University of Groningen
The reactive extrusion of thermoplastic polyurethaneVerhoeven, Vincent Wilhelmus Andreas
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The Reactive Extrusion of
Thermoplastic Polyurethane
Vincent Verhoeven
RIJKSUNIVERSITEIT GRONINGEN
The Reactive Extrusion of Thermoplastic
Polyurethane
Proefschrift
ter verkrijging van het doctoraat in de
Wiskunde en Natuurwetenschappen
aan de Rijksuniversiteit Groningen
op gezag van de
Rector Magnificus, dr. F. Zwarts,
in het openbaar te verdedigen op
vrijdag 24 maart 2006
om 16:15 uur
door
Vincent Wilhelmus Andreas Verhoeven
geboren op 24 mei 1973
te Waalre
Promotor: Prof. dr. ir. L.P.B.M. Janssen
Beoordelingscommissie: Prof. dr. A.A. Broekhuis
Prof. dr. S.J. Picken
Prof. dr. A.J. Schouten
ISBN 90-367-2520-8
ISBN 90-367-2521-6 (Electronic version)
1 INTRODUCTION 7
1.1 POLYURETHANE EXTRUSION 7 1.2 SCOPE OF THE THESIS 8
2 AN INTRODUCTION TO EXTRUSION AND POLYURETHANES 9
2.1 EXTRUSION 9 2.2 THE CLOSELY INTERMESHING COROTATING TWIN-SCREW EXTRUDER 10 2.3 POLYURETHANES 19 2.4 LIST OF SYMBOLS 30 2.5 LIST OF REFERENCES 32
3 RHEO-KINETIC MEASUREMENTS IN A MEASUREMENT KNEADER 35
3.1 INTRODUCTION 35 3.2 EXPERIMENTAL SECTION 37 3.3 THEORY OF MEASUREMENT OF THE KINETICS 39 3.4 RESULTS 43 3.5 CONCLUSIONS 51 3.6 LIST OF SYMBOLS 52 3.7 LIST OF REFERENCES 53
4 A COMPARISON OF DIFFERENT MEASUREMENT METHODS FOR THE KINETICS OF POLYURETHANE POLYMERIZATION 55
4.1 INTRODUCTION 55 4.2 REACTION KINETICS 57 4.3 EXPERIMENTAL 59 4.4 RESULTS 65 4.5 CONCLUSIONS 79 4.6 LIST OF SYMBOLS 80 4.7 LIST OF REFERENCES 81
5 THE REACTIVE EXTRUSION OF THERMOPLASTIC POLYURETHANE 83
5.1 INTRODUCTION 83 5.2 THE MODEL 84 5.3 EXPERIMENTAL SECTION 92 5.4 RESULTS 96
5.5 CONCLUSIONS 114 5.6 LIST OF SYMBOLS 115 5.7 REFERENCES 117
6 THE EFFECT OF PREMIXING ON THE REACTIVE EXTRUSION OF THERMOPLASTIC POLYURETHANE 119
6.1 INTRODUCTION 119 6.2 MIXING 120 6.3 EXPERIMENTAL SETUP 122 6.4 MATERIALS 123 6.5 ADIABATIC TEMPERATURE RISE ANALYSIS 123 6.6 RESULTS 125 6.7 CONCLUSIONS 133 6.8 LIST OF SYMBOLS 134 6.9 REFERENCES 135 6.10 APPENDIX 1 136
7 CONCLUSIONS 139
8 APPENDIX 143
8.1 SUMMARY 143 8.2 SAMENVATTING 149 8.3 LIST OF PUBLICATIONS 155 8.4 DANKWOORD 157
1 Introduction
1.1 Polyurethane extrusion
Polyurethanes are mostly known for their widespread usage as building foam (PUR-
foam). However, their applications extend much further than ´just foam´.
Polyurethanes are in fact a broad class of polymers with the urethane bond as a
common element. As for foam, thermoplastic polyurethane (TPU), the key player in
this thesis, forms an important subclass in the field of polyurethanes.
Thermoplastic polyurethane (TPU) is a versatile elastomer that is used in automotive
products, electronics, glazing, footwear and for industrial machinery. For all these
applications thermoplastic polyurethanes show a good performance regarding
resistance to chemicals and hydrolysis, tear and abrasion resistance, low-
temperature flexibility and tensile strength. Thermoplastic polyurethane is a block
copolymer that owes its elastic properties to the phase separation of so-called ‘hard
blocks’ and ‘soft blocks’. Hard blocks are rigid structures that are physically cross-
linked and give the polymer its firmness; soft blocks are stretchable chains that
give the polymer its elasticity. By adapting the composition and the ratio of the hard
and the soft blocks, polyurethane can be customized to its application. As for most
polymers, further tailoring of the material properties occurs through additives.
TPU can be produced in several ways. The most common production method for
thermoplastic polyurethane is reactive extrusion. For slow reacting systems, batch
processes are used. An alternative process for extrusion is to ´cure´ premixed
monomer pellets on a conveyor belt. Space requirements in combination with
longer reaction times make the latter process less favorable. For the reactive
extrusion process, the monomers are separately fed to the extruder by a precise
metering system. In the extruder, reaction and transport take place, and the
polymer formed is peletized at the die.
These TPU-extruders are, to the best of our knowledge, mainly operated based on
experience. This empirical approach is caused by the fact that flow and reaction are
directly connected in an extruder, which makes the prediction of the outcome of a
reactive extrusion process a difficult task. Moreover, the fact that numerous
combinations of monomers and catalysts are used to produce a variety of TPU’s
does not improve the situation. Therefore, to control the extrusion process, a
reliable extruder model in combination with reliable knowledge of the kinetics of
the system used is highly desirable.
Chapter 1
1.2 Scope of the thesis
In the introduction the two key components of this thesis, extrusion and
polyurethane, are discussed. An elaboration on these subjects is presented in the
second chapter, giving more insight into the basics and relevant areas regarding
polyurethane extrusion. Subsequently, the kinetics of the polyurethane reaction is
addressed. The emphasis of this part of the thesis lies on the effect of mixing and
temperature on the kinetics of the reaction. For many polyurethane applications,
low-temperature no-mixing kinetic measurements suffice. However, considering the
working range of an extruder, this approach may be insufficient. Due to the
immiscibility of the monomers, the reaction will initially take place at the interface.
Depending on the temperature and the mixing conditions, diffusion limitations may
predominate. Because of this competition between diffusion and reaction, the
measurements of the kinetics for TPU polymerization are best performed at the
temperature and the mixing situation of the application for which the investigation
is intended. To bring this idea into practice, a new kinetic measurement method is
introduced in the third chapter, based on torque kneader experiments. In the
fourth chapter, the results of these kneader experiments are compared with other
kinetic methods.
The attention then shifts to the extruder. A reactive extrusion model is presented in
chapter 5, in which the relevant effects for polyurethane extrusion are taken into
account. Special emphasis is put on the depolymerization reaction, which is an
important factor in polyurethane extrusion. The effect of premixing on the extruder
performance is presented in chapter 6. Finally, the conclusions of this thesis are
presented in chapter 7.
8
2 An Introduction to extrusion and polyurethanes
2.1 Extrusion
Extruders have a widespread application in food and polymer technology. In general,
extruders find their use in processing of medium to high viscosity materials that do
not need a long processing time. Compounding of polymers, production of powder
coatings and hot melts, paper pulp processing, and cooking extrusion of pasta,
chips, pet food, and cereals are among others the working area of extruders.
Extruders are even found to be useful for more ´exotic´ applications such as for
production of explosives, ice cream manufacturing, and metal extrusion. The
general working principle of an extruder is straightforward: a screw rotates in a
closely fitted barrel; material is transported through the rotating action of the screw
in the downstream direction.
Extruders come in different forms, each with their own advantages. The
classification of extruders is straightforward. First, there is the difference between
single and twin-screw extruders. Based on costs, a single screw extruder is always
first choice. However, for several applications single screw extruders are less
suitable, which only leaves the choice for a twin-screw extruder. The most
predominant inconvenience of a single screw extruder is the transport mechanism.
Transport is only based on drag flow, which makes a single screw extruder sensitive
to viscosity changes and slippage. Twin-screw extruders have this disadvantage to a
much lesser extent. Twin-screw extruders come in different varieties; several types
of extruders are shown in figure 2.1. More details on the benefits and limitations of
every type of extruder can be found in Janssen (1), Rauwendaal (2), and Todd (3).
