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In Situ Observation of Plastic Foaming under Static Condition,
Extensional Flow and Shear Flow
by
Anson (Sze Tat) Wong
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by Anson (Sze Tat) Wong 2012
ii
In Situ Observation of Plastic Foaming under Static Condition,
Extensional Flow and Shear Flow
Anson (Sze Tat) Wong
Doctor of Philosophy, 2012
Department of Mechanical and Industrial Engineering University of Toronto
ABSTRACT
Traditional blowing agents (e.g., hydrochlorofluorocarbons) in plastic foaming processes
has been phasing out due to environmental regulations. Plastic foaming industry is forced to
employ greener alternatives (e.g., carbon dioxide, nitrogen), but their foaming processes are
technologically challenging. Moreover, to improve the competitiveness of the foaming industry,
it is imperative to develop a new generation of value-added plastic foams with cell structures that
can be tailored to different applications. In this context, the objective of this thesis is to achieve a
thorough understanding on cell nucleation and growth phenomena that determine cell structures
in plastic foaming processes. The core research strategy is to develop innovative visualization
systems to capture and study these phenomena. A system with accurate heating and cooling
control has been developed to observe and study crystallization-induced foaming behaviours of
polymers under static conditions. The cell nucleation and initial growth behaviour of polymers
blown with different blowing agents (nitrogen, argon and helium, and carbon dioxide-nitrogen
mixtures) have also been investigated in great detail. Furthermore, two innovative systems have
been developed to simulate the dynamic conditions in industrial foaming processes: one system
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captures a foaming process under an easily adjustable and uniform extensional strain in a high
temperature and pressure environment, while the other achieves the same target, but with shear
strain. Using these systems, the extensional and shear effects on bubble nucleation and initial
growth processes has been investigated independently in an isolated manner, which has never
been achieved previously. The effectiveness of cell nucleating agents has also been evaluated
under dynamic conditions, which have led to the identification of new foaming mechanisms
based on polymer-chain alignment and generation of microvoids under stress. Knowledge
generated from these researches and the wide range of future studies made possible by the
visualization systems will be valuable to the development of innovative plastic foaming
technologies and foams.
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To my awesome mom and dad, my beloved girlfriend, Gladys, my brothers, Andy and Clement, and my sister-in-
law, Wendy, for your unconditional support, encouragement and patience throughout the journey of my
graduate studies. I could not have done it without you.
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ACKNOWLEDGMENT
It is beyond words for how grateful I am to those who have helped me through my
academic career at the University of Toronto. Without their help, encouragement and support, my
Ph.D. experience would never be as successful and rewarding as it had been.
First of all, I would like to express my deep and sincere gratitude to my supervisor,
Professor Chul B. Park, for his valued supervision, personal guidance and encouragement
throughout my research in the Microcellular Plastics Manufacturing Laboratory. Throughout the
years, I have learned from him a wealth of knowledge that is integral for my growth as a
researcher, and will be a solid foundation for my future career.
I would like to thank my Ph.D. committee, Professor Hani Naguib and Professor Glenn
Hibbard, who have given me valuable guidance and encouragement throughout my Ph.D. studies.
Their insight and help are instrumental for me to overcome the challenges I faced in this journey.
Also, I am grateful for Professor Markus Bussmann and Professor Marie-Claude Heuzey for their
valuable feedback in my Ph.D. final oral examination.
My gratitude is also extended to the Department of Mechanical and Industrial
Engineering and the School of Graduate Studies at the University of Toronto, Natural Sciences
and Engineering Research Council of Canada and the Ontario Research Foundation, for
providing scholarships and financial support for my research. In addition, I would like to thank
the Consortium for Cellular and Micro-Cellular Plastics and AUTO21 for providing me with
funding and opportunities to expand my research and professional networks.
I would also like to take this opportunity to acknowledge the support from my previous
and current colleagues. Their friendships are integral parts of my graduate studies experience.
Many of my research works would not have been as successful without their advice and
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assistance. Special thanks goes out to Dr. Saleh Amani, Dr. Amir Ameli, Dr. Maridass
Balasubramanian, Dr. Reza Barzagari, Dr. Amir Behravesh, Dr. Nan Chen, Dr. Qingping Guo,
Dr. Dong-won Jung, Dr. Babu Adhikary Kamal, Dr. Mehdi Keshtkar, Dr. Ryan Kim, Dr. Young
Wook Kim, Dr. John Lee, Dr. Kevin Lee, Dr. Kyungmin Lee, Dr. Patrick Lee, Dr. Richard Lee,
Dr. Sunghyo Lee, Dr. Gary Li, Dr. Guangming Li, Dr. Takashi Kuboki, Dr. Bhuwneesh Kumar,
Dr. Maridass Balasubramanian, Dr. Mohammed Serry, Dr. Yongrak Moon, Dr. Bo Sung Shin,
Dr. Chunmin Wang, Dr. Jin Wang, Dr. Jing Wang, Dr. Mingyi Wang, Dr. Qingfeng Wu, Dr. Jae
Dong Yoon, Dr. Wentao Zhai, Dr. Jingjing Zhang, Dr. Wenge Zheng, Dr. Changwei Zhu, Dr.
Wenli Zhu, Dr. Zhenjin Zhu, Dr. Jin Ho Zong, Raymond Chu, Weidan Ding, Thomas
Goetz, Yanting Guo, Ivan Gutierrez, Mohammed Hasan, Davoud Jahani, Peter Jung, Kamlesh
Katihya, Ryohei Koyama, Esther Lee, Hasan Mahmood, Tero Malm, Lun Howe Mark, Tara
McCallum, Nemat Neossiny, Reza Nofar, Ali Rizvi, Mehdi Saniei, Vahid Shaayegan, Alireza
Tabatabaei, Hui Wang, Lilac Wang, Stephan Wijnands, Mo Xu, Hongtao Zhang, Ying Zhang,
Anne Zhao, as well as everyone else who helped me in my Ph.D. studies. Also, I am grateful for
the many undergraduate students who have assisted me in research throughout the years.
Furthermore, to our machine shop specialists: Ryan, Jeff, Gordon, Fred, Tai and Terry:
thank you for the professional machining services and the numerous advice you have given me
for the development of my foaming systems. Also, to the administrative staff in our department:
Brenda, Donna, Sheila and Jho: thank you for your help and advice on various administrative
issues that allow me to focus on my research work.
Last but not least, I owe a big thanks to my awesome mom and dad, my beloved
girlfriend, Gladys, my brothers, Andy and Clement, and my sister-in-law, Wendy, for their
unconditional support, encouragement and patience throughout the years. Their caring support
carried me through the difficult times and always inspired me to go forward in this long journey.
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TABLE OF CONTENT
ABSTRACT ....................................................................................................................... II
ACKNOWLEDGMENT .................................................................................................... V
TABLE OF CONTENT .................................................................................................. VII
LIST OF TABLES ......................................................................................................... XIV
LIST OF FIGURES ......................................................................................................... XV
LIST OF SYMBOLS ...................................................................................................... XX
CHAPTER 1 INTRODUCTION ..................................................................................... 1
1.1 Preamble .............................................................................................................................. 1
1.2 Classification of Plastic Foams and their Applications ....................................................... 2
1.3 Plastic Foam Manufacturing Technologies ......................................................................... 5
1.3.1 Blowing agents ............................................................................................................. 5
1.3.1.1 Chemical Blowing Agent (CBA) .......................................................................... 5
1.3.1.2 Physical Blowing Agent (PBA) ............................................................................ 6
1.3.2 Generation of a Uniform Polymer-Gas Mixture .......................................................... 7
1.3.3 Plastic Foaming Technologies ................................................................................... 10
1.3.3.1 Batch Foaming .................................................................................................... 10
1.3.3.2 Extrusion Foaming .............................................................................................. 10
1.3.3.3 Injection Foam Molding ...................................................................................... 12
1.3.3.4 Bead Foaming ..................................................................................................... 13
1.4 The Current Challenges and Future Outlook .................................................................... 14
1.4.1 Replacement of Hazardous Blowing Agents ............................................................. 14
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1.4.2 Waste Reduction of Plastic Products ......................................................................... 16
1.4.3 Development of Innovative Foams with Specific Functions ..................................... 17
1.5 Objective of the Thesis ...................................................................................................... 18
1.5.1 Key Research Strategy ............................................................................................... 19
1.6 Overview of the Thesis ..................................................................................................... 21
CHAPTER 2 LITERATURE REVIEW AND THEORETICAL BACKGROUND ..... 23
2.1 Introduction ....................................................................................................................... 23
2.2 Nucleation Theory ............................................................................................................. 24
2.2.1 Types of Nucleation ................................................................................................... 24
2.2.1.1 Classical Homogeneous Nucleation .................................................................... 26
2.2.1.2 Classical Heterogeneous Nucleation ................................................................... 26
2.2.1.3 Pseudo-Classical Nucleation ............................................................................... 26
2.2.2 Classical Nucleation Theory ...................................................................................... 27
2.2.2.1 Classical Homogeneous Nucleation .................................................................... 27
2.2.2.2 Classical Heterogeneous Nucleation ................................................................... 30
2.2.2.3 Prediction of Nucleation Rate ............................................................................. 35
2.2.3 Pseudo-Classical Nucleation Theory ......................................................................... 36
2.2.3.1 Homogeneous Cell Nucleation from an Existing Microvoid .............................. 38
2.2.3.2 Heterogeneous Cell Nucleation from an Existing Microvoid ............................. 40
2.2.4 Stress-Induced Nucleation .......................................................................................... 43
2.2.5 Crystal-Induced Nucleation ........................................................................................ 47
2.2.6 Nucleating Agents for Heterogeneous Nucleation ..................................................... 49
2.3 Bubble Growth and Deterioration Mechanisms ................................................................ 50
ix
2.3.1 Cell Growth ................................................................................................................ 51
2.3.2 Cell Coalescence ........................................................................................................ 54
2.3.3 Cell Coarsening and Collapse .................................................................................... 56
2.4 Numerical Simulation of Cell Nucleation and Growth ..................................................... 59
2.5 Foaming Visualization Studies .......................................................................................... 63
2.5.1 Dynamic Foaming Visualization ................................................................................ 63
2.5.2 Static Foaming Visualization ..................................................................................... 66
2.6 Imaging Technology ......................................................................................................... 67
2.7 Summary and Assessment of Research Directions ........................................................... 69
CHAPTER 3 IN SITU VISUALIZATION OF PLASTIC FOAMING PROCESSES UNDER
STATIC CONDITIONS ................................................................................................... 72
3.1 Introduction ....................................................................................................................... 72
3.2 Development of a Foaming Visualization System with Accurate Heating and Cooling
Control ........................................................................................................................................ 73
3.2.1 Background ................................................................................................................ 73
3.2.2 New Foaming Chamber with Accurate Heating and Cooling Control ...................... 73
3.2.3 Optical Lens Assembly .............................................................................................. 78
3.2.4 New IO Control Board and Software ......................................................................... 79
3.3 Crystallization and its Effects in Cell Nucleation and Growth ......................................... 81
3.3.1 Background ................................................................................................................ 81
3.3.2 Research Methodology ............................................................................................... 82
3.3.2.1 Experimental Materials and Sample Preparation ................................................ 82
3.3.2.2 Isothermal Crystallization ................................................................................... 82
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3.3.2.3 Foaming Visualization ........................................................................................ 83
3.3.3 Results and Discussion ............................................................................................... 84
3.3.3.1 Isothermal Crystallization ................................................................................... 84
3.3.3.2 Foaming Visualization ........................................................................................ 86
3.4 Foaming Behaviour of Plastics Blown with Environmentally Friendly Blowing Agents 92
3.4.1 Comparison of Inert Blowing Agents: Argon, Nitrogen, and Helium ....................... 92
3.4.1.1 Background ......................................................................................................... 92
3.4.1.2 Experimental Materials and Sample Preparation ................................................ 93
3.4.1.3 Experimental Procedure ...................................................................................... 93
3.4.1.4 Results and Discussion ........................................................................................ 96
3.4.2 Plastic Foaming with Blowing Agent Blends: Carbon Dioxide and Nitrogen ........ 100
3.4.2.1 Background ....................................................................................................... 100
3.4.2.2 Experimental Materials, Sample Preparation and Procedure ............................ 101
3.4.2.3 Results and Discussion ...................................................................................... 103
3.5 Conclusion ....................................................................................................................... 108
CHAPTER 4 IN SITU VISUALIZATION OF PLASTIC FOAMING PROCESS UNDER
EXTENSIONAL STRESS .............................................................................................. 110
4.1 Introduction ..................................................................................................................... 110
4.2 Development of a Foaming Visualization System with Extensional Stress-Inducing
Ability ....................................................................................................................................... 111
4.2.1 Function I: Application of a Uniform Extensional Strain to a Plastic Specimen under
High Temperature and Pressure ........................................................................................... 112
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4.2.2 Function II: Gas Saturation in Plastic Melt and Subsequent Inducement of Foaming
by Rapid Depressurization ................................................................................................... 114
4.2.3 Function III: Capture of Bubble Formation and Growth Processes with Fine
Temporal and Spatial Resolution ......................................................................................... 116
4.2.4 Experimental Procedure ........................................................................................... 117
4.2.5 Verification of System Capability in Application of Extensional Strain ................. 118
4.3 PS and PS-Talc Composite Foaming under Extensional Stress ...................................... 119
4.3.1 Experimental Materials and Sample Preparation ..................................................... 119
4.3.2 Experimental Cases .................................................................................................. 119
4.3.3 Results and Discussion ............................................................................................. 120
4.3.3.1 PS Foaming ....................................................................................................... 120
4.3.3.2 PS-talc Composite Foaming .............................................................................. 123
4.4 Effect of Talc Particle Size and Surface Treatment on Foaming Behaviour of PS-Talc
Composites under Extensional Stress ...................................................................................... 130
4.4.1 Background .............................................................................................................. 130
4.4.2 Experimental Materials, Sample Preparation and Procedure ................................... 131
4.4.3 Characterization of Talc Distribution in PS-Talc Composites ................................. 134
4.4.4 Foaming Results and Discussion .............................................................................. 137
4.5 Investigation on the Interrelationships among Extensional Stress, Crystallization, and
Foaming Behaviour .................................................................................................................. 145
4.5.1 Background .............................................................................................................. 145
4.5.2 Experimental Materials, Sample Preparation and Procedure ................................... 145
4.5.3 Crystallization Study Results ................................................................................... 147
4.5.4 Foaming Visualization Results................................................................................. 149
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4.6 Conclusion ....................................................................................................................... 154
CHAPTER 5 IN SITU VISUALIZATION OF PLASTIC FOAMING PROCESS UNDER
SHEAR STRESS............................................................................................................. 156
5.1 Introduction ..................................................................................................................... 156
5.2 Development of a Foaming Visualization System with Shear Stress-Inducing Ability . 157
5.2.1 Function I: Generate a Uniform Simple Shear Flow to a Plastic Melt under High
Temperature and Pressure .................................................................................................... 157
5.2.2 Function II: Saturate the Plastic Melt with a High Pressure Gas and Induce Foaming
by Rapid Depressurization ................................................................................................... 162
5.2.3 Function III: Capture Bubble Formation and Growth Processes with Fine Temporal
And Spatial Resolution ......................................................................................................... 164
5.2.4 Verification of System Capability in Application of Shear Strain ........................... 167
5.2.5 Experimental Materials and Procedure .................................................................... 168
5.3 PS and PS-Talc Composite Foaming under Shear Stress ............................................... 169
5.3.1 Experimental Materials and Sample Preparation ..................................................... 169
5.3.2 Experimental Cases .................................................................................................. 169
5.3.3 Results and Discussion ............................................................................................. 171
5.3.3.1 PS Foaming with CO2 ....................................................................................... 171
5.3.3.2 PS-Talc Composites Foaming with CO2 ........................................................... 175
5.4 Conclusion ....................................................................................................................... 179
CHAPTER 6 SUMMARY AND CONCLUDING REMARKS .................................. 180
6.1 Summary ......................................................................................................................... 180
6.2 Key Contributions ........................................................................................................... 180
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6.2.1 Development of Foaming Visualization Systems .................................................... 180
6.2.1.1 Scope of the Visualization Systems .................................................................. 181
6.2.2 Experimental Work .................................................................................................. 182
6.3 Recommendation for Future Works ................................................................................ 185
REFERENCES ................................................................................................................ 190
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LIST OF TABLES
Table 3-1 – Experimental cases for PP/CO2 foaming under presence of crystals ......................... 86
Table 3-2 – Experimental cases of PP foaming with inert gases ................................................... 96
Table 3-3 – PS/CO2-N2 experimental matrix ............................................................................... 102
Table 4-1 – Experimental cases for PS and PS-talc/CO2 foaming under extensional stress ....... 120
Table 4-2 – Summary of talc characteristics ................................................................................ 132
Table 4-3 – Experimental cases for PS-talc foaming under extensional stress ............................ 133
Table 4-4 – Experimental cases for PP/CO2 foaming with crystals and extensional stress ......... 146
Table 5-1 – Experimental cases for PS and PS-talc foaming under shear stress ......................... 171
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LIST OF FIGURES
Figure 1-1 – Typical plastic foaming process ................................................................................ 12
Figure 1-2 – Research methodology of this thesis ......................................................................... 20
Figure 1-3 – Overall research structure .......................................................................................... 21
Figure 2-1 – Types of nucleation ................................................................................................... 26
Figure 2-2 – ΔFhom vs. Rbub plot...................................................................................................... 28
Figure 2-3 – Bubble shape vs. contact angle on a planar surface .................................................. 32
Figure 2-4 – Bubble nucleation at a conical cavity ........................................................................ 34
Figure 2-5 – Change of density at polymer-gas interface .............................................................. 37
Figure 2-6 – Cell nucleation for CNT vs. foaming through growth of a microvoid ...................... 40
Figure 2-7 – Cell nucleation for CNT vs. foaming through growth of a microvoid on a conical
cavity .................................................................................................................................. 43
Figure 2-8 – Foaming simulator developed by Chen et al. [99] .................................................... 45
Figure 2-9 – Foaming simulator developed by Zhu et al. [101] .................................................... 45
Figure 2-10 – Bubble growth-induced cell nucleation ................................................................... 46
Figure 2-11 – PS-talc foaming visualization under static condition (Tsys = 180 °C) [107] ............ 47
Figure 2-12 – Foaming visualization study by Villamizar and Han [161] ..................................... 64
Figure 3-1 – Schematic of the batch foaming visualization system [53] ....................................... 73
Figure 3-2 – Detailed foaming chamber design for static visualization system ............................ 75
Figure 3-3 – Overall foaming chamber design for static visualization system .............................. 77
Figure 3-4 – Temperature profile in foaming chamber vs. HPDSC at 139 °C .............................. 77
Figure 3-5 - Batch foaming visualization system with accurate heating/cooling control .............. 80
Figure 3-6 – Finalized foaming chamber setup for the static visualization system ....................... 81
xvi
Figure 3-7 – Foaming visualization at the suspended region ......................................................... 84
Figure 3-8 – Isothermal crystallization of DM55 using HP DSC (Psat = 6 MPa) .......................... 85
Figure 3-9 – Isothermal crystallization of SEP550 using HPDSC (Psat = 6 MPa)......................... 85
Figure 3-10 – Crystallinity & VER vs. Tsys (DM55)....................................................................... 85
Figure 3-11 – Crystallinity & VER vs. Tsys (SEP550) .................................................................... 85
Figure 3-12 – Crystal formation of PP during isothermal stage at Psat = 6 MPa ........................... 86
Figure 3-13 – Sample foaming visualization images of DM55 ..................................................... 91
Figure 3-14 – Sample foaming visualization images of SEP550 ................................................... 91
Figure 3-15 – Solubility of He, Ar, & N2 in PP copolymer [35] ................................................... 95
Figure 3-16 – Snapshots of PP foaming processes with inert gases at Psat = 2000 psi .................. 98
Figure 3-17 – Nunfoam vs. time (Psat = 2000 psi) .............................................................................. 98
Figure 3-18 – Nunfoam vs. time (C = 0.432 mol of gas/g of polymer).............................................. 98
Figure 3-19 – dNunfoam/dt vs. time (Psat = 2000 psi) ....................................................................... 98
Figure 3-20 – dNunfoam/dt vs. time (C = 0.432 mol of gas/g of polymer) ....................................... 98
Figure 3-21 – Rbub,avg vs. time (Psat = 2000 psi) ............................................................................. 99
Figure 3-22 – Rbub,avg vs. time (C = 0.432 mol of gas/g of polymer) ............................................. 99
Figure 3-23 – Sample foaming video of the 75% CO2-25% N2 case foamed at 100°C............... 103
Figure 3-24 – In situ PS/CO2-N2 foaming images ....................................................................... 104
Figure 3-25 – Nunfoam vs. time of PS/CO2-N2 foaming (Tsys = 100 °C) ........................................ 107
Figure 3-26 – Nunfoam vs. time of PS/CO2-N2 foaming (Tsys = 140 °C) ........................................ 107
Figure 3-27 – Nunfoam vs. time of PS/CO2-N2 foaming (Tsys = 180 °C) ........................................ 107
Figure 3-28 – Max. Nunfoam of PS/CO2-N2 foaming ..................................................................... 107
Figure 3-29 – dDbub/dt|avg vs. Tsys of PS/CO2-N2 foaming ........................................................... 108
Figure 4-1 – Stress effect on cell nucleation in extrusion process ............................................... 111
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Figure 4-2 – Counter-rotating roller design ................................................................................. 112
Figure 4-3 – Foaming chamber design for visualization system with extensional stress ............ 114
Figure 4-4 – Preliminary setup for visualization system with extensional stress ........................ 115
Figure 4-5 – Revised setup for visualization system with extensional stress .............................. 115
Figure 4-6 – Schematic of foaming visualization system with extensional stress-inducing ability
.......................................................................................................................................... 117
Figure 4-7 – Finalized foaming visualization system with extensional stress-inducing ability ... 117
Figure 4-8 – Deformation of PS sample under an applied extensional strain .............................. 118
Figure 4-9 – PS sample foamed at 100 °C: a) ε = 0; b) ε = 1.2 .................................................... 122
Figure 4-10 – Snapshots of PS foaming at 100 °C (ε of 1.2 at dε/dt of 0.5/s) ............................. 122
Figure 4-11 – PS-talc foamed at 100°C: a) ε = 0; b) ε = 0.6; c) ε = 1.2 ....................................... 124
Figure 4-12 – PS-Talc sample: a) before applied ε; b) after applied ε of 1.2 ............................... 126
Figure 4-13 – Snapshots of PS-talc foaming at 100°C (ε = 0) ..................................................... 127
Figure 4-14 – Snapshots of PS-talc foaming at 100°C (ε = 0.6 at dε/dt = 0.5 s-1) ....................... 128
Figure 4-15 – Snapshots of PS-talc foaming at 100°C (ε = 1.2 at dε/dt = 0.5 s-1) ....................... 128
Figure 4-16 – Nunfoam vs. time for PS-talc samples foamed at 100 °C.......................................... 129
Figure 4-17 – Dbub vs. time graph for PS-talc samples foamed at 100 °C ................................... 129
Figure 4-18 – PS-talc sample foamed at 140°C: a) ε = 0; b) ε = 1.2 ............................................ 130
Figure 4-19 – Snapshot of PS-talc foaming at 140°C: a) ε = 0; b) ε = 1.2 ................................... 130
Figure 4-20 – Sample SEM pictures of PS-talc composites a) Cimpact CB7 talc wt% = 5; b)
Stellar 410 talc wt% = 5 ................................................................................................... 135
Figure 4-21 – Summary of particle density, size distribution, and surface area vs. talc wt% ..... 137
Figure 4-22 – Foaming sequences of PS with talc wt% = 5.0 under extensional stress .............. 139
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Figure 4-23 – Nunfoam vs. time and maximum Nunfoam for PS with 0.5 wt% talc ........................... 140
Figure 4-24 – Nunfoam vs. time and maximum Nunfoam for PS with 2.0 wt% talc ........................... 141
Figure 4-25 – Nunfoam vs. time and maximum Nunfoam for PS with 5.0 wt% talc ........................... 141
Figure 4-26 – Effect of dε/dt on Nunfoam vs. time and maximum Nunfoam for PS with 5.0 wt% talc
.......................................................................................................................................... 142
Figure 4-27 – Maximum Nunfoam vs. Ntalc,avg for PS-talc foaming under extensional stress ......... 144
Figure 4-28 – The effect of high pressure CO2 on Tm of unfoamed polymers ............................. 148
Figure 4-29 – Melting behaviour of foamed PP samples under atmospheric pressure ................ 149
Figure 4-30 – Snapshots of PP foaming videos showing effects of the applied ε ....................... 153
Figure 4-31 – Bubble growth-induced nucleation with the presence of crystals (SEP550) ........ 153
Figure 4-32 – Crystallinity vs. ε for foamed PP samples ............................................................. 154
Figure 4-33 – Foaming behaviour of SEP550 under ε = 1.65 in two different regions ............... 154
Figure 5-1 – The high pressure sliding plate rheometer [223] ..................................................... 158
Figure 5-2 – Design requirement of shear mechanism for rapid gas saturation process ............. 158
Figure 5-3 – Mechanism of the moving plate assembly with sliding wedges ............................. 159
Figure 5-4 – Adjustment shaft assembly on rectangular frame ................................................... 163
Figure 5-5 – a) Coaxial lighting; b) Ring lighting; c) Transmissive lighting .............................. 165
Figure 5-6 – Final foaming chamber design for visualization system with shear stress .............. 165
Figure 5-7 – Operation of the moving plate assembly with sliding wedges ................................ 166
Figure 5-8 – Schematic of foaming visualization system with shear strain inducing ability....... 167
Figure 5-9 – Finalized foaming visualization system with shear stress-inducing ability ............ 167
Figure 5-10 – Deformation of PS sample under an applied shear strain ...................................... 168
Figure 5-11 – Snapshots of PS/CO2 foaming videos under shear stress ...................................... 172
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Figure 5-12 – Nunfoam vs. time of PS/CO2 foaming under shear stress ......................................... 173
Figure 5-13 –Dbub,avg vs. time of PS/CO2 foaming under shear stress ......................................... 173
Figure 5-14 – Snapshots of PS-5% talc/CO2 foaming videos under shear stress ........................ 177
Figure 5-15 – Nunfoam vs. time of PS-5% talc/CO2 foaming under shear stress ............................ 178
Figure 5-16 – Dbub,avg vs. time of PS-5% talc/CO2 foaming under shear stress ........................... 178
Figure 5-17 – Maximum Nunfoam for PS and PS-talc foaming under shear stress ......................... 179
Figure 5-18 – dDbub/dt|avg for PS and PS-talc foaming under shear stress ................................... 179
xx
LIST OF SYMBOLS
a Equatorial radius of a prolate spheroid, m
A(Rcr) Surface area of a critical bubble, m2
Ac Area of circular boundary for cell density and size characterization, m2
Ahet Surface area of nucleating agents per unit volume of polymer melt, m2/m3
Ahet,avg Average surface area of nucleating agents per unit volume of polymer melt,
m2/m3
ΔAhet,avg Errors of Ahet,avg, m2/m3
Alg Surface area of a liquid-gas interface, m2
Asg Surface area of a solid-gas interface, m2
At Area of circular boundary for talc density and size characterization, m2
b Equatorial radius of a prolate spheroid, m
c Polar radius of a prolate spheroid, m
C Gas concentration within polymer, mol/m3
-dC/dt Gas depletion rate, mol/m3-s
Cavg Average gas concentration within polymer, mol/m3
Csat Dissolved gas concentration within polymer at the saturated state, mol/m3
da Abbe diffraction limit, m
D Diffusivity, m2/s
Do Pre-exponential coefficient of diffusivity equation, m2/s
Dbub Bubble diameter, m
dDbub/dt|avg Average bubble diameter growth rate, m/s
Dbub,avg Average bubble diameter, m
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Dbub,eq Equivalent bubble diameter, m
Dr Diameter of rollers in the visualization system with extensional stress-
inducing ability, m
E Elastic modulus, N/m2
Ea Activation energy for gas diffusion, J
F Ratio of the volume of the nucleated bubble to the volume of a spherical
bubble with the same radius of curvature, dimensionless
ΔFhom The change in free energy for the homogeneous nucleation of a bubble, J
ΔFhet The change in free energy for the heterogeneous nucleation of a bubble, J
h The gap height between the static and moving plates in the visualization
system with shear stress-inducing ability, m
H Henry’s Law Constant, N-m/mol
J Bubble nucleation rate, #/m2-s
Jhet Heterogeneous nucleation rate (per unit area of nucleating agent), #/m2-s
Jhom Homogeneous nucleation rate (per unit volume of polymer), #/m3-s
kB Boltzmann constant, m2kg/s2-K
l Length of gas diffusion path, m
lc Center-to-center distance between rollers in the visualization system with
extensional stress-inducing ability, m
Lo Original length of sample, m
ΔL Change in sample length, m
ΔLmax Maximum change in sample length, m
m Molecular mass of gas molecules, kg
xxii
n(Rcr) Number density of critical bubbles, #/m3
ni Frequency of talc particles in the i-th length group within a circular boundary
with an area of At, #
nr Refractive index of the medium between a lens and an object, dimensionless
N Number of gas molecules per unit volume of polymer, #/m3
N(t) Number of cells within a circular boundary with an area of Ac
Nfoam Cell density with respect to foamed volume, #/m3
Ntalc Total talc particle density, #/m3
Ntalc,avg Average Talc particle density, #/m3
ΔNtalc,avg Errors in Ntalc,avg, #/m3
Ntalc,i Talc particle density in the i-th length group, #/m3
Nunfoam Cell density with respect to unfoamed volume, #/m3
dNunfoam/dt Cell nucleation rate with respect to unfoamed volume, #/m3-s
Pbub Bubble pressure, N/m2
Pbub,cr Bubble pressure of a critical bubble, N/m2
Pcr Critical pressure, N/m2
Psat Saturation pressure, N/m2
Psys System pressure, N/m2
-dPsys/dt System pressure drop rate, N/m2-s
-dPsys/dt|avg Average system pressure drop rate, N/m2-s
-dPsys/dt|max Maximum system pressure drop rate, N/m2-s
ΔPlocal Local pressure variation, N/m2
Q Ratio of the surface area of the nucleated bubble to the surface area of a
xxiii
spherical bubble with the same radius of curvature, dimensionless
r Radial position from the center of bubble, m
Rbub Bubble radius, m
Bubble growth rate, m/s
Rbub,avg Average bubble radius, m
Rbub,i Radius of the i-th bubble at time t within a circular boundary with an area of
Ac, m
dRbub/dt|avg Average bubble growth rate, m/s
Rbub,1 Radius of an existing microvoid at the initial state, m
Rbub,2 Radius of an existing microvoid at a subsequent state, m
RG Universal gas constant, J/K-mol
Rshell Radius of the shell of the polymer-gas solution surrounding the bubble in the
cell model, m
s Talc particle size, m
savg Average talc particle size, m
Δsavg Errors in savg, m
S Corrected solubility, g of gas/g of polymer
Sa Apparent solubility, g of gas/g of polymer
t Current time, s
td Time needed for gas saturation, s
Tc Crystallization temperature, K
Tcr Critical temperature, K
Tm Melting temperature, K
xxiv
Tsys System temperature, K
V Speed of the moving plate in the visualization system with shear stress-
inducing ability, m/s
Vf(r) Fluid velocity at r, m/s
Vg Volume of a bubble, m3
Vmax Maximum V, m/s
Vps Volume of a prolate spheroid, m3
W Activation energy for n(Rcr), J
Whet Free energy barrier to heterogeneously nucleate a bubble, J
Whom Free energy barrier to homogeneously nucleate a bubble, J
X
Displacement of the moving plate in the visualization system with shear
stress-inducing ability, m
y Transformed Lagrangian coordinate, m3
Z Zeldovich factor that accounts for thermodynamic fluctuation that affects
n(Rcr), dimensionless
Greek Letters
α Half opening angle of an objective lens, °
αt Coefficient of linear thermal expansion, m/m-K
β Semi-conical angle of a heterogeneously nucleating site, °
γ Engineering shear strain, dimensionless
dγ/dt Engineering shear strain rate, s-1
dγ/dt|max Maximum engineering shear strain rate, s-1
γlg Surface tension along the liquid-gas interface, N/m
xxv
γmax Maximum engineering shear strain, dimensionless
γsg Surface tension along the solid-gas interface, N/m
γsl Surface tension along the solid-liquid interface, N/m
γo Strain rate tensor, s-1
ε Engineering extensional strain, dimensionless
dε/dt Engineering extensional strain rate, s-1
dε/dt|max Maximum engineering extensional strain rate, s-1
εmax Maximum engineering extensional strain, dimensionless
η Viscosity, N/m2-s
ηo Zero-shear viscosity, N/m2-s
θc Contact angle, °
λ Relaxation time, s
λl Wavelength of light, m
μg,gas Chemical potential of the gas inside the bubble, J/mol
μg,liquid Chemical potential of the gas in the polymer/gas solution, J/mol
ν Rate at which molecules strike against an unit area of the bubble surface,
#/m2-s
ρR Probability density function of Rbub,1, dimensionless
ρβ Probability density function of β, dimensionless
σ Tensile stress, N/m2
τ Stress tensor, N/m2
τo Upper convected time derivative, N/m2-s
τrr Stress component in the radial direction, N/m2
xxvi
τθθ Stress component in the tangential direction, N/m2
φ Turning angle, °
ω Angular speed of the rollers in the visualization system with extensional
stress-inducing ability, s-1
ωmax Maximum angular speed of the rollers in the visualization system with
extensional stress-inducing ability, s-1
1
CHAPTER 1
INTRODUCTION
1.1 Preamble
Plastic foaming is a technology that involves the generation of porous or cellular structures
in plastic materials. The demand and production for foamed plastics have grown significantly
over the last few decades owing to their low processing energy and time requirement,
lightweight, thermal and acoustic insulation properties, good dielectric properties, high corrosion
resistance, and mechanical properties that can be tailored to different applications (e.g., flexible
foams for cushioning/packaging applications, rigid foams for structural support). Also, in typical
plastic parts manufacturing processes, the material cost accounts for 50-70% of the total
production cost. Therefore, there is a significant economic interest to use foamed plastics to
reduce material usage amid the increasing cruel oil prices in recent years. Many products that
were manufactured with the conventional materials (e.g., metal, ceramic or wood) have now been
replaced by foamed plastics, such as food packaging, automotive parts (e.g., bumper core, interior
trim) and building insulation, due to their superior quality and/or low cost. Moreover, with the
development of plastic foams, new applications (e.g., bio-scaffolds) have emerged. In the future,
the applications of plastic foams will continue to expand, which will ultimately lead to products
with higher quality and better functions as well as lower cost at the same time. However, despite
the success and the bright future prospect of the plastic foaming industry, many technological
2
challenges lie ahead. To overcome these challenges, it is imperative to achieve clear
understanding in cell nucleation, growth, deterioration and stabilization processes that determine
the cellular structure of foams and hence their applications. Clear understanding in these
phenomena will facilitate the development of innovative foaming technologies to utilize greener
blowing agents and/or plastic materials to produce foam with controllable cellular structures (e.g.,
cell density, void fraction, open- and closed-cell contents) that can be tailored to specific needs
and applications. However, despite the numerous research studies conducted in the last few
decades, the fundamental mechanisms of the aforementioned phenomena have yet to be clarified
thoroughly.
1.2 Classification of Plastic Foams and their Applications
The foaming of thermoplastics is typically achieved using the following steps: 1)
Dissolution of a blowing agent into a plastic matrix; 2) Generation of pores or cells by phase
separation of the blowing agent from the plastic matrix; and 3) Stabilization of the porous or
cellular structure. Foam morphologies are often categorized in these three ways: 1) Foam density,
which is often measured by the volume expansion ratio (VER) that is defined to be the
volumetric ratio of a plastic foam to the unfoamed plastic material; 2) Average cell diameter
(Dbub,avg) and cell density with respect to unfoamed volume (Nunfoam); and 3) Cell structure. To be
specific, foam densities can be categorized as: high-density foam (VER < 4), medium-density
foam (VER = 4 – 10), low-density foams (VER = 10 – 40), and very low-density foams (VER >
40). Meanwhile, cell diameter and cell density can be categorized as: conventional plastic foams
(Dbub,avg < 300 µm and Nunfoam < 106 cells/cc), fine-cell plastics (10 < Dbub,avg < 300 µm and
Nunfoam = 106 – 109 cells/cc) and microcellular plastics (0.1 < Dbub,avg < 10 µm and Nunfoam = 109 –
3
1015 cell/cc) [1]. Microcellular plastics were first defined and developed by Dr. Nam P Suh at the
Massachusetts Institute of Technology (MIT) in 1980s.
