CONNECTING FUNDAMENTAL PROPERTIES OF CONJUGATED …

The Pennsylvania State UniversityMECHANICAL PERFORMANCE IN STRETCHABLE ELECTRONICS
A Dissertation in
December 2018
The dissertation of Renxuan Xie was reviewed and approved* by the following:
Enrique D. Gomez
Dissertation Co-Advisor
John B. Asbury
*Signatures are on file in the Graduate School
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ABSTRACT
Although conjugated polymer is promising for applications in stretchable electronics, no
rational design exists due to the lack of characterization of the fundamental properties of conjugated
polymers and their interrelationships with chemical structures and performances. Regarding the
mechanical performance, the fundamental properties include the glass transition temperature (Tg),
the entanglement molecular weight (Me) and the tie chain density (ρx), which dictate the
stretchability of a homopolymer in different states (i.e., glassy, semicrystalline, melt). Therefore,
the focus of this dissertation is to first characterize these fundamental properties for various
conjugated polymers, and then uncover their correlations with the chemical structure in order to
ultimately predict the mechanical performance of stretchable electronics.
The glass transition temperatures (Tg) for regioregular (RR) and regiorandom (RRa)
poly(3-hexylthiophene-2,5-diyl) (P3HT) and poly-((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-
linear shear oscillatory rheology. This method then allows systematic investigation of the effects
of molecular weight and side chain regioregularity of P3HT on Tg. In addition, both side chain and
backbone Tgs are identified for P3HT, while only the backbone Tg is found for PFTBT. The
molecular weight dependence of backbone Tg is modeled by the Flory-Fox equation, yielding Tg =
22 °C, 6 °C and 144 °C in the long chain limit for RR P3HT, RRa P3HT and PFTBT, respectively.
Furthermore, for RR P3HT, a different molecular weight dependence of Tg is seen below Mn = 14
kg/mol, suggesting this is the typical molecular weight of intercrystalline tie chains, based on our
hypothesis that RR P3HT has 16 K higher Tg than RRa P3HT due to stretched tie chains.
A general correlation between Tgs and chemical structures of 32 conjugated polymers with
drastically different backbone and alkyl side chain structures is found through a newly defined
effective atomic mobility, m. This effective atomic mobility is directly calculated from the assigned
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mobility values for atoms belonging to different groups in the repeat unit. This semi-empirical
correlation requires only one adjustable parameter on the relative difference in atomic mobility
between a conjugated and a non-conjugated atom and predicts the Tg ± 25 °C with 95% confidence
for nearly all conjugated polymers with alkyl side chains. Other attempts of correlating Tg with side
chain mass fraction and packing length are also illustrated but deemed as unsatisfactory because of
the limited applicability in only certain groups of conjugated polymers.
Because nematic phase is ubiquitous in conjugated polymer, the role of nematic coupling
on entanglement molecular weight (Me) is explored with multiple molecular weights of PFTBT and
poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)]
(PCDTBT). We first verify the existence of nematic phases in both PFTBT and PCDTBT and
identify nematic-isotropic transition temperatures, TNI, between 260 and 300 °C via a combination
of differential scanning calorimetry, polarized optical microscopy, temperature dependent wide-
angle X-ray scattering, and rheology. Then, the entanglement molecular weight (Me) in the isotropic
phase is extracted to be 11 ± 1 kg/mol for PFTBT and 22 ± 2 kg/mol for PCDTBT by fitting the
linear viscoelastic response with a tube model. Mes are significantly enlarged during the isotropic
to nematic transition by 10 fold for PFTBT and 15 fold for PCDTBT, suggesting that the local
chain alignment via nematic ordering substantially reduces chain entanglements.
Entanglement molecular weight (Me) for RR P3HT (~16 kg/mol) is also determined to be
about a factor of 3 larger than that for RRa P3HT (5 kg/mol) by modeling the linear viscoelastic
data and analyzing the molecular weight dependence of zero-shear viscosity. Because the
persistence lengths for RR and RRa P3HT are nearly the same based on static light scattering and
intrinsic viscosity measurements in dilute solutions, the difference in Me could be due to the
possible nematic phase in only RR P3HT (not RRa P3HT). This is a reasonable hypothesis, because
of the apparent increase in Me via the nematic ordering as observed for PFTBT and PCDTBT. But
unlike PFTBT and PCDTBT, no clear signatures of nematic-isotropic transition is observed
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currently for RR P3HT, except for some suggestive evidence from wide-angle X-ray scattering,
validity check of Cox-Merz rule, and polarized Raman spectroscopy. Future experiments that probe
the nematic ordering in RR P3HT are warranted.
The density of tie chains (ρx) in RR P3HT is estimated by examining the linear shear
semicrystalline rheology for different molecular weights of RR P3HT and multiple blends ratios of
RR and RRa P3HTs. As the molecular weight of pure RR P3HT decreases, the possibility of
forming tie chains in RR P3HT decreases, eventually leading to isolated crystal domains and
viscoelastic liquid behavior at long times. By adding more RRa P3HT to the blends, the mass
crystallinity determined by differential scanning calorimetry decreases from 0.58 to nearly zero,
and the intercrystalline distance increases drastically from 10 to 40 nm based on the small-angle
X-ray scattering. As a result, the estimated number density of tie chains (ρx) decreases by orders of
magnitude till the percolation threshold of about 4% RR P3HT, below which the reported charge
mobility of the blends abruptly drops off to that of pure RRa P3HT.
Finally, some preliminary results are also included as a part of the future work to better
understand the nature of nematic ordering and the universal correlation between chain dimensions
and entanglements in conjugated polymers. Specifically, with hexyl side chains added onto the
thiophene rings of PFTBT and PCDTBT, both PFT6BT and PCT6BT appear to be entirely
amorphous within the temperature range, where PFTBT and PCDTBT show strong evidence of
nematic phase. This behavior suggests that the nematic ordering in conjugated polymers may
profoundly depend on the propensity of π-π stacking, which can be distorted by significant side
chain steric hindrance, thus supporting the possible nematic phase in RR P3HT but not in RRa
P3HT. Furthermore, data for multiple conjugated polymers with estimated persistence lengths and
plateau moduli (or Me) agree reasonably well with the previously proposed universal relationship
between the dimensionless Kuhn monomer density and the dimensionless rubbery plateau modulus.