For reactive processing, a closely intermeshing corotating twin-screw extruder is
often the preferred choice. Due to the self-wiping action, the transport of material is
largely independent of the viscosity of the material. Of course, this is an advantage
for a reactive system, since the viscosity rises exponentially along the screw.
Moreover, the high average shear-rate promotes a well-mixed reaction mass, and
the diversity in screw build-up make a twin-screw extruder a versatile reactor, which
can be tailored to its application.
Chapter 2
Figure 2.1 Different types of extruders, a) single screw, b) tangential extruder, mixing
emphasis, c) tangential extruder, transport emphasis, d) closely intermeshing
counterrotating, e) conical closely intermeshing counterrotating, f) closely
intermeshing corotating (1).
In general, if we look at the extruder as a polymerization reactor, the benefits and
disadvantages are well known. The high investment costs (expensive reactor
volume), in combination with the unsuitability for time-consuming processes
compete with a narrow residence time distribution, a fair heat transfer, no need of
solvents and good mixing properties. Most important, in an extruder a ´one-shot´
polymerization and pellet forming process can be carried out. For several high-end
polymers, as for polyurethane, the extruder is the preferred reactor.
2.2 The closely intermeshing corotating twin-screw extruder
2.2.1 Working principle
In a closely intermeshing corotating twin-screw extruder, material is transported
from the feed zone to the die. The conveying mechanism in this type of extruder is
similar to a single screw extruder. However, for the twin-screw extruder the
´seconds screw´ wipes the ´first screw´, which prevents slippage and guarantees
forward conveying (figure 2.2). Because of the requirement that one screw wipes
the other, the screw cross section has a unique shape for a given diameter, pitch,
centerline distance, and number of tips (parallel channels).
10
An introduction to extrusion and polyurethanes
Figure 2.2 Two closely intermeshing corotating screws.
Booy (4, 5) derived the mathematical expressions from which the geometry of fully
wiped corotating twin-screw extruders can be calculated. Due to the constraints on
the screw geometry, the screw has a relatively large channel width compared to the
flight width. As a result, hardly any decrease of the channel area is found in the
intermeshing zone between the two screws. Roughly speaking, a screw channel
continues from one screw to the next, giving one continuous channel. Due to the
multiple thread starts that are common practice for corotating extruders, several
parallel channels exist; the number can be calculated from the number of thread
starts (1).
Figure 2.3 Parallel channel representation of a corotating closely intermeshing twin-screw
extruder (6).
A common way to represent the flow in a screw channel is related to the idea of an
infinite channel. As shown in figure 2.3, the flow in a corotating intermeshing
extruder can be envisaged as several parallel channels, with the barrel wall sliding
11
Chapter 2
as a ´infinite plate´ over the channels. In figure 2.3, the curvature of the channels
is ignored, and the flow in and the geometry of the intermeshing zone is not
captured completely in this way. The route the material travels in a channel is
shown in figure 2.4.
vb,x
vb,zv
barrelwall
x
z
Figure 2.4 The helical flow pattern in a single channel.
Near the barrel wall, material flows in the positi
´movement of the wall´) until it meets the upcoming
forced to the bottom of the channel (negative y-dir
material flows back in the x-direction. This time, the
pushes the material upwards (y-direction) and this com
z-component of the barrel wall velocity, the net
downstream direction of the channel; the material the
Experiments and 3D-simulations (7) confirm this flow
2/3th of the channel height a stagnation point exist.
2.2.2 Energy considerations
This helical flow pattern has clear consequences for the
channel. The material that resides at the center of rota
the barrel wall, while other material passes the barre
heat with the barrel. Therefore, temperature gradients
especially, since viscous dissipation and reaction heat h
heat balance. This effect is particularly important for la
5 cm). Still, due to the helical flow pattern, the heat t
what would be expected for flow between two movi
estimate of the effect of reaction, viscous dissipation a
wall on the energy balance, a dimensionless number a
12
y
ve x-direction (due to the
flight. The material is then
ection); at the bottom, the
presence of the flight-wall
pletes the cycle. Due to the
flow of material is in the
refore follows a helical path.
pattern and show that at
temperature gradient in the
tion does not come close to
l wall regularly, exchanging
in the channel are inevitable,
ave a dominant effect in the
rger extruder diameters (D ≥
ransfer is much better than
ng plates. To obtain a first
nd heat transfer through the
nalysis can be made. Three
An introduction to extrusion and polyurethanes
dimensionless numbers are relevant: DamköhlerIV (Da
IV) number, the Brinkmann (Br)
number, and the Graez (Gz) number (equation 2.1).
transferheatconvectivetransferheatconductive
QLa
Gz
heatofconductionndissipatioviscous
TDN
Br
heatoftransportconductivereactionofheat
DTQH
Da
22
RIV
=⋅
=
=∆⋅λ⋅⋅µ
=
=⋅∆⋅λ⋅∆⋅ρ
=
( 2.1 )
For the reactive extrusion of polyurethane (for the system and extruder used in this
thesis), an evaluation of these numbers shows that the heat of reaction is lower
than the viscous dissipation (DaIV / Br < 1). Moreover, the extruder operates
somewhere in between isothermal and adiabatic conditions (Gz ≈ 1).
For more specific information, the energy balance of the extruder has to be solved.
Due to the complicated flow pattern, only a fully developed three-dimensional flow
model can take care of all effects. However, a more simple approach will give
reasonable insight. Commonly, a one-dimensional heat balance over short sections
of the extruder is used (chapter 5).
2.2.3 Flow behavior
As for the heat balance, the three-dimensional flow pattern in the screw channel
must be condensed to a more simple equation, in order to estimate the filling
degree and pumping characteristics of a corotating intermeshing extruder. A basic
approach is to express the throughput of an extruder in a drag and a pressure flow
term (8):
ϕ⋅⋅η
−⋅=+= sindLdPB
NAQQQ pressuredrag ( 2.2 )
Equation 2.2 states that the net throughput in an extruder equals the maximum
drag flow capacity (A·N) minus the pressure flow, which occurs in the opposite
direction. The pressure flow is proportional to the pressure build-up capacity
13
Chapter 2
divided by the viscosity. Equation 2.2 can be derived from a momentum balance
over a screw channel. The constants A and B are specific for an element type and
represent the curvature of the channel. The A and B terms can be obtained from a
geometrical analysis (1, 9, 10, 11) or through an experimental approach (12).
Several effects are not taken into account by applying Equation 2.2:
1. The leakage flows
2. The effect of the intermeshing zone
3. Non-Newtonian flow behavior
4. The effect of radial temperature gradients (and resulting viscosity
gradients).
These phenomena cause a deviation of the linear dependence of the pressure drop
on the rotation speed. Several measures can be taken to obtain a more precise
description.
1. The leakage flows
The leakage flows can be taken into account by adapting equation 2.2:
LQdLdPB
NAQ −⋅η
−⋅= ( 2.3 )
Of all the leakage flows present in a corotating intermeshing extruder (1), the
leakage over the flight predominates. The other leakage gaps, which are located
near the intermeshing zone, are less important, due to the smaller leakage area,
and because in this part the two screws rotate in the opposite direction, giving no
net flow through the leakage gaps. The leakage over the flight can be introduced
using a pressure and a drag flow term (13):
( ) ( )ψ−π⋅δ⋅+⋅=
⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅ηδ
⋅ϕ
+⋅ϕ⋅
∆∆
+δ⋅ϕ⋅ϕ⋅=
R
flight
3R
R0
L
2D2u
e12tanew
sinLP
cossin2
vuQ
( 2.4 )
Drag Pressure
Due to the small gap size δR, the pressure driven leakage flow would seem to be a
small contribution to the leakage flow. However, for non-Newtonian fluids, the
14
An introduction to extrusion and polyurethanes
leakage over the flight is of importance; the high shear rate over the flight results in
a low apparent viscosity causing the pressure driven leakage flow to become
important.
2. The effect of the intermeshing zone
To refine equation 2.3, the flow in the intermeshing zone can also be introduced.
The intermeshing zone forms a local restriction in the channel; the material
undergoes no net drag flow since it is not in contact with the barrel wall. Moreover,
a small contraction of the channel area is present in the intermeshing area. Michaeli
et al. (11) and Vergnes et al. (14) each came up with a solution to account for the
intermeshing zone, based on a pressure driven flow through this zone.