Microcellular plastics exhibit improved mechanical properties (e.g., impact strength [2-6],
fatigue life [7]), thermal properties (e.g., thermal stability [8], insulation [9]), acoustical
insulation [9], and optical properties [10] over their conventional foams or their unfoamed
counterparts. While the compressive strength of solid polymers is still superior to microcellular
plastics, the latter demonstrates significant improvement in this regard over fine-cell and
conventional foams. Consequently, this technology has spurred numerous research activities
since its introduction in order to achieve microcellular plastics with different materials and
properties. Meanwhile, in the last 10 years, increasing efforts have been directed to achieving
foams with Dbub,avg < 1 µm. While many of these foams can still be categorized as microcellular
plastics based on its original definition, some researchers have adopted the term nanocellular
plastics for foams with Dbub,avg < 1 µm. It has been demonstrated that nanocellular plastics exhibit
superior mechanical strength that are comparable to solid plastics, as well as thermal insulation
properties that are far superior to microcellular plastics. On the other hand, nanocellular foams
have only been produced into thin sheets in batch processes, and large-scale productions of
nanocellular foams have yet to be achieved, which vastly limits its industrial applications.
Cell structures can be categorized into three major types: closed-cell foams, open-cell
foams, and reticulated foams. In closed-cell foams, individual cells are completed separated by
cell walls. In open-cell foams, pores exist on the cell walls so adjacent cells are interconnected.
Reticulated foams are a special class of open-cell foams where cells are completely devoid of cell
walls, leaving only skeletal structure intact. While closed-cell and open-cell foams can have a
wide range of foam density, reticulated foams typically have very low foam density (VER > 50).
4
Closed-cell foams generally have higher mechanical strength than open-cell or reticulated foams,
so closed-cell foams are often used as structural materials. Closed-cell foams also have higher
thermal insulation properties since heat transfer by gas is limited by cell walls. For thermal
insulation applications with closed-cell foams, it is preferred to use a blowing agent with low
thermal conductivity and diffusivity through the polymer, hence the blowing agent remain within
the foams for a long time during its uses. Closed-cell foams are also used when gas/liquid
permeation is undesirable (e.g., floatation devices). Open-cell foams can be used for liquid
adsorption (e.g., a sponge) due to its porous structure, acoustic insulation and filtration due to its
tortuous nature, and as cushioning or packaging foams due to its flexibility and energy absorbing
properties. Open-cell foams produced with polymers that are biodegradable and biocompatible,
such as poly(lactic-co-glycolic acid) (PLGA), are also used new applications such as bioscaffolds
for tissue re-engineering. Reticulated foams are generally used for filtration and acoustic
insulation. Due to its extremely opened structure, reticulated foams are well suited to filtration
processes with high flow rates. For example, nickel reticulated foams are used as diesel
particulate filters in exhaust systems of automobiles to capture soot particles before the exhausted
gas is released.
In general, plastic foams can also be categorized into two major groups: rigid foams or
semi-flexible/flexible foams. The rigidity of foam depends on the base polymer material, foam
density (i.e., rigidity increases with foam density) and cellular structure (e.g., rigidity decreases
with open cell content). Both rigid and semi-flexible/flexible foams are used in industries such as
packaging, furniture, and transportation. In addition, rigid foams are specialized in applications
such as building and construction materials, appliances, tank/pipes, floatation, as well as food and
drink containers. Meanwhile, flexible/semi-flexible foams are specialized in areas such as carpet
underlay, bedding and seat foams.
5
1.3 Plastic Foam Manufacturing Technologies
In general, foaming can occur by mechanical perturbation, or introduction of a blowing
agent (BA) via chemical reaction or physical injection and the subsequent phase separation of the
BA. In mechanical foaming, cells are generated as gas is mechanically mixed into a plastic melt.
Surfactant can be added to the plastic melt/solution to enhance the foaming process. As the
plastic melt stabilizes, the gas remained entrapped in the plastic melt, hence a cellular structure is
achieved. However, in most thermoplastics foaming processes, a chemical or physical blowing
agent is used.
1.3.1 Blowing agents
1.3.1.1 Chemical Blowing Agent (CBA)
The chemical method involves the blending of a chemical blowing agent (CBA) that
generate gases, typically CO2 or N2, when they are heated above its decomposition temperature.
CBAs are usually dry-blended with plastics resins or powder at solid state, or are compounded
with plastics in an extruder at a temperature below their decomposition temperature before the
plastic/CBA blends are fed into foam processing equipment. A key to choose an appropriate
CBA lies on its decomposition temperature, which must match with that used for plastic foaming.
If its decomposition temperature is too low, gas could be generated prematurely, thus leading to
gas loss and/or premature generation of cells. Conversely, if the decomposition temperature is too
high, the CBAs might not be activated completely, which might result in non-uniform cell
structure and/or limited foam expansion. In some cases, kickers or activators are added to a CBA
to lower the decomposition temperature to tailor for the plastic material and foaming process. For
example, addition of zinc oxide to azodicarbonamide (ADC) can reduce the decomposition
temperature of ADC from 205 – 215 °C to approximately 150 °C [11]. Another key selection
6
criterion is that the residue products from the decomposition of CBA must be compatible with the
plastic to be foamed. For example, certain CBA generates water upon decomposition, which can
affect the properties of moisture sensitive polymers such as polycarbonate (PC) and polyesters.
Also, for food packaging foams, the toxicity of both the CBA and the residue products must be
considered.
CBAs can be categorized into two groups: exothermic and endothermic. Exothermic CBAs,
such as ADC and azobisisobutyronitrile (AIBN), generate N2 upon decomposition. Due to the
exothermic nature of these CBAs, the decomposition of one CBA particle can trigger the
decomposition of neighbouring particles; hence exothermic CBAs tend to release gas more
readily than endothermic CBAs. Meanwhile, CO2 is the primary gas generated from most
endothermic CBAs, such as sodium bicarbonate (NaHCO3) and zinc carbonate. Many
endothermic CBAs are non-toxic, which make them a popular choice for the production of food
packaging foam. .
The main advantages of CBAs lie in its ease of use: CBAs are uniformly distributed into
polymer matrix prior to a foaming process, hence it is easier to disperse and dissolve the
generated blowing agents into the polymer matrix to generate a homogeneous polymer-gas
mixture prior to the foaming stage. It can also be used in conventional extrusion or injection
molding systems directly to produce foamed plastics without the need to modify the systems.
1.3.1.2 Physical Blowing Agent (PBA)
Physical blowing agents (PBAs) are directly injected into foam processing equipment via
an injection port under high pressure. Due to the localized injection method, a better mixing
technique is necessary to achieve a homogeneous polymer-gas mixture. Also, a higher processing
pressure and/or temperature are often needed to accelerate the gas dissolution process.
Furthermore, modifications to conventional extrusion or injection molding systems are also
7
required for gas injection and mixing. However, despite the additional technical challenges,
PBAs are common in industries due to its lower cost and effectiveness, especially in their
production of low-density foams. Traditionally, chlorofluorocarbons (CFCs) were widely used as
PBAs for the production of foams with low foam density, good mechanical properties and very
good thermal insulation properties. Their high solubility, low toxicity, thermal conductivity, non-
flammability, good thermal and chemical stability, as well as low cost made them very ideal
choice as PBAs. However, the chemical stability of CFCs also leads to their diffusion into the
stratosphere, where they break down and generate chlorine atoms that destroy the ozone layer
[12]. This ultimately leads to significant increase in UV-B radiation that is harmful to human and
other biological systems. Consequently, an international protocol, known as the Montreal
Protocol, was established to phase out the use of CFCs, as well as other substances that can
damage the ozone layer [13]. This protocol has profoundly changed the development of the
plastic foam industry, as industry look for alternative PBAs and faces various technical
challenges and other environmental concerns. This is further discussed in Section 1.4.1.
1.3.2 Generation of a Uniform Polymer-Gas Mixture
For foaming with a chemical or physical blowing agent, a complete dissolution of gas
generated from chemical reaction or directly injected into the plastic melt to generate a uniform
polymer-gas mixture prior to the foaming stage is very important. This is a key step to the
production of high-quality plastic foams with high cell density and uniform cell structures. If
there exist undissolved gas pockets at the foaming stage, gas molecules tend to diffuse into these
pockets, which can vastly undermine the ability of the plastic-gas solution to generate new cells.
Small cells that are nucleated around these large gas pockets can also collapse due to cell
coarsening, which drives the diffusion of gas from a bubble with high pressure (i.e., the small
bubble due to its small radius of curvature) to low pressure (i.e., the big gas pocket due to its
8
large radius of curvature). Consequently the resulting foam structure tend to be very non-uniform
and with low cell density. This severely undermines the properties (e.g. mechanical, thermal,
acoustical, etc.) of the foamed product. In order to eliminate undissolved gas pockets, the
pressure within plastic foaming equipment must be at least equal to the solubility pressure of the
blowing agent in the plastic used at the processing temperature. In this context, accurate
measurement of solubility data for various blowing agents is imperative to plastic foaming
processes.
Among various techniques, the pressure decay method developed by Newitt and Weale in
1948 [14] is a relatively popular method due to its simplicity and low equipment cost. Its
principle is based on the measurement of pressure drop as gas is dissolved into a plastic sample
enclosed inside a pressurized chamber of known volume at a constant temperature. One of the
limitations of this method lies in its long measurement time as a large sample is required. Also, it
is not suitable to operate at elevated temperature/pressure because a pressure sensor that can
operate accurately with high precision at these conditions is not available. Gravimetric method is
another popular technique for solubility measurement in polymer, which involves direct
measurement of weight gain of a plastic sample after gas sorption. The simplest method involves
gas dissolution into a plastic sample at high pressure inside a chamber, and subsequent weighting
of the sample upon its removal from the chamber. However, this method can only be used in low
temperature (i.e., not molten state), and gas loss between the sample removal and weighting
processes is inevitable and unquantifiable in an accurate manner. Together, these limitations
vastly limited its application. More advanced gravimetric methods were developed subsequently
to measure the weight gain during the saturation process under high temperature and pressure
with an electro-balance [15], but the convection-induced density variation of blowing agent
affected the accuracy of the solubility data. This shortcoming has been overcome by the
9
introduction of the magnetic suspension balance [16], where the sample is weighted in a
compartment that is isolated from the chamber containing it and thus the convection effect is
eliminated. Meanwhile, for MSB and other in situ gravimetric methods, the buoyancy effect of
the blowing agent increases as the plastic sample swells and the density of the blowing agent
increases, so the measured weight gain and hence solubility is less than the actual amount. To
account for this error, the pressure-volume-temperature behaviour is often estimated by various
equations of state (EOS) to determine the swelling amount, thus compensating for the buoyancy
effect [17-19]. The commonly used EOS for measurement of gas solubility in plastics are
Sanchez-Lacombe EOS and Simha-Somcynsky EOS. Alternatively, Li et al. [20] developed an
apparatus to measure the PVT behaviour experimentally via direct observation of a polymer
sample under high temperature and pressure. This equipment can be used to verify the accuracy
of the EOS for estimating the swelling effect of specific polymer/gas mixtures. Recently, this
system has also been used in conjunction with the MSB to determine the solubility of CO2 in
polypropylene (PP) experimentally without the use of an EOS [21].
In industrial foaming processes, the pressure is often set significantly higher than the
solubility pressure to accelerate the gas dissolution process. Even so, the diffusivity of most
commonly used PBAs are not high enough to allow them to dissolve into the polymer-gas matrix
uniformly based on diffusion process alone. Moreover, temperature uniformity is also very
important since it influences gas solubility and diffusivity, as well as rheological behaviour of the
polymer-gas mixture. All of these material parameters ultimately govern the plastic foaming
behaviour. Therefore, a good distributive and dispersive mixing technique to achieve a uniform
polymer-gas mixture with uniform gas concentration and temperature distribution is essential to
the production of a uniform polymer-gas mixture, which is discussed further in Section 1.3.3.2.
10
1.3.3 Plastic Foaming Technologies
1.3.3.1 Batch Foaming
Many plastic foaming technologies have been developed since the invention of plastic
foams. In particular, batch foaming is one of the most studied processes due to its ease of setup
and control. In a batch process, a plastic sample is placed inside a high-pressure chamber where it
is saturated with a blowing agent (e.g., CO2) under ambient temperature. After the gas dissolution
process, a rapid depressurization and subsequent heating causes a sudden drop of gas solubility,
which generates a thermodynamic instability for cell nucleation. As the plastic sample is heated,
the viscosity of the polymer reduces, hence the foam expands as cells are nucleated and grew.
The plastic sample is cooled afterward to stabilize the foam structure. Due to the very low gas
diffusion into the polymer at ambient temperature, the gas saturation process typically takes very
long time (e.g., 24 hours or longer depending on the thickness of the sample). Alternatively, the
gas saturation process can be done at an elevated temperature to reduce the time required, but an
effective cooling strategy is needed to stabilize the foam after depressurization. Otherwise, cell
deterioration can occur which leads to non-uniform cell structure and low volume expansion.
Nevertheless, the long production cycle associated with batch foaming processes vastly limits
their application in industrial foaming processes. However, batch process is still widely used in
plastic foaming research, such as for the development of specialized and innovative foams (e.g.,
nanocellular foams, bioscaffolds, acoustic foams) due to its simple operation and easy control in
various experimental parameters to produce foams with tailorable properties.
1.3.3.2 Extrusion Foaming
The three most common types of manufacturing processes for thermoplastic foams are
extrusion foaming, injection foam molding, and bead-foam molding. In extrusion foaming
processes, plastic resins and additives are first fed into a heated barrel with a rotating screw. The
11
plastic and additives are compacted, melted and mixed by the distributive and dispersive mixing
action of the rotating screw, which also pushes the plastic melt downstream. Subsequently, a
gaseous phase is introduced to the plastic melt via decomposition of CBA or direct injection of
PBA. To achieve a homogeneous plastic-gas mixture with uniform temperature, additive, and
blowing agent distribution, screw designs with good mixing and energy transfer capability (e.g.,
Barr screw, Turbo screw) have been developed. Static mixers are often installed at the end of a
screw to enhance the mixing quality. A second extruder can also be connected downstream and in
series with the primary extruder, where the polymer-gas mixture is mixed further and is often
cooled to a lower temperature before it reaches the foaming stage. These mixing techniques
improve the homogeneity of the polymer-additive-gas mixture and its temperature distribution,
which is critical for foaming. The mixing is achieved by series of division and deformation of
plastic melt to disperse local gas pockets and additive agglomerate into smaller sections (i.e.,
dispersive mixing) as well as distribute these sections to other regions of the plastic melt (i.e.,
distributive mixing). In this process, the energy and mass transport are accelerated due to
increased polymer-gas interface area and decreased striation thickness.
Subsequently, the uniform polymer-gas mixture is forced through a die and foaming is
induced by a rapid depressurization as the mixture exit the die. Foam stabilization is achieved by
cooling under ambient conditions or immersion in water. Figure 1-1 depicts this foaming process,
which is the most common method to generate plastic foams. The foamed plastic is extruded
continuously, which can be cut to specific length afterwards. Typical products manufactured by
extrusion foaming processes are foamed rods, tubes, sheets and boards. By controlling various
material and processing parameters, the foam density, cell density and cell structures can be
tailored to specific applications. The geometry of the foamed products depends on the shape of
12
the die opening, but they must be symmetric along the extruding direction, hence a complex 3D
shape cannot be produced with this process.
Figure 1-1 – Typical plastic foaming process
1.3.3.3 Injection Foam Molding
Injection foam molding processes are similar to extrusion foaming processes except that
the die used for the latter case is replaced with a mold. In injection foam molding, molten plastic-
gas mixtures passes through a gate into a mold cavity. Depending on the back pressure and mold
pressure, foaming occurs at the gate or inside the mold cavity during the injection process, and
the plastic foam expands to take on the geometry of the mold. Subsequently, the foam structure is
stabilized as it is cooled down by the mold, and the foamed part is released from the mold as it
opens. Typically, an unfoamed skin-layer is produced along the outer surface of the foamed part
because it is quickly cooled by the mold surface. The void fraction and hence the foam density is
determined by the shot size. Besides reducing material usage, foaming processes can eliminate or
significantly reduce part warpage and shrinkage that cause residue stresses and dimensions errors,
which are typically related to unfoamed injection molded parts. Injection foam molding processes
allows the production of parts with complex 3D geometry (no symmetry constraint) and good
surface finish, but the foam density is typically quite high (e.g., VER < 2).
13
1.3.3.4 Bead Foaming
Bead foaming technology involves generation of foamed beads, which are subsequently
sintered together in a steam-crest molding process to form the geometry of the part. The most
common bead foams are expandable polystyrene (EPS) and expanded polypropylene (EPP). EPS
is widely used in disposable cups, coolers, and general packaging materials due to its lightweight,
good thermal insulation and cushioning properties. Meanwhile, EPP generally possess very good
mechanical strength despite its lightweight, hence it is often used in automotive parts (e.g.,
bumper cores, side impact protection), sport protective gears (e.g., helmet, knee pads) and
construction materials. The preparation processes of foamed beads prior to steam chest molding
stage are very different between EPS and EPP. EPS beads are typically polymerized with n-
pentane in an unexpanded state. Afterward, they are shipped to a steam chest molding facility,
where they are first expanded in a pre-expander prior to the molding process. Since EPS beads
are shipped in the unexpanded state with high bulk density, their transportation cost can be kept
low. Meanwhile, to produce EPP beads, a blowing agent (e.g., CO2) is first dissolved into solid
plastic beads under high pressure while the beads are immersed in a rotating fluid mixture (e.g.,
water, dispersion agent, surfactant, and blowing agent) to prevent beads agglomeration.
Subsequently, cells are generated within each bead upon depressurization. The cost of EPP beads
are significantly higher than EPS due to its batch foaming process and the high transportation
cost of EPPs beads, which have low foam density, to steam-chest molding facility. This limits the
use of EPP products to higher end engineering products. Meanwhile, in the conventional EPS
bead foam process, the n-pentane used is a volatile organic compound (VOC), so there is fire and
explosion hazards during the transportation and storage of EPS beads. EPS also have a limited
shelf life since the n-pentane can gradually diffuse out of the EPS bead. Currently, expanded
polyethylene (EPE) and expanded poly lactic acid (EPLA) are also attracting significant interests
14
due to their wide range of market potentials and biodegradability, respectively. Bead foam
technologies can be used to generate foamed products with complex 3D structure as well as low
foam density. However, the surface finish of bead-foamed products cannot match those of
injection foam molding due to the grainy texture of the sintered beads. Also, despite its high
compressive strength, it typically possesses low flexural strength, especially for EPS, due to
shear-induced delamination of foamed beads.
1.4 The Current Challenges and Future Outlook
Despite the success and the bright future prospect of the foaming industry, many
technological challenges lie ahead, which are related to various environment concerns and
development of new generation of specialized foams. The major ones are discussed briefly in the
following sections.
1.4.1 Replacement of Hazardous Blowing Agents
As mentioned in Section 1.3.1.2, the use of CFCs has been completely phased out (i.e., in
1996 in developed countries and 2010 in developing countries) by the Montreal Protocol due to
their serious ozone depletion potentials (ODPs). Hydrochlorofluorocarbons (HCFCs) are
chemically less stable than CFCs and hence tend to break down before they reach the
stratosphere. However, they still pose, albeit to a lesser degree, potentials for damaging the ozone
layer. Consequently, they were eventually phased out in Europe for the production of foams in
2004 [22]. In other countries, the use of HCFCs are now being restricted in stages by the
Montreal Protocol, and they will be completed phased out in 2020 in developed countries and
2040 in developing countries [13].
Hydrofluorocarbons (HFCs) [23] have no chlorine atoms and hence do not exhibit any
ODPs, but their high cost and limited benefits in thermal insulation performance when compared
15
to the other alternatives (e.g., hydrocarbons, CO2) has limited their wide-spread use. Moreover,
many HFCs are known to exhibit high global warming potentials (GWPs), hence they are
currently under scrutiny and are expected to be replaced by more environmentally friendly BAs
in the future. Hydrocarbons (HCs) [24] are also being used as alternative BAs due to their
availability, lower cost, no ODP and no GWP or are “greenhouse neutral”, as well as high
solubility and low diffusivity in polymers. However, HCs (e.g., butane, pentane) are flammable,
which leads to safety concerns in their storage, handling, foam manufacturing, as well as the final
foamed products. Besides the needs to implement stricter safety regulations in these processes, a
prolonged storage time for the produced foam products is needed to allow the BAs to safely
diffuse out of the foamed product prior their uses, which lead to additional storage time and cost.
Also, HCs are considered as volatile organic compounds (VOCs), which cause generation of
smog; hence the emissions of these BAs also lead to environmental concerns.
As a result, attention has been shifted towards using greener and safer BAs, which have
no ODP and no GWP or is “greenhouse neutral”. Among them, the most widely used are
supercritical CO2 [25-30] and N2 [31-33]. Argon (Ar) [34, 35] has also been considered but it is
still rarely used in the industry. These BAs are more volatile than the aforementioned BAs, which
might result in better cell nucleating performance. Also, these BAs are often used at their
supercritical states due to their moderate critical temperature (Tcr) and pressure (Pcr). For
example, the Tc and Pc of CO2 are 31 °C and 7.38 MPa. These supercritical BAs, notably
supercritical CO2, have very good plasticization effect that permits the operation of foaming
processes at lower temperatures. However, their solubility is significantly lower than those of
HCFCs, HFCs or HCs [36-40]. As a result, better distributive and dispersive mixing techniques
and higher system pressure are needed to fully dissolve these supercritical BAs into the polymer
melt prior to the foaming process. In addition, due to their high diffusivity, significant gas loss
16
from foam during its stabilization stage can occur, which limits foam expansion. Together, these
limitations pose technical challenges to produce foams with very low density and/or open-cell
structures by using these BAs.
1.4.2 Waste Reduction of Plastic Products
Most of the commonly used plastics are derived from petroleum and are generally not
biodegradable, so large amount of plastic wastes have been generated at increasing rates over the
years. While innovative plastic materials that are both bio-based and biodegradable have been
developed (e.g., PLA), their costs are often higher than the petroleum-based materials. Also, the
processability of these emerging plastic materials in foaming application and the properties (e.g.,
mechanical strength, resistance to heat/moisture) of these foamed plastics are often inferior to the
conventional plastic foams, which limits their applications. Consequently, their production
volume is still very small compared to petroleum-based plastics, and technological advancement
in material formulation (e.g., additives to control/accelerate crystallization or as mechanical
reinforcement) and foam-processing techniques is imperative to expand their usage and
application.
A key strategy to reduce the consumption of the petroleum-based plastics and hence its
waste generation is to replace solid plastic parts with foamed plastics. However, solid plastics
still exhibit better mechanical strength (e.g., compressive strength) than foamed parts, which
limits the usage of foamed plastics in many applications. Plastic foams with very fine cell
structures, especially microcellular and nanocellular foams, have demonstrated mechanical
strength that are similar to their solid counterparts. However, this is technologically challenging
in many industrial foaming processes. In injection foam molding processes, cell sizes uniformity
is also difficult to achieve due to the transient pressure and heat transfer characteristics within a
mold cavity. Since individual large voids constitute weak spots in molded parts, cell sizes non-
17
uniformity can severely undermine the mechanical properties of foamed parts. Therefore,
innovative technologies to generate high cell density and uniform cell structures are imperative to
the replacement of solid plastic products with foamed parts and the reduction of plastic waste.
In addition, thermoset plastics, notably polyurethane that is widely used in cushioning
foams, are cross-linked during the manufacturing processes, which limits its recyclability. In
comparison, the recyclability of thermoplastic foams is higher since they can be re-melted, and
hence these materials are more environmentally friendly. However, effective strategies to
produce thermoplastic foams with similar cellular structures, notably foams with very high open-
cell content (> 98%) and ultra-low density (> 100 times), and mechanical properties (long fatigue
life), as thermosetting foams are limited. Meanwhile, although thermoplastics foams are
recyclable, the use of various fillers (e.g., cell nucleating agents, mechanical reinforcement) and
polymer grades with different material characteristics can be detrimental to their recyclability due
to immiscibility issues.
1.4.3 Development of Innovative Foams with Specific Functions
A key area of plastic foam development is to apply foaming technologies to emerging
materials with various characteristics, such as superior mechanical properties and heat resistance
(e.g., polyether ether ketone (PEEK)), and biocompatibility and biodegradability (e.g., PLGA,
PLA, and polycaprolactone (PCL)). Another key area is to develop innovative plastic foam
products with specialized foam structures that are not available in current products. In particular,
nanocellular foams has attracted increasing research interest in recent years due to their unique
characteristics. Production of nanocellular plastics is challenging due to the extremely short time
span between the nucleation and collapse of nano-sized cells [41]. This is due to cell coarsening
[41] and collapse [42]. However, as cell sizes decreased to sub-micrometer regions, the
mechanical strength (e.g., compressive strength) of cellular plastics can be drastically improved
18
[3], reaching or even surpassing the strengths of unfoamed plastics by also utilizing
crystallization [43]. The enhanced mechanical strength in nanocellular foams can be attributed to
polymer chains alignment and enhanced crystallization due to foaming. In addition, improved
thermal insulation characteristics have also been demonstrated [44]. It has been pointed out that if
cell sizes are reduced below 50 nm, the contribution of the gas phase in thermal conduction can
be neglected due to the Knudsen effect, which is a result of the limited vibration of gas molecules
within cells with sizes below this limit [45]. Also, owing to the small bubble sizes, nanocellular
foams of amorphous polymers can appear as transparent, which is an important characteristic in
some automotive or aerospace applications. Currently, nanocellular foams are produced with
polymer blends or co-polymers with nano-scale domain in batch processes, and are typically
produced in small thin sheets only. Some examples of polymer blends or co-polymer used in
nanocellular foams are: poly(2,6-dimethyl-1,4-phenylene ether)/poly(styrene-co-acrylonitrile)
(PPE/SAN) [46], PE/rubber [47], polysulfone/polyimide (PSU/PI) [48], PP/styrene-ethylene-
butylene-styrene (PP/SEBS) [43], poly(ether ether ketone)/para-diamine poly(ether imide)
(PEEK/p-PEI), PEEK/meta-diamine poly(ether imide) (PEEK/m-PEI) [49], PS-block-
poly(perfluorooctylethyl methacrylate) (PS-PFMA) diblock copolymer [50, 51], and PS-
poly(methyl methacrylate) (PS/PMMA) copolymer [52]. In summary, the successful production
of foams using emerging materials or foams with nanocellular structures will hinge on
development of innovative technologies that permit higher production rates while achieving
precise control of cell nucleation, growth, deterioration, and stabilization phenomena.
1.5 Objective of the Thesis
With the impending bans on the current blowing agents, the adoption of the
environmentally friendly alternatives (e.g., CO2, N2 and Ar) by plastic foaming industries is
19
inevitable and urgent. Meanwhile, the global usage of thermoplastic foams is expected to increase
exponentially due to its availability, versatility, and superior recyclability when compared to
thermosetting materials. Therefore, it is imperative to overcome the many technical challenges
pertain to the production of innovative thermoplastics foams with environmentally friendly
blowing agents. In this context, the primary objective of this thesis is to advance our
understanding on cell nucleation and growth phenomena in foaming of thermoplastics with
environmentally friendly blowing agents. The resulting knowledge will provide guidance for
industry to improve the current plastic foaming technologies to better control the cellular
structures of plastic foams for different needs and applications.
1.5.1 Key Research Strategy
The core research strategy of this thesis is to develop three innovative foaming
visualizations systems to capture and study plastic foaming processes in situ under different
conditions: 1) Static condition; 2) Extensional stress; and 3) Shear stress. The first system
simulates batch foaming processes while the second and third one simulates the dynamic
conditions in many industrial plastic foaming processes (e.g., extrusion foaming and injection
foam molding). Figure 1-2 depicts the research methodology of this thesis. Together, these three
systems permit in situ observation of plastic foaming processes with direct control of material
formulation (i.e., base polymers, additives and blowing agents) and experimental conditions (i.e.,
temperature, gas content via saturation pressure setting, pressure drop rate, extensional strain,
extensional strain rate, shear strain, shear strain rate) in microscopic-scale (i.e., maximum spatial
resolution of ~2 μm) and under high speed (i.e., up to 120,000 frames/second). Using these
systems, each of the parameters mentioned above can be controlled and investigated individually
as well as together to evaluate their combined effects. In particular, direct observation of bubble
nucleation and growth phenomena under an extensional or shear flow has never been achieved in
20
an isolated manner previously. The visualization systems serve as an important bridge between:
1) Scientific investigation in material characteristics (i.e., surface tension, viscosity, relaxation
time, solubility, diffusivity, pressure-volume-temperature relationships) and foaming theories via
numerical and theoretical modeling; and 2) Processing studies with lab-scale, pilot-scale, and
eventually industry-scale foaming equipment. On one hand, the cell nucleation and growth data
obtained from the visualization systems can be used to verify the numerically simulated results
and to improve the underlying theories, as well as to identify the interrelationships between
material parameters measured in other studies and plastic foaming behaviours. On the other hand,
the visualization data can be used to help improving processing strategies in typical foaming
equipment. Therefore, successful development of innovative foaming visualization systems will
significantly expand our capability to investigate and understand the fundamental mechanisms in
plastic foaming processes. Figure 1-3 illustrates the overall research structure for which this
thesis is part of.
Figure 1-2 – Research methodology of this thesis
21
Figure 1-3 – Overall research structure
This thesis details the development processes of each system, and various experimental
studies to verify the capability of the systems and to elucidate various foaming mechanisms in
plastic foaming processes. Due to the versatility of the systems, they are expected to generate a
wide range of future research opportunities, so the potential impact of this thesis is very high.
1.6 Overview of the Thesis
Chapter 2 presents a literature review and theoretical background on cell nucleation,
growth, and deterioration phenomena in plastic foaming processes. It encompasses the classical
and pseudo-classical cell nucleation theories, cell growth mechanisms, and cell deterioration
mechanisms. It outlines the previous studies in numerical simulations and in situ observation of
plastic foaming processes. It also discusses various imaging techniques for the development of
the visualization systems. Finally, it summarizes the research direction of this thesis based on an
assessment of the previous research works.
22
Chapter 3 focuses on investigation of plastic foaming processes by foaming visualization
under static conditions. It describes the development of a static foaming visualization system that
was designed based on an existing system by Guo et al. [53]. The aim of the new system is to
expand the capability of the existing one, notably with an accurate heating/cooling control. It
presents experimental studies to advance the current understanding of bubble nucleation and
growth in the following areas: 1) Crystal formation and its effects on foaming of PP; 2) The use
of inert gases (i.e., N2, Ar and He) in PP foaming and blowing agent blends (i.e., CO2-N2) in PS
foaming. This information is directly usable in batch foaming processes, and can serve as
baseline information for dynamic processes such as extrusion foaming.
Chapter 4 illustrates the investigation of plastic foaming processes by foaming
visualization under extensional stresses. It describes the development of a novel foaming
visualization system to observe plastic foaming processes under uniform and controllable
extensional strain and strain rate. It also presents experimental studies to clarify the effects of
extensional stresses on the foaming behaviour of PS and PS-talc composites, as well as the
interrelationships between extensional stresses, crystal formation, and foaming behaviour of PP.
Chapter 5 describes the investigation of plastic foaming processes by foaming
visualization under shear stresses. It details the development process of a novel foaming
visualization system to observe plastic foaming processes under uniform and controllable shear
strain and strain rate. It also illustrates experimental studies to investigate the effects of shear
stresses on the foaming behaviour of PS and PS-talc composites.
Chapter 6 serves as a summary of this thesis. The major contribution of this thesis is also
outlined. Finally, this chapter provides a list of recommendation for future research with the
developed visualization systems to fully utilize their capability.
23
CHAPTER 2
LITERATURE REVIEW AND
THEORETICAL BACKGROUND
2.1 Introduction
Since the introduction of plastic foams, there has been multitude of research studies by
academia and industry to explore ways to improve the properties or processability of plastic
materials and foaming technologies to produce foamed parts with better quality and
characteristics. These research efforts have led to the widespread application of plastic foams,
and also formed a valuable knowledge base that is key for the plastic foaming industry to
overcome the previous, current, and future challenges, as well as for the scientific community to
continue to advance our understanding in plastic foaming processes. In this context, this chapter
serves as a thorough review of the previous theoretical studies of cell nucleation, growth, and
deterioration phenomena via conceptual and analytical models, numerical simulation, and
experimental visualization of these processes. The current imaging technologies are also
reviewed to lay the foundation for the discussion of visualization system development in Chapter
3, 4 and 5.
24
2.2 Nucleation Theory
2.2.1 Types of Nucleation
Nucleation is the formation of a new phase from a bulk phase and is a commonly
observed phenomenon in both nature and technology. It can be considered as the first-order phase
transition where a metastable phase transforms into another stable one with multiple phases.
Examples of nucleation are formation of bubble or a crystal within a liquid, and liquid droplets in
saturated vapor. Among these processes, an important form of nucleation is the formation of gas
bubbles from a liquid phase by boiling or cavitation. The Classical Nucleation Theory (CNT)
[54] has been developed based on thermodynamics to predict the kinetic instability limit for
bubble nucleation. According to the CNT, a bubble that has a radius greater than the critical
radius (Rcr) grows spontaneously, while one that has a radius smaller than Rcr collapses; hence a
critical bubble (i.e., a bubble with radius equals to Rcr) is at an unstable equilibrium, where the
free energy of the system is at a maximum (i.e., the free energy barrier). The Rcr is determined by
the state of the system (e.g., temperature, pressure, gas concentration). A bubble is nucleated
when it grows beyond the size of a critical bubble. For the case of plastic foaming, nucleation is
typically achieved by first dissolving a blowing agent into a polymer under high pressure, and
then quickly decreases the solubility of the blowing agent by a rapid depressurization. Due to the
sudden decrease in solubility, the polymer-gas solution becomes supersaturated, and the system
tends to seek a lower energy and stable state by forming bubbles in the polymer-gas solution.
According to the CNT, nucleation occurs either within a continuous liquid phase (i.e.,
homogeneous nucleation), or along a liquid/liquid or liquid/solid interface (i.e., heterogeneous
nucleation). The CNT describes boiling or cavitation phenomena in many single component
systems accurately when extreme care has been used to remove any existing gas bubbles in the
25
liquid phase. However, in plastic foaming processes, it has been demonstrated by various
researchers that the CNT overestimated the degree of supersaturation needed to initiate
nucleation; the observed nucleation rates were significantly higher than were predicted by the
CNT [55]. In this context, other researchers proposed that microvoids exist in polymer-gas
solutions as free volumes between polymer chains, or gas cavities on solid particles (e.g.,
nucleating agents, impurities) due to incomplete wetting between polymer and the solid particles
even under high temperature and pressure [56, 57]. These microvoids could serve as seeds for
bubble nucleation.
Jones et al. [58] classified nucleation into four categories. The first two are classical
homogeneous and heterogeneous nucleation, respectively. The third and fourth types are given as
pseudo-classical and non-classical nucleation. In both of these cases, nucleation occurs at pre-
existing cavities, which require less energy to initiate nucleation. In Type 3, the radius of
curvature of the microvoids are smaller than Rcr, hence a certain amount of energy is needed to
initiate nucleation, whereas in type 4, the radius of curvature of the microvoids are bigger than
Rcr, hence nucleation occur spontaneously. In this thesis, a similar classification is adopted except
that Type 3 and Type 4 are grouped together into one category as Pseudo-Classical Nucleation.