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Chapter 1 Introduction ............................................................................................................. 1
1.1 Motivation .................................................................................................................. 1 1.2 Measurement of Mechanical Properties ..................................................................... 4 1.3 Glass Transition and Chain Entanglements ............................................................... 10
1.3.1 Glass Transition............................................................................................... 11 1.3.2 Chain Entanglement ........................................................................................ 13
1.4 Characterization of Thermal Phase Transitions ......................................................... 19 1.4.1 Liquid Crystalline Phase ................................................................................. 20 1.4.2 Semicrystalline Morphology ........................................................................... 23
1.5 Determination of Chain Dimensions .......................................................................... 31 1.5.1 Static Light Scattering ..................................................................................... 32 1.5.2 Predicting Persistence Length ......................................................................... 36 1.5.3 Dynamic Light Scattering ............................................................................... 37 1.5.4 Intrinsic Viscosity Measurement ..................................................................... 39
1.6 Dissertation Overview ................................................................................................ 42 1.7 References .................................................................................................................. 46
Chapter 2 Glass Transition Temperature of Conjugated Polymers by Oscillatory Shear
Rheometry ........................................................................................................................ 55
2.1 Abstract ...................................................................................................................... 55 2.2 Introduction ................................................................................................................ 56 2.3 Materials and Methods ............................................................................................... 58
2.3.1 P3HT Characteristics ....................................................................................... 58 2.3.2 PFTBT Characteristics .................................................................................... 63 2.3.3 Linear Viscoelastic Shear Rheology ............................................................... 65
2.4 Results and Discussion ............................................................................................... 65 2.4.1 Backbone and Side Chain Glass Transitions of P3HT .................................... 65 2.4.2 Molecular Weight Dependence of Glass Transition Temperatures for
P3HTs ............................................................................................................... 68 2.4.3 Flory-Fox Modeling of the Molecular Weight Dependent Tαs for RR and
RRa P3HTs ....................................................................................................... 71 2.4.4 Molecular Weight Dependence of Glass Transition Temperatures of
PFTBTs ............................................................................................................ 75 2.5 Conclusions ................................................................................................................ 79 2.6 References .................................................................................................................. 81
Chapter 3 Glass Transition Temperature Correlation with Chemical Structure for
Conjugated Polymers ....................................................................................................... 85
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3.1 Abstract ...................................................................................................................... 85 3.2 Introduction ................................................................................................................ 86 3.3 Materials and Methods ............................................................................................... 88 3.4 Results and Discussion ............................................................................................... 92
3.4.1 Measurements of the Glass Transition Temperature ....................................... 92 3.4.2 Correlation of Tg with the Alkyl Side Chain Mass Fraction............................ 101 3.4.3 Correlation of Tg with the Packing Length ...................................................... 103 3.4.4 Correlation of Tg with the Effective Atomic Mobility .................................... 106
3.5 Conclusions ................................................................................................................ 112 3.6 References .................................................................................................................. 114
Chapter 4 Local Chain Alignment via Nematic Ordering Reduces Chain Entanglement in
Conjugated Polymers ....................................................................................................... 118
4.3.1 Synthesis and Molecular Weight Distribution ................................................ 121 4.3.2 Differential Scanning Calorimetry .................................................................. 123 4.3.3 Rheometry ....................................................................................................... 124 4.3.4 X-ray Scattering .............................................................................................. 125 4.3.5 Optical Microscopy ......................................................................................... 126
4.4 Results ........................................................................................................................ 126 4.4.1 Thermal Transitions of PFTBT and PCDTBT ................................................ 126 4.4.2 Chain Entanglement in the Isotropic Phase ..................................................... 141 4.4.3 Effect of Nematic Phase on Entanglements .................................................... 146
4.5 Discussion and Conclusions ....................................................................................... 152 4.6 References .................................................................................................................. 156
Chapter 5 Impact of Side Chain Regioregularity on Chain Entanglements and Chain
Conformation of Conjugated Polymer ............................................................................. 160
5.3.1 P3HTs .............................................................................................................. 162 5.3.2 Static Light Scattering ..................................................................................... 163 5.3.3 Intrinsic Viscosity Measurement ..................................................................... 165 5.3.4 Melt Rheology and Linear Viscoelastic Modeling .......................................... 166 5.3.5 X-ray Scattering .............................................................................................. 169
5.4 Results and Discussion ............................................................................................... 170 5.4.1 Chain Conformation in Dilute Solution .......................................................... 170 5.4.2 Chain Entanglements by Melt Rheology ......................................................... 175 5.4.3 Hints of Nematic Ordering in RR P3HT ......................................................... 179 5.4.4 Checking the Universal Prediction of Plateau Modulus with RRa P3HT ....... 183
5.5 Conclusions ................................................................................................................ 184 5.6 References .................................................................................................................. 185
Chapter 6 Semicrystalline Morphology and Networks of P3HT ............................................. 188
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6.3.1 P3HTs .............................................................................................................. 191 6.3.2 Semicrystalline Rheology ............................................................................... 192 6.3.3 Small-angle X-ray Scattering .......................................................................... 194
6.4 Results and Discussion ............................................................................................... 195 6.4.1 Molecular Weight Effect on Semicrystalline Morphology of RR P3HT ........ 195 6.4.2 Semicrystalline Morphology of the Regiorandom and Regioregular P3HT
Blends ............................................................................................................... 197 6.5 Conclusions ................................................................................................................ 209 6.6 References .................................................................................................................. 211
Chapter 7 Conclusions and Future Outlook ............................................................................. 214
7.1 Conclusions ................................................................................................................ 214 7.2 Future Outlook ........................................................................................................... 217
7.2.1 Effect of Side Chain Steric Hindrance on Liquid Crystalline Ordering .......... 217 7.2.2 Verify the Universal Relationship between Plateau Modulus and Chain
Dimensions using Conjugated Polymers .......................................................... 221 7.2.3 Rational Design of Stretchable Electronics ..................................................... 225
7.3 References .................................................................................................................. 227
Appendix B Smectic Phase of Conjugated Polymers .................................................................. 230
Appendix C Dynamic Light Scattering for P3HTs ...................................................................... 237
Appendix D Raman Spectroscopy for RR and RRa of P3HTs .................................................... 240
Appendix E Static Light Scattering for PFO in Dilute Solution .................................................. 244
Appendix F SAXS for Different Molecular Weights of RR P3HTs ............................................ 246
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LIST OF FIGURES
Figure 1-1: Comparison of two common mechanical measurement techniques for thin
films of conjugated polymers: (a) tensile test on water and (b) compressional
buckling test on elastomer. Regioregular P3HTs with different molecular weights
are shown as an example.33 (c) The molecular weight dependence of the fracture
strain and fracture stress obtained by these two methods for regioregular P3HTs.
Data are taken from 33. ..................................................................................................... 5
Figure 1-2: Thin-film DMA for conjugated polymers. Solution-cast conjugated polymer
films are reinforced by woven glass fibers.37 This approach is more sensitive for
glass transition temperatures (Tg and sub Tg) of conjugated polymers than DSC, but
accurate modulus values cannot be extracted due to a poorly defined sample
geometry.37 ....................................................................................................................... 7
Figure 1-3: Examples of the tensile and the shear measurements of bulk samples for
conjugated polymers. (a) Uniaxial tensile test at room temperature for melt-pressed
regioregular P3HT strips of different molecular weights.52 (b) Schematic of a
vacuum-assisted molding setup to obtain void-free and undegraded P3HT disks
(pictures shown with 3-mm diameter and 1-mm thickness) for shear rheology
measurements. .................................................................................................................. 8
Figure 1-4: Example of the master curve of regiorandom P3OT for (a) storage and loss
moduli at a reference temperature of 0 °C and (b) frequency shift factors (aT) based
on the time-temperature-superposition principle.58 .......................................................... 10
Figure 1-5: (a) Loss modulus versus temperature for regiorandom P3ATs with different
alkyl side chain lengths at a frequency of 10 rad/s and heating rate of 2 °C/min.
Curves are shifted vertically for clarity.58 (b) Glass transition temperatures of
regiorandom P3ATs for both backbone (Tα = Tg, green symbols) and side chain
(TαPE, orange symbols) as a function of the side chain lengths (squares) 58 and the
effect of molecular weight for P3HT (triangles)28. .......................................................... 12
Figure 1-6: Demonstration of various stress-relaxing motions incorporated in the BoB
program using monodispersed molten polyethylene as an example. The storage and
loss moduli generated by the full BoB program (blue lines) are compared with those
generated by successively excluding the longitudinal stress relaxation (red lines), the
constraint release (grey lines) and the contour length fluctuation (black lines) from
the BoB program.60, 61 ....................................................................................................... 14
Figure 1-7: The cumulative weight fraction of a regioregular P3HT is approximated by
20 monodispersed components with the corresponding weight fraction, which are
input to BoB program to predict the viscoelastic response of the P3HT melt. ................ 16
Figure 1-8: Dimensionless plateau moduli as a function of the dimensionless number
density of Kuhn segments: Experimental data vs predictions. Red symbols indicate
experimental data for various loosely entangled polydiene, polyolefine, and
polyacrylate melts and loosely entangled theta-solutions of polystyrene and
x
polybutadiene. Blue symbols represent the tightly entangled F-actin and fd-phage
solutions. Colored lines represent theoretically derived power laws for tightly81 and
loosely entangled systems76. Black line represents the universal scaling prediction by
Everaers with slight modification to the fit for the loosely entangled region.80
Adapted from Everaers’ plot.82 ........................................................................................ 19
Figure 1-9: (a) Example of identifying the liquid-crystal-to-isotropic transition
temperature (246 °C shown on the inset) for P3HT by DMA. 1.0 Hz: E’, black line;
tan(δ), black squares. 10 Hz: E’, red dashed line; tan(δ), red triangles.36 (b) A typical
rheology signature for identifying the nematic-to-isotropic transition of a polymer
(structure shown above) is the increase in complex viscosity upon heating (open
symbols) for ramp rates of 0.1 K/min (◊) and 2.0 K/min (), and this trend is fully
reversible when cooling (filled symbols). Dashed line is the nematic-to-isotropic
transition temperature from DSC.83 ................................................................................. 22
Figure 1-10: (a) Schematic of a chain in a semicrystalline matrix with crystal thickness
(lc), amorphous region thickness (la) and (1 + f) crystal stems in one run.111
Schematic of different types of folding (b) in a single given fold plane and (c) on the
plane perpendicular to fold plane. (1), (2), (3) are considered as tight folds, while (4)
is considered as a loop.111 ................................................................................................. 25
Figure 1-11: Schematic of the semicrystalline structure of conjugated polymers showing
tie chains in red, entanglements in green and filler effect in blue.115 ............................... 29
Figure 1-12: (a) Example of the stress relaxation test for isostatic polypropylene shows
the continuous slow relaxation without reaching a plateau modulus in the
semicrystalline state, indicating the possible origin of this connected crystals
morphology similar to the schematic drawn for P3HT thin films spin-coated from
trichlorobenzene.118 (b) Effect of solvent on the microstructure and the charge
mobility of P3HT thin films spin coated from either chlorobenzene or
trichlorobenzene. High mobilities are attributed to an interconnected crystal
morphology.120 ................................................................................................................. 30
Figure 1-13: Zimm plot of RRa P3HT in THF. Solid circles are data and crosses are
extrapolations to the zero angle and the zero concentration limits. K is the optical
constant, c is concentration that varies between 1.0 and 4.0 mg/ml, Rθ is the
Rayleigh ratio, θ is the scattering angle that varies between 30° and 150°, and k is an
arbitrary constant (= 104 ml/g in this plot).122 The overlap concentration is also
determined to be 7.4 mg/ml based on the intrinsic viscosity measurement.122 ................ 33
Figure 2-1: Zimm plots generated by static light scattering of dilute chlorobenzene
solutions of (a) RRa 4 (110 ± 2 kg/mol, Rg = 15.4 ± 1.1 nm) and (b) polymer 8 (67 ±
2 kg/mol, Rg = 14.2 ± 2.1 nm). The weight-average molecular weight (Mw) was
calculated from the intercept of zero angle and zero concentration extrapolations in
the plot, while Rg was obtained from the slope of the fit for the low concentration
limit. (K: optical constants, 2.89 × 10-7 for RR and 2.17 × 10-7 mol ml/g2 for RRa;
c: polymer concentration (g/ml); Rθ: Rayleigh ratio; θ: scattering angle.) ....................... 60
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Figure 2-2: (a) Difference in refractive index versus concentration for RR P3HT 7 (2
sets of solutions), RRa 3, and RRa 4 in chlorobenzene at 30.0 C at a wavelength of
620 nm. (b) Frequency dependence of the real permittivity (ε’) for RR P3HT 7
(amplitude of 0.5 V) and RRa 3 & 4 (amplitude of 1.5 V) at -40 C from DRS. ............ 61
Figure 2-3: GPC traces of RR P3HTs 1, 2, 3, 4, 5, 6, 7, 8 and RRa P3HTs 1, 2, 3, 4 in
chlorobenzene at elevated temperature whose characteristics are shown in Table 2-1. .. 62
Figure 2-4: (a) Second heating scans of RR P3HTs at 20 C/min from DSC. Data is
vertically shifted for clarity. (b) Derivative of heat flow shown in (a). ........................... 63
Figure 2-5: GPC traces of PFTBTs in 1,2,4-trichlorobenzene at 150 C determined
from a universal calibration that relies on refractive index and viscometer detectors. .... 64
Figure 2-6: Two examples of master curves for (a) storage and loss moduli and (b)
tan(δ) for RR P3HT 6 and RRa 4. Tref of 0 C. Strain amplitude of 0.001. (c)
Frequency shift factors (aT) used to generate master curves shown in (a), (b) and (d).