3. Non-Newtonian flow behavior
To take into account the non-Newtonian behavior of the material in the screw
channel, the average or the local shear rate must be known. For a one-dimensional
approach, the average shear rate in the channel can be expressed as in equation
2.5:
HDN ⋅⋅π
=γ& ( 2.5 )
so that equation 2.3 becomes:
L
n
QsindLdP
kB
HDN
NAQ −ϕ⋅⋅⎟⎠
⎞⎜⎝
⎛ ⋅⋅π−⋅=
−
( 2.3a )
A better estimate of the average shear rate can be obtained through a two-
dimensional analysis of the flow (x and z direction in figure 2.3), taking into
account the actual channel geometry as for example was done by Michaeli et al.
(11). However, no analytical equation appears in that case. With the approach of
Potente et al. (15), based on single screw calculations of Tadmor and Gogos (16),
this disadvantage is not present.
4. The effect of radial temperature gradients
A further refinement of the flow model, for example by taking into account the
temperature gradients, results in two- or three- dimensional models.
15
Chapter 2
2.2.4 Kneading paddles
So far, all emphasis has been placed on the regular transport elements. One of the
benefits of a corotating intermeshing extruder is its flexibility. Not only transport
elements, but also numerous types of other elements can be applied in endless
combinations to tailor the extrusion process. A survey of possible elements is for
example presented by Todd (3). For this thesis, the most important class of
elements (besides the transport elements) are the kneading blocks (figure 2.5). The
main function of the kneading blocks is to enhance mixing. Kneading blocks
consist of staggered kneading paddles. The stagger angle of the successive paddles
and the width of the paddles can be varied. With a larger stagger angle, the forward
conveying capacity diminishes, but the kneading action improves at the cost of
more energy dissipation. The forward conveying capacity diminishes with a larger
stagger angle because the leakage gaps between two paddles (figure 2.5) increases.
Kneading paddles reorient the fixed flow lines that are present in the regular
transport elements, which give a distributive mixing effect. Moreover, going from
paddle to paddle, further distributive mixing takes place due to the staggering of
the paddles (extra reorientation of the flow lines) and the backflow through the
leakage gaps. Besides distributive mixing, the kneading paddles also promote
dispersive mixing. Material is squeezed between two neighboring paddles, giving
large extensional flow rates compared to the normal transport elements. In general,
by widening the paddles width, the mixing emphasis shifts from distributive to
dispersive mixing. By using wider kneading paddles, the material has less
possibilities to escape when it is squeezed together, giving larger elongational and
shear forces.
Figure 2.5 A kneading block for a corotating intermeshing twin-screw extruder.
16
An introduction to extrusion and polyurethanes
Many investigations have been directed towards understanding and describing the
flow and the mixing behavior in kneading blocks (7, 10, 13, 14, 17-23). The most
straightforward way is to consider the kneading blocks as modified transport
elements. In that case, the equations that are used to calculate the transport
capacity of a transport element can be used, with some modifications:
stag,LL QQsindLdPB
NAQ −−ϕ⋅η
−⋅= ( 2.6 )
Compared to equation 2.2, an extra leakage flow is introduced due to the
staggering of the kneading paddles. This extra leakage flow can be defined in
different ways, as done by Potente et al. (10) or Meijer et al. (9).
2.2.5 The filling degree and residence time
Through residence time distribution measurements or modeling efforts, the
residence time in an extruder can be determined. Especially for reactive extrusion,
the residence time is an important parameter, since it is directly related to the yield
that is obtained with the extrusion process.
Corotating extruders are usually starved fed. Consequently, sections of the
extruder are not completely filled. To calculate the residence time, the filling degree
of the partially filled zones and the length of the fully filled zones must be
determined.
Figure 2.6 A typical screw profile for a corotating intermeshing twin-screw extruder (1).
A typical extrude profile is shown in figure 2.6. As pointed out, partially filled zones
alternate with fully filled zones along the screw. The filled regions are created by
17
Chapter 2
upstream elements that form local restrictions and create backpressure. Examples
are reverse elements, 90° (non-conveying) kneading blocks, or, as a special case,
the die. The length of each fully filled zone is dependent on the pumping
characteristics of both the backpressure and forward-pressure creating screw
elements. The pumping characteristics can for example be calculated using
equation 2.2, or a modified version of this equation, depending on the desired
accuracy and the element type under consideration. For the die, a different
approach must be taken. The pressure over the die is very dependent on the die
geometry. For cylindrical dies, the most straightforward equation is based on the
flow in a tube:
die4L
d
Q128P
⋅ρ⋅π
η⋅⋅=∆ ( 2.8 )
The second parameter that is important for calculating the residence time is the
filling degree in the partially filled zones. A general expression gives:
max
feed
Q
Qf = ( 2.7 )
Qfeed
is the feed rate of material. For Qmax
, the A·N-term of the right side of equation
2.2 may be used. In case other types of elements are taken into consideration, the
A-factor for Qmax
changes.
18
An introduction to extrusion and polyurethanes
2.3 Polyurethanes
As explained in paragraph 1.1, polyurethanes are a group of polymers that have the
urethane bond in common. Polyurethane can be regarded as a linear block
copolymer as shown in figure 2.7. This segmented polymer structure can vary its
properties over a wide range of strengths and stiffness by modification of its three
basic building blocks: polyol, diisocyanate, and chain extender (diol). Essentially,
the hardness range covered is that of soft jelly-like structures to hard rigid plastics.
Material properties are related to segment flexibility, chain entanglement, inter
chain forces, and cross-linking.
Figure 2.7 The basic unit in a urethane block-copolymer (24).
Evidence from X-ray diffraction, thermal analysis and mechanical properties strongly
support the view that these polymers can be considered in terms of long (100 – 200
nm) flexible segments and much shorter (15 nm) rigid units which are chemically
and hydrogen bonded together (24). The structure becomes oriented via extension
as indicated in figure 2.8. The stretching of an elastomer proceeds by the
stretching of the coiled flexible polyol segments while the hard segments stay
bonded to each other.
19
Chapter 2
Figure 2.8 Flexible and rigid segments in a polyurethane elastomer.
Modulus-temperature data usually show at least two definite transitions, one below
room temperature, related to segmental flexibility of the polyol and one above
100°C due to dissociation of the inter chain forces in the rigid units. Multiple
transitions may also be observed if mixed polyols and rigid units are present in the
polymer structure.
2.3.1 Isocyanates
CH H
N NC CO O
CH H
NCO
N C O
Figure 2.9 Structure of 4,4’-MDI (left) and 2,4’-MDI (right).
Only the diisocyanates are of interest for linear urethane polymer manufacturing,
and relatively few of these are used commercially. The most important ones in
elastomer manufacturing processes are 2,4- and 2,6-toluene diisocyanates (TDI),
4,4’-diphenylmethane diisocyanate (MDI) and its aliphatic analogue 4,4’-
dicyclohexylmethane diisocyanate. Also 1,5-naphtalene diisocyanate (NDI) and 1.6
hexamethylene diisocyanate (HDI) are used. The diisocyanates used in this research
20
An introduction to extrusion and polyurethanes
are 4,4’-diphenylmethane diisocyanate (4,4’-MDI) and a mixture of 50% 4,4’-
diphenylmethane diisocyanate (4,4’-MDI) and 50% 2,4’-MDI. The structures of these
compounds are shown in figure 2.9.
2.3.2 Polyols
Although diisocyanates are the intermediates responsible for chain extension and
the formation of urethane links, much of the ultimate polymer structure is
dependent on the nature of the components carrying the groups with which the
isocyanates react. An example component can be a simple short diol, as such was
employed in the early work on linear polyurethanes (24). Linear polyurethanes of
this type are crystalline, fiber-forming polymers but have a lower melting
temperature than the corresponding polyamides, and none have become of real
importance either as a synthetic fiber or as a thermoplastic material.
However, replacement of the simple diols by polymeric analogues has resulted in an
extensive commercial development. This arose from the finding that linear
polyesters or polyester-amides, of molecular weights of about 2000 and carrying
terminal OH groups, can react with hexamethylene diisocyanate (HDI) and toluene
diisocyanate (TDI). Through a chain lengthening process, tough elastomeric or
plastic materials can be formed, which can be cross-linked by using additional
isocyanate.