The rationale behind this is that in both cases, nucleation occurs at pre-existing cavities, and the
bubbles’ growth and collapse are still dictated by Rcr. As foaming occur, Rcr would evolve over
time, and nucleation at pre-existing cavities would occur as Type 3 or 4 depending on the value
of Rcr and the sizes of the pre-existing cavities. Consequently, three types of nucleation are used
in this thesis. Figure 2-1 illustrates the various types of nucleation.
26
Figure 2-1 – Types of nucleation
2.2.1.1 Classical Homogeneous Nucleation
This involves nucleation in the liquid bulk phase of a homogeneous solution. There exist
no gas cavities prior to the system being made supersaturated. The required level of
supersaturation is very high, and it is generally not applicable to plastic foaming processes.
2.2.1.2 Classical Heterogeneous Nucleation
This involves nucleation on a liquid/liquid or liquid/solid interface and requires a smaller
level of supersaturation than the first type. In the beginning, there are no gas cavities in the
system. The system is then made to become supersaturated and gas cavities form in a pit or
surface of a nucleating agent. Each bubble then grows and detaches, leaving behind a small
pocket of gas on the pit or surface of the nucleating agent where the bubble was originally
formed. The first bubble formed, without any pre-existing gas pocket, is referred to as classical
heterogeneous nucleation.
2.2.1.3 Pseudo-Classical Nucleation
This form of nucleation includes homogeneous and heterogeneous nucleation at pre-
existing gas cavities (e.g., free volume between polymer chains, gas pockets at the surface of
27
equipment and nucleating agents, etc.). At the time when the system is made supersaturated, Rcr
starts to drop. As the Rcr decreases below the radius of curvature of a pre-existing gas pocket, it
grows in size spontaneously to become a nucleated bubble.
2.2.2 Classical Nucleation Theory
The CNT and the concept of Rcr was first developed by Gibbs [54]. Over the years,
various researchers have built on this theory to examine the necessary conditions and free energy
barrier for homogeneous nucleation [59-64] as well as heterogeneous nucleation with different
surface geometries [65-72]. For example, Tucker and Ward [63] experimentally observe the
growth and collapse of bubbles in a water-oxygen solution to verify the concept of Rcr.
2.2.2.1 Classical Homogeneous Nucleation
According to the CNT, the free energy change (ΔFhom) from a metastable liquid-gas
solution to the homogeneous formation of a gas bubble within the liquid can be given as [60, 63]:
Equation 2-1
where Pbub is the pressure inside the bubble; Psys is the system pressure surrounding the bubble;
Vg is the bubble volume; γlg is the surface tension of the bubble-liquid interface; and Alg is the
bubble surface area. The first term on the left hand side (i.e., -(Pbub-Psys)Vg) is the work done by
the expansion of gas volume inside the bubble, and the second term (i.e., γlgAlg) is the work
required to create the liquid-gas interface that constitutes the bubble. Assuming that the bubble is
spherical in shape, Equation 2-1 can be rearranged as:
Equation 2-2
where Rbub is the radius of the bubble. Based on Equation 2-2, a ΔFhom vs. Rbub plot can be
generated (see Figure 2-2), which exhibits a maximum ΔFhom value. In Figure 2-2, the maximum
ΔFhom represents the free energy barrier for homogeneous nucleation (Whom) and the Rbub at which
28
ΔFhom is at the maximum is the Rcr. Since a system tends to seek a low energy configuration, a
bubble smaller than Rcr tends to collapse, and a bubble larger than Rcr tends to grow
spontaneously. By taking the derivative of ΔFhom with respect to Rbub and equating it to zero, the
Rcr can be determined as [60, 63]:
Equation 2-3
where Pbub,cr is the pressure inside a critical bubble. By substituting Equation 2-3 into Equation
2-2, the free energy barrier for homogeneous nucleation (Whom) can be determined to be [60, 63]:
Equation 2-4
Equation 2-4 indicates that Whom is strongly dependent on γlg and the degree of supersaturation,
which is defined to be (Pbub,cr - Psys). A lower γlg and a higher degree of supersaturation would
cause Rcr and Whom to decrease, which lead to a higher tendency for bubble nucleation.
Figure 2-2 – ΔFhom vs. Rbub plot
Since Pbub,cr is not directly measureable, attempts has been made to estimate its value. Since a
critical bubble is at an unstable equilibrium state, the chemical potentials of the gas in the liquid
phase (i.e., μg,liquid) and gas phase (i.e., μg,gas) must be equal:
Equation 2-5
29
where C is the concentration of the gas in the liquid phase. Assuming that the liquid is not
volatile (e.g., polymer) and the gas in both the liquid and gas phase is an ideal gas, μg,gas can be
expressed as [73]:
Equation 2-6
Similarly, by further assuming that the polymer-gas mixture is a weak solution (i.e., no
interactions between gas molecules), μg,liquid can be expressed as [73]:
Equation 2-7
where Csat is the saturated gas concentration in the liquid phase at Tsys and Psys. By combining
Equation 2-5, Equation 2-6 and Equation 2-7, Pbub,cr can be determined to be [73]:
Equation 2-8
Consequently, the expressions for Rcr and Whom can be updated by substituting Equation 2-8 into
Equation 2-3 and Equation 2-4, respectively, as follows [73]:
Equation 2-9
Equation 2-10
Alternatively, Henry’s Law could be used to simplify Equation 2-9 and Equation 2-10:
Equation 2-11
where H is the Henry’s Law Constant, which could be determined empirically. Consequently,
Equation 2-9 and Equation 2-10 could be rewritten to:
30
Equation 2-12
Equation 2-13
In a typical plastic foaming process, a polymer-gas mixture forms at an elevated temperature and
pressure. Subsequently, a rapid depressurization causes Psys to drop, which leads to a sudden
decrease in Csat and hence the solution becomes supersaturated (i.e., (CPsys/Csat – Psys) > 0).
Consequently, both Rcr and Whom decrease, which cause foaming to occur.
It has been demonstrated in numerous experimental plastic foaming studies that a high
gas content leads a high cell density [24, 31, 74-76]. This can be explained by the decrease in γlg
at a higher gas content [77, 78], and a higher degree of supersaturation upon depressurization due
to the increase of C. In addition, a higher pressure drop rate (-dPsys/dt) is favorable for cell
nucleation [1]. This phenomenon can also be explained by the increase of the degree of
supersaturation since Psys decreases rapidly while C remained high initially. In both cases, Whom
drops according to Equation 2-10 and cell nucleation occurs more easily.
2.2.2.2 Classical Heterogeneous Nucleation
The derivation of Rcr and the free energy barrier for heterogeneous nucleation (Whet) can
be proceeded in a similar fashion. To be specific, the free energy change (ΔFhet) from a
metastable liquid-gas solution to the heterogeneous formation of a gas bubble within the liquid on
a liquid/solid interface can be given as [65-72]:
Equation 2-14
where γsg and γsl are the surface tension along the solid-gas interface and solid-liquid interface;
and Asg and Alg is the surface area along the solid-gas and liquid-gas interface. Similar to the case
of homogeneous nucleation, the first term on the left hand side (i.e., -(Pbub-Psys)Vg) is the work
31
done by the expansion of gas volume inside the bubble. The second term is the energy required to
replace the solid-liquid interface (e.g., nucleating agent-polymer interface) with a solid-gas
interface (e.g., nucleating agent-bubble interface). The third term (i.e., γlgAlg) is the work required
to create the liquid-gas interface that constitutes the bubble. Considering the second term, if the
affinity between the solid and liquid phases is low, especially if it is lower than that between the
solid and gas phases (i.e., γsl > γsg), there would be a higher tendency for the solid-liquid interface
to be replaced by the solid-gas interface. This is favorable for bubble nucleation. This behaviour
can also be explained by the expression of ΔFhet, whose value decreases when γsl increases and/or
γsg decreases. Considering the third term, if the affinity between the liquid and gas phases is high
(i.e., small γlg) and Alg is small, the energy required to generate the bubble surface also decreases.
Physically, a smaller Alg means that a smaller liquid-gas interface is needed for bubble nucleation
when compared to the homogeneous case. This effectively decreases the free energy required for
bubble nucleation. To achieve this, it is usually desirable to have a large contact angle (θc)
between the solid and liquid phase. This is illustrated in Figure 2-3, which compares the bubble
shape on a planar surface at different contact angles. As shown in this figure, Alg increases
significantly as θc decreases, and eventually approaching the case of homogeneous nucleation
where the entire spherical surface area is needed for nucleation. The contact angle is a material
properties that is related to the interfacial energies by the Young’s Equation [73]:
Equation 2-15
From this equation, it is clear that in order to have a large θc, it is desirable to have a large γsl and
small γsg. In summary, heterogeneous nucleation occurs via the replacement of a high-energy
solid-liquid surface by a low energy solid-gas interface and the generation of a new liquid-gas
interface with a smaller area than the case of homogeneous nucleation. Due to this mechanism,
32
the free energy needed to initiate heterogeneous nucleation is generally lower than the
homogeneous case.
Figure 2-3 – Bubble shape vs. contact angle on a planar surface
The expressions for Whet and Rcr could be derived in a similar way as the homogeneous
case. Using a planar nucleating surface as a case example, Equation 2-14 can be expressed as
[69]:
Equation 2-16
where πRbub3(2 + 3cosθc - cosθc)/3 is the volume of the bubble; πRbub
2(1 - cos2θc) is the area of
the solid-liquid interface; and 2πRbub2(1 + cosθc) is the area of the liquid-vapor interface; and Rbub
is the radius of curvature of the meniscus that constitutes the bubble on the solid surface. By
rearranging Equation 2-15 into:
Equation 2-17
and substitutes the resulting equation into Equation 2-16. The expression of ΔFhet can be
simplified to:
33
Equation 2-18
By taking the derivative of ΔFhet with respect to Rbub and equating the resulting equation
to zero, it can be shown that the expression for Rcr is the same as the homogeneous nucleation
case (Equation 2-3). The expression for Whet can then be determined by substituting Equation 2-3
into Equation 2-18, which, after simplification, differs slightly from Whom, as follows [69]:
Equation 2-19
where F is a geometric factor that equals to the ratio of the volume of a heterogeneously
nucleated bubble to that of a spherical bubble having the same radius of curvature. The
expression of F for planar surface is [69]:
Equation 2-20
Using this equation, it has been demonstrated that as θc increases, F also decreases, which
ultimately causes Whet to drop.
While planar surface is a good approximation for foaming processes on surfaces like
platelet-shaped nucleating agents and smooth equipment walls, it might not be suitable for
describing surfaces on small domains (e.g., rubber particles, talc, nano-silica). Inorganic
nucleating agents are often added to polymer matrix to enhance bubble nucleation. Many of these
particles (e.g., talc, nanoclay) and their agglomerates often have rough surface geometries in
micro- or nano-scale. Previous researchers model this surface non-uniformity as a conical cavity.
By using Equation 2-14, Equation 2-15, and the expressions for areas and volumes, a similar
analysis as the case with planar surface can be used to determine the expressions of Rcr and Whet.
34
It turns out that the expression for Rcr also remains the same as the homogeneous case (see
Equation 2-3). The expression of Whet is the same as Equation 2-16 except that a different
expression of F is determined [67]:
Equation 2-21
where β is the semi-conical angle (refer to Figure 2-4). In this thesis, this model has been adopted
to study the effectiveness of inorganic nucleating agents (i.e., talc) in plastic foaming processes.
Figure 2-4 – Bubble nucleation at a conical cavity
In addition to planar and conical cavity, other surface geometries have also been
investigated. For example, nucleation on the outer surface and inner surface of a spherical
interface have been examined by Wilt [68] and Cole [67], respectively. The first case constitute
foaming on a hard spherical surface, while the latter describe foaming within a soft spherical
domain that is dispersed in a hard matrix. Meanwhile, if the compliancy of the two domains is
similar, the interface is not fixed (e.g., a polymer matrix with infusion of mineral oil droplets).
This situation has also been examined by Apfel et al. [71] and Javis et al. [72].
35
2.2.2.3 Prediction of Nucleation Rate
The concept of Rcr, Whom, and Whet in the CNT provide information on the conditions to
generate a metastable state necessary for bubble nucleation. However, the CNT cannot predict
when a system would transfer, through molecular perturbation or external work, from a
metastable liquid-gas solution to one where a bubble with size Rcr is generated within the liquid-
gas mixture. It is necessary to consider kinetics to determine the rate of bubble nucleation. In this
context, Blander and Katz [59] defined bubble nucleation rate, J, as the rate at which critical
bubbles gain gas molecules, which trigger their spontaneous growth to become nucleated
bubbles. They prescribe an expression for J as follows:
Equation 2-22
where ν is the rate at which gas molecules strike a bubble surface per unit area; A(Rcr) and n(Rcr)
are the surface area and number density of critical bubbles; and Z is the Zeldovich factor that
accounts for thermodynamic fluctuation that affects n(Rcr). The expression for ν is given in the
following [59]:
Equation 2-23
where m is the mass of a gas molecule. Moreover, it has been assumed that n(Rcr) follows the
Arrhenius equation [59]:
Equation 2-24
where N is the number of gas molecules per unit volume of polymer, kB is the Boltzmann’s
Constant, and W is the activation energy that can be considered as Whom or Whet depending on the
type of nucleation. By combining Equation 2-22, Equation 2-23, and Equation 2-24, the
homogeneous nucleation rate (Jhom) has been derived as [59]:
36
Equation 2-25
Similarly, the expression for heterogeneous nucleation rate (Jhet) has been determined [59]:
Equation 2-26
where Q is the ratio of the surface area of the heterogeneously nucleated bubble to that of a
spherical bubble with the same radius of curvature. In this thesis, the expression of Q for conical
cavity is used to study plastic foaming with inorganic nucleating agents. However, it is noted that
the most dominant term affecting the cell nucleation rates is the exponential term (i.e., -W/kBTsys).
Considering the case of rough or irregular surfaces that are modeled as conical cavities,
the value of β is unlikely to be constant. A probability density function, ρβ(β), can be used to
model the uncertainty of the value of β. In particular, Leung et al. [79] has numerically simulated
the cell nucleation behaviour using the normal and uniform distributions to study the effects of
ρβ(β). The ρβ(β) can be incorporated into the expression for Jhet as follows [80]:
Equation 2-27
2.2.3 Pseudo-Classical Nucleation Theory
Experimental studies, reviewed and summarized by Lubetkin [55], have shown that
bubble nucleation often takes place at supersaturation levels much lower than those determined
with the CNT. The CNT was derived on the basis that continuum mechanics holds. However, for
a nano-sized bubble, the curvature of the bubbles surface and the size of polymer molecules are
comparable, hence continuum mechanics might not be valid. In particular, Kim et al. [81] pointed
out that the CNT’s representation of a bubble surface as a flat interface significantly
37
overestimates the surface energies of the bubble surface. This is because polymer molecules can
explore more conformations on a curved surface than on a flat surface, so the actual surface
energy of a bubble interface is lower than what the CNT predicts. Moreover, as the radius of a
bubble is reduced to the nano-scale, the CNT’s assumption of an abrupt change of density at the
polymer-gas interface no longer holds (see Figure 2-5). At such scale, the diffuse walls collide
causing increased mixing of polymer and gas molecules, which causes further reduction of
internal energy associated with the bubble interface [81]. However, despite the shortcomings of
the CNT, it is capable to explain plastic foaming behaviour and the effects of various material
and experimental parameters in a qualitative manner. Therefore, the concepts of CNT have been
adopted in this thesis for its simplicity.
Figure 2-5 – Change of density at polymer-gas interface
On the other hand, the CNT’s assumption that no microvoids existed prior to cell
nucleation is not realistic and might lead to incorrect interpretation of foaming mechanisms.
Since impurities, nucleating agents and/or their agglomerates might have rough or porous
surfaces, they cannot be completely wetted by the plastic melt due to high viscosity of plastic
melt and contact angle restraint [56, 66, 82]. Therefore, pre-existing gas cavities might act as
seeds for bubble nucleation. Various researchers have suggested that this is a dominant plastic
foaming mechanism. For example, Biesenberger and Lee [83-86] concluded that foaming in a
plastic devolatilization process occurs primarily through heterogeneous nucleation at microscopic
38
cavities on nucleating agents or contaminants in which gas is entrapped. Extending the analysis
by Kweeder et al. [87], Ramesh et al. [88] proposed a bubble nucleation model that considered
nucleation as the survival and growth of microvoids. They verified the model with the batch
foaming processes of a PS-rubber composite, where cavitations were created in the rubber phase
and/or the PS-rubber interface during the cooling process of sample preparation by utilizing the
thermal expansion mismatch between PS and rubber [89]. Using a “metastable cavity model” that
was developed based on the cavitation theory identified by Harvey et al. [56] to describe bubble
formation in blood vessels, Lee and Biesenberger [86] argued that shear flow is needed to detach
gas cavities on the surfaces of nucleating agents or contaminants to form bubbles. This shear-
induced foaming behaviour is discussed further in Section 2.2.4. In summary, the assumption that
no microvoids exists fails to describe the cell nucleation mechanisms in plastic foaming in a
comprehensive manner. Therefore, the CNT has to be modified to include cell nucleation from
microvoids. Park et al. [90] has considered homogeneous cell nucleation from microvoids, which
is briefly outlined in the following section. The heterogeneous case is also examined in this
thesis.
2.2.3.1 Homogeneous Cell Nucleation from an Existing Microvoid
Based on Figure 2-6b, the free energy change (ΔFhom) from a microvoid with a size of
Rbub,1 within a liquid to a larger gas bubble with a size of Rbub,2 within the liquid can be given as:
Equation 2-28
By assuming that the bubble is spherical, Equation 2-28 can be simplified to be:
39
Equation 2-29
Both Pbub,1 and Rbub,1 are independent of Rbub,2. By taking the derivative of ΔFhom with respect to
Rbub,2 and equating it to zero, the expression of Rcr can be shown to be the same as the CNT case
(see Equation 2-3). By substituting the expression of Rcr to Equation 2-29, the free energy barrier
of homogeneous cell nucleation from an existing microvoid (Whom) can be determined to be [90]:
Equation 2-30
The first term on the right hand side is the free energy barrier to nucleate a critical bubble
homogeneously within a liquid-gas solution without the presence of an existing microvoid (see
Equation 2-4). The second term on the right hand side is the free energy change from a
metastable liquid-gas solution to the homogeneous formation of a gas bubble with a size of Rbub,1
within the liquid. As demonstrated by this equation, the overall free energy is decreased if cell
nucleation occurs through the growth of an existing microvoid. Therefore, if there are microvoids
within a polymer-gas mixture, cell nucleation are likely to occur via the growth of these
microvoids as supposed to be homogeneously nucleated from the bulk phase of the polymer-gas
mixture. Also, due to the presence of existing microvoids, the cell nucleation rate and cell density
is expected to increase. Based on the expression for classical homogeneous cell nucleation rate
(Jhet) (Equation 2-25), the homogeneous cell nucleation rate from microvoids can be derived as:
40
Equation 2-31
where ρR(Rbub,1) is the probability density function of Rbub,1. If no microvoid exists (the case for
the classical homogeneous nucleation), then ρR(Rbub,1 = 0) = 1. In that case, Equation 2-31 would
be reduced to the original form (Equation 2-25).
Figure 2-6 – Cell nucleation for CNT vs. foaming through growth of a microvoid
2.2.3.2 Heterogeneous Cell Nucleation from an Existing Microvoid
Based on Figure 2-7b, the free energy change (ΔFhet) from a gas cavity with a radius of
curvature of Rbub,1 on a nucleating site within a liquid to a larger gas cavity with a radius of
curvature of Rbub,2 on the same nucleating site within the liquid can be determined using a similar
approach as the homogeneous case. Assuming that the nucleating site is a conical cavity, ΔFhet
can be determined as follows:
41
Equation 2-32
By using Equation 2-15 and the expressions for areas and volumes, Equation 2-32 can be
simplified to:
Equation 2-33
where F is the geometric factor that equals to the ratio of the volume of a heterogeneously
nucleated bubble to that of a spherical bubble having the same radius of curvature, which has
been given in Equation 2-21. Similar to the homogeneous case, both Pbub,1 and Rbub,1 are
independent of Rbub,2. By taking the derivative of ΔFhet with respect to Rbub,2 and equating it to
zero, the expression of Rcr can be shown to be the same as the CNT case (see Equation 2-3). By
substituting the expression of Rcr to Equation 2-43, the free energy barrier of heterogeneous cell
nucleation from an existing microvoid (Whet) on a conical cavity can be determined to be:
Equation 2-34
The first term on the right hand side is the free energy barrier to nucleate a critical bubble
heterogeneously on a conical cavity within a liquid-gas solution without the presence of an
existing microvoid (see Equation 2-4). The second term on the right hand side is the free energy
change from a conical cavity within a metastable liquid-gas solution to the formation of a gas
bubble on the conical cavity with a size of Rbub,1 within the liquid. As shown by this equation, the
overall free energy is decreased if cell nucleation occurs through the growth of an existing
42
microvoid on a cavity, which is similar to the homogeneous case. Therefore, if there are
microvoids on cavities (on impurities or nucleating agents), cell nucleation are likely to occur via
the growth of these microvoids as supposed to be heterogeneously nucleated from a nucleating
site. Also, due to the presence of existing microvoids on the cavities, the cell nucleation rate and
cell density is also expected to increase. Based on the expression for classical heterogeneous cell
nucleation rate (Jhet) (Equation 2-27), the heterogeneous cell nucleation rate from microvoids can
be derived as:
Equation 2-35
where ρβ(β) is the probability density function of the semi-conical angle of the conical cavities (β)
and ρR(Rbub,1) is the probability density function of Rbub,1. Note that the value of β can also
influence the distribution of Rbub,1. If no microvoid exists (the case for the classical heterogeneous
nucleation), then ρR(Rbub,1 = 0) = 1. In that case, Equation 2-35 would be reduced to the original
form (Equation 2-27).
43
Figure 2-7 – Cell nucleation for CNT vs. foaming through growth of a microvoid on a conical
cavity
2.2.4 Stress-Induced Nucleation
In 1981, via direct observation of plastic foaming processes via a transparent mold in
structural foam molding processes, Han and Yoo [91] suggested that the level of stress in a
plastic melt might have a significant effect on bubble formation and growth. In a subsequent
extrusion foaming study, Han and Han [92] pointed out that, in addition to nucleation by thermal
fluctuations and cavitation, both shear stress near the die wall and flow around the die center
could induce cell nucleation. Similar results were also reported by Tsujimura et al. [93], Taki et
al. [94], and Tatibouët and Gendron [95]. A possible explanation was given by Lee and
Biesenberger [86], who, as mentioned in Section 2.2.3, argued that shear flow is imperative for
bubble nucleation. They hypothesized that gas cavities, modeled as conical pits, exist on rough
surfaces of nucleating agents or contaminants due to incomplete wetting. Upon depressurization,
the gas cavities tend to expand towards the lip of the cavity. A shear flow would help to detach
44
this expanding gas pocket from the conical cavity; hence a bubble would be formed. In a
subsequent study, Lee [96] identified that both shear rate and shear force induced cell nucleation.
He attributed the increase in cell nucleation to the conversion of the mechanical energy from the
shear flow to the interfacial energy needed for bubble nucleation. Guo and Peng [97] and Guo et
al. [98] conducted extrusion foaming experiments with a slit die. They observed that the cell
density of foamed samples was higher near the die wall at low throughput rate due to the higher
amount of shear stress at these regions. As the throughput rate increased, the cell density
increased significantly and becomes more uniform throughout the sample thickness. Similar to
Lee’s theory [96], they attributed the enhancement of cell nucleation to the increased shear
energy as the throughput was increased.
To investigate the effect of shear stresses on plastic foaming in isolation, some researchers
also developed batch foaming systems that induced shear stresses [99, 100] or a combination of
shear stresses and vibrations [101, 102] to a plastic-gas mixture at high temperatures and
pressures, which, when depressurized, generated foams (see Figure 2-8 and Figure 2-9). In
particular, Chen et al. [100] developed a “cell stretch model” to explain shear-induced nucleation
whereby bubble nuclei are stretched during shear flow. They hypothesized that these nuclei
would expand more easily than spherical bubbles due to their larger size (along the shear
direction) and surface area. Both Zhu et al. [101] and Gao et al. [102] demonstrated that the
bubble densities were increased and bubble size uniformity were improved by superimposing an
oscillatory vibration onto a shear flow in an orthogonal direction. Holl et al. [103], and Handa
and Zhang [104] also investigated stress-induced bubble nucleation, but their foaming
experiments were only conducted in a solid state at relatively low temperatures. Also, in these
studies where stresses were applied to plastic samples in batch processes [99-104],
characterizations were carried out with scanning electron microscopy (SEM) after the foams had
45
cooled and stabilized. Since cell coalescence, coarsening, and collapse could occur to nucleated
cells before they were stabilized, the shear stress effect on cell nucleation could not be
determined in an isolated manner.
Figure 2-8 – Foaming simulator developed by Chen et al. [99]
Figure 2-9 – Foaming simulator developed by Zhu et al. [101]
In a plastic devolatilization study by Albalak et al. [105] with a falling strand apparatus,
some micro-sized bubbles were observed along the surface of bigger bubbles in a series of SEM
pictures of foamed plastic strands. They proposed that bubble expansion could generate tensile
stresses in the surrounding melted plastic that would result in decreased local system pressure.
46
This would increase the degree of supersaturation and cause secondary micro-bubbles to nucleate
around the bubble. Similar results were obtained by Yarin et al. [106]. They argued that elastic
energy would be stored in the vicinity of a primary bubble as it grows and that it is then released
due to mechanical degradation near the primary bubble, which subsequently causes secondary
bubbles to form. Using the batch foaming visualization system developed by Guo et al. [53], a
similar bubble growth-induced cell nucleation phenomenon was observed in situ in the foaming
of PS-talc composites with CO2 by Leung et al. [107]. Figure 2-10 depicts this foaming
behaviour. Meanwhile, Wang et al. [108] simulated the pressure profile around a solid particle
near the presence of a growing cell under the following three constraints for the solid particle: 1.
static; 2. simple rotation; and 3. a combination of translation and rotation. It was demonstrated
that tensile stresses could exist around a particle, which supported the extensional stress-induced
cell nucleation theory proposed by Albalak et al. [105] and confirmed by Leung et al. [107] (refer
to Figure 2-11).
Figure 2-10 – Bubble growth-induced cell nucleation
47
Figure 2-11 – PS-talc foaming visualization under static condition (Tsys = 180 °C) [107]
In this thesis, innovative experimental studies based on direct observation of plastic
foaming processes under various dynamic conditions are conducted to evaluate the stress-induced
foaming mechanisms described in this section, as well as to improve our understanding in this
subject area.
2.2.5 Crystal-Induced Nucleation
In extrusion foaming processes, polymer is first melted to a high temperature above its
melting temperature (Tm) during the melting and gas injection section, and then subsequently cool
down to below its Tm downstream (e.g., in the second extruder of a tandem extrusion foaming
line or the static mixer in a single extrusion foaming line). When a semi-crystalline polymer-gas
mixture is cooled down to below its Tm, which is typically lower than the Tm of the polymer in the
ambient condition due to the plasticization effect of gas, the polymer will start to crystallize. The
crystallization starts in regions near the barrel wall due to its lower temperature, and the crystals
are mixed into the polymer-gas matrix by the screw motion. The nucleation and growth of
crystals continue downstream to the die where foaming occur. The crystals’ density and sizes
depend on the processing temperature and the residence time. On one hand, crystals help to
induce cell nucleation and maintain foam structure during the foam stabilization process as the
foams exit the die and cool. On the other hand, an excessive amount of crystals causes the
48
viscosity of the polymer-gas mixture to increase significantly, which hinders the expansion of
foams (See Section 2.3.3 for further details). Also, gas cannot be dissolved into the crystalline
regions effectively, which ultimately leads to non-uniform cell nucleation in regions with
different crystallinity and structures. Consequently, a non-uniform foam structure is generated.
Previous studies have shown that with proper selection of processing parameters and
technique, it is possible to tailor the crystallization kinetics for different cell morphology and
mechanical properties. For example, Xu [109] conducted an extensive study of PP foaming with
CO2 and showed that by varying the system temperature (154 to 160 °C), saturation pressure (9
to 16 MPa) and depressurization rate (1.4 to 15 MPa), different cellular structures (uniform or
bimodal cellular structure) could be obtained with the presence of crystalline phrases.
Several crystal-induced foaming mechanisms have been discussed previously. Koga and
Saito [110] investigated the morphology of high-density polyethylene (HDPE) and
poly(vinylidene fluoride) (PVDF) crystallized under high pressure CO2 with polarized optical
microscopy, and observed a fine-layered porous structure for both materials. Based on the
crystallization study by Oda and Saito [111], they attributed such characteristic to the exclusion
of CO2 from the crystal growth front to the intercrystalline amorphous region and the growth of
bubbles by the supersaturation of CO2 in the constrained amorphous region. Taki et al. [112]
demonstrated this mechanism with in situ observation of the foaming processes of polylactide
(PLA), where the majority of bubbles were observed to be nucleated around crystals spherulites
foamed in PLA. Reignier et al. [113] used ultrasonic measurement to detect the onset of cell
nucleation in the foaming of poly(ε-caprolactone) with CO2; they demonstrated that the presence
of crystals led to a 5 to 10 times increase in the degassing pressure (the pressure at which cell
nucleation occurred during the decompression process) when compared to the amorphous case.
49
This further demonstrated that crystals could induce cell nucleation. Meanwhile, by comparing
the crystallization kinetics and foaming behaviour of linear and branched PP, Liao et al. [114]
demonstrated that a large density of crystals with small sizes are favorable for generating foams
with high cell density. They suggested that the crystals acted as heterogeneous nucleating sites to
promote cell nucleation.
Despite these pioneering studies, the fundamental mechanisms of crystal-induced cell
nucleation still need to be clarified further. This is addressed in this thesis through foaming
visualization studies of semi-crystalline polymers under static and dynamic conditions.
2.2.6 Nucleating Agents for Heterogeneous Nucleation
Nucleating agents are often used in plastic foaming processes to produce foams with high
cell densities, small cell sizes, and narrow cell size distributions. As mentioned in Section 2.2.2.2
to Section 2.2.3, the bubble nucleation enhancement could be attributed to the lower free energy
barrier (Whet) in heterogeneous nucleation and the presence of microvoids on nucleating agents
due to incomplete wetting. Dating as early as Hansen and Martin’s work in the 1960s [115],
several studies have investigated the effectiveness of various nucleating agents in plastic foaming
processes. For example, Yang and Han [116] compared the foamability of low density
polyethylene (LDPE) blended with nine different nucleating agents (aluminum stearate, calcium
carbonate, calcium hydroxide, calcium stearate, Celogen CB, sodium bicarbonate, sodium
bicarbonate/citric acid mixture, talc, and zinc stearate). Colton and Suh [117, 118] carried out
theoretical and experimental studies on heterogeneous cell nucleation phenomena using
polystyrene (PS) filled with zinc stearate, stearate acid, and carbon black. In a subsequent study
by Colton [119], the microcellular foams of semi-crystalline polymers (polypropylene) were
produced by using talc and sodium benzoate as nucleating agents. Chen et al. [120] investigated
the effects of the filler size of calcium carbonate, talc, and titanium oxide on the foamability of
50
high density polyethylene (HDPE). They found that a smaller additive size led to a higher cell
density when the gas saturation pressure was high. Kim et al. [121] found that there was a critical
size of rubber particles in the foaming of thermoplastic olefin (TPO) to achieve the maximum cell
density. In theory, a smaller nucleating agent has a higher number density- and surface area-to-
weight ratio. Hence, the number of nucleating sites and the total area for heterogeneous
nucleation are also higher than for larger particles when the same weight content of nucleating
agents is used. Consequently, a number of researchers have also investigated the feasibility of
such nano-particles as nanoclay [25, 122, 123], nanosilica [124-126], nanocellulose [127], carbon
nanofiber [128], and carbon nanotubes [129] as nucleating agents.
Of the nucleating agents mentioned above, talc is one of the most widely used due to its
effectiveness, the ease with which it disperses in polymer, and its low cost. Many research studies
have been conducted to identify the optimal talc content and processing conditions for the
foaming of various polymer-talc composites, such as LDPE [116, 130], HDPE [31, 120], PP
[119, 131, 132], PS [74], and PLA [133]. Due to its wide applications, talc was chosen as the
main nucleating agent used in the experimental studies of this thesis to elucidate the
interrelationships between the use of nucleating agents, applied extensional and shear stresses,
and the plastic foaming behaviour.
2.3 Bubble Growth and Deterioration Mechanisms
Bubble growth and collapse in plastic foaming processes are generally driven by mass
transfer of gas molecules and momentum transfer between the bubble and the surrounding
polymer-gas solution. At the onset of bubble growth upon nucleation, the bubble pressure (Pbub)
is typically quite high owing to its small radius. The large pressure difference between the gas
and liquid phase causes bubble to grow. At the same time, the gas concentration gradient across
51
the bubble interface causes gas to diffuse into the bubble. As the bubble grows in size, the Pbub
decreases, and the bubble growth process become more diffusion-driven. Eventually, the gas
concentration within the polymer-gas solution diminishes, and bubble growth ceases. In typical
foaming processes, the depressurization that causes foaming to occur also exposes the unstablized
foam to a low-pressure environment (e.g., the ambient pressure). This leads to a concentration
gradient that causes gas diffusion from the polymer-gas solution to the surrounding. Therefore,
the gas concentration in the polymer-gas solution decreases, which decreases the bubble growth
rate. If the foam sample is not cooled and stabilized rapidly, the gas loss can eventually cause gas
diffusion out of the bubble, hence the bubble shrinks and even collapses. Other bubble
deterioration mechanisms can also accelerate this mass transfer phenomenon and they are
discussed in Section 2.3.2 and 2.3.3.
2.3.1 Cell Growth
In plastic foaming processes, bubbles grow simultaneously in close proximity to generate
a cellular structure. In this context, Amon and Denson [134] proposed the cell model whereby a
polymer-gas solution is divided in spherical units with limited amounts of dissolved gas. This is a
significant improvement over the “Single Bubble Growth Model”, which model a single bubble
immersed in an reservoir with unlimited supply of gas [135, 136]. Consequently, the cell model
has been widely adopted in the subsequent bubble growth research in plastic foaming processes
[137-139]. To analyze a bubble growth process, it is necessary to simultaneously solve a set of
governing equations: the continuity, momentum balance, and gas diffusion equations for a
polymer-gas solution around a bubble interface, the constitutive equation that describes the
viscoelastic nature of polymer-gas solutions, and the conservation of mass equation for gas
molecules. A brief summary of this analysis using the cell model is given here.