Equation (2-1) is fitted to aT for RRa 3 at temperatures just above Tα, which should
be between 0 and 10 C when the data deviate from the WLF fit. Below Tα the
activation energy is 65 ± 3 kJ/mol. (d) Master curve for storage and loss moduli for
RRa 3 P3HT from the terminal region to the glassy region. Tref of 0 C. ........................ 67
Figure 2-7: (a) Storage modulus (b) loss modulus as function of temperature heating
from -120 to 40 C at fixed frequency of 10 rad/s, strain amplitude of 0.001 and
heating rate of 5 C/min. Only from -35 to 40 C for RR P3HT 1 and 2. ........................... 69
Figure 2-8: G’ for the αPE side chain glass transition as a function of molecular weight.
G’ was calculated between the two local minima of G’’ of the master curves
generated for RR and RRa P3HTs shown in Figure 2-6a. ............................................... 71
Figure 2-9: Molecular weight dependence of glass transition temperatures for both RR
and RRa P3HTs. Star symbols represent Tα’s measured by DRS, while square
symbols represent rheology results measured at 10 rad/s and heating rate of 5
C/min. Green symbols correspond to the backbone segmental relaxation
temperature, Tα, and orange symbols represent the side chain relaxation temperature,
TαPE. Open symbols refer to RR P3HTs and filled symbols refer to RRa P3HTs.
Green lines (both dash and solid) correspond to the linear fits of the Flory-Fox
equation (2-2) for RR and RRa P3HTs. Orange dashed and solid lines represent the
average TαPE’s that is independent of Mn for RR P3HT (-101 ± 2C) and RRa P3HT
(-94 ± 3C), respectively. ................................................................................................. 72
Figure 2-10: (a) Frequency dependence of the dielectric loss (ε’’) and the in-phase
conductivity (σ’) for RRa 3 and RR 7 P3HTs at 20 C from 107 to 0.63 rad/s. The H-
N function is used to fit the α relaxation (ε’’ peak) for RRa 3 P3HT, and ωmax and
the dielectric strength (ε) are extracted. (b) Tα‘s are determined to be 262 K, 271 K,
274 K and 278 K for RRa 1, RRa 2, RRa 3 and RRa 4 P3HTs, respectively, by
extrapolating the VFT fits of the ωmax to 0.01 rad/s. ........................................................ 74
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Figure 2-11: In-situ heating WAXS data for PFTBT 2 that was previously quenched
from 270 C to room temperature in the rheometer. ........................................................ 76
Figure 2-12: Storage and loss moduli versus temperature for PFTBT 2 at 1 rad/s for
samples with two different crystallization procedures: quenched from 270 oC to
room temperature (Quenched) and isothermally crystallized at 195 C for 30 mins
before cooling to room temperature (Crystallized). ......................................................... 76
Figure 2-13: DSC traces for the three PFTBTs after isothermal crystallization at 195 C
for 30 mins, at a heating rate of 20 C/min. ..................................................................... 77
Figure 2-14: (a) Temperature ramp results at frequency of 1.0 rad/s and heating rate of
5 C/min, after isothermally crystallizing at 195 C for 30 mins. For temperatures
below 220 C, 3-mm diameter parallel plates were used, while 8-mm plates were
used above 220 C. Only data above 80 C are shown for PFTBT 1, due to the loss
of adhesion on the parallel plates at lower temperatures. (b) Molecular weight
dependence of Tg determined from the G’’ peak at frequency of 1.0 rad/s for
isothermally crystallized PFTBTs. The dashed line is a fit to the Flory-Fox equation.
Tg determined from rheomery at 10 rad/s and by DSC are also shown for
comparison. ...................................................................................................................... 78
Figure 3-1: Chemical structures of conjugated polymers used in this work. Each of them
has conjugated backbone with alkyl side chain. Polymers that are highlighted in red
belong to Group 1 (thiophene-rich polymers), others belong to Group 2 (phenyl-rich
polymers). ........................................................................................................................ 91
Figure 3-2: Finding the glass transition temperature using rheology. (a) Storage (G’) and
loss (G”) moduli for regiorandom P3ATs with different side chain lengths (P3BT,
P3HT, P3OT and P3DDT). (b) G’ and G” for regioregular P3BT (50 °C), P3OT (-17
°C), P3DT (-27 °C) and P3DDT (-18 °C), and (c) PBTTT-C14 HH (5 °C) with head-
to-head configuration. Strain amplitude of 0.001, frequency of 1.0 rad/s, heating rate
of 5 °C/min. ...................................................................................................................... 94
Figure 3-3: Tg measurements of the “push-pull” conjugated polymers for (a) PCDTBT
and PCT6BT, (b) PFTBT (126 °C), PFT6BT (79 °C) and PDPT6BT (90 °C), (c)
PF8BT (112 °C) and PF82T (102 °C), and (d) three molecular weights of
PCDTBT(107 °C, 116 °C, 119 °C). Oscillatory frequency of 1 rad/s, 5 °C/min
heating and strain amplitude of 0.001. ............................................................................. 95
Figure 3-4: Tg measurements of the polyfluorene family, namely PFH (101 °C), PFO
(71 °C) and PFDD (16 °C) with hexyl, octyl, and dodecyl side chains, respectively.
Oscillatory frequency of 1 rad/s, 5 °C/min heating and strain amplitude of 0.001. ......... 96
Figure 3-5: (a) Tg measurements by rheology for the semicrystalline conjugated
polymers with branched alkyl side chains, including PII-2T, PffBT4T-2OD,
P(NDI2OD-T2) and PTB7, are conducted at a heating rate of 5 °C/min, an
oscillatory frequency of 1 rad/s and a strain amplitude of 0.001. The side chain Tg is
more apparent and at a lower temperature than the backbone Tg. The data for PTB7
are stopped at 100 °C, above which the glue (i.e. polycyanoacrylate) between the
xiii
plate and sample softens and the data no longer represent the modulus of the sample.
The extraction of backbone Tgs of (b) PffBT4T-2OD, (c) PII-2T, (d) P(NDI2OD-
T2), (e) PTB7 are shown by fitting the temperature dependence of the loss modulus
with Gaussian peaks. The peak temperature that corresponds to each Gaussian fit is
shown in the legend, and the backbone Tgs are marked in bold. Chemical structures
of these low bandgap polymers with branched side chains are also shown as well. ........ 98
Figure 3-6: Second DSC heating scans of the polyarylene (PA) family with butyl, hexyl,
octyl, decyl side chains at 10 °C/min. Tgs are identified as the midpoints of the step
changes in heat flow: 58 °C for PA-butyl, 87 °C for PA-hexyl, 117 °C for PA-octyl,
164 °C for PA-decyl. ........................................................................................................ 99
Figure 3-7: Second DSC heating scan of the polythiophene (PT) powder at 10 °C/min.