The original polyols used in PU elastomer synthesis are structurally simple and
three classes have been recognized, namely polyesters, polyethers and more
recently polycaprolactones. For elastomer synthesis, these are available in various
molecular weights, and products in the range of 600-2000 g/mol are commonly
used industrially.
The polyol used in this research was a polyester-based polyol of the type P765
(Huntsman Polyurethanes), based on an ester of mono-ethylene glycol, di-ethylene
glycol and adipic acid. The influence that different polyester backbones have on the
properties of polyurethane elastomers is large. Tensile strengths and moduli
depend largely upon the presence of a side chain in the polyester. For example,
polyesters that contain methyl side chains give elastomers that have significantly
lower tensile strengths than those from the linear polyesters.
2.3.3 Diols (chain extenders)
The flexible (polyol) blocks primarily influence the elastic nature of the product. In
addition, they make important contributions towards the hardness, tear strength,
and modulus. But chain extenders for example a diol like butanediol particularly
21
Chapter 2
affect the modulus, hardness and tear strength, and determine the maximum
application temperature by their ability to remain associated at elevated
temperatures. Rigid segments are usually formed by the reaction of diisocyanate
with a glycol or a diamine. In this research mainly glycol is used as a chain extender,
namely methyl-1,3-propanediol.
2.3.4 Polyurethane chemistry
In figure 2.10, the most common reactions that occur when making polyurethanes
are shown (25). Figure 2.10 shows overall reaction schemes so no details on the
order of the reaction can be concluded. For the production of thermoset
polyurethane foam (PUR) reaction 5 is indispensable. For thermoplastic
polyurethane (TPU) production, water is excluded, so that only reactions 1, 2, 3 and
4 can take place.
For ´normal´ condensation polymerization, in which always a small molecule
(mostly water) is formed, equilibrium between the forward and the reverse reaction
can be prevented by removing this small molecule (e.g. evaporation of water). For
all isocyanate reactions, this option is not present; therefore, the reverse reaction
can have a substantial impact. For the polyurethane formation reaction (reaction 1),
an equilibrium state has been demonstrated. Dissociation of the polyurethane bond
has been observed with DSC and rheology (26). In addition, it was shown by Ando
(27) that for a bulk system without catalyst and at temperatures between 180 and
220 °C the molecular weight decreases with polymerization temperature. Ando (27)
attributes this effect to the depolymerization reaction (i.e. the reverse of reaction 1).
Which of the reactions shown in figure 2.10 take place during polyurethane
production depends on the temperature, and the presence and the type of solvent
and catalyst used. Solvent and catalyst can greatly enhance the rate of one (or
sometimes more) reactions. Moreover, the temperature affects the reaction rate and
the equilibrium of each of the reactions specified. Normally, the type and ratio of
monomers and the type of catalyst is chosen in such a way that the polyurethane
reaction will dominate. However, even the occurrence of a limited amount of side
reactions may interfere with the final material properties. In the literature, some
articles have been published that take the side reactions during polyurethane
formation into account. However, most of the publications on polyurethane kinetics
use the kinetics as input for modeling purposes (e.g. for reactive injection molding),
and the side reactions are neglected. Moreover, for these systems the kinetics are
very fast which makes a detailed analysis of the reaction difficult.
In the next paragraphs, a short overview of the relevant reactions will be presented.
22
An introduction to extrusion and polyurethanes
(5) Urea Formation: + N C OH2O N C
H
O
OH
NH
H+ CO2N C
H
N
O
HN C O
(1) Urethane Formation: N C O + OH N C
H
O
O
Possibly catalyzed
(3) Allophanate Formation: N C
H
O
O
+ N C ON C
C
O
O
O
N
H
(4) Uretidione Formation: 2 N C O NC
NC
O
O
(2) Isocyanurate Formation:N
CN
C
NC
O
OO
3 N C O
Figure 2.10 The most commonly occurring isocyanate reactions.
2.3.5 Reaction 2: Isocyanurate formation
At lower temperatures (up to 50°C) and with N,N´,N´´-pentamethyl dipropylene
triamine (PMPT) as a catalyst, it was shown that up to 30% isocyanurate can be
formed (28). HPLC measurements showed that allophanate appears as an
intermediate during this reaction. A second publication of these authors (29) shows
that the type of tertiary amino catalyst determines if and at what speed
isocyanurate is formed. A mechanism for isocyanurate formation is proposed by
Kresta et al. (30). A catalyst-isocyanate complex is formed in an equilibrium step;
23
Chapter 2
subsequently two isocyanate units are added. During the last step, a fourth
isocyanate replaces the trimer that is formed at the catalyst site. However, this
mechanism does not concur with the observations of Wong and Frish (28, 29) that
allophanate acts as an intermediate for isocyanurate formation. Vespoli and
Albetino (31) have fitted adiabatic temperature rise data for a MDI-polyol system
with this mechanism. They assumed that only at a higher ratio of isocyanate to
alcohol isocyanurate is formed. Sun et al. (32) used the mechanism of Kresta et al.
(30) for modeling a RIM-process for thermoset polyurethane production. They
observed during their ATR experiments that the isocyanurate activation energy is
higher and the polyurethane reaction is slower. Therefore, at higher temperatures
the isocyanurate formation predominates. Sun et al. (32) concluded further that
urethane oligomers cause a diffusion limitation for the isocyanurate formation. A
free-volume model was used to consider this effect.
Isocyanurate formation is sometimes desirable because it enhances thermal and
dimensional stability and decreases the combustibility and smoke production of the
resulting polymer. Conditions that favor isocyanurate formation are a high
isocyanate to alcohol ratio and the presence of certain types of catalyst (for
instance tertiary amino catalysts like PMPT enhance isocyanurate formation). If
these factors are not present, as is the case for the extrusion process presented in
this thesis, isocyanurate formation will not be of importance.
2.3.6 Reaction 3: Allophanate formation
In contrast to the isocyanurate bond, which is still remarkably stable at 200°C,
allophanates dissociate more readily. Malwitz et al. (33) took a computational
chemistry approach to calculate the rate of allophanate formation. They found an
equilibrium temperature of 165°C. According to their calculations, the rate of
allophanate formation is slow without catalyst, but is quite considerable in the
presence of catalyst. Generally, it is assumed that formation in bulk and without
catalyst occurs only at temperatures higher than 120°C (34, 35). Jöhnson and Flodin
(36) showed with NMR-study that in a non-catalyzed system at temperatures lower
than 100°C no allophanate is formed. They also stated that allophanate formation
would only happen at higher temperatures. Imawaga et al. (37) measured reaction
products of a bulk system without catalyst at 85°C. No side products were found
though it was stated that at higher temperatures side reactions may well occur.
Dorozhkin et al. (38) reported a second order kinetic constant for allophanate
formation: ln (k2) = 19 – 60 / R·T.
24
An introduction to extrusion and polyurethanes
The short list of publications on allophanate formation indicates that there is
limited knowledge on this subject. Based on the publications as presented above,
allophanate formation does not take place below 120°C, but above this temperature,
the formation rate can be substantial. For polyurethane extrusion, allophanate
formation may therefore interfere with the polyurethane reaction. Allophanate
formation interferes with the stoichiometric ratio of alcohol and isocyanate,
resulting in a lower final molecular weight. Moreover, allophanate will give
branched polymer chains at low concentrations and at high concentrations, even a
cross-linked polymer network would result.
In fact, for polyurethane production at high temperatures (> 150°C, for example
during extrusion), a constant amount of isocyanate will be present due to the
reverse reaction. These free isocyanate groups can ´choose´ between a relatively
low concentration of alcohol groups and a relatively high concentration of urethane
groups. Depending on the reaction rate constants and the equilibrium constants of
the urethane and the allophanate reaction, a gradual increase of allophanate groups
may therefore occur when keeping polyurethane at a high temperature for a longer
time. Hentschel and all showed this effect indirectly by rheological experiments (26).
2.3.7 Reaction 4: Uretidione formation
Uretidione formation (reaction 3) in most cases does not influence polyurethane
extrusion. Because of its low equilibrium temperature, uretidione readily dissociates
at normally used reactive extrusion temperatures. The two free isocyanate groups
that appear upon dissociation will react further to form polyurethane. Problems
with uretidione formation may arise when heating the isocyanate prior to the
reactive extrusion. Uretidione is insoluble in isocyanate, so a precipitate will form.
2.3.8 Polyurethane kinetics
Reaction mechanism
N C O + OH N C O
OH
-OH
OH
N C
H
O
O
+
OH
:.... ..