52
It is assumed that the polymer-gas solution is an incompressible fluid, and the bubble is
spherically symmetric. In this case, the continuity equation for a polymer-gas solution
surrounding a bubble interface can be reduced to [137]:
Equation 2-36
where r is the radial position and Vf(r) is the fluid velocity at r. Since the fluid velocity at the
bubble interface equals the growth rate of the bubble ( , the Vf(r) can be expressed as:
Equation 2-37
The inertial force is assumed to be negligible since polymer-gas solution is highly viscous with a
Reynold’s number < 1. In this case, the momentum equation for a polymer-gas solution
surrounding a bubble interface can be simplified to [140]:
Equation 2-38
where τrr and τθθ are the stress components in the radial and tangential direction, respectively. In
order to relate the stresses within the fluid to the pressure of gas inside the bubble, Equation 2-38
can be integrated from the bubble surface (i.e., R = Rbub) to the outer boundary of the shell of the
polymer-gas solution surrounding the bubble (i.e., R = Rshell). By combining the resulting
equation with the force balance condition at the bubble interface (Equation 2-39) [140]:
Equation 2-39
the momentum equation can be expressed as [140]:
Equation 2-40
53
In order to solve Equation 2-40, it is necessary to determine the expressions for the stress
components (i.e., τrr and τθθ) using a constitutive equation that relate the stresses with the rate of
deformation of the polymer-gas solution. In particular, Arefmanesh and Advani [140] and Leung
et al. [138] have adopted the upper convected Maxwell model to describe the viscoelastic nature
of the polymer-gas solution. This model has been shown to accurately describe important
viscoelastic behaviour such as stress relaxation and normal stress effects [140]. The upper
convected Maxwell model can be represented as [140]:
Equation 2-41
where τ is the stress tensor; λ is the relaxation time; τo is the upper convected time derivative of τ;
η0 is the zero-shear viscosity of the polymer-gas solution; and γo is the strain rate tensor. τo is
defined as [141]:
Equation 2-42
where D/Dt is the substantial derivative operator. By combining Equation 2-37, Equation 2-41,
and Equation 2-42, and applying a Lagrangian coordinate transformation of ,
the constitutive equation can be reduced to the following ordinary differential equations [140]:
Equation 2-43
Equation 2-44
Assuming that the accumulation of gas molecules on the bubble interface is negligible, the
conservation of mass dictates that the rate of change of the gas mass within the bubble must be
equal to the net mass transfer of gas molecules across the bubble interface. By further assuming
54
that the gas molecules behave like an ideal gas, the bubble pressure (Pbub) can be determined
based on the mass transfer through diffusion at the bubble interface [137]:
Equation 2-45
where RG is the universal gas constant and D is the gas diffusivity in the polymer-gas solution. In
order to solve this equation, it is necessary to determine the concentration gradient at the bubble
interface, which can be achieved by solving the gas diffusion equation for the polymer-gas
solution [137]:
Equation 2-46
By simultaneously solving Equation 2-40 and Equation 2-43 to Equation 2-46 with appropriate
initial and boundary conditions, the bubble growth dynamics for plastic foaming processes can be
determined. Due to the complexity and coupling nature of the governing equations, numerical
methods are generally used to obtain such solutions.
2.3.2 Cell Coalescence
When two neighboring cells grow, the polymer-gas solution between them (i.e., the cell
wall) is subjected to an approximate biaxial stretching. Consequently, the cell wall could be
ruptured due to overstretching. This is not acceptable for close-cell foams. For the production of
open-cell foams, this process of cell wall rupture (i.e., cell opening) is necessary to generate
interconnectivity between cells. The foam must be stabilized quickly (i.e., via cross-linking in
thermoset and cooling in thermoplastics) to maintain the cellular structure. On the other hand, if
the foams are not stabilized rapidly, adjacent cells can combine together, and the cellular
structure collapse non-uniformly. This phenomenon is termed cell coalescence, which is
undesirable to the foam quality (e.g., detrimental to its mechanical properties). Also, due to cell
55
coalescence, gas loss to the environment is also accelerated, hence the foam expansion decreases.
Due to the difficulty to control this phenomenon to generate high-quality open-cell foams, other
strategies, such as salt-leeching and puncturing of stabilized foams, have also been investigated
and utilized for this purpose.
To reduce or eliminate cell coalescence, attempts have been made to develop polymers
with optimized the extensional properties to prevent cell wall ruptures. Many of these studies
focused on linear PP due to its low melt strength that causes cell coalescence during plastic
foaming processes. One common method to solve this issue is to introduce branching in PP
molecules. For example, Park and Cheung [142] and Naguib et al. [24] investigated foaming with
long-chain-branched PP (LCB-PP), which exhibits significant strain hardening under extension.
Through extrusion foaming, they demonstrated that much higher cell densities and volume
expansion ratios could be generated with LCB-PP when compared to linear PP. Similar results
were obtained by McCallum et al. [143] in batch foaming processes. All of these three studies
attributed the better foaming behaviour of branched PP to its higher melt strength that lead to
reduced cell coalescence during the early stage of cell growth. Spitael & Macosko [144] and
Stange & Münstedt [145] characterized the uniaxial extensional viscosities of linear PPs, LCB-
PPs, and their blends at foaming conditions, and attempted to relate rheological properties to cell
morphology. They found that even a small amount of LCB-PP (e.g., 10% by weight) in the blend
can improve the expansion and reduce the cell opening of linear PP. Stange & Münstedt [40]
attributed the higher volume expansion of LCB-PP and blends containing LCB-PP to their higher
strains at rupture and higher uniformity in their deformation during extension compared to linear
PP. In addition to branching, other ways to suppress cell coalescence is to decrease the melt
temperature [146] and to incorporate additives (e.g., nano-particles [147]) into the polymer
matrix. In the cases of plastic composites, additive particles could orient along the cell walls
56
during the foaming processes to enhance the melt strength, which is desirable for suppressing cell
coalescence [147]. This strengthening effect is believed to be more significant for additives with
high aspect ratio. Meanwhile, these additives can also act as nucleating agents and barrier for gas
diffusion. Consequently, more cells would be nucleated while gas loss to the environment is
decelerated. As a result of the increased foam expansion, the cell wall thickness might decrease at
faster pace, which could ultimately cause cell opening and hence cell coalescence, so it is
necessary to control the melt temperature at the same time to prevent this behaviour.
2.3.3 Cell Coarsening and Collapse
During foam processing, cell growth and collapse processes is driven by the pressure and
concentration differences between a cell and its surrounding. The gas concentration in small cells
is higher than bigger ones. Therefore, gas tends to diffuse from a small bubble to an adjacent
bubble with a bigger size, and the small bubble shrinks and collapses eventually. This cell
deterioration mechanism is termed cell coarsening. Therefore, if there exist a non-uniform cell
size distribution during the stabilization stage, the larger cells would continue to grow while the
smaller ones shrink, and the final stabilized foams would have highly non-uniform cellular
morphology. Compounding with the fact that cell growth is thermodynamically favorable to cell
nucleation, it is clear why undissolved gas pockets in plastic matrix is hugely detrimental to the
resulting foam quality and must be avoided. On the other hand, even if cell coalescence and cell
coarsening are suppressed, gas diffusion to the environment could still cause rapid decrease in
gas concentration in a polymer. This leads to gas transfer away from bubbles, and hence they
shrink and collapse. Studies in the past have investigated the mechanisms for cell coarsening and
cell collapse, and developed strategies to prevent them.
To understand the cell coarsening process in plastic foaming, Zhu and Park used finite
element analysis to simulate the stability of nano-sized bubbles in the presence of neighboring
57
bubbles [41]. The simulation demonstrated that nano-sized bubbles collapse rapidly upon
interaction with adjacent cells with larger sizes due to cell coarsening. This study demonstrates
the difficulty in generating nanocellular foams as mentioned in 1.4.3.
Meanwhile, Xu et al. investigated the bubble growth and collapse phenomenon in the
foaming of low-density polyethylene (LDPE) blown with a CBA under atmospheric pressure
using computer simulation [148], and the results were compared with empirical data obtained
from in situ foaming observation. It was shown that a higher gas concentration increases a bubble
life span. On the other hand, an increase in elasticity or surface tension decreases the life span of
a bubble. Furthermore, a bubble life span decreases with temperature due to increased gas
diffusivity. Guo et al. used a high pressure batch foaming visualization system to study the effect
of system pressure on bubble sustainability of LDPE/CBA foaming systems [149]. It was found
that a bubble life span increases with the system pressure, which is believed to be due to the
higher gas content that sustained the bubble growth.
These aforementioned studies used diffusion phenomena to explain the cell growth and
collapse processes. Meanwhile, these processes can also be explained by the CNT [54]. As
mentioned in Section 2.2.2, a bubble that is larger than Rcr, grows, whereas one that is smaller
than Rcr collapses. Leung et al. [42] investigated the continuous change of Rcr during plastic
foaming processes of LDPE with CBA and the effect of Rcr on bubble sizes using computer
simulation. The results were also compared with in situ observation of the bubble growth and
collapse phenomena in a batch process. The computer simulation shows that a lower diffusivity, a
higher solubility, and a lower surface tension will enhance the sustainability of bubbles formed in
CBA-based, pressure free foaming processes.
In the past, various researchers have developed methods to improve foam morphology by
preventing cell coalescence, coarsening and collapse. In particular, Naguib et al. [146]
58
demonstrated that there is an optimal foaming temperature to achieve foams with high expansion
while suppressing cell coalescence. If the foaming temperature is too low, polymer foams would
cool quickly and stabilize before bubbles could grow to their maximum sizes. On the other hand,
if the foaming temperature is too high, the initial cell growth rate would also be high, but the
bubbles would eventually shrink to smaller sizes or cell coalescences might occur before the
foam stabilized.
A number of previous studies have shown that the solubility of CO2 in PDMS and PMMA
is higher than that in other commodity plastics such as PS, polyethylene (PE) and PP [19, 144]. In
this context, various researches have been done to blend PDMS or PMMA into commodity
plastics to increase the amount of CO2 dissolved in the polymer matrix. It was believed that the
dispersed phase (i.e., PDMS or PMMA) could act as gas reservoirs to promote cell nucleation,
sustain cell growth, and prevent cell collapse. In particular, Wu et al. [150] observed increased
cell density and better foam morphology when PDMS was added to PP and PP copolymer,
respectively. A similar result was also observed by Han et al. [151] in PS/PMMA/nanoclay
foams. According to the CNT, the increased gas concentration from the PMMA or PDMS would
suppress the increase of Rcr and hence enhance the sustainability of a bubble. Therefore, more
bubbles would survive up to the stabilization stage, and thus the overall cell density would
increase. Furthermore, Okamoto et al. demonstrated that nanoclay particles would align along
cell walls due to extensional stress [147]. It was hypothesized that the aligned particles would
decrease gas diffusion from bubbles, so they are less likely to collapse due to cell coarsening or
gas loss to the environment.
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2.4 Numerical Simulation of Cell Nucleation and Growth
To achieve thorough understanding of the mechanisms governing plastic foaming
processes, numerous research have developed numerical simulation to model these processes.
Many of these studies are based on the mathematical formulation of cell nucleation and growth
detailed in Section 2.2.2 and 2.3.1, respectively. In particular, in regards to the modeling of cell
growth in plastic foaming, various researches have adopted the cell model and demonstrated
good qualitative or quantitative agreements between numerically simulated and experimentally
observed cell growth profiles [138-140, 152] in static conditions. Meanwhile, other researchers
have attempted to simultaneously simulate bubble nucleation and growth in plastic foaming
processes [88, 138, 153-156]. For example, Han and Han [156] simulated foaming of PS/toluene
solutions by assuming constant bubble growth rates. Shafi et al. [155] developed the “influence
volume approach” whereby each bubble is surrounded by a thin shell of polymer-gas solution
(i.e., the influenced volume) within which cell nucleation does not occur due to insufficient gas
concentration as gas is diffused into the bubble. Cell nucleation was assumed to start upon an
instant pressure drop and ceased when the non-influenced volume drops to zero. The initial
bubble pressure was assumed to be the same for all bubbles and was determined by the initial gas
concentration and the Henry’s Law constant. Shimoda et al. [153] simulated cell nucleation and
growth in a flow field through a rectangular channel. In their simulation profile, they accounted
for the pressure drop profile in the flow channel and changes in viscosity and flow rate during the
cell nucleation stage. Ramesh et al. [88] simulated plastic foaming by considering the survival
and growth of microvoids in PS-rubber composites. They suggested that voids are generated in
the rubber particles due to stresses generated due to a mismatch of volume contraction between
PS and rubber particles during the cooling process. When the polymer-gas solution becomes
60
supersaturated, the Rcr decreases, thus triggering the microvoids with radius bigger than Rcr to
grow. Based on a similar concept of bubble nucleation from existing microvoids and the shear-
induced nucleation model by Lee [96], Feng and Bertelo [157] simulated cell nucleation and
growth from the detachment of microvoids that reside on conical cavities. Leung et al. [80, 158]
used the Sanchez-Lacombe Equation of State (SL-EOS) to determine the Pbub,cr inside a critical
bubble, and incorporated this method to simulate bubble nucleation and growth in plastic
foaming processes. In their study [80], the bubbles were assumed to be nucleated
heterogeneously on conical cavities without the consideration of microvoids. A computer
simulated PS foaming process blown with CO2 was compared with in situ foaming video in a
batch process using a foaming visualization system developed by Guo et al. [53], and good
agreement between the two results was observed.
All of these computer simulation studies contribute significantly to our understanding of
plastic foaming processes as they evaluated the validity of various underlining theories, and
clarified the importance of material and processing various parameters (e.g., pressure drop rate,
diffusivity of gas in polymer, viscosity and elasticity of polymer-gas solution) in cell nucleation
and growth via various sensitivity studies. However, discrepancy between experimental data and
computer-simulated results were often observed. There are three major reasons for the
discrepancy.
The first reason is the possible errors or insufficiency in the set of governing theories used
in the numerical model. For example, the CNT has been criticized to overestimate the free energy
needed for nucleation. While much efforts have been directed to modify the CNT to account for
its shortcoming (e.g., correction for γlg variations according to cluster sizes [159]), continued
advancement in this theory is necessary to close the gaps between observed and predicted results.
In addition, as mentioned in Section 2.2.4, stresses can significantly affect cell nucleation.
61
Therefore, it is imperative to incorporate the effect of a flow field in the simulation model. While
attempts have been made in this regard, such as by Shimoda et al. [153], the models used in the
previous studies might not be sufficient in various ways to completely describe the simultaneous
cell nucleation and growth process under dynamic conditions.
The second reason is the possible errors in various assumptions made in the numerical
model due to difficulty in devising a simulation scheme or to lighten the computation time
requirement (e.g., spherical bubble and no bubble-to-bubble interaction). For example, the
average gas concentration of the polymer-gas solution at each time instant (Cavg(t)) is often used
to determine the termination point of cell nucleation (i.e., nucleation ceases when Cavg(t) is
sufficiently low). However, growth in existing cells affect local gas concentration and hence it is
not accurate to prescribe this single boundary condition for termination of cell nucleation for the
entire polymer-gas solution. Furthermore, the assumption of no bubble-to-bubble interaction is a
significant simplification from actual foam processing. While this assumption can be valid at the
initial stage of a foaming process when no heterogeneity exists in the polymer-gas solution, it
fails to capture the stress-induced cell nucleation mechanism whereby the grow of an existing
bubble causes cell nucleation in the surrounding [105-107]. As it is further demonstrated in the
latter sections of this thesis, this could be a dominant cell nucleation mechanism in typical plastic
foaming processes.
The third reason is the unavailability of material parameters (e.g., θc, viscosity and
relaxation time of polymer-gas solution), hence fitting parameters are often introduced to fit
computer simulation results to experimental results. Due to the fitting procedure used, it is
difficult to confirm the validity of the computer models despite good agreement between
numerical and experimental results. One way to solve this challenge is to fix the fitting
parameters once they have been determined from an experiment and to use these values in other
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simulation runs. However, discrepancy between numerical and experimental results are often
observed, possibly due to changes in these parameters at different conditions that could not be
accounted for accurately. While errors in some of these parameters might not significantly affect
the foaming behaviour at the relevant processing conditions as demonstrated by various
sensitivity analysis (e.g., relaxation time on bubble growth [138]), the opposite is also true for
other parameters. For example, it has been demonstrated that the simulated cell density varied by
four orders of magnitude (i.e., from 105 to 109 cells/cm3) as the θc changed from 85.5° to 87.5°
[80]. Therefore, until the sensitive material parameters are determined accurately, as well as
solutions to the other two issues listed above are developed, it is challenging to achieve
quantitative agreements between numerical and experiments results on a consistent basis.
In summary, despite its many merits and versatility, the applications of computer
simulation in achieving thorough understanding on cell nucleation and growth behaviour remain
to be challenging even with the accelerated advancement of computing power in recent years.
Moreover, in order to verify the validity of a numerical model for cell nucleation and growth and
to improve the underlying theories, it is imperative to compare the numerical results with
experimental data. Direct comparison between numerical results with cell morphology of foamed
samples might not be accurate since the interaction of cells during their growth (i.e., deformation
of cells, cell coalescence, cell coarsening) are often not considered in computer simulations.
Therefore, it is imperative to obtain experimental data that captures the foaming processes in situ.
However, this is not a trivial task since these processes are often encapsulated within foaming
equipment. In this context, the next section discusses the pioneering research studies on in situ
observation/detection of plastic foaming processes.
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2.5 Foaming Visualization Studies
Bubble nucleation, growth and deterioration phenomena in plastic foaming are key
research subjects because they determine the final foam structure of the plastic (e.g., bubble size
distribution and density, porosity, and volume expansion ratio). These factors determine the
plastic’s mechanical, thermal, acoustical, and optical properties that relate to a wide range of its
applications. However, bubble nucleation and growth phenomena are often encapsulated within
the foam processing equipment, such as in extrusion foaming and injection foam molding, so it is
difficult to study these phenomena in detail with typical processing studies. Therefore, in many
cases, optimization in processing strategies and parameters were largely based on a trial-and-see
approach, which is inefficient. While numerical simulation were used to model the cell
nucleation, growth, and collapse processes to achieve better understanding of the underlying
mechanisms, various assumptions and limitations, as discussed in Section 2.4, undermined the
validity of the simulated results. On the other hand, direct observation of plastic foaming
processes provides information on cell nucleation, growth and deterioration phenomena without
the need for any assumptions or simplification. However, due to the spatial limit of optical
microscopy and other operating requirements (e.g., high pressure and temperature) that is further
discussed in Section 2.6, nano-sized cells could not be observed clearly, so the initial instances of
cell nucleation might not be captured in foaming visualization studies. Nevertheless, foaming
visualization is one of the most useful tools to analyze plastic foaming processes. In the following
sections, the pioneering visualization studies are discussed.
2.5.1 Dynamic Foaming Visualization
Han et al. [160] and Villamizar [161] conducted pioneering research on in-situ
observations of plastic foaming processes through transparent slit dies and transparent mold
64
cavities with a video camera in 1978 (see Figure 2-12 for details). Despite various technological
limitations at that time that restricted the operating range (i.e., temperature and pressure) and
resolution of images, these studies provided valuable insight that were not achievable by other
methods and demonstrated the wide research potential of in situ visualization in plastic foaming
research, and thus they sparked numerous research efforts in in-line foaming observation in
industrial foaming processes (e.g., extrusion foaming or injection foam molding) [93, 94, 162-
165]. Han et al. [92, 156, 166] also investigated a light-scattering method to detect the onset of
cell nucleation by monitoring the electrical signal from a photomultiplier that collected scattered-
light caused by phase separation in plastic melt. This system allowed them to detect bubbles with
sizes down to 1 – 2 μm, but the detection method was not suitable for cases with broad cell size
distributions. Another in-line foaming detection technique based on ultrasonic measurements
through a transparent slit die was also reported by Tatibouët and Gendron [95], where phase
separation due to foaming were detected by sound attenuation and velocity. This equipment
permits the determination of the onset of cell nucleation easily, but cell size distributions and
cell-to-cell interactions information cannot be directly observed.
Figure 2-12 – Foaming visualization study by Villamizar and Han [161]
65
Through direct observation, Han and Yoo [91] realized that the level of stress in a plastic
melt might have a significant effect on bubble formation and growth in structural foam molding
process. In a subsequent extrusion foaming study, Han and Han [92] pointed out that, in addition
to nucleation by thermal fluctuations and cavitation, both shear stress near the die wall and flow
around the die center could induce cell nucleation. Similar suggestions were also pointed by
Tsujimura et al. [93], Taki et al. [94], and Tatibouët and Gendron [95] in their in-line foaming
visualization/detection studies. Using these equipment, some researcher also studied the dynamic
solubility of gas by detecting the system pressures at the onset of bubble nucleation within a
continuous flow of polymer-gas mixture through a slit die using optical microscopy [162] and
ultrasonic measurement [95, 167]. All of these pioneering studies have provided useful
knowledge on plastic foaming behaviours within processing equipment. However, bubble
nucleation and growth phenomena in a continuous flow of plastic-gas solutions are highly
complex, and their coupled thermodynamic, multi-phase fluid dynamic, and rheological
processes are difficult to thoroughly understand. Moreover, in these cases, the effects of shear or
extensional stresses could not be examined in isolation.
Other researchers developed visualization system to capture bubble dynamics under a
stress field. For example, Favelukis et al. [168] used a Couette apparatus developed by Canedo et
al. [169] to observe bubble nucleation and growth in a viscous liquid under a simple shear flow.
However, the apparatus is incapable of working under the high temperatures and high pressures
required in plastic foaming processes. Mackley et al. [170] and Mackley and Spitteler [171]
developed a capillary rheometer with an optical section for viewing foaming processes under
stressed conditions. These instruments are capable of simulating a wide range of flow situations
in extrusion and injection molding. However, due to the nature of pressure-driven flows, the
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pressure and rate of deformation are non-uniform, and hence, so is the induced stresses.
Therefore, the stress effects on the foaming behaviour remained unclear.
2.5.2 Static Foaming Visualization
In the 1970s, Ward et al. used a visualization technique to study bubble nucleation and
growth dynamics in various liquid/gas solutions (e.g., oxygen/nitrogen in water [73], oxygen in
water [63], nitrogen in ethyl ether [61]). Meanwhile, dedicated visualization system for observing
plastic foaming processes under static conditions were developed by Otake et al. [172], Taki et al.
[94], and Guo et al. [53], and Salejova and Kosek [173], in which a small plastic sample is placed
inside a pressurized chamber and the foaming processes are captured using a video camera or
high-speed camera with optical microscope. These systems could offer valuable insight by
suppressing the stresses to decouple the analysis of various material compositions (e.g., base
polymer, cell nucleating agents), experimental parameters (e.g., temperature, pressure, pressure
drop rate). For example, these systems have been used to study the foaming behaviour of various
materials (e.g., PP [94, 126, 174-176], TPO [121, 143], PS [53, 107, 177, 178], PLA [112, 178]),
as well as the effects of various additives (e.g., talc [107], nanoclay [174], nanosilica [126]),
blowing agents (e.g., CO2 [53, 107, 112, 177], N2 [121, 143, 175], Ethanol [179]), and various
processing conditions (e.g., pressure drop rate [177], gas content [53, 177]). In particular, Taki et
al. [94, 174] observed that bubble nucleating and growth occurred simultaneously and that bubble
nucleation was suppressed around existing bubbles (i.e., the influence region). They also
observed that the cell densities increased with pressure drop rate. Based on in-situ bubble growth
observation, Leung et al. [177] numerically simulated the same process to fit to the growth
profile of the bubble. The resulting data was used to estimate the pressure at the onset time of
bubble nucleation at various temperature, gas content and pressure drop rates.
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Meanwhile, some researchers [42, 148, 180-182] used a hot stage device coupled to a
video camera to capture the foaming processes of polymers blended with CBA under atmospheric
pressure. Despite the valuable insights generated, the apparatus used in these studies might not be
ideal for understanding the foaming behaviour in industrial plastic foaming processes where
polymer is subjected to both shear and extensional stresses, which have been shown to
significantly affect the cell nucleation and growth phenomena as described in the previous
sections.
All of the aforementioned dynamic and static foaming visualization studies have made a
significant contribution to the understanding of plastic foaming processes. At the same time, to
verify and improve the existing theories of stress-induced plastic foaming, it is crucial to obtain
clear, empirical bubble nucleation and growth phenomena data under the effects of extensional
and shear stresses in an isolated manner. This has not been achieved by any of the pioneering
works, or reported anywhere else.
2.6 Imaging Technology
In plastic foaming processes, cell nucleation could occur in nano-scale. Therefore, it would
be ideal to adopt an imaging technology with high magnification and spatial resolution to capture
the instant of nucleation onset. However, due to the diffraction limits of optical microscopy,
observation in nano-scale is difficult. To be specific, the Abbe diffraction limit (da) generally
describes the smallest feature that can be resolved based on the wavelength of the light (λl) (i.e.,
visible light has λl from 400 to 780 nm), refractive index of the medium between the lens and the
object (nr), and the half opening angle of the objective lens (α) that is described by its aperture.
The Abbe diffraction limit is given as [183]:
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Equation 2-47
where nrsinα is also known as the numerical aperture. In modern optics, a large numerical
aperture can be used to decrease the diffraction limit to approximately 250 nm assuming green
light is used (λ = 550 nm). However, to achieve this, an objective with a large aperture (hence
large α) has to be used. Also, the sample should be immersed in a medium with a uniform nr to
prevent light reflection that effectively decreases useful range of α. However, both of these
strategies are not feasible for plastic foaming visualization. First of all, an objective with a large
aperture angle requires that the specimen to be placed very closed to the specimen, hence the
working distance (the distance between the lens surface and the specimen), is very small (e.g.,
less than 5 mm). However, in order to observe plastic foaming under high temperature and
pressure, the plastic specimen needs to be enclosed within a high temperature/pressure chamber.
This necessitates the use of a lens with long working distance, and hence the spatial resolution
decreased. Moreover, the plastic sample is required to be immersed in a specific blowing agent
(e.g., CO2, N2) for gas sorption. The incident light has to pass through this gas medium, a
transparent window (e.g., sapphire, quartz) installed on the chamber, and finally the ambient air
before it reaches the lens. These mediums have different nr, hence the light reflection at the
boundary of medium changes is unavoidable. Due to these reasons, it is difficult to achieve a
spatial resolution below a few microns using optical microscopy in this application. Some other
imaging technique such as scanning electron microscopy (SEM) and transmission electron
microscopy (TEM) uses electron beams instead of light to detect images. The de Broglie
wavelength of electrons is significantly smaller than the wavelength of visible light, hence they
could achieve spatial resolutions in nano-scale. However, they need to be operated in vacuum, so
they are not feasible for observation of plastic foaming processes under high pressure.
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Moreover, in typical industrial foaming processes, a high depressurization rate is used to
generate cell high cell density and uniform cell sizes. In these processes, cell nucleation and
initial growth occur very quickly, and could be completed within 0.5 second or less. Therefore, in
order to capture the initial stage of the plastic foaming processes to probe the evolution of cell
formation and growth, a high speed imaging technique should be used (i.e., high speed camera).
Because of the high-speed requirement, many imaging techniques (e.g., X-Ray microscopy) that
require relatively long imaging scanning time are unfeasible for this application despite that they
might have higher spatial resolution than optical microscopy and could image specimens
contained in a high temperature/pressure chamber.
In summary, due to the requirement for high-speed imaging, long working distance, and
high temperature/pressure environment for plastic sample, optical microscopy consisting of a
high-speed camera coupled to an optical microscope is a viable option for plastic foaming
visualization, which is also adopted in this thesis.
2.7 Summary and Assessment of Research Directions
The introduction and literature review given in Chapter 1 and Chapter 2 have described
the state of the art and challenges for plastic foaming industries and research. Evidently, there is a
wealth of previous research in plastic foaming: from measurement of material parameters, to
computer simulations of cell nucleation, growth, and deterioration, to foaming experiments with
small-scale foaming equipment and specialized systems that allow in situ observation or
detection of foaming processes. Despite significant progresses made on all fronts, thorough
understanding in cell nucleation and growth phenomena in plastic foaming processes has yet to
be achieved due to various limitations discussed in the previous sections. In particular, in order to
verify and improve the foaming theories generated from experimental and numerical foaming
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studies, it is imperative to devise effective strategies to observe foaming processes in situ.
Pioneering studies in this research field have retrofitted transparent windows to die or mold
cavity for direct observation. However, bubble nucleation and growth phenomena in a continuous
flow of plastic-gas solutions are highly complex, so it was difficult to study and hence understand
the effects of individual parameters in an isolated manner, notably the individual effects of
extensional and shear stresses on cell nucleation and growth. Since plastic is subjected to these
stresses in typical industrial foaming processes, especially at the foaming stages, it is imperative
to study their individual effects and fundamental mechanism in inducing cell nucleation and
affecting cell growth. For example, stresses could influence material characteristics (e.g.,
crystallization, viscosity) that affect foaming behaviour. Meanwhile, other experimental
parameters (e.g., temperature, gas content) can also affect the rheological behaviour that changes
the stress-strain relationships of the plastic melt. While previous researchers have developed
dedicated batch foaming visualization systems for direct observation of plastic foaming processes
to study the effects of various material and experimental parameters in isolated manner, none of
them were equipped to induce an easily controllable and uniform stress field. On the other hand,
other researchers have developed foam systems to induce shear stresses to polymer during the
foaming processes, but they were not equipped with visualization capability, and the foamed
samples were only characterized after their stabilization. Therefore, new visualization systems
that allow investigation of plastic foaming processes under both static and dynamic conditions in
isolated manner are imperative to identify the fundamental foaming mechanisms. To be specific,
the extensional and shear effects on bubble nucleation and growth should be investigated
independently in isolated manner to unfold the stress-induced nucleation mechanisms.
Since heterogeneity (e.g., talc) has been demonstrated to trigger bubble-growth induced
cell nucleation, it is foreseeable that crystals in semi-crystalline polymers can generate similar
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effects. A preliminary study has been conducted by Leung et al. [178] in the foaming of PLA
blown with CO2 using a static foaming visualization system developed by Guo et al. [53]. On the
other hand, that system is not equipped with any cooling capability, hence it is difficult to achieve
customizable heating/cooling cycles to study the effects of thermal history on the foaming
behaviour, notably the effects of crystallization. Therefore, an improved visualization system
with accurate and programmable heating/cooling control is needed to advance this research.
Due to the urgent need to replace the existing blowing agents, more research effort is
needed to clarify the foaming behaviour of polymers blown with alternative blowing agents that
are greener and safer to use, such as CO2, Ar, N2, and He. In this context, blowing agent blends
(e.g., CO2-ethanol, CO2-N2) have also been investigated to evaluate their feasibility in plastic
foaming processes, and promising results (e.g., higher cell density and foam expansion) have
been observed in previous studies. However, the synergistic effects of blowing agent blends on
plastic foaming are still not well understood.
It has been demonstrated in previous studies that extensional strain induces crystallization
in polymers [184]. Therefore, the interrelationship between extensional strain, crystallization, and
foaming behaviours are highly coupled and difficult to model numerically. In this context,
foaming visualization with semi-crystalline polymers with the presence of crystals under
dynamic conditions would serve to clarify these interrelationships. However, this has yet to be
elucidated yet. In addition, previous foaming visualization studies have attempted to clarify the
effect of nucleating agents on foaming behaviour [107, 174], but these studies were conducted
under static conditions. Since stress could also induce cell nucleation, it is unclear what would be
the combined effects of nucleating agents and applied stresses on cell nucleation and growth. In
this context, foaming visualization studies of polymer composites under dynamic conditions
would be a key study to further our understanding in this subject area.
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CHAPTER 3
IN SITU VISUALIZATION OF PLASTIC
FOAMING PROCESSES UNDER
STATIC CONDITIONS
3.1 Introduction
In situ observation of plastic foaming processes under static condition is an effective tool to
study the effects of material (e.g., plastic resins, additives, blowing agents) and processing
parameter (e.g., temperature, gas content, pressure drop rate) on bubble nucleation, growth, and
deterioration behaviours in the absence of applied stress. The visualization data provide important
knowledge on the fundamental mechanisms of foaming and is baseline to foaming visualization
studies conducted under dynamic conditions. In this context, this chapter describes the
development of a static foaming visualization system with accurate heating and cooling controls
and a foaming study of PP to verify its capability and to elucidate the effect of crystals on the cell
nucleation and growth behaviour, which have been detailed in reference [185]. Moreover, the
effectiveness of inert blowing agents (i.e., N2, Ar and He) and CO2-N2 blends in plastic foaming
processes was examined, and the preliminary results have been published in reference [35] and
[186], respectively.
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3.2 Development of a Foaming Visualization System with Accurate
Heating and Cooling Control
3.2.1 Background
The foaming visualization system developed by Guo et al. [53] is a versatile research tool
that allows the observation of plastic foaming processes in high spatial and temporal resolution
under static conditions (see Figure 3-1). It consisted of a foaming chamber with visibility through
transparent sapphire windows. Foaming processes was initiated by depressurization and captured
using a high-speed camera (FASTCAM – Ultima APX, CMOS camera sensor, 1024 x 1024
pixels, pixel width at 17 μm). However, there were a few drawbacks that limit its functionality
and operability. In this thesis, a new foaming visualization system has been developed that also
utilized some of its elements. A key new feature is an accurate heating and cooling control that
allowed direct correlation between visualization of crystallization and foaming, and thermal
characteristics obtained in high-pressure differential scanning calorimetry (HPDSC).
Figure 3-1 – Schematic of the batch foaming visualization system [53]
3.2.2 New Foaming Chamber with Accurate Heating and Cooling Control
The visualization system developed by Guo et al. [53] lacked a cooling system to
accurately controls the heating and cooling cycles. This is essential to studies where the thermal
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history of a plastic sample impact its foaming behaviour, notably the foaming of semi-crystalline
polymers at temperatures where crystallization occurs, such as in many bead foaming processes.
Therefore, a new foaming chamber has been developed that incorporates a water-cooling system.
The new foaming chamber used a smaller chamber body than the existing one in order to
achieve a faster heating/cooling response. The contact area between the chamber and its
supporting stand has also been minimized to suppress heat dissipation. It adopted a cylindrical
uni-body design in place of the multi-layered existing chamber. This new design eliminated the
need to realign the chamber layers during sample loading and replacement of high-pressure gas-
sealing gasket in between experimental runs. A sapphire window was installed at the bottom
surface of the chamber to provide transmissive lighting, while another sapphire window was
installed on the top cover for bright field observation. The sapphire-to-metal sealing mechanism
for both the top and bottom sapphire windows has been designed based on O.M. Suleimenov’s
design [187] that utilized the Bridgman’s unsupported area principle [188]. The basic concept of
the unsupported area principle is to generate a pressure on the sealing element (e.g., an o-ring)
that is higher than the internal pressure of the chamber. The increased pressure deforms the
sealing element, which then penetrates the surrounding gaps and improves the seal’s
performance. To utilize this principle, a mushroom-shaped sapphire window has been used to
guide a sealing o-ring (see Figure 3-2 for details). A compression nut was installed to provide the
clamping force required for the initial seal. The area of the sapphire window under pressure was
designed to be larger than the facial area of the o-ring, thus the pressure exerted on the o-ring
would be higher than the internal pressure. The mushroom-shaped sapphire window prevented
the o-ring from deforming excessively towards the center under pressure that could cause
damages to the o-ring. To avoid damaging the sapphire window against the chamber body during
the initial seal, a copper ring was sandwiched in between the window and the chamber. This
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sealing mechanism was superior to the previous design where an o-ring was sandwiched between
the chamber body and the sapphire window because the latter relies on an external clamping
force to deform the o-ring to form a seal. The clamping force must be uniform along the sealing
surface to avoid damages to the o-ring and/or the sapphire window. Also, as pressure increased,
the clamping force required to prevent leakage also increased. On the other hand, the new design
only required a slight clamping force for initial seal, and the performance of the seal improved as
the internal pressure increased, hence it was more robust than the previous design. The material
of the sealing o-ring has been chosen to be PTFE with 25% glass-fiber due to PTFE’s inertness
and high serviceable temperature limit (i.e., 260 °C), and the high mechanical strength of glass-
fiber that prevented excessive deformation of the o-ring even at high temperatures and pressures.
Figure 3-2 – Detailed foaming chamber design for static visualization system
This sealing mechanism has been used for both the top and bottom sapphire windows. At
the bottom side, a threaded compression nut was used to clamp the sapphire window and sealing
components together to provide an initial seal. The compression nut also secured an optic fiber
that was connected to a halogen lamp as a transmissive light source. The design of the top
compression nut was different from the bottom one such that the top sapphire window and the
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sealing o-ring were housed within the compression nut. This design allowed for easier access to
load or remove a plastic sample. However, this design also generated an additional leakage path
between the top compression nut and the chamber body, which was sealed with a silicon-based o-
ring installed on a slot on the nut. Four M6 bolts have been used to provide the clamping force
for the top compression nut, instead of a threaded nut design, to avoid potential damages of
threads from the frequent open and close operation of the top nut for sampling loading and
removal. The top nut has a cylindrical lead-in that mates with the chamber body to a close-
tolerance slide-fit, hence proper alignment between the top nut and the chamber was guaranteed.
This foaming chamber design has been tested to maintain good sealing performance after
repeated uses without the need to replace any of the sealing o-rings on a frequent basis. A
resistive thermal detector (RTD) (Omega PT110) and a pressure transducer (Dynisco PT160)
have also been installed to measure the temperature and pressure inside the chamber.