Tg of PT is identified at 215 °C where shows a small step change in heat flow (more
clearly seen in the derivative). ......................................................................................... 99
Figure 3-8: Correlation between the side chain mass fraction (w) and the glass transition
temperature (Tg) for conjugated polymers in this work. Two groups, representing the
thiophene-rich polymers (Group 1) and the phenyl-rich polymers (Group 2), are
modeled by Equation (3-1) with fitting parameters shown in Table 3-2. ........................ 102
Figure 3-9: Extraction of the persistence length (lp = Np x l0) from the exponentially
decaying tangent-tangent correlation obtained by the freely rotating chain model for
(a) PBTTT-C14 (lp = 2.98 x 1.36 nm = 4.1 nm) and (b) PFTBT (lp = 2.65 x 2.08 nm
= 5.5 nm). ......................................................................................................................... 104
Figure 3-10: Correlation between the packing length (p) and the glass transition
temperature (Tg) on log-log scale for conjugated polymers with alkyl side chain, and
the outliers are the polyarylene (PA) family, TFB and P(NDI2OD-T2). The solid
curve is the power law fitting through most of the conjugated polymers. ....................... 105
Figure 3-11: The strength of correlation represented by the coefficient of determination
(R2) between Tg and m depends on a. The strongest correlation is achieved when the
mobility per ring is 3.6 or equivalently a = 0.6, while the correlation becomes poor if
atoms in a conjugated ring are assigned to be too immobile (a < 0.45) or too mobile
(a > 0.68) relative to the atoms on the side chain. ............................................................ 108
Figure 3-12: The general correlation between the glass transition temperature (Tg) and
the effective mobility value (m) for all 32 conjugated polymers with different
backbones and alkyl side chains. Black solid line represents the best linear fit
through all data with the coefficient of determination (R2) shown above. Group 1 is
thiophene-rich backbones and Group 2 is phenyl-rich backbones, as introduced in
Figure 3-8. ........................................................................................................................ 109
Figure 3-13: (a) Data for MPE-PPV and PS lie far below the correlation based on the
original assignment of the atomic mobility values in Table 3-2. (b) Data for MPE-
PPV and PS agree with the correlation after increasing the effective atomic value in
a phenyl ring from 0.60 to 0.72. Chemical structures of PS and MPE-PPV are shown
above. ............................................................................................................................... 111
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Figure 4-1: Chemical structure of (a) PFTBT and (b) PCDTBT. (c) Molecular weight
distribution of PFTBTs and PCDTBT obtained by high temperature 1,2,4-
trichlorobenzene GPC at 150 °C using universal calibration that relies on refractive
index and viscometer detectors. ....................................................................................... 123
Figure 4-2: The second heating scans of PFTBT 2 and PCDTBT at 20 °C/min after
isothermal annealing at 194 °C for 30 mins. The glass transition temperatures (Tg =
133 °C for PFTBT 2 and 129 °C for PCDTBT), nematic-to-isotropic transition
temperatures (TIN = 293 °C for PFTBT 2 and 274 °C for PCDTBT) and melting
temperature (Tm = 267 °C for PFTBT 2) are identified accordingly on the plot. Data
are vertically shifted for clarity. ....................................................................................... 127
Figure 4-3: Optical micrographs under crossed polarizers taken for (a) PFTBT 1 at
semicrystalline (150 °C), nematic (250 °C) and isotropic states (290 °C) and for (c)
PCDTBT at nematic (150 and 200 °C) and isotropic states (300 °C). Normalized
transmitted intensity either with or without crossed polarizers (CP) as a function of
temperature for (b) PFTBT 1 and (d) PCDTBT. Corrected normalized intensity
(hollow circles) and its derivative (solid circles) are also shown. Thicker parts of
cast films (aggregates or dust particles) appear as the black spots surrounded with
brighter region in both PFTBT and PCDTBT under crossed polarizers. ......................... 129
Figure 4-4: Temperature dependent wide-angle X-ray scattering of (a) PFTBT 2 and (b)
PCDTBT. ......................................................................................................................... 130
Figure 4-5: Temperature dependence of complex viscosity (η*), storage modulus (G’)
and loss modulus (G’’) of (a) PFTBT 2 and (b) PCDTBT at frequency of 1 rad/s and
ramp rate of 2 °C/min under oscillatory shear verifies the reversibility of the
nematic-isotropic transition. ............................................................................................. 132
Figure 4-6: (a) Strain amplitude sweep for PCDTBT at 1 rad/s and 250 °C in nematic
phase. (b) Large Amplitude Oscillatory Shear (LAOS) of PCDTBT at 250 °C with
frequency of 1 rad/s and strain amplitude of 1 for 30 mins. ............................................ 134
Figure 4-7: (a) Schematic of beam direction for 2D WAXS experiment on LAOS-
sheared PCDTBT (250 °C, 1 rad/s, 100% strain for 30 mins). 2D WAXS images
were obtained at five different positions within the sample puck, corresponding to
different local strain amplitudes (γ) as labeled from 0.05 to 0.95. (b) Relative
intensity as a function of azimuthal angle (ψ) at q = 0.4 Å-1 shows increase in
anisotropy with local strain, with strong anisotropy for strain amplitude exceeding
0.5. .................................................................................................................................... 135
Figure 4-8: (a) Isotropic-to-nematic temperature (TIN) is identified as the local minimum
of complex viscosity under cooling at 2 °C/min and 1 rad/s for different molecular
weights of PFTBTs. (b) The number-average degree of polymerization (N)
dependence on TIN is fitted by Equation (4-1) such that TIN in the long chain limit is
extrapolated to 350 °C for PFTBT. .................................................................................. 137
Figure 4-9: (a) Fits of previously reported molecular weight dependences of the
nematic-isotropic transition temperatures for DEH-PPV44, P3DDT20, and P3EHT20
xv
by Equations 4-3a and 4-3b to extract nematic coupling constants. (b) Comparison
of the experimentally extracted nematic coupling constants for DEH-PPV, P3DDT,
P3EHT and PFTBT with the prediction from simulations for P3HT19. ........................... 140
Figure 4-10: Mismatch between the master curve of PFTBT 2 at Tref of 300 °C (data
points) and the BoB predictions (curves) with Mw input from universal calibration.
Red curves are BoB predictions using Me of 3.4 kg/mol in order to match the width
of the rubbery plateau for the master curve, but leading to too high modulus level
than the data. But if Me of 11 kg/mol is chosen (Green curves), which is the best
fitted parameter in Figure 4-11 for PFTBT 2, BoB predicts a barely entangled
response. ........................................................................................................................... 143
Figure 4-11: (a) Predictions from the BoB model for the master curve of PFTBT 2 in its
isotropic phase at a reference temperature of 300 °C by (a) varying Me while fixing
Mw = 115 kg/mol and the shape of the molecular weight distribution, and (b) varying
Mw while fixing Me = 11 kg/mol and the shape of the molecular weight distribution.