.. :
OH
N C O....k1
k2
k3
Figure 2.11 Lewis base catalysis for urethane formation.
25
Chapter 2
Several studies have been conducted on polyurethane kinetics. Two reaction
mechanisms are used as the basis for a kinetic equation: A Lewis acid catalyzed
reaction and a Lewis base catalyzed reaction. Actually, uncatalyzed reactions do not
exist for polyurethane formation, since the alcohol group itself works as a Lewis-
base catalyst. The mechanism for the Lewis-base catalysis is shown in figure 2.11
(the alcohol group in this case is the base-catalyst), the mechanism for the Lewis-
acid catalysis is shown in figure 2.12 (35).
N C O + HA H...A ROH N C
H
O
O[ ] HA+:..
..N C Ok1
k2 k3
Figure 2.12 Lewis acid catalysis for urethane formation.
Tertiary amino catalysts (for example DABCO), are Lewis-base catalysts. It is clear
from literature (39) that the transition metals (Co, Mn) form a complex with the
isocyanate group while the post-transition metals (Sn, Sb, Pb) form a complex with
the alcohol group. In the literature, if the catalyst complex is taken into account in
the kinetic equation a Lewis-base catalyzed reaction is always assumed. The most
elaborate kinetic equation (for metal-complex catalysis) has been proposed by
Richter and Macosko (40). They used the mechanism in figure 2.11 with an extra
equilibrium step: dissociation of the catalyst in Metal+ and Rest-. The resulting
kinetic equation did not have an analytical solution but Richter and Macosko (40)
observed four limiting cases:
[ ] [ ] [ ]
[ ] [ ] [ ] [
[ ]
]
[ ] [ ] [ ]
[ ] [ ] [ ] [ ]OHNCOCatkdt
NCOd
OHNCOCatkdt
NCOd
OHNCOCatkdt
NCOd
OHCatkdt
NCOd
5.0f
f
5.05.0f
f
⋅⋅⋅=
⋅⋅⋅=
⋅⋅⋅=
⋅⋅=
( 2.10 )
Which equation prevails depends on the degree of dissociation of the metal-
complex and the degree of association of the metal+ and the isocyanate group. Of
course, the k in these equations is a lump sum k that consists of a combination of
26
An introduction to extrusion and polyurethanes
rate and equilibrium constants. Dissociation of the metal complex has not been
mentioned in the literature on polyurethane catalysis.
Steinle et al. (41) used the mechanism in figure 2.11 for an analytical rate equation.
This equation has a hyperbolic form:
[ ] [ ] [ ] [[ ]
]OHK1
NCOOHCateKdt
NCOd
2C
T1
T1
RE
1CR
C
+⋅⋅⋅⋅
=⎟⎟⎠
⎞⎜⎜⎝
⎛−
( 2.11 )
The main assumption Steinle et al. (41) make is that EA of k
2 is equal to E
A of k
3. The
rate equation of Steinle et al. (41) is both used for uncatalyzed reactions and
reactions with tertiary amines as a catalyst.
No decisive evidence has been presented on the exact reaction mechanisms during
the polyurethane bond formation. The developed kinetic equations are therefore
quite general, without any deep knowledge on which intermediate steps are rate
limiting, and what the activation energy of each step is. In practice, this knowledge
does not seem to be necessary to describe reactive injection molding processes.
However, with reactive extrusion, the experiments on the kinetics are performed at
different temperatures than the reactive extrusion process is operated, which may
give an incorrect extrapolation of the reaction rate constant.
Most authors report that up to 50 % conversion, the kinetics follow a second order
trend but at higher conversions different effects are observed. Both acceleration
and deceleration of the reaction velocity have been reported. Acceleration is mostly
ascribed to the autocatalytic effect of the polyurethane bond. However, this
autocatalytic effect has never been quantified. Deceleration is attributed to
diffusion effects which may become important (especially in bulk systems) at higher
conversions. In case of diffusion limitation, the idea that the reactivity of a
functional group is independent of the chain length is no longer valid.
For relatively short chain lengths, Król (42) has shown that a higher molecular
weight causes a slower reaction rate, but this effect is only observable up to a
carbon backbone of five units. The slowing-down of the reaction at high
conversions is therefore not explained by his findings. However, the findings of Król
(42) could mean that for polyurethane polymerization the chain extender reacts
faster than the polyol. This difference in reaction rate is hardly ever taken into
account for bulk polyurethane polymerization. The underlying reason is that the
experimental difficulties related to the tracking of the two species (chain extender -
OH and polyol -OH) in a fast reacting high-temperature bulk process are hard to
27
Chapter 2
resolve. Moreover, for many applications it is sufficient to be able to predict the
overall reaction rate, since longer oligomers are rapidly formed.
A further assumption for polycondensation kinetics is that the reactivity of a
reactive group on a molecule is independent of whether another reactive group on
the same molecule has reacted. With all these conditions in mind, a general rate
equation for polyurethane polymerization can be written:
[ ]
TRE
m0
TR
E
Uncat,0f
nfCat,NCOUncat,NCONCO
AUncat,A
e]cat[AeAkwith
]NCO[kRRdt
NCOdR
⋅−
⋅
−
⋅⋅+⋅=
⋅−=+== ( 2.12 )
In equation 2.12 a stoichiometric amount polyol and isocyanate is assumed. For an
isothermal batch reactor, the isocyanate balance can be solved to give:
[ ] ( ) n11
1n0f0 t]NCO[)1n(k1NCO]NCO[ −− ⋅⋅−⋅+= ( 2.13 )
Often a second order rate equation is found to be valid for polyurethane
polymerization, which gives for the isocyanate concentration:
[ ]t]NCO[k1
NCO]NCO[
0f
0
⋅⋅+= ( 2.14 )
The number and weight average molecular weight are related to the isocyanate
concentration. The increase in number and weight average molecular weight in time
for a second order reaction gives (43):
( )t])cat[,T(k]NCO[1MM f0repN ⋅⋅+⋅=
( 2.15 )
[ ] )t])cat[,T(kNCO21(MM 0repW ⋅⋅⋅+⋅=
In this equation Mrep
is the molecular weight of a repeating unit and [NCO]0 is the
initial isocyanate concentration.
28
An introduction to extrusion and polyurethanes
As explained in paragraph 2.3.4, the reverse reaction of polyurethane formation
occurs at higher temperatures. To incorporate the reverse reaction, the rate
equation (equation 2.12) changes:
]NCO[]NCO[]U[and
eA
kk,eA]Cat[kwith
]U[k]NCO[kdt
]NCO[dR
0
TR
E
eq,0
fr
TRE
0m
f
r2
fNCO
eq,A
A
−=
⋅
=⋅⋅=
−==
⋅
−⋅
−
( 2.16 )
Depending on the reactor type, equation 2.16 can be solved analytically to give the
isocyanate concentration as a function of time.
The equilibrium constant can be expressed in several ways (43):
( )TR
E
eq,00
2rep
repNN
2eq
eq
r
feq,A
eA]NCO[M
MMM
]NCO[
]U[
kk
K ⋅⋅=⋅
−⋅=== ( 2.17 )
This equation can be used to calculate the effect of the reverse reaction.
29
Chapter 2
2.4 List of Symbols
a Thermal diffusivity m2/s
A Geometrical constant kg
A0 Reaction pre-exponential constant mol/kg s
B Geometrical constant kg⋅m
[Cat] Catalyst concentration mg/g
D Diameter m
e Flight land width m
EA Reaction activation energy J/mol
f Filling degree of a not fully filled element -
H Height of the screw channel m
∆HR Heat of reaction J/mol
k Power law consistency Pa·sn
kf Forward reaction rate constant kg/mol⋅s
kr Reverse reaction rate constant 1/s
K Equilibrium constant kg/mol
L Length m
n Reaction order -
n Power law index -
N Rotation speed 1/s
[NCO] Concentration isocyanate groups mol/kg
[NCO]0 Initial concentration isocyanate groups mol/kg
m Catalyst order -
MN Number average molecular weight g/mol
Mrep
Average weight of repeating unit g/mol
MW Weight average molecular weight g/mol
[OH] Concentration alcohol groups mol/kg
∆P/∆L Pressure gradient in the axial direction of the extruder Pa/m
Q Throughput kg/s
R Gas constant J/mol K
RNCO
Rate of isocyanate conversion mol/kg⋅s
t Time s
T Temperature K
∆T Temperature difference K
u Circumference of the eight-shaped barrel m
30
An introduction to extrusion and polyurethanes
[U] Concentration urethane bonds mol/kg
v Velocity m/s
v0 Circumferential velocity of the screw m/s
w Width of the screw channel m
Greek symbols
δR Clearance between barrel and flight tip m
γ& Shear rate 1/s
η Viscosity Pa⋅s
ϕ Pitch angle -
λ Heat conductivity W/m·K
µ Kinematic viscosity m2/s
ρ Density kg/m3
ψ Intermeshing angle -
Subscripts
b Barrel wall
Cat Catalyzed
Die Die
Eq Equilibrium
L Leakage
Uncat Uncatalyzed
31
Chapter 2
2.5 List of References
1. L.P.B.M. Janssen, Reactive extrusion systems, Marcel Dekker Inc., New York, Basel
(2004).