The accurate heating and cool function was achieved with two electric cartridge heaters
and a water-cooling module, respectively, and they were controlled by a single temperature
controller (Omega CN7833). The cooling module consisted of a customized cooling jacket with
surrounding metal tubes soldered to its surface. The tubes circulate cool water (maintained at 20
°C) that was supplied by a water line to achieve the cooling function. The water flow was
controlled via the opening of a solenoid valve that was operated by the temperature controller.
The cooling jacket was installed onto the chamber’s cylindrical surface. Thermal paste has been
added to their contact area to ensure effective heat transfer. Figure 3-3 shows the design of the
overall foaming chamber. The temperature of the system was recorded into a computer program
(Omega CN7-A) in real-time. To demonstrate the heating and cooling capability of the system,
the temperature controller has been programmed to achieve a temperature profile for the foaming
chamber, pressurized to 6 MPa with CO2, as follows: 1) heat from 20 °C to 200 °C at 10 °C/min;
77
2) maintain at 200 °C for 10 minutes; 3) cool to 139 °C at 10 °C/min; 4) maintain at 139 °C for
60 minutes; and 5) cool to 20 °C at 10 °C/min. Initially, the auto-tuning feature has been used to
tune the PID parameters for the temperature control. However, during the cooling stage from 200
°C to an isothermal temperature, the temperature overshot a few degrees below the set isothermal
temperature. Since isothermal crystallization phenomenon in semi-crystalline polymers is
strongly depended on temperature, an overshoot in temperature decrease might accelerate the
nucleation of crystals, which causes inconsistency in experimental results. To overcome this
issue, the proportional, integral and differential parameters of the controller has been tuned
manually to eliminate the overshoot while maintaining the specified heating/cooling rate and the
holding temperature at each stage. The temperature readings are shown in Figure 3-4. The same
temperature profile obtained with a high-pressure differential calorimeter (HPDSC) (NETZSCH
DSC 204 HP, Germany) has also been included for comparison, which shows that the two
profiles are very similar. This demonstrated the systems’ heating/cooling capability.
Figure 3-3 – Overall foaming chamber
design for static visualization system
Figure 3-4 – Temperature profile in foaming
chamber vs. HPDSC at 139 °C
0
20
40
60
80
100
120
140
160
180
200
220
0 20 40 60 80 100 120
Time (min.)
Tem
pera
ture
(o C)
High pressure DSCFoaming chamber
78
3.2.3 Optical Lens Assembly
The existing lens assembly for the high-speed camera incorporated an objective lens with
high magnification power (50x) to achieve a high spatial resolution, but its working distance (i.e.,
the distance between the objective lens and the sample for observation) was limited (i.e., 13 mm).
This posed technical challenge since a longer working distance was needed to accommodate the
new sealing mechanism. Moreover, the objective lens could be damaged if it is placed very close
to a high temperature environment (i.e., near the foaming chamber). In this context, an improved
optical lens assembly with a significantly longer working distance (i.e., 33 mm) and similar
levels of maximum magnification and spatial resolution has been incorporated. To be specific,
the smallest field of view (i.e., the length of image in actual size) was 0.42 mm and the spatial
resolution was 0.6 μm. However, due to birefringence around bubbles, unavoidable impurities in
many polymer melts, and the limitation on the pixels numbers of the high-speed camera, the
smallest bubbles that could be detected was around 2 – 4 μm in diameter. The long working
distance was obtained by using an objective lens with lower magnification (10x) (Mitutoyo M
Plan APO) while the overall magnifying power was maintained by the addition of a zoom lens
element (0.7x to 4.5x) (Navitar 6000 UltraZoom) and a magnifying coupler (2x). The zoom lens
element also provided variable zoom that allowed continuous adjustment from a field of view of
2.69 mm to 0.42 mm for visualization of foaming processes under different length scales. In
addition to providing extra magnifying power, the coupler with an F-mount also suppressed
vignetting (i.e., a reduction of an image's brightness at the periphery region relative to the center
region) that was apparent in the existing lens assembly that used a C-mount (i.e., smaller
opening). Therefore, consistent brightness could be achieved throughout the entire image with the
new optical lens. The high-speed camera and lens assembly was installed onto a stand taken from
79
the existing system. In addition, a linear-guide with micro-adjustment (spatial resolution = 0.5
um) along two orthogonal directions was installed onto the stand, which provided easier
adjustment to achieve proper focus on the plastic sample. This is very important, because the
depth of view (i.e., the distance between the nearest and furthest object that gives an image that
appears in focus) is typically small for lenses with high magnification. In particular, the depth of
field ranged from 6 μm (high magnification setting) to 39 μm (low magnification setting), so the
fine-adjustment tool was needed to achieve a proper focus. This optical lens assembly was
important not only for the static visualization system, but also for the development of the
dynamic visualization systems that has been detailed in Section 4.1 and 5.1. Near UV lens and
UV lens utilize incident light with shorter wavelength than visible light for observation. Due to
the shorter wavelength, a higher spatial resolution could be achieved. However, they have not
been used in the new setup because they cost significantly higher than normal lens, while the gain
in spatial resolution is not significant (up to approximately 2 times theoretically).
3.2.4 New IO Control Board and Software
In the existing system, a software has been developed in the LabVIEW (Laboratory
Virtual Instrumentation Engineering Workbench, National Instrument) environment to monitor
and save pressure data, and to trigger the simultaneous opening of a gas exit value to initiate
foaming and the recording of the high-speed camera. These I/O commands were received/sent via
an Advanced Data Acquisition and Control (ADAC) board (IOtech) to the pressure sensor and
high-speed camera. The software had an ergonomically friendly graphical interface and usability.
However, due to various compatibility issues between the LabVIEW and the ADAC board, the
software has to incorporate various specialized modules to carry out the I/O commands, which
made it difficult to maintain and troubleshoot when problem arise. In this context, the existing
I/O control system has been replaced with a simpler setup. The new software was also
80
programmed in the LabVIEW environment, which has been coupled to a data logger with digital
I/O control (NI6009, National Instrument) that was directly compatible to the LabVIEW
commands. Also, the control board and software could be easily transferred to another system
that requires similar I/O capability. This is because the control board was interfaced with a USB
port, and the software could be adapted to another data logger from National Instrument simply
by adjusting the I/O channels. In summary, not only was the new I/O control module simpler to
maintain and troubleshoot, it was also easily transferrable to other systems. Figure 3-5 shows the
overall foaming visualization system with accurate heating and cooling control. Figure 3-6 shows
the finalized chamber setup. In the following section, the capability of the new foaming
visualization is demonstrated via a foaming study of PP blown with CO2.
Figure 3-5 - Batch foaming visualization system with accurate heating/cooling control
81
Figure 3-6 – Finalized foaming chamber setup for the static visualization system
3.3 Crystallization and its Effects in Cell Nucleation and Growth
3.3.1 Background
As mentioned in Section 2.2.5, crystals in semi-crystalline polymers could significantly
affect their foaming behaviour, but the underlying mechanisms still need to be clarified further.
In particular, PP accounted for approximately 14% of the global plastic usage by weight in 2007
[189]. Foamed PP exhibits excellent impact strength and toughness, durability, as well as strength
to weight ratios. Many recent foaming studies investigated the foamability of PP using
supercritical fluids as BAs (e.g., CO2 and N2) by way of batch foaming [35, 109, 174, 175, 190,
191], foam extrusion [28, 132, 142, 192, 193], and injection foam molding [194-197]. Despite the
various insights offered by these researches, the effect of crystals on the foaming behaviour
remained unclear due to a lack of empirical data on cell nucleation and growth phenomena of PP
foaming. Guo et al. [175, 198] and Taki et al. [174] studied PP and PP-nanoclay composites
foaming with direct foaming visualization, but crystals were not present because of the high Tsys
used. In this context, this study investigated the foaming behaviour of linear homo PP in the
presence of crystals via direct observation of crystallization and foaming to elucidate these
82
mechanisms. In addition, the crystallization behaviour of the PP in the presence of high pressure
CO2 has been evaluated with high-pressure differential scanning calorimetry (HPDSC).
Therefore, the crystallinity at the foaming condition could be evaluated accurately and related to
the cell nucleation and growth characteristics obtained by direct observation. The same study has
also been conducted with a PP-ethylene random copolymer, which typically has a wider
processing Tsys window due to its higher melt strength, as comparison. The insight drawn on the
PP-copolymer would also be valuable for expanded PP (EPP) bead foams technologies.
3.3.2 Research Methodology
3.3.2.1 Experimental Materials and Sample Preparation
The plastics used were a linear PP (DM55, Borealis) and a PP-ethylene random co-
polymer (SEP550, Honam). The melting temperature (Tm) and crystallization temperature (Tc) of
both polymers were measured using DSC analysis (TA Instruments DSC Q2000, US). The Tm
and Tc of DM55 are 163oC and 117 °C, respectively, while the Tm and Tc of SEP550 are 146 °C
and 107 °C, respectively. The polymer resins were compression molded to films 0.4 mm in
thickness with a hot press at 200 °C. Upon pressure release, the molded films were immediately
quenched with a large reservoir of water at 13 °C. Afterwards, the films were cut into circular
discs that are 4 and 6.5 mm in diameter for HPDSC analysis and foaming visualization
experiments, respectively. The blowing agent used was CO2 (99.8% pure, Linde Gas Inc.).
3.3.2.2 Isothermal Crystallization
The goal of this study was to investigate the effect of crystals on the foaming behaviour of
PP. Therefore, it was imperative to analyze the crystallization kinetics of each PP, which was
studied with HPDSC (NETZSCH DSC 204 HP, Germany). Each polymer sample was first
heated from 20 °C to 200 °C and was maintained at 200 °C for 10 minutes to completely melt the
83
existing crystals. Afterwards, the sample was cooled down to an isothermal temperature, and was
maintained at the temperature for 60 minutes. Finally, it was cooled down to 20 °C. The
heating/cooling rate for the entire cycle was kept at 10 °C/min. The saturation pressure (Psat) used
in the HPDSC analysis was 6 MPa. Figure 3-4 shows a sample temperature profile vs. time. This
heating/cooling cycle simulates a typical extrusion foaming process, where polymer is first
melted at a high temperature and then cooled downstream. Crystallization might occur as the
polymer melt is subsequently cooled to a temperature around or below Tm prior to foaming.
3.3.2.3 Foaming Visualization
Using the improved foaming visualization system described in Section 3.2, PP foaming
experiments were conducted at temperatures at which isothermal crystallization occurred, which
were determined by the HPDSC analysis. To conduct an experiment, a circular disc shaped PP
sample was placed inside the high temperature/high pressure chamber. A clear polyethylene
terephthalate (PET) film (0.127 mm in thickness) with a 1 mm hole punched out in the center was
placed beneath each PP sample, so that the sample was partially suspended in air. Observation of
foaming processes was focused upon that region (see Figure 3-7). This minimized the effects of
heterogeneous nucleation and/or formation of cells from pre-existing cavities along the PP-
sapphire and PP-PET interfaces, which would be more thermodynamically favourable to cell
nucleation within the bulk phase of polymer [199]. Consequently, the effects of crystals on the
foaming behaviour could be studied in an isolated manner. The neighbouring regions where PP
was in contact with PET were also captured to demonstrate the differences in foaming behaviour
in these two regions. The chamber was first maintained at 20 °C for 5 minutes and then it was
subjected to the same temperature profile as the HPDSC analysis until after foaming occurred.
High pressure CO2 was injected into the chamber via a metered stream of gas controlled by a
syringe pump upon the chamber reaching 200 °C. After holding for 60 minutes at the isothermal
84
temperature, a gas release valve was triggered to open, which caused a sudden release of gas
pressure. The rapid pressure drop caused a thermodynamic instability within the polymer to
initiate the foaming process, which was captured by a high-speed camera in situ. By adjusting the
resistance of the gas exit path with a metered valve, a specific pressure drop rate was obtained.
Figure 3-7 – Foaming visualization at the suspended region
3.3.3 Results and Discussion
3.3.3.1 Isothermal Crystallization
The HPDSC results (Psat = 6 MPa) for the isothermal sections of DM55 and SEP550 are
shown in Figure 3-8 and Figure 3-9, respectively. The isothermal temperature ranges used for
DM55 and SEP550 are 124 to 130 °C and 112 to 121 °C, respectively, at 3 °C intervals. For both
materials, the crystallinity decreased as temperature increased. Figure 3-10 and Figure 3-11
summarizes the crystallinity at the end of the 60 minutes isothermal phase (i.e., at the time when
foaming would be induced for the foaming visualization experiments) for all cases. Furthermore,
using the foaming visualization system, images of PP samples were taken at 1-minute intervals
during the 60 minutes isothermal stage to capture the crystallization behaviour. Figure 3-12
shows a sample of the crystallization behaviour for DM55. It was observed that there were two
categories of crystal growth behaviours. One started from a central nucleus, and then grew
radially in all directions to become spherulites. Subsequently, these spherulites continued to grow
until they came in contact with adjacent crystals, which are called spherulite truncation (Type I
crystals). The other one developed into a sheaf-like lamellar structure initially, and then attained
85
the spherical shape via continuous branching and fanning of the sheaf-like structure. The lamellae
of these spherulites formed a crosshatched structure when they came in contact with adjacent
ones without showing obvious boundaries (Type II crystals). As the temperature increased, the
crystals’ sizes decreased, which agreed with the decrease of crystallinity measured in HPDSC.
Figure 3-8 – Isothermal crystallization of
DM55 using HP DSC (Psat = 6 MPa)
Figure 3-9 – Isothermal crystallization of
SEP550 using HPDSC (Psat = 6 MPa)
Figure 3-10 – Crystallinity & VER vs. Tsys
(DM55)
Figure 3-11 – Crystallinity & VER vs. Tsys
(SEP550)
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
Time (min.)
Hea
t flo
w (W
/g)
124 degC127 degC130 degC
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
Time (min.)H
eat f
low
(W/g
)
112 degC115 degC118 degC121 degC
86
Figure 3-12 – Crystal formation of PP during
isothermal stage at Psat = 6 MPa
Table 3-1 – Experimental cases for PP/CO2
foaming under presence of crystals
Material Tsys [°C] Material Tsys [°C]
DM55
124
SEP550
112
127 115
130 118
133 121
136 124
139 127
130
Note: Psat = 6 MPa, -dPsys /dt|avg = 2.1 MPa/s
3.3.3.2 Foaming Visualization
The Tsys profile in each foaming experiment followed the HPDSC analysis except that a
faster cooling rate was used at the end of the 60 minutes isothermal stage, at which point pressure
was released to initiate the foaming processes. The faster cooling rate was used to stabilize the
foam structure quickly for volume expansion measurement. This would not hinder the
comparison of the HPDSC isothermal crystallization results with the foaming visualization data.
For the foaming experiments, the Tsys ranges used for DM55 and SEP550 are 124 to 139 °C and
112 to 130 °C, respectively, at 3 °C intervals. These ranges covered those used in the HPDSC
analysis, as well as the higher Tsys to study the foaming behaviour where fewer and/or smaller
crystals were present. The Psat and the average pressure drop rate (-dPsys /dt|avg) were kept
constant at 6 MPa and 2.1 MPa/s in all cases. Table 3-1 summarizes the experimental conditions.
Each experiment was conducted three times to ensure that the results were repeatable.
Foaming visualization images from selected experiments of DM55 and SEP550 are
shown in Figure 3-13 and Figure 3-14, respectively. At a low foaming Tsys (Tsys = ~8 °C above
87
their individual Tc) and in the region where the polymer was suspended in the air, the majority of
the bubbles were nucleated around existing crystals (Tsys = 124 °C for DM55 and Tsys = 115 °C
for SEP550). They grew rapidly in the outward radial direction away from the crystal nuclei due
to the high stiffness of the crystals. This crystal-induced cell nucleation could be explained by
two main mechanisms. The first one was the exclusion of CO2 at the crystal growth front that led
to surrounding region becoming supersaturated and hence foaming occurred. This theory was
first proposed by Koga and Saito [110] and also demonstrated by Taki et al. [112] in their
foaming visualization study of PLA. Another main reason was the polymer chain networks
formed around crystals. As crystallization occurred, polymer tended to shrink at the crystal sites.
Consequently, the amorphous regions surrounding the crystals were constrained and tensile
stresses were generated. When a bubble was nucleated in this constrained region, the growth of
this bubble caused deformation to the surrounding polymer chains. Since these chains were
constrained by the crystals, additional tensile stresses were generated in these regions. Due to the
tensile stresses, the local system pressure (Psys) was reduced. This decrease in Psys would increase
the degree of supersaturation (i.e., Pbub,cr – Psys), hence cell nucleation was accelerated. To further
explain this point, Equation 2-3, Equation 2-30, Equation 2-34, Equation 2-31 and Equation 2-35
have been modified to include the local pressure variations (ΔPlocal) as follow:
Equation 3-1
Equation 3-2
88
Equation 3-3
Equation 3-4
Equation 3-5
When there is a compressive stress, ΔPlocal is positive, thus the local Psys is increased. Conversely,
when there is a tensile stress, which is believed to be the case in this study, ΔPlocal is negative,
thus the local Psys is decreased. Therefore, the level of supersaturation would have increased,
which led to reduction in Rcr, Whom, Whet. Consequently, some existing microvoids that had radius
greater than the decreased Rcr would grow spontaneously to become nucleated cells. In addition,
the homogeneous and heterogeneous nucleation rates (i.e., Jhom and Jhet) would also increase due
to the increased level of supersaturation. This stress-induced nucleation mechanism explained
why new bubbles were nucleated around existing bubbles and this created a chain effect that
propagated into the surrounding regions quickly (refer to Figure 3-13 and Figure 3-14). These
phenomena was similar to that observed by Leung et al. [107] in the foaming of PS-talc
89
composites, where the presence of talc was believed to cause local stress fluctuations similar to
that generated by crystals in this case. Importantly, it is noted that, while the exclusion of CO2 at
crystals growth fronts was successful in explaining the initial foaming along the crystals’
boundary, it could not describe the bubble-growth induced nucleation phenomena observed;
Stress-induced nucleation is believed to be the dominant foaming mechanism in this study.
At higher Tsys, these two foaming mechanisms became less apparent as the crystallinity
and the viscosity of the polymer-gas mixtures decreased. As the crystallinity decreased, the
exclusion effect of CO2 became less significant. Also, the amorphous regions became less
constrained and had lower viscosity, so the tensile stresses induced to polymer chains by bubble
growth also decreased. Combined, these two phenomena caused reduction in nucleation rate,
especially in the suspended region. In the region where PP was wetted on the PET surface, the
PET-PP contact provided an additional constraint to polymer chains and hence they would be
subjected to a higher amount of tensile stresses. This explained why the bubble-growth induced
nucleation phenomena was still apparent in these regions but the propagation stopped at the
suspended regions (see Figure 3-14, Tsys = 121 °C). At even higher temperatures, the bubble
growth-induced nucleating phenomena were not observed due to the absence of crystals and the
low viscosity of the polymer-gas mixture. However, bubbles were still nucleated on the PP-PET
contact regions due to the heterogeneous nucleation effect of the PET. Meanwhile, no bubbles
were nucleated in the suspended region, but the area of that region decreased as bubbles in the
neighbouring area grew in sizes and caused deformation to this region.
Although it was observed that crystals induced cell nucleation, an excessive amount of
large-sized crystals might hinder cell structure uniformity as cell growth around crystals would be
restricted. The volume expansion ratio (VER) would also decrease due to the high viscosity of
90
the polymer-gas mixture that restricted cell growth. An appropriate amount and sizes of crystals
would induce cell nucleation uniformly, allow sufficient cell growth, as well as provide enough
melt strength to prevent cell coalescence and collapse. Figure 3-10 and Figure 3-11 show the
VER of the stabilized foams obtained in the foaming experiments vs. the isothermal/foaming
temperature. The VER data was evaluated using the water-displacement technique based on
ASTM D792-00. For both materials, a typical single-peak behaviour [146] that captured the
limited cell growth due to rapid crystallization at low temperatures and cell deterioration at high
temperatures was observed. The peak for DM55 was very narrow when compared to that of
SEP550, which demonstrated the challenges in processing linear PP: it crystalizes quickly at low
temperatures and exhibits a low melt strength at high temperatures. It was observed that a high
crystallinity (~25%) was needed for DM55 to achieve the maximum VER. This could be due to
the low melt strength of linear PP, hence a larger amount of crystals were needed to increase the
melt strength and to prevent significant gas loss. However, for processes with faster cooling (e.g.,
extrusion foaming), foam stabilization occurs in shorter time, hence a lower melt strength and
hence crystallinity would be needed to prevent cell deterioration. Therefore, the Tsys at which
maximum VER occurred would expect to be higher. Meanwhile, for SEP550, the volume
expansion ratio maintained at the highest level (i.e., approximately 13 times) even when the
crystallinity dropped below 10%. This was due to the inclusion of the ethylene chains in SEP550,
which exhibited higher extendibility that prevented rupture of cell walls and hence foam
shrinkage. Therefore, a large amount of crystals was not necessary to stabilize the foam structure.
91
Figure 3-13 – Sample foaming visualization images of DM55
Figure 3-14 – Sample foaming visualization images of SEP550
92
3.4 Foaming Behaviour of Plastics Blown with Environmentally
Friendly Blowing Agents
As mentioned in Section 1.4.1, there is an urgent need to replace the hazardous blowing
agents that are currently used in plastic foaming industries, such as HCFCs and HFCs. In this
context, the following studies investigated the feasibility of utilizing inert blowing agents (Ar, N2
and He) and blends of environmentally friendly blowing agents (CO2-N2 blends) in plastic
foaming processes by in situ visualization at static conditions.
3.4.1 Comparison of Inert Blowing Agents: Argon, Nitrogen, and Helium
3.4.1.1 Background
In the past, experimental studies have been conducted to evaluate the feasibility of using
inert gases as blowing agents for plastic foaming processes. Dey et al. [200] studied extrusion
foaming of Polyvinyl chloride (PVC) foam with CO2 and Ar. Jacob et al. [34] studied the
foamability of PS blown with CO2, Ar and N2 using a single extrusion system. Lee et al. [31]
studied high density PS (HIPS) foaming blown with N2 using an extrusion foaming system. In
particular, Lee et al. [31] pointed out that due to a higher specific volume of N2 than CO2, a
higher volume expansion ratio can, in theory, be achieved using N2. This idea can be extended to
the case of Ar and He since they both have higher specific volumes than CO2. Therefore, foaming
with these inert gases might be feasible in industrial processes. However, despite the valuable
insight offered by the previous researches, thorough understanding in this subject has not been
fully achieved yet. In particular, plastic foaming with He has not been reported in the past. In this
context, this study compares the cell nucleation and initial growth behaviour of a PP-ethylene
random copolymer blown with three inert gases: Ar, N2 and He via in situ foaming visualization.
93
3.4.1.2 Experimental Materials and Sample Preparation
The polymer used in this study is a high melt strength PP-ethylene random copolymer
(Daploy PP WB260HMS, Borealis). The MFI and density of WB260HMS is 2.4 g/10 min and
0.9 g/cm3, respectively. The BAs used is Ar, N2, and He (99% pure from BOC Canada Ltd.). To
prepare the plastic sample for the batch foaming experiments, the PP copolymer resins were first
molded to 200 μm thick discs using a hot press. Then, they were annealed at 180 ºC for five
minutes to release the stress of the polymer before they were allowed to cool down under the
ambient condition. The molding and cooling conditions (i.e., temperature and pressure) were kept
constant to ensure that all samples had similar thermal histories.
3.4.1.3 Experimental Procedure
This study was conducted using the batch foaming visualization system developed by Guo
et al. [53] to capture in situ plastic foaming processes of PP copolymers. The setup of the system
is depicted in Figure 3-1. Unlike the study described in Section 3.3, all experiments in this study
was conducted at a high temperature (180 °C) to ensure that all crystals has been melted, hence
the effect of the blowing agents could be studied in an isolated manner. To conduct an
experiment, a sample is loaded into the foaming chamber at room temperature. The chamber was
heated to 180 °C, and a high-pressure blowing agent was injected into the chamber via a metered
stream of gas controlled by a syringe pump. The chamber was held at constant temperature and
pressure for 30 minutes, after which a rapid depressurization was induced by the opening of a gas
exit valve while the high-speed camera captured the foaming processes.
This study is composed of two major parts. First, foaming visualization experiments were
conducted for Ar, N2, and He by keeping the processing temperature (Tsys), saturation pressure
(Psat) and the maximum pressure drop rate (-dPsys/dt|max) constant at 180 ºC, 2000 psi, and 20
MPa/s, respectively. Since each gas has a different solubility in the PP copolymer, the dissolved
94
gas content in these cases was also different. Therefore, the effects of the BA type could not be
decoupled from those of the gas content in this study. However, this study aims, as the first
endeavor, to evaluate the feasibility of using these gases as BAs for extrusion foaming or
structural foam injection molding processes. To explain this, it is noted that in order to generate
high quality foams with high cell density and uniform cell sizes, it is imperative to achieve a
homogeneous polymer-gas mixture prior to foaming (see Section 1.3.2 for explanation). For
complete dissolution of gas into the polymer, the system pressure prior to foaming must be higher
than the solubility pressure (or saturation pressure) corresponding to the amount of gas that is
injected. Also, in order to speed up the gas dissolution process, it is desirable to set the system
pressure to be much higher than the solubility pressure, but this imposes difficulties in
processing. Therefore, by studying the foaming behaviour of these insert gases at a fixed
saturation pressure, the feasibility of each gas as blowing agents for foam processing could be
determined.
Secondly, foaming experiments were conducted by keeping the molar concentration of
these inert gases the same. This study is aimed to investigate which BA has the higher nucleating
power per molar concentration of gas. To achieve this, the solubility of these gases in the PP
copolymer has been measured by Mr. Mohammad Hasan. To be specific, the solubility data was
measured using a gravimetric method with a magnetic suspension balance (MSB). Due to the
buoyancy effect of the swelled polymer upon gas dissolution, the mass reading of the dissolved
gas in the MSB, denoted as apparent solubility (Sa), is lower than the actual solubility. The
Sanchez Lacombe EOS (SL EOS) was used to estimate the swelling effect on the solubility of N2
in the PP copolymer to obtain the corrected solubility (S). For Ar and He, however, only the
apparent solubility was available. From Figure 3-15, it could be seen that the solubility of He,
expressed by wt%, is very low. Therefore, it is expected that the swelling effect of He is very
95
small and was neglected. For Ar, however, the solubility is the highest among the three gases,
and hence the swelling effect might be significant. Therefore, only He and N2 were used in this
part of the study. Further investigation will be needed in the future when the corrected solubility
of Ar and He becomes available. For this study, the Tsys, -dPsys/dt|max, and molar concentration of
gas were fixed at 180 ºC, 15 MPa/s and 0.432 mol of gas/g of polymer, respectively.
Figure 3-15 – Solubility of He, Ar, & N2 in PP copolymer [35]
Each case was conducted three times to test the repeatability of the experimental results.
Table 3-2 summarizes the experimental cases discussed above. For analysis, cell density data was
extracted from the foaming visualization data. To achieve this, N(t), the number of cells within a
superimposed circular boundary with an area of Ac at time t was counted at each time frame. The
radiuses of 10 randomly selected bubbles at time t (i.e., Rbub,i(t), where i = 1…10) were also
measured. The cell density with respect to the foamed volume, Nfoam(t), and the cell density with
respect to the unfoamed volume, Nunfoam(t), were calculated using the following equations:
Equation 3-6
Equation 3-7
96
Equation 3-8
The data was collected from t = 0 to after the completion of the cell nucleation process to extract
the cell density profiles with respect to time. The cell nucleation rate profiles with respect to the
unfoamed volume were computed by direct differentiation of the cell density data. Note that the
smallest bubbles that could be observed are approximately 2 to 5 μm in diameter. Therefore,
there could be a small time delay between the moment of bubble nucleation and the time at which
the bubbles were observed. Therefore, the cell density and cell nucleation rate profiles are based
on the observable bubbles only. Also, the average cell radius growth profiles with respect to time
were obtained from the measured cell radius data.
Table 3-2 – Experimental cases of PP foaming with inert gases
Expt. #
BA Tsys
[°C] Psat
[psi] Molar C
[x 103mol/g] -dPsys/dt|max
[MPa/s]
1 He 180 2000 0.280* 20 2 N2 180 2000 0.875 20 3 Ar 180 2000 1.297* 20 4 He 180 2500 0.432* 15 5 N2 180 949 0.432 15
* Based on apparent solubility
3.4.1.4 Results and Discussion
Figure 3-16 shows snapshots of the in situ foaming processes in which the Psat was kept
constant at 2000 psi. Figure 3-17 and Figure 3-20 show the cell density and cell nucleation rate
vs. time, respectively, for all experiments where Psat = 2000 psi. Since the pressure drop profiles
are very similar for all cases, only the average pressure drop profile is shown in Figure 3-17. This
figure shows that the maximum cell density for the He case is much lower than that of Ar or N2,
97
which could be attributed to the higher dissolved gas content in the polymer in the latter two
cases. When the gas content increases, the chance of forming gas clusters larger than the size of a
critical bubble increases, thus resulting in more bubble nucleation. To be specific, when a high
gas content was used, γlg decreased [77, 78]. Meanwhile, the supersaturation (i.e., Pbub,cr – Psys)
increased since Pbub,cr is a positive function of gas concentration (C) while the Psys profile was the
same for all three cases (i.e., Pbub,cr = CPsys/Csat, which is valid for a weak polymer-gas solution
where the gas is an ideal gas). According to Equation 3-4 and Equation 3-5, the decrease in γlg
and increase in supersaturation would increase cell nucleation rate and hence the overall cell
density. Also, from Figure 3-17, the maximum Nunfoam of the N2 case was slightly higher than that
of Ar despite that the onset of nucleation of Ar was earlier than N2. Figure 3-21 shows the
average bubble radius (Rbub,avg) vs. time data, which demonstrates that that the average bubble
growth rates of the Ar and He cases were similar, while that of the N2 case was slightly lower.
This could be attributed to the higher gas diffusivities of Ar and He than N2 [201]. Therefore, for
the Ar case, more gas might have been used for bubble growth than nucleation as compared to
the N2 case. This could explain why the maximum cell density for the latter case was higher even
when the dissolved gas content of Ar was higher than N2 as per wt% and per molar concentration
basis (refer to Figure 3-15 and Table 3-2, respectively). This demonstrates that N2 has a higher
nucleating power than Ar.
98
Figure 3-16 – Snapshots of PP foaming processes with inert gases at Psat = 2000 psi
Figure 3-17 – Nunfoam vs. time (Psat = 2000 psi)
Figure 3-18 – Nunfoam vs. time (C = 0.432 mol
of gas/g of polymer)
Figure 3-19 – dNunfoam/dt vs. time (Psat = 2000
psi)
Figure 3-20 – dNunfoam/dt vs. time (C = 0.432
mol of gas/g of polymer)
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Figure 3-21 – Rbub,avg vs. time (Psat = 2000 psi)
Figure 3-22 – Rbub,avg vs. time (C = 0.432 mol
of gas/g of polymer)
Figure 3-18 and Figure 3-20 summarize the cell density profiles and cell nucleation rate
vs. time, respectively, for cases where the molar C was kept constant at 0.432 mol of gas/g of
polymer. It was observed that the maximum cell density of He was higher than that of N2 (i.e.,
less than one order of magnitude difference). On the other hand, the onset times of nucleation for
the two cases seem to be quite similar, based on the times when bubbles were first observed.
These results seem to suggest that the nucleating power of He is higher than N2 when the same
molar concentration of gas is used. However, this could be because the total amount of pressure
drop for the He case was higher than that of the N2 case, since a higher Psat was needed for the He
case to achieve the same molar concentration of gas (i.e., 2500 vs. 949 psi). Furthermore, Leung
et al. [177] showed that the pressure drop rate has no effect on the pressure drop threshold (i.e.,
the amount of pressure drop beyond the saturation pressure that is required to induce foaming), so
the pressure drop rate prior to the onset of nucleation is irrelevant. Therefore, even through the
maximum pressure drop rate are matched in these two cases, the pressure drop rate beyond the
pressure drop thresholds, which is not currently available, might not be same. Therefore, further
investigation is required to confirm this result when the pressure drop threshold data becomes
available. Figure 3-22 shows the average bubble growth profiles for these experimental cases. It
100
was observed that the bubble growth rate of the N2 case was higher than that of the He case. This
could be explained by the higher cell density of He than N2, hence more gas might have been
used for cell nucleation than cell growth for He that resulted in a lower bubble growth rate.
3.4.2 Plastic Foaming with Blowing Agent Blends: Carbon Dioxide and Nitrogen
3.4.2.1 Background
Current PS foam processes utilize a blend of supercritical CO2, and an alcohol or a HC as
blowing agents to improve the foamability of PS blown with CO2 [202-204]. Foaming of other
polymers (e.g., PMMA and PCL) with similar BA blends has also been studied. Similar to the PS
cases, improved foams, when compared to those blown with CO2, were observed [205, 206].
Most of the previously mentioned studies attributed the improved foaming behaviour to increases
in BA solubility, permeability and plasticization effects due to the addition of an alcohol and/or a
HC. Furthermore, the additional cooling effect from the vaporization of the alcohol or HC upon
depressurization helped to stabilize the cell structure. However, they are flammable, and therefore
potentially hazardous if these BAs are not diffused out of the foams prior to usage [207].
Therefore, it is imperative to reduce the usage of the hazardous component of these BA blends
with a safer alternative that provides greater ease in handling and storage. One possible option is
to replace the alcohols with supercritical N2. Both Maio et al. [208] and Kim et al. [33] have
suggested that the nucleating power of N2 was higher than CO2 per wt% of BA. However, the
solubility of CO2 is much higher than that of N2 [209]. Therefore, by blending these two BAs, it
might be possible to produce foams with high cell density and volume expansion. In a subsequent
study conducted by Maio et al. [208], it was demonstrated that PCL foams blown with a blend of
CO2 and N2 resulted in high cell density while maintaining a low overall foam density. These
results were later used to create porous PCL scaffolds for tissue engineering [210]. Despite these
pioneering studies, a thorough understanding of the fundamental mechanisms of plastic foaming
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using CO2-N2 blends has not yet been achieved. In this context, this study examined the foaming
behaviour of PS blown with various supercritical CO2-N2 blends by observing the cell nucleation
and growth processes in situ.
3.4.2.2 Experimental Materials, Sample Preparation and Procedure
The polymer used for the foaming experiments was PS (Styron PS685D, Dow Chemical
Ltd.), which has a melt flow index (MFI) of 1.5 g/10 min and a density of 1.04 g/cm3. Polymer
pellets were compression molded into films 200 µm in thickness by using a hot press. Five BAs
with various CO2-N2 compositions (Linde Gas Inc.) were used: N2 (99.998% pure), 75% N2-25%
CO2 blend (99.99% pure), 50% N2-50% CO2 blend (99.99% pure), 25% N2-75% CO2 blend
(99.99% pure) and CO2 (99.8% pure). The foaming visualization system developed by Guo et al.
[53] has been used in this study. The experimental procedure for the foaming visualization
experiments has been detailed in Section 3.4.1.3. By adjusting the resistance of the gas exit path
with a metered valve, the same pressure drop rate was obtained for each BA composition. In
addition, similar to the study outlined in Section 3.3.2.3, foaming observation was conducted in a
region where a PS sample was suspended in air by placing a clear PET film (0.127 mm in
thickness, with a 1 mm hole in the center) beneath it. In this study, the main goal was to study the
foaming behaviour of PS when different compositions of CO2-N2 gas blends were used.
Therefore, the Psat and –dP/dt|max were kept constant at 10.34 MPa (1500 psi) and 15 MPa/s
(2176 psi/s), respectively. To study the effect of temperature on the performance of BAs, three
Tsys were used: 100°C, 140°C and 180°C. It is well known that the solubility of CO2 decreases
with increasing temperature while that of N2 increases [211]. Since each blend has a different
solubility in the PS polymer at each temperature, the amount of dissolved gas in each
experimental case is also different. However, by studying the foaming behaviour of plastics
102
blown with these gases at a fixed saturation pressure, the ease of use of each BA in industrial
plastic foam processes could be clarified. This study would provide valuable insight on the
foaming mechanisms of these BA blends and guidance to identify an optimal composition for
plastic foaming processes.