(c) Master curves of PFTBT 1, PFTBT 2 and PCDTBT at same Tref of 300 °C with
the best BoB prediction (fitting parameters shown in Table 4-3). ................................... 144
Figure 4-12: Temperature ramp for quenched PFTBT 1 and PFTBT 2 from 50 to 150 °C
with a frequency of 1 rad/s and a strain amplitude of 0.002 at a heating rate of 5
°C/min. Tg = 112 oC for PFTBT 1 and Tg = 116 oC for PFTBT 2. Smaller τe for
PFTBT 1 leads to smaller τ0 and faster Kuhn monomer relaxation, meaning a lower
glass transition temperature.............................................................................................. 145
Figure 4-13: Good agreement between master curves at Tref of 240 °C and the BoB
predictions with Mws from static light scattering (SLS) for two different batches of
RRa P3HTs. Mws from SLS for these two RRa P3HTs are 101 kg/mol and 110
kg/mol, respectively11. ..................................................................................................... 146
Figure 4-14: (a) Frequency sweep results of PFTBT 2 at 270 °C (in the nematic phase)
and at 295 °C (in the isotropic phase) show the effect of nematic ordering on chain
entanglements. (b) Frequency sweeps of PCDTBT at 250 °C (in the nematic phase)
and at 270 °C (in the isotropic phase). (c) Temperature dependence of the G’, G’’
crossover frequency (ωc), which represents the lower frequency boundary of the
entanglement plateau and is obtained by multiwave temperature ramp test from 300
to 240 °C at 2 °C/min at a frequency of 1 rad/s and harmonics of 2, 4, 7, 14, 27, 52,
100 for PFTBT 2. Black symbols represent the directly measured crossover
frequency within the probed region, namely between 1 and 100 rad/s. Gray symbols
represent the extrapolated crossover frequencies based on the 2nd order interpolation
fit to measured multiwave frequency data. The change in the entanglement plateau
width is caused by the isotropic to nematic transition. .................................................... 147
Figure 4-15: (a) Master curves of G’, G’’, and tan(δ) with Tref = 300 °C, (b) horizontal
shift factors, aT, and vertical shift factors, bT, in the isotropic phase (red) and the
nematic phase (blue) for molten PFTBT 2. Time-Temperature superposition (tTs)
fails for PFTBT 2 between 285 and 270 °C (not shown) because this is the biphasic
region and below 230 °C (not shown) due to crystallization. (c) Master curves with
Tref = 300 °C and (d) shift factors in the isotropic phase (red) and the nematic phase
xvi
(blue) for molten PFTBT 1. tTs fails for PFTBT 1 between 270 and 250 °C (not
shown) because this is the biphasic region and below 190 °C (not shown) due to
crystallization. The dashed lines in (b) and (d) are Arrhenius fits to extrapolate
activation energies in both the nematic (111 ± 10 kJ/mol for PFTBT 1 and 96 ± 10
kJ/mol for PFTBT 2) and the isotropic phases (203 ± 12 kJ/mol for PFTBT 1 and
211 ± 10 kJ/mol for PFTBT 2). ........................................................................................ 150
Figure 4-16: (a) Master curves of G’, G’’ and tan(δ) with Tref = 300 °C, (b) horizontal
shift factors aT, and vertical shift factors, bT, in the isotropic phase (red) and the
nematic phase (blue) for PCDTBT. tTs fails for PCDTBT between 250 and 270 °C
(not shown) because this is the biphasic region. (c) The full master curve for the
nematic glass-former PCDTBT between 90 and 250 °C. Black guidelines are drawn
to extract different time scales for Kuhn monomer relaxation (τ0), reptation in the
nematic phase (τrep,nem), and reptation in the isotropic phase (τrep,iso). The dashed line
in (b) is an Arrhenius fit in the isotropic phase and a WLF fit in the nematic phase. ...... 151
Figure 4-17: Schematics of entanglement tubes for test chain (purple) in the nematic
phase (blue) and the isotropic phase (red). Two constraining tubes imposed by the
surrounding chains in the nematic phase can be imagined to be perpendicular and
parallel to the backbone, leading to two different tube diameters, dt,nem,⊥ (green) and
dt,nem,// (orange), respectively. The average tube diameter in the nematic phase is
represented by dt,nem (black), which is still larger than dt,iso in the isotropic phase, thus
providing an explanation of the decrease in tube diameter when transition from the
nematic to the isotropic phase. ......................................................................................... 154
Figure 5-1: (a) Zimm plot of RRa 4 P3HT in chlorobenzene. (Mw: weight-average
molecular weight, 110 ± 2 kg/mol; Rg: radius of gyration, 15.4 ± 1.1 nm). (b) Zimm
plot of RR 6 P3HT in chlorobenzene. (Mw: weight-average molecular weight, 75 ± 2
kg/mol; Rg: radius of gyration, 13.8 ± 1.7 nm). K: optical constants, 2.17 × 10-7
mol ml/g2 for RRa 4 and 2.89 × 10-7 for RR 6; c: polymer concentration (g/ml);
ΔRθ: Excess Rayleigh ratio; θ: scattering angle. .............................................................. 164
Figure 5-2: The cumulative weight fraction versus the log of molecular weight for RR 1
P3HT by GPC (blue curve) which is discretized into 20 monodispersed components
(red “stair steps”). ............................................................................................................ 169
Figure 5-3: Huggins plot for multiple molecular weights of (a) RR P3HTs and (b) RRa
P3HTs in chlorobenzene at 30.0 °C. (c) Mark-Houwink plot of both RR and RRa
P3HT on log-log scale that shows same power exponent of 0.76 (good solvent). .......... 171
Figure 5-4: Stockmayer-Fixman extrapolations of the intrinsic viscosity to the θ solvent
condition that allows calculating the unperturbed chain conformations and the
corrected persistence lengths for both RR and RRa P3HTs. ............................................ 174
Figure 5-5: Master curves and BoB predictions for (a) RRa P3HTs and (b) RR P3HT at
the reference temperature of 240 C. (c) Comparison of RR 6 and RRa 4 P3HT
showing the difference in chain entanglements at same Tref of 240 °C. ........................... 176
xvii
Figure 5-6: Extrapolation of zero shear viscosity by fitting the frequency dependent
complex viscosity with the Carreau model for (a) RR P3HT and (b) RRa P3HT. (c)
The molecular weight dependence of the zero shear viscosity for both RR and RRa
P3HTs. Tref = 240 °C. ....................................................................................................... 178
Figure 5-7: Temperature dependent wide-angle X-ray scattering for (a) RRa 4 P3HT
and (b) RR 3 P3HT. ......................................................................................................... 181
Figure 5-8: Check the Cox-Merz rule by comparing the steady shear ( η(γ)) and the
dynamic viscosities (|η*ω|) for both RR and RRa P3HTs at 240 °C using a cone and
plate geometry. ................................................................................................................. 182
Figure 5-9: Comparing the experimentally measured RRa P3HT with the universal
prediction between the dimensionless plateau modulus and the dimensionless Kuhn
monomer density proposed by Everaers et. al.14 b is the Kuhn Length (twice of lp)
and k is the Boltzmann constant. ...................................................................................... 183
Figure 6-1: (a) The molecular weight dependence of the long-time stress relaxation for
RR P3HT at 130 °C, except for RR 1 at 25 °C. (b) Vertically shifted stress relaxation
results with respect to RR 5 display a faster relaxation rate for a lower molecular
weight of RR P3HT. Step strain = 0.01 is well within the linear region. RR 5, RR 4,
RR 3, and RR 2 each have tie chains, while RR 1 does not, because the crystallinity
is only 0.15. ...................................................................................................................... 196
Figure 6-2: (a) Frequency sweep for semicrystalline RR 5 P3HT at different
temperatures with an oscillatory strain of 0.01. (b) Stress relaxations at 100 and 230
°C for RR 5 P3HT with a step strain of 0.08 and 0.03, respectively. .............................. 197
Figure 6-3: (a) Vertically shifted second heating scans for RR 4 and RRa P3HT blends
at 10 °C/min in DSC. (b) The crystallinities in the blends calculated from (a) are
compared with the expected crystallinities from the product of crystallinity in pure
RR 4 P3HT and the RR blend ratios. The crystallization temperature is chosen to be
200 °C for both 0% RRa and 50% RRa P3HT, 180 °C for both 90% RRa and 95%
RRa P3HT, and 170 °C for both RRa 96% and RRa 98%. .............................................. 199
Figure 6-4: Master curves at Tref = 130 °C in the semicrystalline state (except for 100%
RRa) between 30 °C and the crystallization temperature: 200 °C for 0% RRa (a) and
50% RRa (b), 180 °C for 90% RRa (c) and 95% RRa (d), and 170 °C for 96% RRa
(e) and 98% RRa (f). (g) The master curve for the pure RRa P3HT is constructed
between 260 and 30 °C. (h) The temperature dependence of the horizontal shift
factors at Tref = 130 °C for all the blends, pure RR 4 P3HT and RRa P3HT.
Horizontal shifts only based on tan(δ). ............................................................................ 202
Figure 6-5: Stress relaxations for all the P3HT blends at 130 °C with a step strain of
0.01. .................................................................................................................................. 203
Figure 6-6: (a) As the RRa content in the blends increases, the entanglement width (i.e.
τrep/τe) decreases and the entanglement molecular weight (Me) increases except for
xviii
the 98% RRa P3HT. (b) The width of the entanglement plateau (τrep/τe) versus the
ratio of RRa P3HT Mw over the extracted Me in the blends. ............................................ 205
Figure 6-7: The extracted tie chain density (ρx) is compared with the previously reported
mobility11 as a function of RRa P3HT content in the blends. .......................................... 206
Figure 6-8: (a) Small-angle X-ray scattering profiles at 130 °C for P3HT blends
collected from our lab X-ray source (Xeuss) and for pure RR P3HT collected from
the beamline in Lawrence Berkeley National Laboratory. (b) The Lorenz-corrected
SAXS profile (Iq2 versus q) in order to better locate the peak position (or the long
period spacing). (c) The long-period spacing (L) and the estimated intercrystalline
distance (la) increases as more RRa P3HT content is added except for the pure RRa
P3HT. ............................................................................................................................... 208
Figure 7-1: Chemical Structures of PF6BT, PCT6BT and PBTTT-C14 HH. ....................... 218
Figure 7-2: (a) Master curves for two different molecular weights of PFT6BTs at Tref of
140 °C. Horizontal shifts only based on tan(δ) only. (b) Grazing incidence wide-
angle X-ray scattering (GIWAXS) of PFT6BT 1 at room temperature. (c) Second
heating scan of PFT6BT 1 at 10 °C/min detects only Tg = 92 °C. ................................... 219
Figure 7-3: Master curve for PCT6BT at Tref of 140 °C spans between 120 and 220 °C.