2. C.J. Rauwendaal, Polymer extrusion, Hanser, Munich (2001).
3. D.B. Todd, Plastic compounding, Hanser, Munich (1998).
4. M.L. Booy, Polym. Eng. Sci., 18, 973 (1978).
5. M.L. Booy, Polym. Eng. Sci., 20, 1220 (1980).
6. W. Michaeli, A. Grefenstein and U. Berghaus, Polym. Eng. Sci., 35, 1485 (1995).
7. D.J. van der Wal, Improving the properties of polymer blends by reactive
compounding, Phd-Thesis, Rijksuniversiteit Groningen (1998).
8. J. Mckelvey, Polymer Processing, John Wiley & Sons, New York (1962).
9. H.E. Meijer, and P.H.M. Elemans, Polym. Eng. Sci., 28, 275 (1988).
10. H. Potente, J. Ansahl and B. Klarholz, Int. Polym. Process., 9, 11 (1994).
11. W. Michaeli, A. Grefenstein and U. Berghaus, Polym. Eng. Sci., 35, 1485 (1995).
12. D.B. Todd, Int. Polym. Process., 6, 143 (1991).
13. W. Michaeli, and A. Grefenstein, Int. Polym. Process., 11, 121 (1996).
14. B. Vergnes, G. Della Valle, and L. Delamare, Polym. Eng. Sci., 38, 1781 (1998).
15. H. Potente, J. Ansahl, R. Wittemeier, Int. Polym. Process., 3, 208 (1990).
16. Z. Tadmor, and G. Gogos, Principles of Polymer Processing, John Wiley & Sons, New
York, Brisbane, Chichester, Toronto (1979).
17. T. Fukuoka, Polym. Eng. Sci., 40, 2524 (2000).
18. V.L. Bravo, A.N. Hrymak, and J.D. Wright, Polym. Eng. Sci., 40, 525 (2000).
19. J.L. White, and Z. Chen, Polym. Eng. Sci., 34, 229 (1988).
20. A. Poulesquen, and B. Vergnes, Polym. Eng. Sci., 43, 1841 (2003).
21. H. Werner, Chemie Ing. Techn., 49, heft 4 (1977).
22. M.A. Huneault, M.F. Champagne, and A. Luciani, Polym. Eng. Sci., 36, 1694 (1996).
23. G. Shearer, and C. Tzoganakis, Polym. Eng. Sci., 40, 1095 (2000).
24. C. Hepburn, Polyurethane elastomers, Elsevier Applied Science, London, New-York
(1992).
25. J.M. Buist, and H. Gudgeon, Advances in polyurethane Technology, Elsevier (1968).
26. T. Hentschel, and H. Münstedt, Polymer, 42, 3195 (2001).
27. T. Ando, Polym. J., 11, 1207 (1993).
28. S.W. Wong and K.C. Frisch, Polym. Sci. Part A: Polym. Chem., 24, 2877 (1986).
29. S.W. Wong and K.C. Frisch, Prog. Rub. Plast. Techn., 7, 243 (1991).
30. J.E. Kresta and K.H. Hsieh, ACS Polym. Prep., 21, 126 (1980).
31. N.P. Vespoli and L.M. Alberino, Polym. Proc. Eng., 3, 127 (1995).
32. X. Sun, J. Toth, and L.J. Lee, Polym. Eng. Sci., 37, 143 (1997).
33. N. Malwitz, Cell. Polym. III, int. Conf., Paper 18, 1 (1995).
34. S.D. Lipshitz, and C.W. Macosko, J. Appl. Polym. Sci., 21, 2029 (1977).
32
An introduction to extrusion and polyurethanes
35. J.H. Saunders and K.C. Frisch, Polyurethanes chemistry and technology. Part 1,
Chemistry, Interscience publishers (1962).
36. K. Jöhnson, and P. Flodin, Brit. Polym. J., 23, 71 (1990).
37. O. Imawaga, F. Ishimaru, Y. Kurahashi and T. Yamada, Polym. React. Eng., 4, 47
(1996).
38. K.J. Dorozhkin, V.J. Kimelblat, and J.A. Kirpikznikov, Vysokomol. Soed. A., 23, 1119
(1981).
39. A. Petrus, Int. Chem. Eng., 11, 314 (1971).
40. E.B. Richter, and C.W. Macosko, Polym. Eng. Sci., 18, 1012 (1978).
41. E.C. Steinle, F.E. Critchfield, and C.W. Macosko, J. Appl. Polym. Sci., 25, 2317 (1980).
42. P. Król, J. Appl. Polym. Sci., 57, 739 (1995).
43. G. Odian, Principles of Polymerization, John Wiley & Sons Inc., New York (1991).
33
3 Rheo-kinetic measurements in a measurement
kneader
3.1 Introduction
To establish reliable kinetics of thermoplastic polyurethane polymerization is not a
straightforward task. The monomers from which thermoplastic polyurethane is
produced in general are poorly miscible. Therefore, a combination of diffusion and
reaction determines the reaction rate observed for each measurement of the
kinetics. Diffusion limitation may be noticeable during the initial part of the
reaction and at high conversions. In the early phase of the reaction, mixing will
enhance the observed reaction velocity, through improvement of the micro-
stoichiometry and through enlargement of the contact surface of the immiscible
monomers. At the end of the reaction, the mobility of the end-groups and of the
catalyst is much lower due to the large polymer molecules that have formed. This
limited diffusion at high conversions may also have an impact on the observed
reaction velocity. As a consequence of the competition between diffusion and
reaction, the measurement of the kinetics for TPU polymerization are best
performed at the same temperature and the mixing conditions as occur in the
application for which the kinetic investigation is intended. For instance, for reactive
injection molding the reaction takes place at temperatures between 30°C and 120°C,
the reaction mass initially experiences a high shear and after the injection the
reaction mass remains stagnant. Adiabatic temperature rise experiments (ATR),
which are performed under the same stagnant conditions, are for that reason best
suited to establish the kinetics in reactive injection molding.
Applying this requirement to reactive extrusion would mean that measurement of
the kinetics should be performed under shear conditions and at high temperatures
(150°C-225°C). These conditions are available in a rheometer and in a measurement
kneader. However, both instruments are not specifically designed for measurement
of the kinetics. Measurement kneaders, for instance, are mostly used for (reactive)
blending of polymers as was done by Cassagnau et al. (1) or for rubber research (2).
Both instruments have a drawback if they are used for measurement of the kinetics:
in both instruments the extent of the reaction can only be followed indirectly
through the increase in torque. In order to correlate the torque to the reaction
conversion, a calibration procedure is necessary for which samples must be taken.
Simultaneous measurement of conversion in the rheometer or kneader would make
Chapter 3
this sampling procedure superfluous. Unfortunately, no obvious method is available.
An adiabatic method as applied by Lee et al. (3) or Blake et al. (4) is not apt, due to
the lack of heat production at higher conversions. A combination of rheology with a
spectroscopic method, for example with fiber optic IR or Raman spectroscopy, has
not been reported yet for polyurethanes. The accuracy at high conversion is not
sufficient, and a stagnant polymer layer may form on the measurement cell.
If we return to the comparison between a rheometer and a kneader, a rheometer
seems more suitable for measurement of the rheo-kinetics, since, in a rheometer,
the viscosity can be measured directly. Nevertheless, a measurement kneader is
preferred in this research. The reasons for this are:
• The mixing behavior in a kneader resembles the mixing behavior in an
extruder more closely, with both dispersive and distributive mixing action
and both simple shear and elongational flow.