Table 3-3 summarizes the experimental conditions. Each experiment was repeated three
times to examine the statistical reliability of the results. From batch foaming videos captured by
the high-speed camera, cell density and size versus time were measured for the region where the
PS samples were suspended in air (i.e., no contact with the sapphire windows or PET film
surface). The characterization methods used were described in Section 3.4.1.3.
Table 3-3 – PS/CO2-N2 experimental matrix
# Blowing Agent Composition [%] Tsys
[°C] Psys
[MPa] -dPsys/dt [MPa/s] CO2 N2
1 0 100
100
10.34 15
2 140 3 180 4
25 25 100
5 140 6 180 7
50 50 100
8 140 9 180 10
75 75 100
11 140 12 180 13
100 0 100
14 140 15 180
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3.4.2.3 Results and Discussion
Figure 3-23 shows snapshots of the 75% CO2-25% N2 case at 100 °C. It was observed
that the cell nucleation rate and cell density were significantly higher in the region where PS was
in contact with the PET; in addition, there was an earlier onset of cell nucleation. This
demonstrated that heterogeneous nucleating effect was substantial, which agreed with Equation
3-5 and the results obtained by Guo et al. [199]. Similar phenomena were observed for the other
experimental cases, except for the cases foamed with 100% N2 and the 25% CO2-75% N2 gas
blend at 100 °C (refer to Figure 3-24), where no cells were formed in either region due to the
limited plasticization effect of these gas blends at 10.34 MPa (gas solubility ≈ 0.0043 and 0.022
g-BA/g-polymer, respectively [211]). In some other cases (i.e., 100% N2 at 140°C, and 100%
CO2 at 140°C and 180°C), cells only nucleated in the region where PS and PET were in contact.
Figure 3-23 – Sample foaming video of the 75% CO2-25% N2 case foamed at 100°C
104
Figure 3-24 – In situ PS/CO2-N2 foaming images
Nunfoam vs. time in the suspended regions of the plastic samples for all five BA cases are
plotted in Figure 3-25 (100°C), Figure 3-26 (140°C) and Figure 3-27 (180°C). In each figure, the
average cell density of the three experiments is shown and the error bars signify the standard
deviations. Comparing these figures shows that as Tsys increased, the onset of cell nucleation
occurred earlier, and cell nucleation took less time to complete. This is due to the decreased
surface tension and the increased mobility of gas molecules at higher temperatures.
Simultaneously, the bubble growth rate also increased with temperature due to the decreased
viscosity and increased diffusivity of gas.
105
The maximum Nunfoam in the suspended region for all cases are shown in Figure 3-28. For
the 100% N2 cases, foaming in the suspended region only occurred at 180°C, with a low average
cell density of 4.26 x 104 cells/cm3. This could be attributed to a relatively increased solubility
and decreased viscosity at high Tsys, which competed with the limited plasticization effect of N2
due to the inherently lower solubility. For the 25% CO2-75% N2 cases, the foaming window
widened slightly (i.e., foam at 140°C and 180°C) due to the increased plasticization effect of
CO2. For the 50% CO2-50% N2 cases, the cells were nucleated at all three temperatures and the
highest cell density was obtained at 140°C. This behaviour could be explained by the opposing
dependency of the CO2 and N2 solubility on temperature: the solubility of CO2 decreases with
increasing temperature, which led to an optimal foaming condition at an intermediate temperature
of 140°C. Also, the nucleation rate at 140 °C was observed to be highest when compared to the
other four BAs. However, the processing temperature window was not as wide as the 75% CO2-
25% N2 case based on the lower cell densities obtained at 100 and 180 °C.
The 75% CO2-25% N2 cases yielded the widest processing window as foams with high
cell density were obtain at all three temperatures (100 °C, 140 °C and 180 °C). The average cell
densities were also the highest (3.71 x 106 to 4.35 x 106 cells/cm3) when compared to the other
gas blends at each temperature. The nucleation rates for this gas blend were also among the
highest when compared to the other four BAs (i.e., highest at 100°C and 180°C and second
highest at 140°C). It was hypothesized that this foaming behaviour was a result of an increased
plasticization effect of CO2 when compared to the cases with lower CO2 content, which helped to
dissolve extra N2 that was required to induce cell nucleation. This hypothesis will be confirmed
once the gas compositional data, which will be derived from the total gas solubility [211],
becomes available in the future. It is noted that the wide processing temperature window of the
75% CO2-25% N2 cases is crucial to industrial foaming processes, where uniform temperature
106
within plastic melt is difficult to achieve due to the low thermal conductivity of plastics and the
large throughput rate in plastics production.
For the 100% CO2 cases, the cells only nucleate at 100°C. This could be attributed to the
increased diffusivity of CO2 as temperature increases [37, 40, 212]. Since the thickness of the
sample film was only 200 µm (which was chosen to ensure clear visibility of the individual
bubbles) and gas could have escaped through both the top and bottom surfaces in the suspended
region, the increased diffusivity could have caused significant gas loss at the higher temperatures.
As a result, the level of supersaturation decreased. Therefore, cell nucleation was less likely to
occur spontaneously. The gas loss effect seemed to be less pronounced for the CO2-N2 blends and
100% N2 cases in this study. This could be due to the lower diffusivity of N2 in molten plastics as
compared to CO2, such as for HDPE [40] and polyethylene oxide (PEO) [213]. Nevertheless, at a
low temperature (100°C) where the gas loss effect is believed to be less significant, the cell
density of the 75% CO2-25% N2 case was still slightly higher than the 100% CO2 case, thus
showing the synergistic or complementary effect of CO2-N2 gas blends. In particular, this suggest
that the addition of N2 to CO2 could help lessen the gas loss effect during foaming processes,
which could lead to foams with higher cell density and volume expansion ratio.
Not only that the 75% CO2-25% N2 cases yielded the highest cell densities with the
widest Tsys processing window, the average bubble growth rates were also the highest among all
BA blends over the entire Tsys range studied (see Figure 3-29 for the average bubble growth rate,
signified by the average rate of change of bubble diameter, for each case). This suggests that
foams with high volume expansion ratios could be achieved in typical foaming processes if the
foams could be stabilized quickly to prevent cell coalescence and collapse.
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Figure 3-25 – Nunfoam vs. time of PS/CO2-N2
foaming (Tsys = 100 °C)
Figure 3-26 – Nunfoam vs. time of PS/CO2-N2
foaming (Tsys = 140 °C)
Figure 3-27 – Nunfoam vs. time of PS/CO2-N2
foaming (Tsys = 180 °C)
Figure 3-28 – Max. Nunfoam of PS/CO2-N2
foaming
(Nunfoam = 100/cm3 signifies no foaming)
108
Figure 3-29 – dDbub/dt|avg vs. Tsys of PS/CO2-N2 foaming
3.5 Conclusion
The capability of an improved foaming visualization system with accurate heating/cooling
program control has been demonstrated. By correlating with the HPDSC studies, this
experimental setup allowed us to investigate the interrelationships between the crystallization
kinetics and the cell nucleation, growth and deterioration phenomena in plastic foaming
processes. Via in situ observation of a linear PP (DM55) and a PP-ethylene copolymer (SEP550),
the effects of crystals on cell nucleation has been demonstrated. It was demonstrated that bubbles
nucleated around crystals at low temperatures, which was due to the exclusion effect of CO2 at
crystal growth fronts and the tensile stresses induced by bubble growth to the constrained
amorphous regions between adjacent crystals. These two effects became less apparent as
temperature increased, and cell nucleation rates decreased.
As part of our research goal to replace the currently used hazardous blowing agents, the
foaming behaviour of a PP random co-polymer using Ar, N2 and He, all of which are inert gases,
and the foaming behaviour of PS with CO2-N2 blends have been studied by in situ batch foaming
visualization experiments under static conditions. The experimental results suggested that the
nucleating power of N2 could be superior to that of Ar. Meanwhile, Ar has the highest solubility
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in the polymer among these inert gases, which also makes it a good candidate as a BA. While He
might have an even higher nucleating power N2 as per molar concentration basis, the ease of use
of N2 is believed to be superior to He since N2 has a higher solubility and hence a lower system
pressure could be used for gas dissolution. Meanwhile, synergistic effects have been observed
when CO2-N2 blends were used. In particular, the 75% CO2-25% N2 gas blend appeared to have
the best foaming performance: it yielded high cell densities and cell growth rates over a wide
processing window from 100°C to 180°C. However, it is also noted that the 75% CO2-25% N2
blends might not be the truly/absolute optimal CO2-N2 composition for the foaming of PS.
Nevertheless, this study provided directions for identifying such an optimal composition: a high
percentage of CO2 and a low percentage of N2. This study also demonstrated that supercritical N2
is a feasible alternative to alcohols as a co-blowing agent to supercritical CO2 in PS foaming
processes. It is expected that this knowledge could be applied to the other polymers that are
currently foamed with blowing agent blends of CO2 and an alcohol.
110
CHAPTER 4
IN SITU VISUALIZATION OF PLASTIC
FOAMING PROCESS UNDER
EXTENSIONAL STRESS
4.1 Introduction
In Chapter 3, the development of a static foaming visualization system has been detailed.
Experimental studies to verify its capability and to investigate various aspects of plastic foaming
have also been conducted. These works provide baseline knowledge for the development of the
dynamic foaming systems with extensional and shear stress-inducing ability and the subsequent
experimental studies, which are detailed in this chapter and the next. These systems model the
stress conditions in extrusion and injection foam molding processes where plastic melt are
subjected to extensional stresses in the converging section of dies and shear stresses near die
walls (see Figure 4-1). In this context, these systems are key research tools to understand the
science behind industrial plastic foaming processes.
This chapter describes the development of a novel foaming system that allows in situ
observation of plastic foaming under a uniform and easily controllable extensional stress field
(refer to reference [214]), which has not been achieved previously. Using the system, foaming
studies of PS and PS-talc composites has been conducted to investigate the effects of extensional
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strain and strain rate on cell nucleation and growth behaviour (refer to reference [214] and [215]).
The interrelationships between extensional strains, crystals, and foaming behaviour of PP have
also been clarified by a foaming visualization study of PP at temperature below its Tm (refer to
reference [216]).
Figure 4-1 – Stress effect on cell nucleation in extrusion process
4.2 Development of a Foaming Visualization System with
Extensional Stress-Inducing Ability
The goal of this research was to develop a novel system to visualize and capture the plastic
foaming process in situ for a plastic sample under extensional stress. The system must carry out
the following three major functions: 1) Apply a uniform extensional strain to a plastic specimen
under high temperature and pressure; 2) Allow dissolution of gas into the plastic melt and the
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subsequent inducement of foaming by rapid depressurization; 3) Capture of the bubble formation
and growth processes with fine temporal and spatial resolution.
4.2.1 Function I: Application of a Uniform Extensional Strain to a Plastic Specimen under
High Temperature and Pressure
A counter-rotating rollers system has been designed to induce extensional strain to a
polymer sample (see Figure 4-2). The visibility to the sample would not be obstructed by the
rollers’ motion and the optical plane would be static irrespective of the rollers’ position.
Figure 4-2 – Counter-rotating roller design
The counter rotating rollers were driven by a stepper motor system with high resolution
(0.01°/pulse) and output torque (320 lb-in) (VEXTA Step Motor ASM98MAE-N36, Oriental
Motors) via two drive shafts and a pair of spur gears that provided the opposite rotating direction.
The stepper motor system, which had a built-in feedback sensor, was controlled by a computer
and could be programmed to run at accurate velocities in specified positions. Two ends of a thin,
rectangular plastic sample would be fixed onto the rollers by two clamps. As the rollers rotated,
the sample would be stretched uniaxially. The strains and strain rates of the plastic specimen
could be easily controlled by adjusting the angular position and velocity, respectively. To be
specific, the maximum strain was limited by the angular displacement of the rollers. In this thesis,
engineering strain (ε) and engineering strain rate (dε/dt) have been used, which are defined to be
113
the change and the rate of change in the sample’s length (ΔL) divided by the original sample
length (Lo), respectively (see Equation 4-1 and Equation 4-2).
Equation 4-1
Equation 4-2
Each of the two rollers could be rotated for up to 0.85 revolution before the clamps started to
interfere with the sample. Based on the diameter of each roller (Dr = 30 mm) and the center-to-
center distance between them (lc = 40 mm), the maximum extensional strain (εmax) could be
calculated to be four using the following equation:
Equation 4-3
The maximum angular speed of the motor (ωmax) was 5000 rpm (523.6 rad/s). The maximum
extensional strain rate (dε/dt|max) could be determined to be 196 s-1 using the following equation:
Equation 4-4
However, the dε/dt|max could only be sustained for 0.02 s due to the εmax constraint. Therefore, a
lower dε/dt must be used to achieve a steadier extensional flow. By using a plastic sample with a
shape of a tensile specimen (i.e., a wider shoulder on each of the two ends of the sample for
gripping and a thinner gauge section in the middle for sample deformation), higher εmax and
dε/dt|max could also be achieved. The two rollers rotated in opposite directions and their angular
speeds would be the same since they were coupled by two identical spur gears. Therefore, the
center of the sample tends to remain stationary as long as the sample was homogeneous and
underwent a uniform deformation. Visualization of foaming was captured in this relatively
stationary region, so that over time its foaming phenomenon could be captured in detail. The
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rollers were installed in a stainless steel housing to maintain their positions. To reduce friction
between the rollers and the housing, a set of four PTFE-coated dry bearings has been installed.
4.2.2 Function II: Gas Saturation in Plastic Melt and Subsequent Inducement of Foaming
by Rapid Depressurization
The counter-rotating rollers system was enclosed in a high pressure and high temperature
stainless steel chamber (see Figure 4-3) to maintain the high-pressure gas for saturation and
foaming via depressurization. It has been found that as the plastic sample was heated, it softened
and the unsupported region of the sample tended to sag under gravity (see Figure 4-4), hence a
design revision was needed to change the orientation of the sample with a new chamber stand.
Consequently, the chamber has been re-positioned so that the plastic specimen’s thinnest side
faced upwards while it stretched horizontally (see Figure 4-5). This orientation prevented
significant deformation of the plastic specimen due to gravity at a high Tsys. The stepper motor
has also been re-positioned to be further away from the chamber so that it would not be
overheated. A tensioned drive belt has been used to transfer the motion of the motor to the drive
shaft that turns the spur gears and subsequently the counter-rotating rollers inside the chamber.
Figure 4-3 – Foaming chamber design for visualization system with extensional stress
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Figure 4-4 – Preliminary setup for visualization system with extensional stress
Figure 4-5 – Revised setup for visualization system with extensional stress
The chamber temperature was controlled by four cartridge heaters with Proportional-
Integral-Derivative (PID) feedback control. The pressure inside the chamber was set and
maintained by a metered gas supply stream from a syringe pump. The chamber was equipped
with a set of two sapphire windows for visualization of the plastic specimen. To foam the plastic
116
specimen, a rapid pressure drop was induced in the chamber by opening the gas exit valve, which
is controlled by the I/O system detailed in Section 3.2.4.
4.2.3 Function III: Capture of Bubble Formation and Growth Processes with Fine
Temporal and Spatial Resolution
For the third function, the optical and computer control system described in the
development of the static foaming visualization system (Section 3.2) has been used. The optical
system consisted of a high-speed camera coupled with a high magnification zoom lens and an
optic fiber transmissive light source. The high-speed camera was installed onto a stand with 3-
orthogonal linear guides to provide adjustments to the camera position. When gas was released
from the chamber to foam the plastic specimen, the computer system controlling the gas exit
valve also triggered the high-speed camera to capture the foaming process viewed through the
sapphire windows as well as a pressure transducer to record the pressure inside the chamber.
The flat surfaces of the mushroom-shaped sapphire windows have been polished, and the
c-axis of the sapphire crystal was parallel to the optical axis. The sapphire-to-metal seal was
created by a PTFE o-ring with a maximum operating temperature of 260 °C. The sealing design
was similar to the one used in the static foaming visualization system (Section 3.2). A threaded
compression nut provided the clamping force for the initial seal. The top compression nut had a
depressed center region to ensure sufficient clearance between the chamber and the lens at high
temperature. The dynamic seal between the chamber and the drive shafts was achieved by a pair
of spring-loaded PTFE cup seals with the maximum operating temperature, pressure, and speed
of 260 °C and 25 MPa, and 2 m/s, respectively. The metal-to-metal seal between the chamber
body and its cover was created by a silicone o-ring that fit into a groove on the top surface of the
chamber body. Figure 4-6 shows a schematic of the overall visualization system. Figure 4-7
shows the finalized foaming system setup.
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Figure 4-6 – Schematic of foaming visualization system with extensional stress-inducing ability
Figure 4-7 – Finalized foaming visualization system with extensional stress-inducing ability
4.2.4 Experimental Procedure
To carry out a foaming experiment, a thin plastic specimen was first clamped onto the
rollers. To be specific, the plastic specimen was fixed at the two ends of the longest dimension by
the clamp installed on each of the rollers. The chamber was then maintained at the designated
foaming temperature and pressure for 40 minutes to allow the blowing agent to dissolve into the
specimen. After gas saturation, the stepper motor was programmed to rotate and generate an
extensional stress on the specimen along the longest dimension. After the desired strain and/or
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strain rate has been reached, the motor was stopped, and the gas was released from the chamber
by opening the gas exit valve. The rapid pressure drop inside the chamber caused foaming to
occur in the plastic specimen. At the same time, the foaming process was captured in situ by the
high-speed camera, and the pressure drop data generated from the pressure transducer was
recorded. By adjusting resistance along the gas exit path via a metered valve, different pressure
drop rates could be obtained. It is noted that the extensional strain, and not stress, was directly
controlled in the experiments. Therefore, the stress relaxation behaviour of the polymer/gas
solution must be considered.
4.2.5 Verification of System Capability in Application of Extensional Strain
To confirm if the foaming system is capable to apply an accurate extensional strain, a PS
sample (Styron PS685D, 0.4 mm in thickness) is marked along its centerline and loaded into the
system at 100 °C. A snapshot of the mark was taken before and after an extensional strain of 0.55
was applied (see Figure 4-8). The overall deformation was quite uniform despite the minor
distortion observed. Meanwhile, due to insufficient/uneven clamp force and sample imperfection,
slippage or necking could be observed in some rare cases. These could be detected easily by
inspecting the sample shape after foaming experiments. In those cases, the experimental results
would be discarded and the experiment would be repeated to avoid any inconsistency.
Figure 4-8 – Deformation of PS sample under an applied extensional strain
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4.3 PS and PS-Talc Composite Foaming under Extensional Stress
4.3.1 Experimental Materials and Sample Preparation
To study the effects of extensional stresses, foaming experiments of PS and PS-talc
composites foamed with CO2 has been conducted. In addition to capturing foaming videos,
scanning electron microscopy (SEM) was also used to observe the cell morphology of the foamed
samples. Same as the other study in this thesis (see Section 3.4.2), the PS and CO2 used for the
foaming experiments were Styron PS685D from Dow Chemical Ltd. and CO2 from Linde Gas,
respectively. In some experimental cases, 5 wt% talc (i.e., Cimpact CB7, Luzenac) was also
added to the PS sample as a nucleating agent. The PS-talc samples were mixed with a 3 piece
C.W. Brabender batch mixer with counter-rotating roller blades from a 20% PS-talc masterbatch
that was produced using the same method. The PS samples were also run through the mixer to
obtain a comparable processing history. Then, the samples were compression molded into thin
films at 0.5 mm thick using a hot press at 190°C, and then cut to 50 mm by 10 mm in size.
4.3.2 Experimental Cases
Firstly, to study the extensional stress effect separately, the Tsys, gas content, and average
pressure drop rate (-dPsys/dt|avg) were kept constant at 100 °C, 2 wt%, and 6 MPa/s, respectively.
Two extensional strains (ε = 0.6 and 1.2) were used. It is noted that the strain and strain rate
values used throughout this thesis were engineering strain and strain rates (i.e., ε = ΔL/L and dε/dt
= d(ΔL/L)/dt). A low Tsys was chosen to reach a high level of stress. The gas content and -
dPsys/dt|avg were also kept at low levels to emphasize the stress effect. Secondly, investigations
were also conducted to observe the effect of the Tsys (100 °C vs. 140 °C) under constant applied ε
and dε/dt. Table 4-1 summarizes the experimental cases. It is noted that, the left-right direction of
the foaming videos were aligned to the longest dimension of the polymer (50 mm) and the optical
120
plane is along the 50 mm x 10 mm plane. On the other hand, the SEM pictures were taken on the
cross-sectional area of the foamed sample (i.e., along the 10 mm x 0.5 mm plane).
Table 4-1 – Experimental cases for PS and PS-talc/CO2 foaming under extensional stress
# -dPsys/dt|avg
[MPa/s] C
[wt%] Talc % [wt%]
Tsys
[°C] ε dε/dt
[s-1] 1 6 2 0 100 0 0
2 6 2 0 100 1.2 0.5/s
3 6 2 0 140 0 0
4 6 2 0 140 1.2 0.5/s
5 6 2 5 100 0 0
6 6 2 5 100 0.6 0.5/s
7 6 2 5 100 1.2 0.5/s
8 6 2 5 140 0 0
9 6 2 5 140 1.2 0.5/s
4.3.3 Results and Discussion
4.3.3.1 PS Foaming
Cases 1 to 4 were used to study the effect of applied ε on PS foaming, as compared with
the unstrained case at different Tsys. For PS foamed at 100 °C, it was found that the sample
without applied ε did not foam at all. On the other hand, the sample with applied ε foamed to a
very low cell density. Figure 4-9 captures images of the stabilized PS samples foamed in both
cases, which clearly show that extensional stress can induce cell nucleation in plastic foaming.
Figure 4-10 shows snapshots of the in-situ foaming video for the stretched case, which
demonstrated that the foaming process was very slow. It is noted that prior to foaming, the
stretched sample thinned. Therefore, it should be more susceptible to gas loss during foaming,
which has a negative effect on cell nucleation. However, a reversed trend was seen. It is
hypothesized that the applied ε generated a tensile stress that counteracted the compression by the
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overall system pressure (Psys). The Psys at each local region within the polymer-gas solution
would be lowered, and the size of reduction would depend on the tensile stress at each local
region. Consequently, the Rcr, Whom and Whet would be reduced, and the cell nucleation rate would
be increased. To explain this, Equation 3-1 to Equation 3-5 have been re-listed in the following:
Equation 4-5
Equation 4-6
Equation 4-7
Equation 4-8
Equation 4-9
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From these equations, it is clear that the decrease in Whom and Whet would effectively increased
Jhom and Jhet, hence the cell density increased. Moreover, as Rcr decreased below the size of pre-
existing microvoids (in the form of free volumes or cavities on impurities in the polymer-gas
solution), the microvoid would grow spontaneously to form a nucleated cell, hence the cell
density would further increased.
Figure 4-9 – PS sample foamed at 100 °C: a) ε = 0; b) ε = 1.2
Figure 4-10 – Snapshots of PS foaming at 100 °C (ε of 1.2 at dε/dt of 0.5/s)
Similar to the 100 °C case, it was found that the sample foamed at 140 °C without applied
ε did not foam at all. A few bubbles were observed in the sample foamed under extensional
strain, but cell nucleation was much less pronounced than in the 100 °C case. This could be due
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to the lower stress and rapid stress relaxation as the polymer’s viscosity and elasticity decreased
at a higher Tsys, which could diminish the effects of applied ε. The lower gas solubility and faster
gas loss as Tsys increased might also contribute to the less pronounced cell nucleation
phenomenon. To be specific, the CO2 concentration at 500 psi is 2.0 wt% at 100 °C and 1.4 wt%
at 140 °C [212]. Moreover, it was observed that many cells collapsed after they had been cooled
and taken out of the chamber.
4.3.3.2 PS-talc Composite Foaming
In cases 5-7, the extensional stress effect for PS with talc as a nucleating agent was
compared with the unstrained case at 100 °C. This study was conducted under the same
conditions as the PS experiments described earlier, except that two levels of applied ε were used
in this study (i.e., ε = 0.6 or 1.2). Similar to the PS cases, it was found that the final cell density of
the foamed sample increased significantly as ε was increased (refer to Figure 4-11 for the SEM
images of the cross-sectional area of the three foamed samples). In all cases, no cells were
observed near the skin layers, which might be due to the rapid gas loss in these regions. The rapid
gas loss might also have resulted in smaller cell sizes for the strained cases near the skin layers.
Similar to the PS case, increasing ε would increase the local tensile stress that would lead to the
promotion of cell formation during the subsequent depressurization process. Due to the presence
of talc, the pressure variations in the PS-talc composites, especially around talc particles, is
believed to be more significant than the PS matrix when ε was applied or during bubble growth,
which could have led to higher tensile stress elements in the PS-talc composites. Similar
explanations have been given by Leung et al. [107] in the foaming of PS-talc composites at static
conditions, where cell nucleation were observed to occur around existing ones. It was believed
that polymer deformation during bubble growth induces extensional stress in some regions
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around the nearby talc particles, reducing the local Psys and hence cell nucleation rate was
increased (refer to Section 2.2.4 for details).
Figure 4-11 – PS-talc foamed at 100°C: a) ε = 0; b) ε = 0.6; c) ε = 1.2
Moreover, since polymer could not completely wet on the talc surfaces, microvoids could
exist at cavities on talc surface. These microvoids would be activated to grow as Rcr decreased
below their sizes. Furthermore, it was observed that when the PS-talc sample was stretched under
high pressure and high temperatures, a large number of unfocused black spots immediately
appeared. Figure 4-12 shows the sample before and after a ε of 1.2 was applied prior to foaming.
The number of black spots increased as ε increased. To explain this, it is first noted that, as the
polymer deformed under extensional stress, talc particles might remain approximately
undeformed due its higher stiffness. This strain mismatch might have caused the polymer chains
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to detach from the talc surfaces prior to depressurization. Therefore, the microvoids that resided
on the polymer-talc interface might change in shape or expand in size. Extra microvoids might
have also been generated in cracks or crevices on talc surfaces due to the dewetting of polymer
chains. All of these microvoids deflected the incident light, and resulted in unfocused black spots
on the camera image. On the other hand, in the PS case, such strain mismatch was minimal;
hence, the unfocused black spots were not observed in that case. As pressure was released, the
microvoids in the PS-talc sample could have seeded cell formation, hence the cell densities for
the PS-talc cases were significantly higher.
Another mechanism could be used to explain the generation of these microvoids. It is
hypothesized that when ε is applied to the polymer, the polymer chains tend to orient along the
extensional direction, which could lead to a decrease in the free volume between the polymer
chains. This decreased the solubility of gas within the polymer melt. As a result, the polymer-gas
mixture became supersaturated, which caused microvoids to form. This theory agrees with the
dynamic solubility measurement conducted in extrusion systems, in which gas solubility
pressures were determined by detecting the system pressures at the onset of bubble nucleation
within a continuous flow of polymer-gas mixture through a slit die using optical microscopy
[162] and ultrasonic measurement [95, 167]. These studies showed that the system pressure at the
phase separation point (gas solubility pressure) increased under higher throughput rate, which
indicated a decrease in gas solubility. Note that a small pressure drop below the gas solubility
pressure would be needed to initiate bubble nucleation [177], so the gas solubility pressures
measured in these two studies should be slightly lower than the actual values. Consequently, the
gas solubility reduction could be even more significant than the measured values indicated.
However, the increase in pressure at phase separation might also be due to stress-induced
nucleation. Also, based on this explanation, microvoids should also be generated in the PS cases,
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but was not observed. It might be due to rapid gas loss since gas could diffuse out from the free
surfaces instead of forming gas clusters. Meanwhile, for the PS-talc case, the expelled gas might
have diffused into gas cavities that resided on talc-surfaces instead since the gas diffusion
distance would be shorter in that case. Nevertheless, based on the available data, the significance
of this mechanism is unknown. Additional investigation will be needed to clarify this behaviour.
Figure 4-12 – PS-Talc sample: a) before applied ε; b) after applied ε of 1.2
Figure 4-13 to Figure 4-15 show the snapshots of the in-situ foaming videos for three
cases (i.e., ε = 0, 0.6, 1.2). Using the foaming videos of the ε = 0 and 0.6 cases, cell density and
cell sizes information was analyzed and plotted over time (see Figure 4-16 and Figure 4-17,
respectively). The characterization method for the cell density and cell size data was described in
Section 3.4.1.3. The case with a higher strain (i.e., ε = 1.2) was not characterized due to the large
number of black spots generated in that case. The black spots caused significantly light scattering
that increased the difficulty in identifying individual bubbles. From Figure 4-16, it could be
observed that the case with ε = 0.6 has an early onset time of nucleation, a higher nucleation rate
and a higher cell density (i.e., over 2 orders of magnitude increase) than the unstrained case (i.e.,
ε = 0). In Figure 4-17, six bubbles were selected at random for each case and their diameters
(Dbub) were plotted vs. time. Using the lines of best fit, the average growth rate for each bubble,
in terms of the rate of change of the bubble diameter, was calculated. The mean of the average
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bubble growth rates was determined to be 0.00027 cm/s (for ε = 0) and 0.00018 cm/s (for ε =
0.6). One-way ANOVA was used to test the significance of the difference in the average growth
rates between these two cases, which showed that the difference was significant (i.e., p < 0.01).
Therefore, it was concluded that the bubble growth rate was higher for the unstrained case. This
could be due to the higher cell nucleation rate for the strained case, so individual bubbles
competed for gas for their growth, thus resulting in a lower average bubble growth rate.
In summary, due to the existing of microvoids on PS-talc interface and the pressure
variations around talc particles, the extensional strain-induced cell nucleation for the foaming of
PS-talc composites was more significant than the PS cases. Although extensional stress could
also be generated around talc particles for the unstretched PS-talc sample due to the growth of
neighboring bubbles, the final cell density for that case was significantly lower than the stretched
PS-talc sample. This result suggests that extensional stress caused by polymer flow in industrial
foaming processes might be a critical factor in determining the effectiveness of nucleating agents
in inducing cell nucleation.
Figure 4-13 – Snapshots of PS-talc foaming at 100°C (ε = 0)
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Figure 4-14 – Snapshots of PS-talc foaming at 100°C (ε = 0.6 at dε/dt = 0.5 s-1)
Figure 4-15 – Snapshots of PS-talc foaming at 100°C (ε = 1.2 at dε/dt = 0.5 s-1)
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Figure 4-16 – Nunfoam vs. time for PS-talc samples foamed at 100 °C
Figure 4-17 – Dbub vs. time graph for PS-talc samples foamed at 100 °C
In cases 8 and 9, the extensional stress effect for PS with talc as the nucleating agent, as
compared with the unstrained case, was examined at 140 °C. This study was conducted under the
same conditions as in the PS experiments described in Section 4.3.3.1. Similar to the PS case, the
effect of extensional stress on cell nucleation seems to be less pronounced, as shown by the SEM
pictures in Figure 4-18. It is believed that this effect could be due to decreased viscosity and
elasticity as Tsys increased. On the other hand, black clouds of microvoids were still observed in
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the stretched case, which suggests the existence of microvoids prior to foaming that could have
helped to promote cell nucleation. This observation is in agreement with a snapshot of the in-situ
foaming videos for the two cases (see Figure 4-19), where more bubbles seem to have nucleated
in the stretched case. The lack of noticeable differences in the final cell densities in the SEM
pictures could be due to a higher occurrence of cell coalescence and coarsening at the elevated
Tsys. Therefore, some cells nucleated in the stretched cases collapsed.
Figure 4-18 – PS-talc sample foamed at 140°C: a) ε = 0; b) ε = 1.2
Figure 4-19 – Snapshot of PS-talc foaming at 140°C: a) ε = 0; b) ε = 1.2
4.4 Effect of Talc Particle Size and Surface Treatment on Foaming
Behaviour of PS-Talc Composites under Extensional Stress
4.4.1 Background
Talc is one of the most widely used nucleating agents due to its effectiveness in
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promoting cell nucleation, the ease with which it disperses in polymer, and its low cost.
Meanwhile, there are many types of talc with different particle sizes and surface characteristics,
and it is of both academic and practical interest to identify the desirable characteristics of talc for
cell nucleation. In particular, Leung et al. [107] investigated the foaming processes of PS-talc
composites (three types of talc with different sizes and surface treatment) by direct in situ
observation of the foaming processes under static conditions. However, the bubble growth-
induced nucleation phenomena caused significant light scattering around the nucleated cells, so
characterization of cell density and sizes could not be made in that study (see Figure 2-11).
Consequently, the effects of talc particle sizes and surface treatment remained unclear. In
addition, in the study detailed above (Section 4.3), it has been demonstrated that the effectiveness
of talc as nucleating agents to generate cells could be significantly affected by the applied
extensional strain. In this context, using the same types of talc that was used by Leung et al.
[107], this study examined the cell nucleation and initial growth processes of PS-talc composites
with different surface treatment and particle sizes under extensional flow.
4.4.2 Experimental Materials, Sample Preparation and Procedure
The plastic material and blowing agent used was PS and CO2, respectively (see Section
4.3.1 for details). Three types of talc from Luzenac were used: Cimpact 710, Cimpact CB7 and
Stellar 410. Table 4-2 summarizes the talc properties. Cimpact CB7 uses the same base talc
particles as Cimpact 710 but with the addition of a surface treatment. Consequently, they have a
very similar talc size distribution and median talc sizes. The surface treatment was proprietary, so
the chemical characteristics were not disclosed. Nevertheless, based on the dispersion of these
talc particles in the PS matrix, the relative affinity of these talcs on PS could be estimated. By
comparing Cimpact 710 and Cimpact CB7, the effect of this surface treatment on the foaming
behaviour of PS was examined. Meanwhile, the surface characteristics of Cimpact 710 and
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Stellar 410 are the same while the median particle size of Stellar 410 was approximately 6 times
that of Cimpact 710, so a comparison between the two would reveal the effects of talc sizes in
plastic foaming processes. PS resins and talc particles in powder form were first compounded to
20% PS-talc in three master batches using a 3 piece C.W. Brabender batch mixer with counter-
rotating roller blades, then further mixed with PS resins to produce PS-talc composite samples
with 0.5, 2.0, and 5.0 wt% of talc. Consequently, a total of 9 different PS-talc composites were
examined in this study. With a hot press maintained at 180°C, the PS-talc samples were then
compression molded to films 400 µm thick. Upon pressure release, the molded films were
quenched with a large reservoir of water at approximately 13°C. Different from the previous
study in which rectangular samples were used, the films were then cut into the shape of tensile
test samples (ASTM D638 Type V) by a standard mold to enhance the uniformity of sample
deformation as extensional strain was applied. During the cutting processes, the mold was
preheated to 100°C to prevent the test samples from fracturing.
Table 4-2 – Summary of talc characteristics
Name Median Particle
Size [μm] Surface
Treatment Stellar 410 10 No
Cimpact CB7 1.8 Yes Cimpact 710 1.7 No
Foaming experiments were carried out with the foaming visualization system with
extensional stress-inducing ability. The experimental procedure has been described in details in
Section 4.2.4. Since our goal was to study the effect of talc size and surface treatment on the
foaming behaviour of PS-talc composites in an extensional flow, the Tsys, Psat, and –dP/dt|avg was
kept constant at 100°C, 3.45 MPa (500 psi) and 6 MPa/s, respectively. Based on Li et al.’s
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PS/CO2 solubility data, the dissolved CO2 content in PS under these conditions was 2 wt% [212].
The actual dissolved gas content might have varied to a small degree due to the addition of talc,
but the differences were expected to be negligible as the gas concentration was relatively low.