Horizontal shifts only based on tan(δ) only. .................................................................... 220
Figure 7-4: (a) Master curves for PBTTT-C14 HH at Tref of 100 °C. Horizontal shifts
only based on tan(δ) only. (b) Oscillatory temperature ramp test for PBTTT-C14 HH
at a heating rate of 5 °C/min and an oscillatory frequency of 1 rad/s. (c) Second
heating scan in DSC for PBTTT-C14 HH at 10 °C/min shows no clear transitions
between 0 and 300 °C. ..................................................................................................... 221
Figure 7-5: Master curves for RRa P3BT, P3HT, P3OT, and P3DDT at Tref of 240 °C........ 223
Figure 7-6: Master curve for polyarylene-decyl at Tref of 100 °C. ........................................ 223
Figure 7-7: Graessley-Edwards plot that includes the data of various conjugated
polymers and the Everaers’ prediction based on the data of flexible polymers and
stiff biopolymers. ............................................................................................................. 225
head-to-head configuration (PBTTT-C14 HH) and with the tail-to-tail configuration
(PBTTT-C14 TT). ............................................................................................................ 226
Figure A-1: Glass transition study of PII-2T-PSx series at a heating rate of 5 ºC/min and
an oscillatory frequency of 1.0 rad/s. Chemical structure of PII-2T-PSx is shown
above. ............................................................................................................................... 229
Figure B-1: DSC heating scans for PBTTT-C14 TT (structure shown above) at 20
ºC/min with different thermal histories show the rich thermal phase transitions: the
xix
melting transitions of side chain (Tm, side chain = 60 ºC) and backbone (Tm, backbone = 120
ºC), and the smectic-to-istropic transition (Tc = 230 ºC). ................................................. 231
Figure B-2: Optical images of PBTTT-C14 TT taken at 150 ºC under (a) no polarizers
(b) cross polarizers. .......................................................................................................... 232
Figure B-3: Temperature dependent wide-angle X-ray scattering for PBTTT-C14 TT. ....... 233
Figure B-4: (a) Master curves of PBTTT-C14 TT for both smectic phase and isotropic
phase at the same Tref of 240 ºC. (b) Oscillatory temperature ramp of PBTTT-C14
TT at a heating rate of 5 ºC/min and a frequency of 1 rad/s. ........................................... 234
Figure B-5: Temperature ramp test for TQ1 at a heating rate of 5 ºC/min and an
oscillatory frequency of 1.0 rad/s. Chemical structure for TQ1 is shown above. ............ 235
Figure C-1: Linear fits of the z-average decay constant (Γ) as a function of the square of
scattering vector (q2) for dilute solutions of RRa P3HT in chlorobenzene (CB) and in
tetrahydrofuran (THF) at 25 ºC with a concentration of 0.5 mg/ml. The diffusion
constant is extracted from the slope (3.67 ± 0.08 x 10-11 in CB and 6.21 ± 0.02 x 10-
11 m2/s in THF), and the y-intercept is set as zero. ........................................................... 238
Figure D-1: (a) Temperature dependent Raman spectroscopy for RR P3HT (Mw = 50.8
kg/mol) from 40 to 270 °C. Peaks are labeled according to the literature.1 (b) Zoom-
in plot of (a) to show the shifting in C=C band position when RR P3HT melts. (c)
Example of probing the orientation alignment in RR P3HT at 120 °C by changing
the polarization angle of the laser from 0° to 90°. A 785 nm laser with a power of
500 μW is used for temperature dependent study while 1 mW for the polarization
study. Grating size is 300. ................................................................................................ 241
Figure D-2: Polarization angle dependence of the C=C peak area for both RR P3HT (Mw
= 50.8 kg/mol) and RRa P3HT (Mw = 110 kg/mol) at (a) 300 K (b) 543 K (270 °C).
A 785 nm laser with a power of 1 mW is used for the polarization study. Grating
size is 300. The area of C=C peak has been normalized by the polarization angular
dependent laser power. ..................................................................................................... 243
Figure E-1: Linear fit of the change in refractive index versus the concentration for PFO
in chlorobenzene (CB) at 30.0 °C. The differential refractive index is extracted from
the slope (0.113 ± 0.002 ml/g), and the y-intercept is set as zero. ................................... 244
Figure E-2: Zimm plot for PFO in chlorobenzene (CB) at 30.0 °C. The weight average
molecular weight (M w ), the z-average radius gyration (R
g,z ) and the second virial
coefficient (A 2 ) are extracted. ........................................................................................... 245
Figure F-1: Temperature dependent small-angle X-ray scattering (SAXS) for different
molecular weights of RR P3HTs: (a) RR 1 (Mw = 29.5 kg/mol), (b) RR 2 (Mw = 32.7
kg/mol), (c) RR 3 (Mw = 50.9 kg/mol), (d) RR 4 (Mw = 57.4 kg/mol), (e) RR 5 (Mw =
74.6 kg/mol). (f) Comparison of SAXS profiles for different molecular weights of
RR P3HTs at 190 ºC. ....................................................................................................... 247
xx
LIST OF TABLES
Table 1-1: Absorption edges for common conjugated polymers in dilute solutions at
room temperature ............................................................................................................. 35
Table 2-1: Characteristics of P3HTs used in this study. ......................................................... 59
Table 2-2: Summary of glass transition temperatures for all P3HTs studied in this work. .... 69
Table 2-3: Flory-Fox equation parameters for RR P3HT and RRa P3HT. ............................ 72
Table 2-4: Fitting parameters of Equation (2-4) for α transition of RRa P3HT by DRS. ...... 74
Table 2-5: Glass transition temperatures of PFTBTs. ............................................................ 78
Table 3-1: Summary of the glass transition temperature (Tg), the determination method,
the effective mobility value (m), the side chain mass fraction (w), the mass density
(ρ), the persistence length (lp), and the packing length (p) of the conjugated polymers
in this work....................................................................................................................... 100
Table 3-2: Fitting parameters of the Fox Equation for Groups 1 and 2 of the conjugated
polymers. .......................................................................................................................... 102
Table 3-3: Assignment of effective atomic mobility value for each atom in different
units, namely phenyl rings, thiophene rings, alkenyl or carbonyl groups, flexible C-C
or C-O side chains. ........................................................................................................... 106
Table 4-1: Characterization of PFTBTs and PCDTBT based on GPC with universal
calibration......................................................................................................................... 123
Table 4-2: Summary of TINs for PFTBT 2 and PCDTBT obtained from different
methods, with heating rate in parentheses. ....................................................................... 133
Table 4-3: BoB fit parameters for PFTBTs and PCDTBT in the isotropic phase at Tref =
300 °C .............................................................................................................................. 145
Table 5-1: Characteristics of P3HTs used in this study. ......................................................... 165
Table 5-2: Intrinsic viscosities and overlap concentrations for RR and RRa P3HTs in
chlorobenzene at 30.0 °C. ................................................................................................ 172
Table 5-3: Extracted entanglement time scale (τe) and entanglement molecular weight
(Me) for RR and RRa P3HTs by BoB fits in Figure 5-5. The tube diameter (dT) is
calculated from the extracted Me and the lp of 3.0 nm. .................................................... 177
Table 6-1: Characteristics of P3HTs used in this work. ......................................................... 192
xxi
Table 6-2: Summary of the directly measured plateau moduli (G and Gt), entanglement
time (τe -1), and reptation time (τrep
-1) from Figure 6-4 and Figure 6-5 for all P3HT
blends and pure RR and RRa P3HTs at 130 °C. .............................................................. 204
Table 6-3: Summary of the extracted parameters for entanglements, tie chains, and
trapped entanglements in all P3HT blends and pure RR and RRa P3HTs at 130 °C. ..... 204
Table 6-4: Predicted probabilities of tie chains (Pt) and tight folds (Ptf), and the average
molecular weight of a tie chain (Mt) based on the Gambler’s Ruin method35 using the
estimated intercrystalline distance in the P3HT blends. The molecular weight of a tie
chain (Mx) extracted from rheology in Table 6-3 is also added here to compare with
Mt. ..................................................................................................................................... 209
Table 7-1: Summary of the chain dimensions and plateau moduli for various conjugated
polymers. .......................................................................................................................... 224
Table C-1: Comparison between the radius of gyration (Rg) and the hydrodynamic
radius (Rh) for RRa P3HT in two different solvents: chlorobenzene and
tetrahydrofuran ................................................................................................................. 238
xxii
ACKNOWLEDGEMENTS
First of all, I would like to thank the loving God and all my church family for the strength
and prayers that helped me over the past few years. Then, I would like to thank my two advisors,
Prof. Enrique Gomez, and Prof. Ralph Colby, for leading me onto a challenging but fulfilling
research journey. Not only I learned a ton from their research expertise, but both of them are my
role models for being an excellent teacher, a critical researcher, a responsible mentor, and a
wonderful human being. I also sincerely appreciate their guidance and patience for helping me
develop a positive attitude when encountering difficult problems in research. Finally, their passion
for research strongly inspired me to keep exploring the unknown and not to be afraid to fail. Also,
I would like to thank my committee members, Prof. Scott Milner, and Prof. John Asbury, for their
time and advice. Special thanks to Prof. Milner for the insightful comments at the monthly NSF
DMREF meeting and a great polymer course that he taught me.