• Highly viscous material can be processed more accurately in a kneader,
because in a rheometer, constant shear experiments at shear rates that are
comparable to those occurring in an extruder are sensitive to edge failure
and demand a high torque.
• Sampling of a small amount of material does not disturb the measurements
in a kneader, whereas rheology measurements are gravely affected by
taking (several) samples.
• Temperature control in a kneader is straightforward. In a rheometer,
temperature control becomes complicated at temperatures above 150°C
since both cone and plate must be heated in that case.
There are several studies known in which the kinetics of TPU polymerization is
measured under mixing conditions (3 - 8). All of these measurements were
performed at relatively low temperatures (<90°C) and mostly on cross-linking
systems. Therefore, no high conversions could be reached, since the gellation
temperature was reached reasonably early in the reaction (around 70% conversion).
Methods for measuring the kinetics that do reach high conversions are largely
‘zero-shear’ methods. As is the case for radical polymerization (9), little attention
has been paid to the interaction between mixing and reaction in step
polymerization. Often it is expected for step polymerization that shear does not
have a major impact on the reaction velocity due to the relatively high mobility of
the reactive end groups of a polymer chain. Malkin et al. (10), for instance, state
36
Rheo-kinetic measurements in a measurement kneader
that any observed acceleration of the reaction speed for poly-condensation
reactions can usually be ascribed to viscous heating of the reaction mass.
Schollenberger et al. (11) performed the only study known to us in a measurement
kneader. Unfortunately, no quantitative data were obtained in this study. So no
reliable data on the kinetics exist on TPU polymerization in an extruder, although
this is a large industrial process. Therefore, this chapter focuses on the acquisition
of relevant data on the kinetics for extruder modeling. A new method is presented,
which is based on performing experiments in a measurement kneader. In a kneader,
the measurement conditions are more similar to those in an extruder in comparison
to existing methods for measuring the kinetics. Quantitative kinetics and
rheological data can be obtained through this method; moreover, the effect of
mixing on the polymerization reaction can be investigated.
3.2 Experimental section
3.2.1 The kneader
The kneader used in this research was a Brabender W30-E measurement mixer. A
picture of the non-intermeshing torque mixer is shown in figure 3.1. Two triangular
paddles counter-rotate in a heated barrel. The barrel can be closed with a (heavy)
plug. The volume of the kneader is 30 cm3.
e
kneading
paddles
Figure 3.1 The Brabender measurement kneader.
The kneader is driven by a Brabender 650-E Plastic
combination with two control thermocouples (one i
kneader section) keep the kneader on the set tem
37
back plat
g e
front platorder. T
n the ba
peratur
plu
wo heating elements in
ck-plate and one in the
e (Tset
). A thermocouple
Chapter 3
sticking in the non-intermeshing zone of the kneading chamber is used for the
measurement of the temperature of the melt (Tmeasure
). The torque and temperature
development in the kneader can be followed by means of a data acquisition system.
3.2.2 Experimental method
Preparations before an experiment
The TPU system for the experiments discussed in this chapter consisted of:
• A polyester polyol of mono-ethylene glycol, di-ethylene glycol and adipic
acid (MW = 2200 g/mol, f = 2).
• Methyl-propane-diol (Mw = 90.1 g/mol, f = 2).
• A eutectic mixture (50/50) of 2,4 diphenylmethane diisocyanate (2,4-MDI)
and 4,4 diphenylmethane diisocyanate (4,4-MDI). (Mw = 250.3 g/mol, f = 2).
The percentage of hard segments was 24%. The reaction was catalyzed using
bismuth octoate. Both the polyester polyol as the methyl-propane-diol were dried
under vacuum at 60°C and stored with molecular sieves (0.4 nm) prior to use. The
isocyanate was used at 50°C. Just before an experiment the polyol, diol, isocyanate,
and catalyst were weighed in a paper cup and mixed, using a turbine stirrer at 2000
rpm for 15 seconds. Experience showed that this premixing was necessary to
obtain reproducible results. About 30 grams of the premixed reaction mixture was
transferred to the kneader with a syringe. The exact amount of reaction mixture
was determined by weighing the syringe before and after filling the kneader. The
kneader measurement was started upon filling.
Sampling
In order to relate torque to molecular weight, samples were taken and analyzed (see
theoretical section). The sampling method consisted of removing the stamp of the
kneader, collecting the sample with tweezers, followed by quenching the material in
liquid nitrogen. After taking a sample the stamp was put back on the kneader; the
whole sampling routine had a negligible influence on the torque during a very short
period. In order to inactivate the still reactive isocyanate end-groups the samples
were dissolved in THF with 5% di-butylamine. The samples were subsequently dried
and used for size exclusion chromatography analysis.
3.2.3 Size Exclusion Chromatography (SEC)
Samples were analyzed for their molecular weight distribution by size exclusion
chromatography (Polystyrene calibrated). The chromatography system consisted of
38
Rheo-kinetic measurements in a measurement kneader
two 10 µm Mixed-B columns (Polymer Laboratories) coupled to a refractive index
meter (GBC RC 1240). The columns were kept at 30°C. Tetrahydrofuran (THF) was
used as mobile phase and the flow rate was set to 1ml/min. The molecular weight
distribution was analyzed using Polymer Laboratories SEC-software version 5.1.
About 25 mg of polymer was dissolved in 10ml of THF; the dissolved samples were
filtered on 0.45-µm nylon filters.
3.3 Theory of measurement of the kinetics
The objective of this study is to determine the reaction rate constant for the
formation of the thermoplastic polyurethane under investigation. Therefore, the
torque and temperature curves measured in the kneader must be translated into a
time-dependent conversion curve. For condensation polymerization conversion,
molecular weight (M) and viscosity (η) are related in a straightforward way. However,
it is impossible to derive the conversion (p) directly from the viscosity. This is called
the ‘direct rheo-kinetic problem’ by Malkin (10). The relationship between viscosity
and molecular weight has to be established first, before conclusions can be drawn
on the reaction pattern (figure 3.2). In addition, there is a complicating factor in a
measurement kneader. Due to the complicated flow profile in a kneader it is not
immediately clear how the measured torque can be related to the viscosity.
Nevertheless, a (simplified) flow analysis can tackle this problem. Subsequently, the
relationship between the torque and the molecular weight can be established.
Chemistry Kinetics p (t)
M (p) M (t)
η (M) η (t) Rheology
Figure 3.2 The rheokinetic scheme (10).
39
Chapter 3
3.3.1 Rheology basics
A simplified model of the kneader forms the basis of the flow analysis. The true
geometry of the kneader is simplified as shown in figure 3.3.
Figure 3.3 A simplification of the flow geometry in the measurement kneader.
The shear stress can then be calculated using a flat-plate approach for which the
paddle is considered stationary and the barrel moves with a velocity Vb. The shear
stress (τ) at the wall is then equal to:
⎟⎠
⎞⎜⎝
⎛ π⋅η−=γη−=τ
HDN
Mappapp & (3.1)
The factor M can be calculated through a flow analysis, for which the height H is a
function of the angular coordinate. The viscosity is written as the apparent viscosity
(ηapp
), since for our polymeric material a Newtonian approach is inaccurate. The
value of the torque acting on a paddle is opposite to the torque value experienced
by the barrel wall, and is equal to the force acting on the wall times the lever arm.
)2/D()DW(ArmLever)StressShearArea(Torque ⋅τ⋅π=⋅⋅= (3.2)
For two paddles, this equals:
appapp
32
NCNH
WDMTorque η⋅⋅=η⋅⋅
π= (3.3)
40
Rheo-kinetic measurements in a measurement kneader
C can be considered as a geometry factor. The manufacturer of the kneader gives a
similar equation to correlate torque to viscosity, with the constant C equal to 50.
Equation 3.3 shows that for a Newtonian fluid the torque is directly proportional to
the viscosity of the material in the kneader. If we consider the polyurethane as a
power-law liquid, equation 3.3 can be rewritten to:
0n' NCTorque η⋅⋅= (3.3a)
The next step, necessary for tackling the direct rheo-kinetic problem is to correlate
the viscosity of the polymer to its weight average molecular weight. It is well
established experimentally as well as theoretically that for an ‘entangled’ linear
polymer:
4.3WM)T(A ⋅=η (3.4)
A(T) is a proportionality-factor that is temperature dependent. For linear amorphous
polymers A(T) can be described with a Williams-Landel-Ferry-equation (WLF-
equation) or with an Arrhenius-type of expression. In general, for a temperature
less than 100°C above the glass transition temperature (Tg) of the polymer, a WLF-
equation is preferable. For higher temperatures, an Arrhenius-type expression is
best-suited (12). For polyurethanes, the value of Tg is dependent on the specific
chemicals used but for most polyurethanes Tg does not exceed 320K (13). An
Arrhenius-type of expression should therefore be suitable to describe the
temperature dependence of viscosity for the temperature range under consideration
(400 - 475K).