The -dPsys/dt|avg was selected at a low level so that the pressure drop rate effect would not
dominate that of extensional strain in the foaming processes. Also, a low temperature of 100°C
was chosen so that a higher level of extensional stress would be induced in the sample with an
applied strain due to the higher viscosity and elasticity at that temperature. Stress relaxation and
gas loss via diffusion would also be slower at this low temperature. Each of the PS-talc
composites was first foamed under static conditions (i.e., ε = 0). Subsequent foaming experiments
were conducted with strain ε = 0.55 and 1.1 while keeping dε/dt constant at 2 s-1. To investigate
the effect of dε/dt, additional experiments using the samples with 5 wt% talc were conducted with
ε = 1.1 but at dε/dt = 0.1 s-1. Each experiment referred to above have been done three times to
ensure the repeatability of the test data.
Table 4-3 – Experimental cases for PS-talc foaming under extensional stress
Expt. #
Tsys
[˚C] Psat
[MPa] -dPsys/dt|avg
[MPa/s] Talc wt%
[%] ε dε/dt
[s-1] 1 100 3.45 (500 psi) 6 0.5 0 2 2 100 3.45 (500 psi) 6 0.5 0.55 2 3 100 3.45 (500 psi) 6 0.5 1.1 2 4 100 3.45 (500 psi) 6 2.0 0 2 5 100 3.45 (500 psi) 6 2.0 0.55 2 6 100 3.45 (500 psi) 6 2.0 1.1 2 7 100 3.45 (500 psi) 6 5.0 0 2 8 100 3.45 (500 psi) 6 5.0 0.55 2 9 100 3.45 (500 psi) 6 5.0 1.1 2 10 100 3.45 (500 psi) 6 5.0 1.1 0.1
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4.4.3 Characterization of Talc Distribution in PS-Talc Composites
Due to Cimpact 710’s and Cimpact CB7’s smaller sized talc particles, we expected that
larger numbers of these would be dispersed into the PS polymer matrix than would Stellar 410
when the same weight content of talc was used. However, the actual talc particle density and size
distribution would also strongly depend on the quality of the distributive and dispersive mixing in
the compounding stage. The talc particles would also be re-oriented during the compression
molding processes. Therefore, to obtain accurate information about talc distribution within the
plastic samples, three pieces of unfoamed samples were randomly selected from each PS-talc
composite, and SEM images were taken along a fractured surface of each sample that was frozen
with liquid nitrogen. In the SEM images, the talc particles appeared to be white platelets of
different sizes. Figure 4-20 shows sample SEM images of a PS-talc composite with 5 wt%
Cimpact CB7 and one with 5 wt% Stellar 410. The size of each talc platelet, denoted as s, was
carefully measured within a known area (At). The measured data was then grouped according to
length, and frequency tables of talc size vs. length were generated from the resulting data.
Subsequently, the particle density of each length group (Ntalc,i) was determined using the
following equation:
Equation 4-10
where i = 1 to k (k equals the total number of length groups) and ni represents the frequency of
talc particles in the i-th length group. This procedure was repeated three times for each PS-talc
composite to obtain the talc particle density vs. the length distribution information. The total
particle density (Ntalc) of each sample was then determined using the following equation:
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Equation 4-11
Finally, the average value of Ntalc, denoted as Ntalc,avg, of each PS-talc composite was calculated
(refer to Figure 4-21).
Figure 4-20 – Sample SEM pictures of PS-talc composites a) Cimpact CB7 talc wt% = 5; b)
Stellar 410 talc wt% = 5
The average particle densities for Stellar 410 were significantly lower than for the other
two types of talc. In particular, the Ntalc,avg of Stellar 410 were close to one order of magnitude
lower than Cimpact 710 and Cimpact CB7 for all three talc wt%. Meanwhile, the surface
treatment seemed to improve the dispersion of talc, as seen in the higher Ntalc,avg of Cimpact CB7
compared with Cimpact 710 at a higher talc content of 2% and 5%. This behaviour was also
observed by Leung et al. [107]. The effect was not as clear in this study because there were
significant variations in Ntalc for the PS-talc composites, as shown by the errors in Ntalc,avg, which
denoted the standard deviation of the Ntalc data in Figure 4-21a. The range of talc sizes for Stellar
410 were much wider than for the other two types of talc. The average value of s for each PS-talc
composite was then taken as the average talc size (savg) in each case (see Figure 4-21b). The
errors represent the standard deviation of the s data. We observed that the savg for Stellar 410 was
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significantly larger than for the other two types of talc, which was reasonable due to the larger
median talc size of Stellar 410. Meanwhile, the difference between the savg of Cimpact 710 and
Cimpact CB7 was insignificant. To estimate the differences in Ahet for each case, we assumed that
each talc platelet had a circular disc shape with diameter equal to savg. We also disregarded the
surface area along the thickness direction; hence, the total surface area of a talc platelet was equal
to twice the area of the circular disc. Therefore, by taking the Ntalc,avg and savg data shown in
Figures 7a and 7b, the average Ahet, denoted as Ahet,avg for each case, was determined through the
following equation:
Equation 4-12
The results are summarized in Figure 4-21c, which demonstrates that Cimpact CB7 has the
highest Ahet, followed by Cimpact 710, and finally Stellar 410, at all talc wt%. The errors of
Ahet,avg, denoted as ΔAhet,avg, were determined by error analysis using the following equation:
Equation 4-13
where ΔNtalc,avg and Δsavg denote the errors in Ntalc,avg and savg, respectively.
a) Ntalc,avg
b) savg
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c) Ahet,avg
Figure 4-21 – Summary of particle density, size distribution, and surface area vs. talc wt%
4.4.4 Foaming Results and Discussion
A sample of the foaming visualization data for is shown in Figure 4-22a to Figure 4-22d
(for talc wt% = 5.0). The cell density (Nunfoam) for each case was characterized based on the
method detailed in Section 3.4.1.3. Figure 4-23, Figure 4-24, and Figure 4-25 show the Nunfoam vs.
time and maximum Nunfoam for each PS-talc composite at different applied ε levels (while keeping
dε/dt constant at 2 s-1) for talc wt% = 0.5, 2.0, and 5.0, respectively. For all PS-composites, the
cell nucleating rate and maximum Nunfoam increased significantly as the applied ε increased. In
most cases, the maximum Nunfoam at ε = 1.1 increased over two orders of magnitude as compared
to the static cases. This phenomenon was especially apparent for Cimpact 710 and CB7.
Furthermore, Figure 4-26 shows that the Nunfoam increased significantly with the dε/dt. To explain
this behaviour, it was assumed that the PS-talc composites as linear viscoelastic materials whose
stress-strain relationship conforms to the Kelvin-Voigt model for simplification purpose as
follows:
Equation 4-14
where the Eε(t) term and the ηdε/dt terms are the elastic and viscous terms, respectively; E is the
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elastic modulus; and η is the viscosity. From this model, it is clear that as ε and/or dε/dt
increased, the tensile stress, σ(t), also increased, which ultimately led to increased cell densities
based on reasons described in Section 4.3.3 and Section 4.3.3.2.
a) ε = 0
b) ε = 0.55 at dε/dt = 2 s-1
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c) ε = 1.1 at dε/dt = 2 s-1
d) ε = 1.1 at dε/dt = 0.1 s-1
Figure 4-22 – Foaming sequences of PS with talc wt% = 5.0 under extensional stress
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a) ε = 0
b) ε = 0.55 at dε/dt = 2 s-1
c) ε = 1.1 at dε/dt = 2 s-1
d) maximum Nunfoam
Figure 4-23 – Nunfoam vs. time and maximum Nunfoam for PS with 0.5 wt% talc
a) ε = 0
b) ε = 0.55 at dε/dt = 2 s-1
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c) ε = 1.1 at dε/dt = 2 s-1
d) maximum Nunfoam
Figure 4-24 – Nunfoam vs. time and maximum Nunfoam for PS with 2.0 wt% talc
a) ε = 0
b) ε = 0.55 at dε/dt = 2 s-1
c) ε = 1.1 at dε/dt = 2 s-1
d) maximum Nunfoam
Figure 4-25 – Nunfoam vs. time and maximum Nunfoam for PS with 5.0 wt% talc
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a) Nunfoam vs. time
b) maximum Nunfoam
Figure 4-26 – Effect of dε/dt on Nunfoam vs. time and maximum Nunfoam for PS with 5.0 wt% talc
Interestingly, despite the lower Ntalc,avg and Ahet,avg of Stellar 410 within the PS polymer,
the PS-stellar 410 composites had the earliest onset of cell nucleation and the highest maximum
Nunfoam in all cases. This might seem counter-intuitive as a higher Ahet,avg should have led to a
larger number of heterogeneous nucleation and hence a higher cell density (see Equation 4-15
below). This is also one of the reasons why there have been significant research efforts directed
to investigate foaming with small-size nucleating agents, especially nanoparticles in recent years.
Equation 4-15
To explain this, it is speculated that the disruption of flow and hence the pressure variation
around a larger particle might also be higher than it would be for a smaller particle since larger
particles constitute larger discontinuities that restrict the polymer flow around them.
Consequently, higher tensile stresses might be generated in some local regions. Because of this,
nucleation was more likely to happened around the larger particles. This explained the higher cell
densities in the Stellar 410 cases, which has higher numbers of large particles than both the
Cimpact 710 and Cimpact CB7 cases.
This effect was most dominant in the static cases. As the level of applied ε increased, the
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differences in the maximum Nunfoam between each PS-composite at the same talc wt% were also
reduced. This was caused by the increased tensile stress that was applied to the polymer as the
level of the applied ε or dε/dt increased. This action effectively lowered the local Psys. Hence, cell
nucleation could occur around smaller particles or through growth of smaller microvoids.
Consequently, the talc size effects became less dominant. Nevertheless, this study demonstrated
that larger nucleating agents might be superior to smaller ones in enhancing cell nucleation
despite its lower particle density and surface area for heterogeneous nucleation.
The surface treatment used in this study did not result in a conclusive trend in the foaming
behaviour. For example, the surface-treated talc (Cimpact CB7) exhibited higher cell density in
some cases (e.g., 0.5 wt% talc with ε = 1.1) but lower cell density in others (e.g., 2.0 wt% talc
with ε = 0.55) than the untreated talc (Cimpact 710). The Ntalc,avg of Cimpact CB7 was higher
than Cimpact 710 especially at high talc content, hence the surface treatment increased the
uniformity of the talc particle dispersion within the PS matrix. This suggested that the surface
treatment might have increased the affinity between the PS and the talc particles. Consequently,
θc would be decreased and cell nucleation would become less favorable on these surfaces. On the
other hand, the higher Ntalc,avg of Cimpact CB7 also led to higher Ahet for heterogeneous
nucleation. The competing phenomena of increased Ntalc,avg and Ahet and decreased θc might have
led to a lack of significant effects of surface treatment on the cell nucleating behaviours. In order
to isolate the effect of surface treatment from the dispersion characteristics, the maximum Nunfoam
vs. Ntalc,avg data has been plotted and is shown in Figure 4-27. However, in the majority of the
experimental cases, the maximum Nunfoam seems to be similar for the two talcs when the particle
densities were similar. Therefore, it is concluded that the surface treatment used in this study did
not significantly impact the foaming behaviour of PS-talc composites.
Importantly, while we observed that the increase of talc wt% and hence Ahet led to a
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higher cell nucleation rate and cell density, the maximum Nunfoam remained at low levels below
106 cells/cm3 in the static condition for all PS-talc composites (see Figure 4-27). To generate a
high cell density, in addition to including a large number of talc particles, it is important to use a
high ε and dε/dt to induce a high level of extensional stress. These results suggest that in
extrusion foaming processes, the dies must be designed to induce sufficient extensional stress to
enhance the effectiveness of the cell nucleation agents.
a) ε = 0
b) ε = 0.55 at dε/dt = 2 s-1
c) ε = 1.1 at dε/dt = 0.1 and 2 s-1
Figure 4-27 – Maximum Nunfoam vs. Ntalc,avg for PS-talc foaming under extensional stress
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4.5 Investigation on the Interrelationships among Extensional
Stress, Crystallization, and Foaming Behaviour
4.5.1 Background
In Section 3.3, the effects of crystals on the foaming behaviour of PP has been studied at
static conditions, which showed that crystals could induce cell nucleation due to exclusion of
CO2 around crystal growth front and tensile stress generation in the constrained amorphous
regions between crystals. Meanwhile, the studies in this chapter have demonstrated that
extensional stress could increase cell nucleation rate and cell density of PS, an amorphous
polymer, and such effect was more significant when nucleating agents (talc) was added. Crystals
might have a similar effect as talc under extensional stress. Moreover, extensional strain is known
to cause crystallization [184]. In this context, this study aimed to clarify the interrelationships
between crystallization, applied ε, and the foaming behaviour of PP with supercritical CO2 as the
blowing agent. Using the batch foaming visualization described in Section 4.2, this study
investigated the foaming behaviour of three different types of PP: a linear PP, a branched PP, and
a PP-ethylene random copolymer, as applied extensional strain were varied.
4.5.2 Experimental Materials, Sample Preparation and Procedure
The polymers used for the foaming experiments were a linear PP (DM55, Borealis), a
branched PP (Daploy WB130HMS, Borealis), and a PP-ethylene random copolymer (SEP550,
Honam). The polymer resins were compression molded to films 400 µm in thickness with a hot
press at 200 °C. Upon pressure release, the molded films were quenched with a large reservoir of
water at 13 °C to 14 °C. Afterward, the films were cut into the shape of tensile test samples
(ASTM D638 Type V) using a standard mold to form the test samples in this study. The blowing
agent used was supercritical CO2 (99.8% pure, Linde Gas Inc.). Foaming experiments were
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carried out with the foaming visualization system with extensional stress-inducing ability. The
experimental procedure has been described in details in Section 4.2.4.
Since our main goal was to study the extensional stress effect on foaming in the presence
of crystals, the Psat and –dP/dt|avg was kept constant at 10.34 MPa (1,500 psi) and 8 MPa/s,
respectively. The dissolved CO2 amount in the PP might varied, but the difference was not
expected to be significant based on the solubility data in literature [209]. The Tsys were selected to
be 10 °C lower than the Tm of the original resins under atmospheric pressure: Tsys = 150 °C for
DM55 and WB130HMS (Tm = ~160 - 163 °C) and Tsys = 135 °C for SEP550 (Tm = ~145 °C). The
following section demonstrated that crystals still existed within the plastic samples at these Tsys
despite the possible Tm depression under high pressure CO2. Three levels of extensional strain (ε
= 0.55, 1.1 and 1.65 at dε/dt = 2 s-1) and the static case were studied for each PP. Each
experiment was conducted three times and summarized in Table 4-4. To investigate the
relationships between the crystallization and the foaming behaviour of these polymers, DSC
measurements with both foamed and unfoamed polymers were also made. The DSC experiments
under atmospheric pressure and high pressure (6 MPa of CO2) were carried out using TA
Instruments DSC Q2000 (US) and NETZSCH DSC 204 HP (Germany), respectively.
Table 4-4 – Experimental cases for PP/CO2 foaming with crystals and extensional stress
Psat [MPa]
-dPsys/dt|avg [MPa/s]
Polymer Tsys [°C]
ε dε/dt [s-1]
10.34 8 DM55/WB130 150 0 0 10.34 8 DM55/WB130 150 0.55 2 10.34 8 DM55/WB130 150 1.1 2 10.34 8 DM55/WB130 150 1.65 2 10.34 8 SEP550 135 0 0 10.34 8 SEP550 135 0.55 2 10.34 8 SEP550 135 1.1 2 10.34 8 SEP550 135 1.65 2
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4.5.3 Crystallization Study Results
As mentioned earlier, dissolved gases could plasticize polymers, which lead to a depression
of Tm. Although the Tsys were lower than the Tm of the polymers under atmospheric pressure, the
polymers could have been melted due to a possible depression of Tm. From Figure 4-28, it could
be observed that the Tm decreased slightly for all polymers in the presence of high pressure CO2
(at 6 MPa). Note that the saturation pressure was 10.34 MPa, so the Tm depression could have
been more significant during the foaming processes, but the exact Tm could not be measured at
that pressure due to the system limitations of the HPDSC. Well-dispersed dots that resembled
crystals were observed in the samples during in situ visualization at Tsys and Psat, but some of the
dots could have been the result of impurities within the polymer. In order to confirm the presence
of crystals during the foaming processes, the effects of annealing and gas pressure on the
melting/crystallization behaviour of each polymer were investigated with unfoamed polymer
samples. It has been shown that annealing without the presence of high pressure CO2 did not lead
to noticeable change in the Tm. However, for all three polymers, the combined effect of high
pressure CO2 (6 MPa) and annealing generated an increased Tm (refer to Figure 4-28), most likely
due to the presence of high-pressure gas that increased the mobility of polymer chains. With the
annealing process, the polymer chains had sufficient mobility and time to form better crystals. As
a result, a new melting peak was generated at a Tm higher than that of the original melting peak.
This crystallization behaviour has been widely utilized in bead foaming technologies [217, 218],
and also investigated further in various studies [109, 191, 219-221]. To confirm that a new
melting peak was also formed in the foaming processes, the foamed samples were cooled down
inside the visualization system and then reheated in the DSC chamber at a heating rate of 10
°C/min. For all three materials, two melting peaks were indeed observed (See Figure 4-29).
These results demonstrated that in each case crystals were present in the plastic samples at the
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foaming conditions. The presence of these crystals was imperative to the foaming visualization
studies detailed in the following section.
a) Without Annealing
b) With annealing for 30 min at Tsys
Figure 4-28 – The effect of high pressure CO2 on Tm of unfoamed polymers
1. heat: 20 to 200°C at 10°C/min (shown on figure) Solid lines (without annealing):
1. heat: 20 to 135°C (SEP550) or 150°C (DM55, WB330) at 10°C/min Dotted/Broken lines (with annealing):
2. hold: 30 min 3. heat: 200°C at 10°C/min (shown on figure)
a) SEP550
b) DM55
145
147
149
151
153
155
157
159
161
163
165
167
169
0 10 20 30 40 50 60
Mel
ting
Tem
pera
ture
(°C
)
Pressure (bar)
DM55WB130SEP550
145
147
149
151
153
155
157
159
161
163
165
167
169
0 10 20 30 40 50 60
Mel
ting
Tem
pera
ture
(°C
)
Pressure (bar)
DM55WB130SEP550
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c) WB130
Figure 4-29 – Melting behaviour of foamed PP samples under atmospheric pressure
4.5.4 Foaming Visualization Results
Foaming videos were captured for all cases. However, for most cases, it was extremely
difficult to obtain clear images of cell nucleation and growth. Due to the presence of crystals
within the polymer-gas solution, the incident light tended to be deflected. Compounded with the
cluster formation of cells in multiple layers, reliable cell density and cell size measurements
could not be made. Thinner plastic samples should have led to clear bubble formation images due
to fewer layers of bubbles, such as that shown in Figure 2-11, which has been captured under a
static condition (i.e., plastic film placed on top of a sapphire window). However, thicker samples
were used in this study to achieve a more uniform stress field, as well as to prevent significant
gas loss during the foaming processes since both the top and bottom surface of the samples were
free surfaces. Despite the difficulty in visualizing individual bubbles, some interesting qualitative
observations could be derived from the foaming videos. Figure 4-30 show snapshots of the
foaming videos of each material at ε = 0 and ε = 1.65. Similar to the PP foaming studies detailed
in Section 3.3, bubble growth-induced nucleation phenomenon was observed in the static cases.
This behaviour is demonstrated clearly in the local region indicated by arrows in Figure 4-31,
where nucleation of multiple cells was observed around an existing cell. The cells’ boundaries
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were not distinct since they were formed very close to each other (i.e., the cells appeared as a
cluster that expand in sizes over time as cell nucleation propagates to the surrounding regions),
but the shape of the cluster clearly demonstrated that there were multiple cells nucleation, rather
than simple growth of the existing cell, as the cluster expanded and propagated to the surrounding
regions. This behaviour was vastly different from the other PP foaming visualization studies
(e.g., the study in Section 3.4) where foaming was conducted at temperatures above the Tm and
hence no crystals were present. In those studies, cell nucleation and growth commenced in a
dispersed manner that was similar to the foaming of amorphous polymers without filler.
In the static cases for all three polymers, cell nucleation was first initiated at a single to a
few locations. Upon the initiation, cell nucleation commenced very rapidly around the existing
cells, covering the whole area within approximately 0.1 sec. When an extensional strain was
applied to the polymer, cells tended to nucleate in a more dispersed manner (i.e., cells nucleation
initiated at many different spots distributed in the polymer-gas solution). This is demonstrated in
Figure 4-30 for the ε = 1.65 cases. It is believed that the applied extensional strain generated the
tensile stresses needed for cell nucleation even in the absence of growing cells. Since the
extensional stress was applied uniformly, cell nucleation occurred in a more dispersed manner.
Besides the tensile stress generated, there could be other reasons for the enhanced cell
nucleation. The applied extensional strain might have accelerated the crystallization process,
which would cause faster discharge of gas to the crystal growth fronts. To investigate the
significance of this effect, the crystallinity of the foamed samples was measured with DSC at
ambient condition. It was found that the crystallinity did not change significantly as the applied ε
was varied (refer to Figure 4-32). The lack of differences could be due to a large amount of
crystallization formed during gas saturation (i.e., annealing under high pressure CO2), foaming,
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or cooling. Since these effects applied to all cases, the additional applied ε effect might have
become less apparent. Since the crystallization did not varied with extensional stress, the effect of
strain-induced crystallization on cell nucleation might not be the dominant factor, but the extent
of such effect was unknown.
Each of these reasons might have enhanced cell nucleation to various extents. Although it
was not possible to isolate each of their contributions, it could be concluded that an applied
extensional strain have caused a significant difference in the foaming behaviour from the static
cases. On the other hand, despite that the cell nucleation occurred in a more dispersed manner
initially, bubble growth-induced nucleation was also observed at a later time around the existing
bubbles formed initially due to the applied ε. Since there were more initially nucleated bubbles to
induce nucleation around them, the bubble growth induced nucleation phenomenon was also
more dispersed than the static cases. In particular, Figure 4-30 shows this process in a finer
temporal resolution, using SEP550 as an example. Interestingly, the propagation of bubble
growth-induced cell nucleation also seemed to be hindered when there were existing bubbles
around their propagation directions. To illustrate this in greater detail, Figure 4-33 compares the
foaming behaviour of SEP550 (ε = 1.65) in a region where existing bubbles are surrounded by
unfoamed polymer (region A) as opposed to where existing bubbles were formed adjacent to
each other uniformly in the presence of the applied ε (region B). In region A, bubble growth-
induced cell nucleation occurred and propagated into the unfoamed regions. On the other hand, in
region B, bubble growth-induced nucleation were not observed in the small unfoamed regions
between existing bubbles that were generated earlier by the applied extensional strain. This
suggested that the applied ε might suppress the bubble-growth-induced cell nucleation
phenomena, which was the primary cell nucleation mechanism in the static cases. Similar
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phenomena were observed in the foaming videos of DM55 and WB130. The cause for the
weakening behaviour might be the gas depletion between adjacent existing cells as gas diffused
into these existing cells. The gas depletion caused a decrease in Pbub,cr in this region. Therefore,
despite that extensional stress were generated between these cells due to their growth (which
decreased Psys), the Pbub,cr was not high enough to generate a sufficient supersaturation level (i.e.,
Pbub,cr – Psys) to induce foaming in the small regions between these adjacent cells (e.g., region B
in Figure 4-33). On the other hand, if the growing cells were surrounded by unfoamed
polymer/gas mixture, the gas concentration might be sufficiently high in these regions, hence
bubble-growth induced nucleation would occur (e.g., region A in Figure 4-33).
a) SEP550
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b) DM55
c) WB130
Figure 4-30 – Snapshots of PP foaming videos showing effects of the applied ε
Figure 4-31 – Bubble growth-induced nucleation with the presence of crystals (SEP550)
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Figure 4-32 – Crystallinity vs. ε for foamed PP samples
Figure 4-33 – Foaming behaviour of SEP550 under ε = 1.65 in two different regions
4.6 Conclusion
Previous researchers have pointed out that stresses could induce cell nucleation and affect
the final cell morphology in plastic foaming processes, but a thorough understanding of the
effects of extensional stress on plastic foaming behaviour was still not established. In this work, a
novel batch foaming visualization system has been developed to capture the in-situ foaming
process of a plastic specimen under extensional stress. Its capability was verified with a set of PS
and PS-talc foaming experiments blown with CO2. By studying the foaming behaviour as the Tsys
and applied ε varied, this study shows that extensional stress could significantly increased the cell
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nucleation rate and final cell density. This behaviour was much more significant with the addition
of talc, and especially at a low Tsys where the extensional stresses induced to the polymer was
expected to be higher due to the increased viscosity and elasticity.
The effects of surface treatment, size, and the weight content of talc particles on the
foaming behaviour of PS under extensional stress have been elucidated. It has been demonstrated
that the talc with the largest particle size yielded the earliest onset of cell nucleation and the
highest Nunfoam at each talc content despite its lower talc particle density and total surface area
than the smaller talc. The surface treatment led result in a better talc particle dispersion, but it did
not cause noticeable differences in foaming behaviours. The enhanced cell nucleation that took
place with the larger talc particles was due to the higher tensile stresses generated around the
larger particles when compared to the smaller particles. As the applied ε or dε/dt increased, the
foaming processes took less time to complete, and the Nunfoam increased significantly in all cases.
This is because of the increased local tensile stresses in the polymer matrix as the applied ε or
dε/dt increased. This caused a decrease of local pressure needed to induce nucleation around the
smaller talc particles. As a result, the effect of talc size became less pronounced.
Furthermore, to investigate if crystals have similar effect as talc to initiate cell nucleation,
the foaming processes of three different PP materials (a linear PP, a branched PP, and a PP-
ethylene copolymer) in the presence of crystals were observed and analyzed with a foaming
visualization system under static and extensionally stressed conditions. Similar to Section 3.3, it
was observed that crystals have similar effects as solid fillers to cause bubble growth-induced cell
nucleating phenomena. As the applied ε increased, the bubbles were nucleated in a more
dispersed manner, and the bubble-growth-induced nucleation behaviour occurred at a later stage
and was less pronounced. These trends were consistent for all three materials.
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CHAPTER 5
IN SITU VISUALIZATION OF PLASTIC
FOAMING PROCESS UNDER SHEAR
STRESS
5.1 Introduction
In Chapter 3 and Chapter 4, the development of a static foaming visualization system and a
dynamic foaming visualization system with extensional stress-inducing ability, respectively, have
been detailed. Experimental studies to verified their capability and to investigate various aspects
of plastic foaming has also been described. Previous studies have demonstrated that shear stress
led to plastic foams with higher cell density. In this context, this chapter describes the
development of a novel foaming system that allows in situ observation of plastic foaming
processes under a uniform and easily controllable shear stress field (refer to reference [222]),
which has not been achieved previously. Using the system, foaming studies of PS and PS-talc
composites have been conducted to investigate the effects of shear strain and strain rate on cell
nucleation and growth behaviour. Together with the two other visualization systems developed in
this thesis, this system will open a wide range of research opportunities to investigate the
fundamental mechanisms of plastic foaming under both static and dynamic conditions.
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5.2 Development of a Foaming Visualization System with Shear
Stress-Inducing Ability
The central objective of our study was to develop a novel system1by which to observe
and capture plastic foaming processes under controllable shear strain and shear strain rate. To do
so, the system employed the following three functions: 1) application of a uniform simple shear
flow to a plastic-gas melt under a high temperature and pressure; 2) saturation of the plastic melt
with gas and the subsequent inducement of foaming by rapid depressurization; and 3) capture of
the bubble formation and growth processes with fine temporal and spatial resolution. These
functions had to be achieved while simultaneously maintaining easy control and adjustment of
the following parameters: applied shear strain (γ), shear strain rate (dγ/dt), Tsys, Psat, -dPsys/dt, type
of plastic and type of blowing agent.
5.2.1 Function I: Generate a Uniform Simple Shear Flow to a Plastic Melt under High
Temperature and Pressure
In addition to providing a shear motion, the shear mechanism has to allow for dissolution
of gas into a plastic sample in a timely manner, which is related to Function II (detailed in the
next section). However, even at Tsys, gas saturation into plastic via diffusion processes could take
a long time. In particular, Koran and Dealy [223] developed the high-pressure sliding plate
rheometer (HPSPR) to measure the shear stresses of a molten plastic film sample, which was
sandwiched between a sliding plate and a static one to generate the shear flow (Figure 5-1). Using
the HPSPR, Park and Dealy [224] demonstrated that 99% saturation of CO2 into the center of a
HDPE sample at 180°C could take 190 to 230 minutes, while two days were required for a PS
sample. An oscillating shear motion applied on the plastic decreased the saturation time (td)
required by half for the HDPE [224], but other plastics with lower gas diffusivity still had a much
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larger td. This could lead to degradation issues, especially for heat-sensitive plastics. One main
factor determining td is the length of the diffusion path (l). If both the top and bottom surface of
the plastic film is in contact with the sliding plates during the gas saturation phase, such as in the
HPSPR case, gas could only diffuse through the four sides of the plastic film to the center of the
sample, which results in a large value of l. Since td ∝ l2 [75], even a small increase of l could
significantly increase td. Therefore, in order to decrease td, it was decided that the revised shear
mechanism must expose the largest face of a plastic film sample to high-pressure gas during the
gas saturation process. Upon completion of the gas saturation process, the shear mechanism has
to move in such a way so that the free surface of the sample made contact with the other shearing
surface prior to the application of shear strain. This requirement increased the design complexity
significantly since motion would be needed in two orthogonal directions (e.g., vertical motion to
achieve contact with sample after gas saturation and horizontal motion to induce shear strain)
(see Figure 5-2 for details).
Figure 5-1 – The high pressure sliding plate rheometer [223]
Figure 5-2 – Design requirement of shear mechanism for rapid gas saturation process
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To satisfy this requirement, a sliding plate assembly has been designed, which consisted
of a bottom moving plate and a top static plate with a plastic sample sandwiched in between
them. The moving plate has been designed to be maintained at a lower position during gas
saturation. To achieve that, the moving plate consisted of two wedges that would slide, with
respect to each other, along a slanted edge. Initially, the upper wedge was maintained at the lower
position, and a plastic sample was placed on top of it for gas saturation. Afterward, it was moved
upward until the sample made contact with the top surface. Subsequently, a shear strain was
applied to the sample as both the upper and lower wedge moved together to the other side of the
chamber (see Figure 5-3 for details).
Figure 5-3 – Mechanism of the moving plate assembly with sliding wedges
The following mechanisms have been used to carry out the steps discussed above. First of
all, a dovetail mechanism was incorporated into both wedges so that they could only slide with
respect to each other along the slanted edge. The upper wedge was made with brass while the
other one was made with stainless steel. The two materials have similar coefficients of linear
thermal expansion (αt) to prevent possible inferences between the dovetail mechanisms of the two
wedges (i.e., αt = 18.7 × 10-6 m/m-K and 17.3 × 10-6 m/m-K for brass and stainless steel,
respectively) as Tsys increased. This use of different materials avoided possible bidding between
the two wedges as they slid relative to each other under high temperature and pressure.
After gas saturation was completed while the upper wedge was maintained at the lower
position, the upper wedge would be pushed towards the lower wedge while the lower wedge
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would be held stationary, thus causing the upper wedge to rise due to the kinematic constraint
between the two wedges. To achieve this, an adjustment shaft, partially threaded with a fine
pitch, would act as a lead screw to push the upper wedge. The adjustment shaft would be actuated
by a threaded adjustment knob that was installed on a rectangular frame outside of a chamber that
housed the moving plate assembly. At the same time, the rectangular frame was also connected to
a drive shaft that was installed on the opposite end as the adjustment shaft. The drive shaft was
connected to the lower wedge to control its position and to hold it in place as the adjustment shaft
pushed the upper wedge toward it. The upward motion of the upper wedge decreased the gap
between the sliding plate and the top plate until the plastic sample made contact with the top
surface, which was needed for the application of shear strain. An excessive upward movement
would compress the sample, thus inducing a normal/compressive stress in it. This could affect the
foaming behaviour of the plastic film and must be avoided. To prevent it, a micrometer was also
installed on the rectangular frame and collinear to the adjustment shaft to accurately monitor its
position and, hence, the vertical position of the upper wedge. The plastic film must also have a
uniform thickness to ensure its proper adhesion to the top shearing plate and to prevent any local
normal stresses.
The adjustment and drive shafts were positioned collinear to each other by two brass
bearings installed on the chamber. The rectangular frame was connected to a linear actuator. As
the actuator moved the rectangular frame, the entire sliding plate assembly (i.e., the upper and
lower wedges, the adjustment shaft, and the drive shaft) would be constrained to move together
as a whole along the shearing direction, thus applying shear strain to the plastic film. Using this
design, the functions of gas saturation and shear strain application could be fulfilled
independently with a simple mechanism, which is a good design practice according to the
Axiomatic Design principles [225]. Also, with few moving parts and kinematic constraints, the
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shear mechanism was manufactured to tight tolerances that were required to induce a uniform
shear field to a thin polymer film, while the risk of causing damages to moving parts due to
interferences at high temperatures was also minimized. Moreover, in this design, different sample
thickness could be accommodated since the gap between the static and moving plate could be
adjusted in a continuous and accurate manner by the position of the adjustment shaft.
The motion of this assembly was controlled by a linear actuator attached to the
rectangular frame. The linear actuator (Oriental Motors EZA6) consisted of a stepper motor with
accurate feedback control and was coupled to a lead screw to convert the rotary motion to linear.
The resolution and maximum speed of the linear actuator was 0.01 mm and 300 mm/s,
respectively, which permitted accurate control of the shear strain and shear strain rate. The
motion of the motor was programmed and executed via the HyperTerminal software. A pair of
photo-interrupters was installed as limit sensors to prevent the moving plate assembly from
colliding with the chamber body. The shear strain (γ) applied to a plastic sample was the
displacement (X) of the moving plate divided by the distance between the plates (h) (see Equation
5-1), which was also equal to the sample thickness. The maximum displacement (X) of the
sliding plate assembly was 40 mm. Using a sample thickness of 0.4 mm, the maximum shear
strain (γmax) that could be applied was 100. Meanwhile, the applied shear strain rate (dγ/dt) was
the velocity (V) of the moving plate divided by h (see Equation 5-2).
Equation 5-1
Equation 5-2
Based on the maximum actuator speed (Vmax = 300 mm/s) and a sample thickness of 0.4 mm, the
maximum shear strain rate (dγ/dt|max) is 750 s-1, but it can only be sustained for a maximum of
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0.13 s due to the displacement constraint. Therefore, to achieve a steadier shear flow, the
maximum dγ/dt chosen was 100 s-1, which could be sustained for a period of 1 s. By using a
thinner plastic sample and hence a smaller value of h, a higher maximum γ and dγ/dt could also
be achieved.
5.2.2 Function II: Saturate the Plastic Melt with a High Pressure Gas and Induce
Foaming by Rapid Depressurization
To achieve the second function of foaming the plastic sample, it was first necessary to
saturate the sample with a blowing agent at a high Tsys and Psat. Foaming could then be induced
by a rapid depressurization. To this end, the sliding plate assembly has been enclosed inside a
stainless steel chamber, as mentioned in the previous section. The chamber was positioned so that
the plastic sample largest side was facing up while it was sheared horizontally. A top cover was
installed onto the chamber to provide assess to the moving plate assembly for sample loading and
removal. An open slot along the shearing direction was incorporated onto the top cover for
visualization. A long sapphire lens is installed under the top cover to act as the top static surface
for shear application, while providing visibility to the plastic sample. The long sapphire lens was
held in position by grooves on the chamber and the top cover. The chamber was installed on a
stand, on which the linear actuator and the gas inlet/release valves were also mounted. The
chamber temperature was controlled by two cartridge heaters with Proportional-Integral-
Derivative (PID) feedback control and a resistance temperature detector (RTD) probe. The
blowing agent was supplied by a gas cylinder via a syringe pump, which set and maintained the
gas pressure inside the chamber.
During gas saturation, the gas pressure within the chamber would induce significant axial
load to the adjustment and drive shafts. In this context, the rectangular frame served to prevent
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the adjustment and drive shafts from being forced out of the chamber by the internal pressure and
minimized the axial load on the motor. The adjustment shaft was also backed by a thrust bearing
on the rectangular frame to minimize the friction on the adjustment knob as it was rotated to push
the upper wedge under high pressure. Figure 5-4 shows the design of the adjustment shaft
assembly on the rectangular frame.