Also, I would not be able to succeed without the help of my labmates, undergraduate
mentees, and collaborators. Thank you to Melissa Aplan and Youngmin Lee for providing me with
various conjugated polymers to perform our study and the helpful discussions about the
fundamentals of polymer synthesis. I also would like to thank Jiho Seo for helping me maintain the
rheometers and many interesting conversations on polymer physics. Sincere thanks to all of my
labmates in both Colby and Gomez groups. I also would like to express my special appreciations
to all of my undergraduate mentees, including Albree Weisen, Su Tang, Jaewook Lee, Mingyue
Zhang, for their contributions in rheology characterization, intrinsic viscosity measurement,
polarized optical microscopy, and X-ray scattering. Thank you to Prof. Christian Müller’s group at
Chalmers University of Technology for the help with GPC measurements, Nichole Wonderling for
training me on the X-ray scattering and Dan Ye for the help on aligning the laser for the light
scattering instrument many times.
xxiii
Finally, I must give special honors to my family members for their unfailing love, care and
support, including my parents, Changlin Xie and Xiaohong Lu, my host parents, Richard &
Mechele Raml, and my dearest wife, Yizhou Fang. Thank you all so much for shaping me into the
person I have become.
This research is supported by the National Science Foundation, Grant DMREF Award No.
1629006. We gratefully acknowledge the financial support. The findings and conclusions in this
dissertation do not necessarily reflect the view of the funding agency.
xxiv
To my one and only love of my life, BeiBei.
Chapter 1
The continued drive towards wearable electronics will require deformability as never
before.1-7 Significant recent advances have demonstrated the potential for stretchable electronics in
artificial skin and wearable biometrics by integrating rigid devices with flexible substrates such as
polydimethylsiloxane, polyethylene terephthalate, and polyimide.6, 8-14 Conjugated polymers may
fill a need beyond substrates as deformable semiconductors, because of their delocalized π orbitals
along a covalently linked backbone that allows electron or hole conduction within a stretchable
network.13, 15, 16 Nevertheless, as materials with more efficient charge transport have been
introduced, empirical trends linking stiffness and charge transport performance have also arisen.17,
18
To first order, stiffer backbone structures that impose longer conjugation lengths lead to
fast intrachain charge mobilities along the backbone, which in turn can lead to macroscopic
enhancement of transport but possibly more rigid behavior as well.19 Aiming to achieve both highly
flexible and conductive properties, one simple solution to circumvent this trade-off is to blend
flexible insulating polymers with semiconducting polymers; nevertheless, the chemical
dissimilarity between the polymers might cause macroscopic phase separation and deteriorated
performance in devices over time.20 Similarly, blends of regiorandom isomers that are amorphous
with low charge mobilities and regioregular counterparts of the same polymer with high charge
transport efficacy, such as in blends of regiorandom and regioregular poly(3-hexylthiophene-2,5-
diyl) (P3HT),21 lead to remarkable materials with high performance and flexibility. Unfortunately,
2
blending of materials with controlled isomerism has not been demonstrated as a general approach
beyond P3HT.
Alternatively, some efforts have attempted to incorporate various flexible moieties as either
a soft block in a block copolymer structure22-24 or as grafted flexible side chains24, 25 of a brush
architecture to improve the overall flexibility of the film without sacrificing charge transport. The
addition of small amounts of plasticizers (2.0 vol%) to active layers can also lower the modulus
significantly without compromising on device performance, and has been demonstrated for
polymer-fullerene solar cells.26, 27 These examples highlight the potential to develop new materials
with the tremendous synthetic versatility of polymeric semiconductors.
The mechanical properties of conjugated polymers have been quantified in terms of the
tensile modulus, elongation to failure, and tensile strength. Beyond these parameters, opportunities
lie in elucidating fundamental insights on charge transport with mechanical measurements. For
example, rheological measurements and dynamic mechanical analysis can map phase behavior and
reveal the complex microstructure of semicrystalline or liquid crystalline polymers. Recent work
has demonstrated that oscillatory shear rheology can clearly delineate the glass transition
temperature (Tg) as a function of molecular weight of conjugated polymers such as regiorandom
P3HT, regioregular P3HT, and poly((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(thiophen-5-yl)-
2,1,3-benzothiadiazole]-2′,2″-diyl) (PFTBT).28 Both a side chain Tg ~ -100 °C and a backbone Tg ~
10 °C were clearly identified for P3HT, while PFTBT shows only one Tg at 144 °C. This is why
the 20 °C modulus of PFTBT is 700 MPa, far exceeding that of regioregular P3HT (~ 150 MPa).
Because chain motion depends on the temperature relative to Tg, these measurements are crucial
for predicting morphological stability and for optimizing thermal or solvent annealing protocols
that aim to enhance performance in electronic devices.
Despite recent progress, many opportunities for new insights exist. Although in principle
rheology yields signatures of the liquid crystal-to-isotropic clearing transition temperature (Tc), this
3
approach for mapping the phase behavior has not been applied to conjugated polymers. The number
of tie chains bridging crystals governs the semicrystalline modulus and is hypothesized to limit
charge conduction, but no current estimates of tie chain densities exist for conjugated polymers.
Entanglements, characterized in terms of the entanglement molecular weight (Me) that is obtained
from the plateau modulus in the amorphous liquid phase, have also not been examined for
conjugated polymers. We propose that Tg, Tc, Me and tie chain density can be obtained from
rheology, and that they are the missing links between molecular parameters such as the persistence
length, packing length and side chain volume fraction, and macroscopic mechanical and conductive
properties.
In this dissertation, we focus on connecting mechanical properties of conjugated polymers
with microstructural insights gained by linear viscoelastic measurements. We begin with recent
progress on mechanical measurements of conjugated polymers as thin films (thickness ≤ 100 nm)
and as bulk samples. Then, we highlight several microstructural parameters, including Tg, Me, Tc
and tie chain density, that directly or indirectly impact charge transport, and discuss the
effectiveness and the challenges of characterizing these parameters through rheology. We also
summarize current empirical correlations trying to connect mechanical and conductive properties
of conjugated polymers based on the proposed semicrystalline morphology. Furthermore, we
summarize some background knowledge on various techniques that determine the chain
dimensions of conjugated polymers in dilute solutions. Finally, we close with a dissertation
overview that outlines the following chapters with a goal of connecting the fundamental properties
of conjugated polymers to the mechanical performances in stretchable electronics.
4
Characterizing the mechanical properties of conjugated polymers can be classified into
either thin film or bulk measurements. Figure 1-1 highlights two methods to measure the modulus
for polymer thin films, buckling of films on elastomers21, 27, 29-31 and tensile tests on water 16, 32, 33.
Three separate thin film experiments on elastomer determine the plane-strain modulus, the yield
strain and the fracture strain of thin films.33, 34 A thin film is prepared on top of a soft and compliant
elastomer, such as cured poly(dimethylsiloxane) (PDMS). Firstly, by applying a small compressive
strain (typically less than 2% strain),29 wrinkles appear on the thin film. The plane-strain modulus
of film is extracted by fitting the wrinkle wavelength dependence on the film thickness with 34

3 (1-1)
where and are the plane strain moduli of the film and the substrate, respectively, and
are the Poisson’s ratios of the film and substrate, respectively, d is the wavelength of the buckled
film, and h is the film thickness. Secondly, by cyclically increasing and then releasing strain on the
film-coated PDMS substrate, the yield strain of the thin film is reached when plastic deformation
occurs and wrinkles remain after the strain release.33 Thirdly, the crack-onset strain can also be
estimated as the strain at which the pinholes and voids start to appear in the film under tension.33
Tensile tests on water use a hydrophobic conjugated polymer thin film, floating on top of water.
PDMS is used to grip the ends of the film and tension is applied at a slow strain rate until the film
ruptures.16 Details of the experimental setup can be found elsewhere.32 The resulting stress-strain
curves show an elastic response at low strain, a yield point, strain hardening/plastic deformation,
and the fracture point, as expected for polymers.
5
Comparing the tensile modulus, the yield stress, and the strain to fracture obtained by both
methods shown in Figure 1-1c for regioregular P3HTs, it is apparent that low molecular weight
polymers have a lower strain at fracture. Most likely, the lack of tie/bridging chains or
entanglements connecting the crystals for low molecular weight chains (Mn = 15 kDa by GPC
relative to polystyrene standards, overestimating actual molecular weight35) makes those films
brittle. Quantitatively, however, the strain at fracture differs dramatically, as shown in Figure 1-1c,
especially for the higher molecular weight P3HTs. Film roughness, voids within films, and different
10 20 30 40 50 60 70 80 90
0
20
40
60
80
100
120
C
Figure 1-1: Comparison of two common mechanical measurement techniques for thin films of
conjugated polymers: (a) tensile test on water and (b) compressional buckling test on elastomer.
Regioregular P3HTs with different molecular weights are shown as an example.33 (c) The
molecular weight dependence of the fracture strain and fracture stress obtained by these two
methods for regioregular P3HTs. Data are taken from 33.
6
strain modes/rates could lead to problems and differences in stress-strain curves between these two
methods.33 Since both fracture strain and fracture stress increase with molecular weight, high
molecular weight polymers are vital for good mechanical properties, as is true for all polymers.
Although dynamic mechanical analysis (DMA) is typically done on bulk samples, DMA
under tension has been recently demonstrated for conjugated polymer thin films by reinforcing the
polymer with either a stainless steel “materials pocket” 36, woven glass fibers37 or thin polyimide
substrate38 before loading. Films are either directly enclosed by the stainless steel pocket, deposited
on thin polyimide substrate, or solvent cast onto the woven glass fibers that are at 45° with respect
to the tensile direction, so that the tensile load is mostly on the polymer film rather than the glass
fibers, as shown for poly[2,3-bis(3-octyloxyphenyl)quinoxaline-5,8-diyl-alt-thiophene-2,5-diyl]
(TQ1) in Figure 1-2.37 The phase angle (δ) is defined as between the applied oscillatory strain and
the measured oscillatory stress, such that tan (δ) can be plotted versus frequency or temperature.
As a consequence, this DMA thin film test offers higher sensitivity than conventional differential
scanning calorimetry (DSC) to probe thermal transitions, such as melting and glass transitions for
the backbone or for side chains. Figure 1-2 shows clear local maxima of tan(δ) that are signatures
of thermal transitions; in this case, the authors attribute the transition near 0 oC to the glass transition
of the side chains, and the transition near 100 oC to the backbone Tg. Nevertheless, due to the
undefined sample geometry for both loading techniques in thin-film DMA, absolute values for the
modulus cannot be extracted. Without accurate moduli, thermal transitions are harder to identify,
as glass transitions, side chain melting, melting or smectic-to-isotropic transitions of conjugated
polymers all exhibit local maxima in tan(δ). While a nematic-to-isotropic transition doesn’t exhibit
such a signature in tan(δ), it is easily detected by the unique behavior of viscosity increasing with
temperature, as detailed in Section 1.4.1.
7
Some methods, such as nanoindentation39 or scanning probe microscopy40, do not rely on
thin film geometries, although they measure mechanical properties near a free surface. As a result,
the measured modulus depends on both the indentation depth and the film thickness; the origin of
these dependences is still under debate, with artifacts, true material response, or surface-probe
interactions as possible candidates. Specifically, the modulus of a thin film is observed to reach the
bulk value only when the indentation depth is relatively large.41, 42 For spin-coated polymer films
with thicknesses below a few hundreds of nanometers, the apparent modulus is considerably higher
than the bulk value, possibly due to a stiffening effect from a rigid substrate43, 44, interactions
between probe and polymer45 or strongly stretched chains in spin-coated films. Only recently, this
substrate stiffening effect has been separated from the thickness dependence of the modulus with
extensive finite element simulations.46 Overall, it remains unclear whether accurate values for the
modulus can be achieved for polymer thin films by nanoindentation that would be representative
of the modulus in a device.
Because conjugated polymers are often used as thin film active layers in electronic devices,
one might assume that mechanical testing in thin film geometries is needed. The glass transition of
Figure 1-2: Thin-film DMA for conjugated polymers. Solution-cast conjugated polymer films are
reinforced by woven glass fibers.37 This approach is more sensitive for glass transition temperatures
(Tg and sub Tg) of conjugated polymers than DSC, but accurate modulus values cannot be extracted
due to a poorly defined sample geometry.37
8
polymer thin films has been shown to differ by as much as 50 degrees from the bulk in some
cases.47-51 But, the tensile modulus extracted from buckling experiments for polystyrene is found
to be independent of film thickness from 30 to 250 nm, and agree well with bulk values.34 Tensile
tests on water for Au thin films show roughly a 15% lower modulus as the thickness decreases
below 100 nm.16, 32 As such, we propose that bulk measurements can yield important insights into
the properties of conjugated polymers, if the morphology of the bulk samples are comparable to
that of thin films.
Conventional mechanical tests of bulk samples, such as tensile tests, are usually carried out
by first melt compressing polymer powders into “tapes” or “dog bone” shapes.52 In Figure 1-3a,
bulk tensile tests on regioregular P3HTs exhibit the expected dependence on molecular weight
similar to that of the thin film tensile test on water. Nevertheless, bulk tensile tests require much
more material (at least 300 mg) than thin film methods (approximately 5mg), and both require
replicate runs for good statistics, particularly for stress and strain at failure.
Figure 1-3: Examples of the tensile and the shear measurements of bulk samples for conjugated
polymers. (a) Uniaxial tensile test at room temperature for melt-pressed regioregular P3HT strips
of different molecular weights.52 (b) Schematic of a vacuum-assisted molding setup to obtain void-
free and undegraded P3HT disks (pictures shown with 3-mm diameter and 1-mm thickness) for
shear rheology measurements.
9
Therefore, another approach that locates Tg with high accuracy and low mass requirement
is to use 3 mm diameter disks in rotational shear rheometry. Only approximately 15 mg of material
is needed and recoverable after the test. Samples can be molded inside a glovebox to remove all
bubbles and minimize degradation as shown in Figure 1-3b. In addition, linear viscoelastic rheology
can distinguish among the various thermal transitions found in conjugated polymers, such as the
glass transition, melting of the backbone or side chains, and liquid crystal to isotropic transitions,
based on a combination of the value for complex modulus and the temperature, time, and frequency
dependence. As described in the next section, solid versus liquid response can be identified from
the magnitude of the storage and loss moduli and their frequency dependence; whether
semicrystalline or not, polymer glasses usually have shear storage moduli between 0.1 and 3 GPa,
and there are unique signatures in the modulus through liquid crystal to isotropic transitions as well.
These various thermal transitions could potentially confound data obtained through techniques such
as DSC or polarized optical microscopy. For instance, reported values for the glass transition
temperature by DSC vary significantly from -14 to 140 C for poly(3-hexylthiophene-2,5-diyl)
(P3HT).36, 53-57
curve by superimposing the linear viscoelastic data at different temperatures fully characterizes the
rheological response of the polymer melt. Example of the master curve is demonstrated in Figure
1-4a that shows the complex moduli that vary between kPa and GPa for about 25 decades in
frequency for a regiorandom (RRa) poly(3-octylthiophene-2,5-diyl) (P3OT) collected with
torsional DMA.58 Furthermore, the temperature dependence of the corresponding shift factors can
be fitted with two known models (i.e. Williams–Landel–Ferry (WLF) equation59, Arrhenius
equation) in Figure 1-4b, thereby extracting more microstructural insights regarding the glass
transition process, such as the Vogel temperature at which the liquid state free volume extrapolates
linearly to zero, the activation energy for the Arrhenius dependent side chain glass transition, and
10
the glass fragility (or the sharpness of the glass transition). In Figure 1-4b, the horizontal shift
factors are shown from the terminal region to the backbone Tg of -20 °C, and, based on the WLF
fit, the backbone relaxation of RRa P3OT corresponds to a relatively “strong” glass with a extracted
Vogel temperature of -99 °C.
1.3 Glass Transition and Chain Entanglements
Two key parameters that dictates the mechanical properties of conjugated polymers are the
glass transition temperature (Tg) and the entanglement molecular weight (Me). At low temperature,
the glassy modulus dominates, while at even higher temperatures, the frequency dependence in the
linear viscoelastic regime might be described by the tube model if well above the entanglement
molecular weight, at least for flexible polymer melts.60-63
Figure 1-4: Example of the master curve of regiorandom P3OT for (a) storage and loss moduli at
a reference temperature of 0 °C and (b) frequency shift factors (aT) based on the time-temperature-
superposition principle.58
1.3.1 Glass Transition
The glass transition is a temperature activated process, such that below the characteristic
temperature Tg the segmental motion of the chain mostly ceases; above Tg, cooperative motion is
allowed in the amorphous phase. For conjugated polymers, the glass transition process is important
not only because of the drastic change in the shear storage modulus between ~ 1 GPa (typically 0.5
– 3 GPa) below the Tg 63 and ~ 1 MPa for amorphous polymers or 100 MPa 64 for semicrystalline
polymers above the Tg, but also because below Tg chain motion is kinetically arrested.
Various experimental techniques have been demonstrated for measuring Tg of conjugated
polymers. Dielectric relaxation spectroscopy (DRS)65, 66 focuses on probing main-chain segmental
relaxations, dynamic mechanical analysis (DMA) usu

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CONNECTING FUNDAMENTAL PROPERTIES OF CONJUGATED …