Figure 5-4 – Adjustment shaft assembly on rectangular frame
Once gas saturation was completed and shear strain was applied, a rapid pressure drop
was induced in the chamber by opening a gas exit valve. Meanwhile, the third function of the
system came into play: a high-speed camera was triggered to record the foaming process. In
order to synchronize the depressurization and video recording processes, both the gas exit valve
(a solenoid valve) and the high-speed camera were triggered simultaneously by a control panel
programmed with the LabVIEW software, which has been described in detail in Section 3.2.4.
The pressure data generated by a pressure transducer was recorded during the depressurization
process, which could be used to determine the pressure drop rate. By adjusting the opening of a
meter valve installed in series along the gas exit path, the pressure drop rate could be adjusted. It
is noted that the shear strain, and not the shear stress, was directly controlled in this system. Due
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to the viscoelastic nature of plastic, the stress applied to a plastic sample would decrease over
time. Therefore, the stress relaxation behaviour of the plastic-gas solution must be considered.
In saturating and foaming a plastic sample, another critical design challenge is to prevent
gas leaking from the chamber over a wide range of Tsys and Psat. The pressure seal between the
long sapphire lens and the chamber was achieved by a silicon o-ring that fits into a groove on the
chamber body. Six M6 cap screws were used to secure the top cover onto the chamber and to
provide the normal force required to form the seal between the long sapphire lens and the
chamber. The dynamic pressure seals for the drive shaft and the adjustment shaft were each made
with a spring-loaded cup seal that fit into a brass bearing installed on the chamber body. The
static seal between each brass bearing and the chamber, and between the top cover and the
chamber, was achieved with an o-ring that fits into a groove on the bearing. Based on the
operating limits of the cup seals, the maximum operating temperature, pressure, and speed of the
system are 260 °C, 25 MPa, and 15 m/s, respectively.
5.2.3 Function III: Capture Bubble Formation and Growth Processes with Fine Temporal
And Spatial Resolution
The high-speed camera (Photron Ultima APX) and magnifying lens setup described in
Section 3.2.3 was used for visualization. Due to the high shutter speed and magnifying power, a
high intensity light source was needed. Ring lighting and coaxial lighting would allow light to be
provided from the top surface to the plastic film and reflected to the zoom lens, so that the
chamber did not need to be transparent from top to bottom along the optical axis (see Figure 5-5a
and b), which would be necessary if transmissive lighting was used (see Figure 5-5c). However,
it was observed that for both ring lighting and coaxial lighting, the incident light was partially
reflected from the top sapphire lens surface, so that the camera images were blurred, and the
contrast level of the images dropped significantly. Consequently, transmissive lighting was used.
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To achieve this, a center slot was incorporated into the upper and lower wedges to allow incident
light from the bottom side to pass through the plastic sample. An additional sapphire lens was
installed on the bottom side of the chamber, where a fibre optic cable was attached as the
transmissive lighting element. The pressure seal between the chamber body and the additional
sapphire lens was achieved with the same sealing mechanism used in the other two foaming
visualization systems (See Section 3.2.2 for details). Figure 5-6 shows the cross-sectional view of
the foaming chamber. Figure 5-7 illustrates the operation of the shear mechanism.
Figure 5-5 – a) Coaxial lighting; b) Ring lighting; c) Transmissive lighting
Figure 5-6 – Final foaming chamber design for visualization system with shear stress
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Figure 5-7 – Operation of the moving plate assembly with sliding wedges
The maximum operating temperature and pressure remained unchanged. The incident
light was provided to the fibre optic cable by a halogen lamp with controllable light intensity.
Visualization took place at the center region of the sample, where the edge effect that impacted
the uniformity of the shear field was minimized [223]. This would be especially important for
elastic materials that were subjected to large strains [226]. Using this strategy, a wide range of
materials with different rheological properties could be tested with various amounts of shear
strains with minimal concern for shear flow non-uniformity. The optical system was mounted on
a 3-way linear stage that allowed for accurate adjustment of its position along three orthogonal
axes: 1) the optical axis; 2) in the shear strain direction; and 3) perpendicular to the first two axes.
Figure 5-8 and Figure 5-9 shows a schematic and a picture of the overall foaming visualization
system, respectively.
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Figure 5-8 – Schematic of foaming visualization system with shear strain inducing ability
Figure 5-9 – Finalized foaming visualization system with shear stress-inducing ability
5.2.4 Verification of System Capability in Application of Shear Strain
The parallelism of shearing surfaces have been confirmed by measuring the gap between
the top and bottom shearing surfaces at four corners of the moving plate at different positions
with a micrometer. To evaluate the system’s capability to induce a uniform shear strain, a PS
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sample (Styron PS685D, 0.4 mm in thickness) is marked along its centerline on both top and
bottom surface and loaded into the system at 200 °C. A snapshot of the mark was taken before
and after a shear strain of 12.5 was applied (see Figure 5-10). The overall deformation was quite
uniform. On the other hand, a small slippage (< 0.2 mm) has been observed at the initiation of
shear strain, but it did not increase in magnitude as the shear strain increased over time. The same
test has also been carried out at a higher shear strain (γ = 25), and the slippage remained to be
small (< 0.2 mm). This demonstrated that despite the existence of slip, its impact on the
performance of the system remained to be low. Nevertheless, the characterization of slip could be
conducted with different materials at various conditions to further confirm this claim.
Figure 5-10 – Deformation of PS sample under an applied shear strain
5.2.5 Experimental Materials and Procedure
To carry out the foaming experiment, a rectangular-shaped plastic film (38 mm by 24 mm
by 0.4 mm) was placed on top of the sliding sapphire window, which was positioned in the lower
vertical position for gas saturation. The chamber was then maintained at a Tsys and Psat for 30
minutes to allow the blowing agent to dissolve into the plastic film. Afterwards, the adjustment
shaft was moved manually to raise the level of the sliding sapphire lens upwards until the plastic
sample connected with the top sapphire window. A small-magnitude oscillatory shear strain was
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then applied to the plastic sample along the longest dimension, which had been shown to improve
the adhesion of the plastic sample in a sliding plate rheometer [227]. The plastic sample was then
held for another 10 minutes to allow the shear stress, induced by the oscillatory shear strain, to
diminish. A desired shear strain along the longest dimension was then induced in the plastic film.
After the desired strain at the desired strain rate had been reached, the motor was stopped, and the
gas was released from the chamber. The rapid pressure drop inside the chamber caused foaming
in the plastic film. At the same time, the foaming process was captured in situ by the high-speed
camera, and the pressure data within the chamber was recorded.
5.3 PS and PS-Talc Composite Foaming under Shear Stress
5.3.1 Experimental Materials and Sample Preparation
To verify the system’s capability, plastic foaming experiments of PS and PS-talc
composites foamed with CO2 were conducted under various processing conditions. The plastic
material and blowing agent used for the foaming experiments was PS (Styron PS685D, Dow
Chemical Ltd.) and CO2 (99% pure, Linde Gas Canada). For the PS-talc composite cases, 5 wt%
talc (Cimpact CB7, Luzenac, median particle size 1.8 µm) was added to the PS sample as a
nucleating agent. The compounding method has been detailed in Section 4.3.1. Subsequently, the
samples were compression molded into thin films 0.4 mm in thickness using a hot press at 180°C.
The samples were released from the hot press afterwards and immediately quenched with water
at approximately 13°C. Then, the samples were cut into rectangular shapes measuring 38 mm in
length, 24 mm in width, and 0.4 mm in thickness.
5.3.2 Experimental Cases
A set of four PS/CO2 and four PS-talc/CO2 foaming experiments were conducted with the
system. In order to study the shear strain effect in isolation, the Psat, -dPsys/dt|avg, and Tsys were
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kept constant at 3.45 MPa (500 psi), 12 MPa/s, and 180°C, respectively. Based on Li et al.’s
PS/CO2 solubility data, the dissolved CO2 content in PS under these conditions was 1.27 wt%
[212]. The levels of Psat and dP/dt|avg were selected at low levels, so that the gas content and
pressure drop effect would not dominate that of the shear strain (γ) in the foaming processes. The
PS and PS-talc samples were first foamed under static conditions (i.e., γ = 0). Subsequent
foaming experiments were conducted with γ = 12.5 and 25 for both materials while keeping dγ/dt
constant at 25 s-1. To investigate the effect of dγ/dt, an additional experiment was conducted with
γ = 25 but at dγ/dt = 6.25 s-1. Table 5-1 summarizes the experimental conditions. It is note that the
top-to-bottom direction of the foaming videos was aligned with the longest dimension of the
plastic (38 mm), which was also the shear strain direction. The optical plane was along the 38
mm x 24 mm plane. Cell density with respect to the unfoamed volume (Nunfoam) and average
bubble diameter (Dbub,avg) vs. time data was characterized based on the foaming videos. Note that
in the cases where γ was applied, many bubbles appeared elongated in shapes. Therefore, the
diameter of each bubble characterized in this study was the equivalent diameter of a sphere that
has the same volume as the bubble, hence an increase in the bubble diameter also constituted a
bubble volume increase. In order to determine the volume of each bubble, it was assumed that
each bubble was in the shape of a prolate spheroid, which is an ellipsoid whose polar radius (c) is
greater than the two equal equatorial radius (a = b). The symmetry assumption (a = b) was a
reasonable one because the applied shear strain was only one dimensional (along the polar axis in
most of the cases). Based on this assumption, the dimensions of a and b were measured to
determined the volume of each bubble using the following equation:
Equation 5-3
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Subsequently, the equivalent bubble diameter (Dbub.eq) of each bubble was calculated with
Equation 5-4, and the Dbub,avg data was determined by taking the averages of the Dbub.eq data.
Equation 5-4
In addition, the average bubble diameter growth rates (dDbub/dt|avg) were determined by the
average slope of the lines-of-best-fits of the Dbub.eq vs. time data for each bubble.
Table 5-1 – Experimental cases for PS and PS-talc foaming under shear stress
Expt.
#
Tsys
[°C]
Psat
[MPa]
-dPsys/dt|avg
[MPa/s]
Talc
[wt%] γ
dγ/dt
[s-1]
1 180 3.45 12 0 0 25
2 180 3.45 12 0 12.5 25
3 180 3.45 12 0 25 25
4 180 3.45 12 0 25 6.25
5 180 3.45 12 5 0 25
6 180 3.45 12 5 12.5 25
7 180 3.45 12 5 25 25
8 180 3.45 12 5 25 6.25
5.3.3 Results and Discussion
5.3.3.1 PS Foaming with CO2
Figure 5-11 shows a set of snapshots of the foaming videos of the PS foaming
experiments that used CO2. The Nunfoam and dDbub/dt|avg vs. time data are shown in Figure 5-12
and Figure 5-13, respectively. Figure 5-13 shows that the bubble nucleation rate and maximum
cell density increased when a shear strain (γ = 12.5 and 25) was applied at a high shear strain rate
level (dγ/dt = 25) in contrast to the static case (γ = 0). Specifically, the maximum Nunfoam
increased from 2.5 ×104 cells/cm3 (γ = 0) to 1.1 × 105 cells/cm3 (γ = 12.5) and 1.6 × 105 cells/cm5
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(γ = 25). Also, the foaming process completion time decreased for the strained cases. However,
when a low strain rate was used (dγ/dt = 6.25 s-1), shear-induced nucleation was significantly less
apparent (maximum Nunfoam = 5.1 × 104 cells/cm3), and the foaming behaviours were similar to
the static case. Pioneering researchers of shear-induced foaming had shown that final cell
densities increased with dγ/dt, and they claimed that cell nucleation rate increased as dγ/dt
increased due to the conversion of shear energy into the interfacial energy needed for cell
nucleation [96, 99-102]. However, since the cell nucleation, growth, and collapse processes were
not observable, it was difficult to confirm if the increased final cell densities were resulted from
increased cell nucleation, decreased cell coalescence and collapse, or a combination of both. This
study visually confirmed that a higher number of cells were nucleated as dγ/dt increased.
Figure 5-11 – Snapshots of PS/CO2 foaming videos under shear stress
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Figure 5-12 – Nunfoam vs. time of PS/CO2
foaming under shear stress
Figure 5-13 –Dbub,avg vs. time of PS/CO2
foaming under shear stress
Several other factors might have increased the bubble nucleation rate in the strained cases.
First, the local Psys around microvoids or contaminants might have changed due to the applied γ,
which could have generated extensional stress components in some local regions. Therefore, the
level of supersaturation (Pbub,cr - Psys) would increase due to the decreased Psys, which
subsequently led to decrease in Rcr, Whom and Whet (see Equation 4-5, Equation 4-6 and Equation
4-7, respectively). Thus, the bubble nucleation rate would increase through the growth of pre-
existing microvoids when the Rcr became less than the size of these microvoids, or through
homogeneous or heterogeneous nucleation (on impurities). However, homogeneous nucleation
was unlikely to have happened due to its high free energy barrier. Due to the viscoelastic nature
of the PS/CO2 mixture, these tensile stresses should be higher when a higher dγ/dt was used,
which would explain the increased Nunfoam when the dγ/dt was increased. Second, the applied γ
might have caused the deformation of the existing microvoids into elongated shapes, which,
according to Chen’s “cell stretch model”, had greater potential to become nucleated cells owing
to their shape and increased surface area [99]. Third, additional gas cavities could have been
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generated when a γ was applied through the detachment of microvoids from contaminants or
from the sapphire surface [86]. Such gas cavities might be the seeds of bubble nucleation, as was
observed for the γ = 12.5 case, where a few elongated cavities were observed after the shear
strain was applied (See Figure 5-11). Shortly after depressurization, these cavities started to
grow.
Similar to the extensional strain case detailed in Section 4.3.3.2, it is also hypothesized
that an applied γ could induce polymer chains alignment that decreased the free volume between
them, so the gas solubility decreased. In the extensional strain case, such behaviour was not
observed for PS case (i.e., only apparent when talc was added). It is believed that gas might have
rapidly diffused out of the polymer sample through all the free surfaces (i.e., top, bottom and
sides) for the PS case. Meanwhile, in the shear strain case, both the top and bottom surfaces of
the polymer sample was in direct contact with the sapphire windows, so gas could not diffuse out
of the sample as easily. This might explain why microvoids were observed for the shear strain
case with PS. However, as mentioned previously, the increase in pressure at phase separation
might also be due to stress-induced nucleation. Therefore, the hypothesis of gas cavity generation
due to a decrease of gas solubility could not be verified based on the available data. Additional
investigation will be needed in the future to clarify this behaviour.
From the Dbub,avg vs. time data in Figure 5-13 and the dDbub/dt|avg data in Figure 5-17, it
could be observed that the bubble growth rates of the strained cases were higher than the static
case. It was hypothesized that the gas diffusion rate might have increased along the applied strain
direction due to polymer chain alignment, which increased the cell growth rates. However, since
changes in gas diffusivity in dynamic conditions were unknown, the validity of this hypothesis
could not be verified in this thesis. Due to the higher bubble growth rates, some submicron-sized
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bubbles could have sustained and/or grew in size to become visible bubbles, hence the overall
cell densities also increased. It is noted that under free expansion, such as in extrusion foaming,
the bubbles would continue to expand and become more spherical in shapes eventually since this
would be the more thermodynamically favorable shape to minimize the surface energy. However,
due to the viscoelastic nature of polymer, the shear stress applied to the polymer as it flow
through the die channel would not be released instantly and would help to increase the bubble
growth rates and the cell nucleating rates, especially in the initial stages of the foaming processes.
5.3.3.2 PS-Talc Composites Foaming with CO2
Figure 5-14 shows snapshots of the foaming videos of the PS-talc samples blown with
CO2. The Nunfoam and dDbub/dt|avg vs. time data are shown in Figure 5-15 and Figure 5-16,
respectively. The shear strain-induced cell nucleation phenomena were more significant than
were the PS cases. Specifically, the Nunfoam increased by two orders of magnitude as γ was
applied. This was from 9.4 × 104 cells/cm3 in the static case (γ = 0), to 8.7 × 105 cells/cm3 (γ =
12.5) and 9.4 × 106 cells/cm3 (γ = 25). All of the PS-talc samples foamed to higher maximum
Nunfoam than the PS samples in every case, and also took much less time (less than 1 s) in contrast
to the PS cases that took 3.5 to 25 s. This confirmed that talc was an effective nucleating agent
under both static and dynamic conditions. Similar to the PS case, the shear-induced cell
nucleating phenomenon was less apparent (Nunfoam = 2.3 × 105 cells/cm3) when a lower dγ/dt was
used (dγ/dt = 6.25 s-1), which was in good agreement with the pioneering researches [96, 99-102].
All of the cell-nucleating mechanisms described in the PS cases were also valid in the PS-
talc cases. On the other hand, the shear-induced cell nucleation effect was more significant for the
latter case. First, similar to the extensional stress case, the presence of talc might have altered
local system pressures and caused some local regions to have experienced extensional stresses
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that led to an increase in the supersaturation level. As mentioned in Section 2.2.4, this concept
has been demonstrated by Wang et al. [108] by numerically simulating the pressure fluctuation
around a solid particle near an expanding bubble. They showed that the system pressure
decreased in some local regions around particles, which might initiate cell nucleation. A large
quantity of gas cavities might also have resided on the rough surfaces of talc particles due to
incomplete wetting of the polymer on the talc surface. As proposed by Lee [86], this would have
provided more seeds for nucleation through the detachment of the gas cavities under shear strain
as pressure decreased. For the γ = 25 case, some unfocused black lines, believed to be
microvoids, approximately 0.01 to 0.2 mm in length, appeared dispersed in the image after a γ
was applied prior to depressurization. The number of the microvoids generated was significantly
higher than the case with PS. It was believed that could be due to the detachment of polymer
chains from talc particles due to the stiffness mismatch between the PS matrix and talc particles.
To be specific, as the PS-talc composite was strained, the PS matrix tended to align to the shear
strain direction. Meanwhile, the talc particles, which have higher stiffness than the PS matrix,
tended to remain undeformed. Since the number of talc particles should be significantly higher
than the number of contaminants in the PS cases, the number of microvoids generated in the PS-
talc composites was significantly higher. Shortly after depressurization, the microvoids
developed into grown cells. This finding also demonstrated that bubbles formation and growth
from pre-existing microvoids could be an important cell nucleation mechanism, as the early
research suggested [86-88]. These mechanisms explained the significantly higher Nunfoam
observed for the PS-talc cases when compared to the PS cases under an applied γ. As discussed in
Section 4.3.3.2, the same mechanisms could be responsible for the similar phenomena observed
for PS-talc foaming under extensional stress.
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From the Dbub,avg vs. time data in Figure 5-16 and the dDbub/dt|avg data in Figure 5-18, the
dDbub/dt|avg of the high dγ/dt cases (γ = 12.5 and 25 at dγ/dt = 25) were slightly higher than the
static experiment. This effect was more apparent for the case of γ = 25. For the low dγ/dt case
(dγ/dt = 6.25 s-1), the dDbub/dt|avg were similar to the static experiment. Similar to the PS cases,
the higher dDbub/dt|avg in the high dγ/dt cases could be explained by the increased gas diffusion
rate as polymer chain aligned to the strain direction. For the low dγ/dt case, the bubble shapes
were approximately spherical and similar to the static case. From this observation, it was believed
that the polymer chain might not be as aligned as the high dγ/dt cases, and hence the increase in
gas diffusion rate in the low dγ/dt case was not significant. Consequently, the cell growth rate of
the low dγ/dt case was similar to the static case.
Figure 5-14 – Snapshots of PS-5% talc/CO2 foaming videos under shear stress
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Figure 5-15 – Nunfoam vs. time of PS-5%
talc/CO2 foaming under shear stress
Figure 5-16 – Dbub,avg vs. time of PS-5%
talc/CO2 foaming under shear stress
Figure 5-17 summarizes the maximum Nunfoam for all of the experimental cases. It
illustrates that shear strain is an effective way to induce cell nucleation, especially in the PS-talc
cases. On the other hand, differences in the maximum Nunfoam between the low and high γ cases (γ
= 12.5 vs. 25 at dγ/dt = 25) were not very significant for the PS cases. This suggests that for each
material, there could be an optimal level of shear strain by which to achieve a high Nunfoam while
preventing melt fracture and cell rupture that could be caused by excessive shear stress.
Moreover, this study shows that shear strain, similar to extensional strain, significantly increased
the effectiveness of the nucleating agents to create plastic foams with high cell densities.
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Figure 5-17 – Maximum Nunfoam for PS and PS-
talc foaming under shear stress
Figure 5-18 – dDbub/dt|avg for PS and PS-talc
foaming under shear stress
5.4 Conclusion
A novel foaming visualization system has been developed to observe and capture plastic
foaming processes an under easily controllable γ and dγ/dt. PS and PS-talc foaming experiments
blown with CO2 verified the capability of the system. This study confirmed the shear-induced
cell nucleating phenomena that were suggested by the pioneering research in this subject area. It
was observed that the cell nucleation rate, Dbub/dt|avg, and maximum Nunfoam increased with the
applied γ and dγ/dt. These results could be attributed to the decrease in gas solubility and local
Psys, as well as the increase in gas diffusion to bubbles, as γ was applied. The shear-induced cell-
nucleating effects were more significant in the PS-talc samples. The enhanced effect was due to
the local pressure variations around talc particles, and the cell nucleation from pre-existing
microvoids at the PS-talc interface. Our study demonstrates that the effectiveness of a nucleating
agent can be significantly improved in the presence of an applied γ when the dγ/dt was high.
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CHAPTER 6
SUMMARY AND CONCLUDING
REMARKS
6.1 Summary
Cell nucleation, growth, deterioration, and collapse phenomena in plastic foaming
processes determine the final foam morphology, and hence the foam’s application and quality.
The successful development of high-quality foams with customizable cell morphology (e.g.,
closed-cell foams with high cell density, open-cell foams with high porosity, and foams with
large volume expansion) for specific applications hinges on the scientific advancement on the
knowledge of thermodynamics, kinetics, and rheological behaviours in these phenomena. In this
context, this thesis investigated the fundamental mechanisms of plastic foaming processes via
series of in situ foaming observation experiments, which are difficult to be achieved in typical
foaming equipment.
6.2 Key Contributions
6.2.1 Development of Foaming Visualization Systems
Three foaming visualization systems have been developed successfully in this thesis: 1) a
static system with accurate heating and cooling control; 2) a dynamic system with extensional
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stress-inducing ability; and 3) a dynamic system with shear stress-inducing ability. The two
dynamic visualization systems are novel: in situ observation of plastic foaming processes under
uniform and easily adjustable extensional and shear flows has not been achieved previously.
The static system permits concurrent studies to be conducted with a high-pressure DSC to
compare crystallization kinetics and foaming behaviour of semi-crystalline polymers. This
system opens a wide range of potential research opportunities, especially with semi-crystalline
polymers where crystallization kinetics significantly influence the foaming behaviour as well as
the mechanical properties of the final foamed products.
The foaming visualization system with extensional stress-inducing ability allows in situ
observation of plastic foaming processes with high spatial and temporal resolution and under a
uniform and easily controllable extensional strain. This is a key contribution to the field of plastic
foaming research because plastics are subjected to extensional stresses in the converging section
of dies or flow channel in extrusion foaming or injection foam molding processes.
The foaming visualization system with shear stress-inducing ability allows observation of
plastic foaming processes with high spatial and temporal resolution and under a uniform and
easily controllable shear strain. Also, a mechanism has been incorporated to accelerate the gas
saturation process significantly, so the system could be used for a wide range of plastic materials,
including ones that are susceptible for degradation due to heat. This is a key contribution to the
field of plastic foaming research because plastics are subjected to shear stresses near the walls of
dies or flow channel in extrusion foaming or injection foam molding processes.
6.2.1.1 Scope of the Visualization Systems
Based on the current optical system, the maximum optical resolution of the three
visualization systems is 2 – 4 μm, which would allow observation of micro-scale fillers, crystals,
and bubbles. However, nano-scale particles, such as nano-silica or nano-clay that are well
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dispersed, as well as nano-sized bubbles and crystals would not be captured. Based on the
pressure seals, the maximum processing Tsys are 260 °C for all three systems and the maximum
processing pressures are 25 MPa (Static and Extensional cases), and 45 MPa (Shear cases). Due
to the wide temperature and pressure ranges, a wide variety of plastics and fillers could be tested
with the system under a wide range of experimental conditions, including many commodity and
engineering thermoplastics. The maximum extensional strain and strain rate are 4 and 196 s-1.
The maximum shear strain and strain rate are 100 and 100 s-1, respectively, and both of which
could be further increased if a thinner sample is used. This system could simulate shear rates that
are typically observed in extrusion processes (102 to 103 s-1). For injection molding processes, the
shear rates are typically very high (103 to 105 s-1), hence the system would not be able to directly
simulate these conditions. Nevertheless, the information on cell nucleation and growth under
dynamic conditions is still valuable to the understanding of these foaming processes.
6.2.2 Experimental Work
1. Using the static system and a HPDSC, the crystallization kinetics and the cell nucleation
and growth phenomena of PP foaming with CO2 has been investigated. It has been
demonstrated that bubbles first nucleated around crystals that were formed at low
isothermal temperatures, and the growth of these bubbles triggered formation of new cells
in the surrounding regions. While previous researchers attributed crystals-induced cell
nucleation to the exclusion effect of CO2 at the crystals growth fronts, this explanation
could not explain the bubble-growth induced cell-nucleating phenomena that were observed
in this study. This study offered an alternative explanation whereby the growth of existing
bubbles induced tensile stresses to the constrained amorphous regions between adjacent
crystals, which caused increased in the level of supersaturation and hence cell nucleation
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rate in the classical sense as well as via the growth of microvoids in these local regions.
This understanding could be extended to the foaming of other semi-crystalline polymers.
2. Via foaming visualization of PP foaming with inert gases (Ar, N2, and He), it has been
demonstrated that Ar is a feasible BA due to its relatively high solubility compared to the
other two BAs, which is an important characteristic for generating foams with high
expansion. Meanwhile, despite its lower solubility, it has been shown that N2 has the
highest nucleating power, which is beneficial for the manufacturing of high-density foams
with high cell density for applications such as injection foam molding processes. On the
other hand, this study demonstrated that He would be an ineffective BA for plastic foaming
processes due to its extremely low solubility.
3. Through foaming visualization of PS with CO2-N2 blends, the synergistic effects of the
high plasticization effect of CO2 and high nucleating power of N2 have been demonstrated.
To be specific, while the gas composition dissolved in the PS was uncertain, the 75% CO2-
25% N2 gas mixture yielded the highest cell densities and cell growth rates over a wide
processing window from 100°C to 180°C. This study provided a direction for identifying
an optimal composition for CO2-N2 blends, and also demonstrated that supercritical N2
could be a feasible alternative to the alcohol as a co-blowing agent to supercritical CO2 in
the current industrial PS foaming processes.
4. Through in-situ observation of PS and PS-talc composites foaming with CO2, the effects of
extensional strain have been examined. It has been shown that the application of
extensional stress significantly increased cell nucleation rate and cell density for both PS
and PS-talc composite. It was hypothesized that the stress-inducing cell nucleation was due
to: 1) decrease in local system pressure; 2) decrease in gas solubility due to polymer chain
184
alignment; and 3) Generation of microvoids. The third reason was more significant for the
PS-talc cases due to strain-mismatch between polymers and talc particles.
5. Three different types of talc have been compounded with PS to elucidate the effects of
surface treatment, size, and the weight content of talc particles on the foaming behaviour of
PS under extensional stress. This study demonstrated that the talc with the largest particle
size yielded the earliest onset of cell nucleation and the highest cell densities despite its
lower talc particle density and total surface area than the other two smaller types of talc. A
new mechanism has been proposed to explain this behaviour: in the presence of nearby
growing bubbles, higher tensile stresses would be generated around larger particles when
compared to smaller particles. The higher tensile stresses caused cell nucleation rate and
cell density to increase. This behaviour became less apparent as the applied extensional
strain or strain rate increased. Also, this study demonstrates that the maximum cell density
remained at low levels for all talc types and weight contents when they were foamed in the
static conditions. This result demonstrated that in extrusion foaming or injection foam
molding processes, the dies or gate must be designed to induce sufficient extensional stress
to enhance the effectiveness of the cell nucleation agents. Meanwhile, it has also been
observed that surface treatment did not cause noticeable differences in their foaming
behaviours despite achieving better talc particle dispersion in the PS-talc composites.
6. The foaming processes of PP have been examined under static and extensionally stressed
conditions at low temperatures to elucidate the interrelationship between crystal formation,
extensional stress, and the foaming behaviour. The bubble-growth-induced nucleation
behaviour was dominant in the static cases due to the presence of crystals. However, as the
applied extensional strain increased, the bubbles were nucleated in a more dispersed
manner; the bubble-growth-induced nucleation behaviour occurred at a later stage and was
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less pronounced. This study demonstrated that extensional stress could alter the
mechanisms of cell nucleation.
7. PS and PS-talc foaming experiments blown with CO2 have been conducted to investigate
the effect of shear strain and strain rate of plastic foaming behaviour. Pioneering
researchers of shear-induced foaming claimed that shear stress could induce cell nucleation
due to the conversion of shear energy into the interfacial energy needed for cell nucleation.
However, the cell nucleation, growth, and collapse processes were not observable, it was
difficult to confirm if the increased final cell densities were resulted from increased cell
nucleation, decreased cell coalescence and collapse, or a combination of both. For the first
time, this study visually confirmed that a higher number of cells were nucleated as the
shear strain rate increased. The mechanisms of shear stress-induced foaming are believed to
be the same as those in the extensional stress cases.
6.3 Recommendation for Future Works
1. According to the classical nucleation theory, Rcr dictates the growth/collapse of a bubble:
Equation 6-1
The values of γlg of polymer-gas mixture could be measured using sessile-drop experiments
and correction factors could be used to correct for the decrease in surface energies at nano-
scale; The Henry’s Law Constant (H) could be determined from solubility measurement;
and Psys is directly measureable. On the other hand, ΔPlocal, which is the key reason for
stress-induced cell nucleation phenomena, has not been measured under plastic foaming
conditions previously. Quantification of ΔPlocal will clarify the impact of stress on cell
nucleation, which will be imperative to the advancement of plastic foaming theory. Using
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a PS/CO2 system (Tsys = 180 °C, C = 2 wt% CO2) as a case example, the impact of ΔPlocal
could be estimated as a first order approximation as follows: 1) The γlg of PS/CO2 mixture
at 180 °C with 2 wt% CO2 was measured to be 2.4 × 10-2 N/m [78]; 2) The Henry’s Law
Constant (H) of a PS/CO2 mixture at the same condition is 11874 Nm/mol [212]. 3) The
Psys is assumed to be zero; 4) It has been numerically simulated that ΔPlocal variations could
exist around an incompressible solid particle in the presence of a growing bubble within a
PS/CO2 mixture at static conditions (Tsys = 180 °C and C = 2 wt% CO2) [108]. In particular,
a tensile stress of 0.2 MPa has been observed under such conditions (ΔPlocal = -0.2 MPa).
Substituting this value of ΔPlocal, as well as the γlg and HC data, into the Rcr equation
(Equation 6-1), the resulting Rcr has been determined to be 8.26 nm. This is lower than the
case where ΔPlocal is assumed to be zero (Rcr = 8.55 nm). It is expected that the effect of
ΔPlocal, and hence the decrease of Rcr, would become much more significant under the
typical processing Tsys for PS foaming (130 - 150 °C) [228], since the viscosity and
elasticity of the polymer-gas mixture would be higher under such conditions. Similarly, the
decrease in Rcr will also be significantly higher for polymer-gas mixture under extensional
and/or shear flow due to the large ΔPlocal generated. In this context, successful evaluation of
ΔPlocal in polymer-gas mixtures, especially in the presence of crystals or additives and
under dynamic flow at the typical processing Tsys, would be critical to the determination of
Rcr and hence the elucidation of plastic foaming behaviours. Numerical simulations, or
birefringence measurements by incorporating polarimetry in the visualization systems,
might help to clarify the stress field of polymers and hence the determination of ΔPlocal.
2. Rheological measurements to investigate the transient and steady state behaviour of
polymer-gas melt under uniaxial and simple shear conditions would compliment the
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foaming visualization results to advance our understanding on the effect of the rheological
behaviours of polymer-gas melt on plastic foaming phenomena.
3. Cell nucleation, either via classical nucleation or growth of existing gas clusters, typically
occurs in the submicron-scale, which could not be captured with the current foaming
visualization systems due to the limitation of optical microscopy and other constraints (e.g.,
requirement of long working distance, high temperature/pressure environment). In this
context, ultrasonic sensor can be incorporated into the visualization system to detect cell
nucleation at the nanometer-scale.
4. New foaming chambers that allow rapid temperature quenching of plastic samples upon
depressurization while maintaining the visualization and stress-inducing ability will allow
examination of cell morphology of stabilized foams even at high processing temperatures.
Consequently, it will be possible to correlate the cell nucleation, growth, and deterioration
processes and the cell morphology directly. Moreover, if it is possible to quench plastic
samples in an initial stage of cell nucleation processes to freeze nanometer-sized bubbles,
SEM or TEM technologies can be used to examine their cell morphology in nanometer-
scale to overcome the optical limitation of the visualization systems.
5. In the current visualization systems, a study of plastic foaming with blowing agent blends
required the use of premixed blowing agents, which limited the use of different blowing
agents and compositions. In this context, multiple gas chambers with known volumes can
be installed to store different blowing agents before the gases are injected into the existing
foaming chamber. Consequently, a wide range of blowing agents can be used as blends and
at customizable compositions for foaming visualization studies.
6. Polarized optical microscopy (POM) can be incorporated to the visualization systems to
better observe and understand crystal formation processes and their effects on foaming
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processes of semi-crystalline polymers under various high temperature/pressure and
dynamic conditions.
7. The formation of crystals is critical to the foaming behaviour, bead sintering, and
consequently mechanical properties of the bead foam products. Therefore, concurrent
foaming visualization study and crystallization kinetics of semi-crystalline polymers using
the static foaming visualization system and HPDSC, respectively, will be imperative to the
advancement of bead foaming technology, especially with the emerging materials (e.g.,
PLA and TPU) where such technologies are still in their developmental stage.
8. Based on the PS/CO2-N2 foaming results in this thesis, PS foaming studies using extrusion
foaming and injection foam molding processes should be conducted in the future to identify
the optimal CO2-N2 blowing agent blend compositions in each of these processes. This will
be a key step to replace hazardous co-blowing agents such as alcohol and butane in the
manufacturing of PS foams with CO2 as the primary blowing agent. It is foreseeable that
the resulting knowledge can also be transferred to other plastic foaming processes as well.
9. The investigation of PS-talc composites foaming in this thesis offered new insight on
heterogeneous nucleation phenomena. This research can be extended to foaming
visualization studies with nanocomposites (e.g., exfoliated vs. intercalated nanoclay,
nanosilica, nanocrystalline cellulose) and other cell nucleating agents of different sizes and
geometries to confirm and improve the proposed foaming mechanisms.
10. Based on the knowledge obtained in the PS and PP studies in this thesis, the effects of
extensional and shear stresses on plastic foaming should be elucidated further with other
polymers and blowing agents in a comprehensive manner to identify general criteria for die
and gate designs to better control stress-induced foaming.
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11. Development of a computer simulation system to model bubble nucleation and growth that
considers local stress and gas concentration variations due to cell-to-cell interactions and
applied extension and shear stresses will be a significant step forward in the field of plastic
foaming research. Using the visualization systems, the validity of the computer simulation
models can be tested and further improvements can be made in an iterative manner.
Ultimately, the knowledge generated will enhance our understanding of the typical plastic
foaming processes such as extrusion foaming and injection foam molding.
12. Based on the foaming visualization studies under extensional and shear stresses, it has been
hypothesized that a decrease in gas solubility and increase in gas diffusion rate might have
enhanced the cell nucleation and cell growth rate. To verify this, measurement of solubility
and gas diffusivity under dynamic conditions would be key to validate these hypotheses.
These data would also be extremely usable for industrial plastic foaming processes.
190
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