If equation 3.3a and 3.4 are combined, the following equation results:
n'4.31
W NC)T(A)T('Awith)T(A
TorqueM ⋅⋅=⎟
⎠
⎞⎜⎝
⎛′
= (3.5)
The torque is now related to the molecular weight. If the function A’(T) is known,
the weight average molecular weight versus time for the TPU-reaction can be
calculated from the logged torque and temperature values. By analogy with the
temperature dependence of the viscosity the temperature dependence of A´(T) can
be described using an Arrhenius-type equation:
41
Chapter 3
TRU
0
A
eA)T('A ⋅⋅= (3.6)
In order to relate torque to the molecular weight, the flow activation energy (UA) and
pre-exponential factor (A0) in equation 3.6 must be known. These constants can be
found through a ‘calibration procedure’. For this procedure, samples are taken from
the kneader and analyzed for their molecular weight with size exclusion
chromatography (SEC). Samples of different molecular weights and samples taken
at different reaction temperatures are necessary for the procedure. The molecular
weight can be calculated from torque and temperature (Tmeasure
) values using
equation 3.5 and 3.6. The calculated and measured molecular weight can be
compared, and the optimal value for A0 and U
A can be found through a least-square
fitting routine.
3.3.2 Basics of the kinetics
From the molecular weight versus time curve, the kinetics of TPU-polymerization
can be obtained. Although the exact reaction mechanism is more complex, the TPU
polymerization reaction is often described successfully with a second order rate
equation (14), as is described in chapter 2.
[ ] )t])Cat[,T(kNCO21(MM 0repW ⋅⋅⋅+⋅= (2.15)
Equation 2.15 shows that the molecular weight increases linearly in time. Since Mrep
and [NCO]0 are constants, the slope of the molecular weight
versus time curve is
proportional to the reaction rate constant k(T,[cat]):
[ ] ])Cat[,T(kNCOM2dt
dM0rep
W ⋅⋅⋅= (3.7)
If A0 and U
A are known, the torque versus time graph can be translated into a
molecular weight versus time graph (equation 3.5). From the slope of this curve and
by applying equation 3.7, the value of the reaction rate constant can be calculated.
If experiments are performed at different temperatures and at a constant catalyst
level, an Arrhenius-expression can be established for the reaction rate constant.
42
Rheo-kinetic measurements in a measurement kneader
There is just one limitation. According to equation 2.15, the molecular weight will
rise to infinity at longer reaction times. In practice, this will not happen. Several
phenomena may cause a leveling off the molecular weight and torque values at
longer reaction times:
• The initial ratio of alcohol groups to isocyanate groups will never be exactly
unity. This stoichiometric imbalance will limit the maximum conversion.
• Chain scission. The long molecules that are present at longer reaction
times are prone to scission due to shearing.
• Depolymerization (chapters 2.3.4, 2.3.8)
• Allophanate formation (chapter 2.3.6). The high concentration of urethane
bonds together with the continuous presence of a small portion of free
isocyanate groups due to depolymerization can give rise to allophanate
formation. Allophanate formation causes branched molecules.
Polydispersity will therefore increase but since also the stoichiometry of
reactants is affected, the net effect on the molecular weight is not clear.
Due to branching the A-factor in equation 4 may change.
• A last reason why MW will not rise to an infinite value is degradation. This
will of course limit the maximum MW.
All of these factors gain importance at longer reaction times and at higher
molecular weights. Therefore, reliable data for the kinetics using the measurement
kneader are best obtained during the initial stage of the reaction.
3.4 Results
3.4.1 A typical kneader experiment
Figure 3.4 shows a typical graph obtained for a kneader experiment. The torque
and the temperature are shown as a function of time. As expected, the torque
increases over time due to the polymerization reaction. The torque curve in figure
3.4 reaches a steady value after 15 minutes. After an initial drop due to the filling
of the kneader, the temperature also rises steadily to a constant value.
43
Chapter 3
0
1
2
3
4
5
0 2 4 6 8 10
Time (min)
Torq
ue (N
m)
130
150
170
190
Tem
pera
ture
(°C
)
Figure 3.4 The torque and temperature versus the time in the measurement kneader. Tset
=
175°C, 80 RPM.
Clearly, viscous dissipation plays an important role in the kneader; the dissipated
heat cannot be completely removed through the walls. In general, the measured
temperature exceeds the set temperature (in figure 3.4 Tset
= 175°C). Analysis of the
experimental curves shows that the temperature increase due to viscous dissipation
(∆Tviscous
= Tmeasure
-Tset
) is proportional to the torque value with a proportionality factor
of 2 °C / Nm.
3.4.2 The determination of the flow activation energy and the pre-
exponential factor
The torque-temperature graph can be converted into a molecular weight versus
time graph using equation 3.5. To do so, the function A’(T) must be known, which
means that the flow activation energy (UA) and flow pre-exponential factor (A
0) have
to be established. To determine these constants, experiments were performed at
four different set-temperatures (125, 150, 175, 200°C). Every experiment was
repeated three times; 4 to 5 samples were taken per experiment at different
reaction times. The molecular weights of these samples were determined and
obviously, the value of the torque and the temperature at the moment a sample was
taken is also known. UA and A
0 can now be established by fitting the measured
molecular weight to equations 3.5 and 3.6, with UA and E
A as the fit parameters.
Figure 3.5 shows the resulting parity plot in which the measured molecular weight
is plotted against the calculated one. For the whole range of molecular weights, the
agreement is good.
44
Rheo-kinetic measurements in a measurement kneader
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 20000 40000 60000 80000 100000
Mw measured
Mw
cal
cula
ted
Figure 3.5 Parity plot for the calculated and measured molecular weight.
The values obtained for UA and A
0 are respectively 42.7 kJ/mol and 7.2⋅10-22
N⋅m⋅mol3.4/g3.4 (see table 3.1). In general, thermoplastic polyurethanes have a much
higher flow activation energy (100 - 200 kJ/mol) than is normally expected for
linear polymers. The hard segments that are present in thermoplastic polyurethanes
cause this effect. Hard segments are associated in hard domains and are physically
cross-linked, which gives rise to a higher resistance to flow. Dissociation of the hard
domains takes place at temperatures between 150°C and 200°C, depending on the
composition of the polyurethane. Beyond that temperature, the flow behavior will
be that of a normal linear polymer. However, for the polymer under investigation,
the hard segments will dissociate at a much lower temperature.
UA (kJ/mol) 42.7 E
A (kJ/mol) 61.3
A0 (N⋅m⋅mol3.4/g3.4) 7.2⋅10-22 k
0 (mol/kg K) 2.18⋅10-6
Table 3.1 The flow and kinetic parameters for the TPU under investigation.
This is caused by the relatively low percentage of hard segments (24%) and the
composition of the hard segments. The hard segments are built from a bulky chain
extender and an isocyanate blend containing 50% 2,4-MDI. Steric hindrance,
therefore, complicates association of the hard segments and improves the
compatibility of the hard and soft segments. The flow activation energy found (42.7
45
Chapter 3
kJ/mol) confirms this expectation, as it falls within the expected range for linear
polymers (15). This result implies that for the TPU under investigation the hard
segments are molten and completely dissolved in the soft segments, already at
125°C.
3.4.2 The determination of the reaction rate constant
The torque and temperature versus time curves of figure 3.4 can be translated into
a plot of molecular weight versus time by applying equations 3.6 and 2.15. Figure
3.6 shows this plot for three repeated experiments at 175°C. The lines represent
the molecular weights as calculated from the torque and temperature and the dots
are the measured molecular weights. The agreement between the three
experiments is reasonably good. In general, the reproducibility was somewhat
better at higher temperatures. Long reaction times in combination with higher
molecular weights seemed to cause the reproducibility to become worse. The initial
slopes are straight, which supports the second order assumption of the rate
equation.
0
30000
60000
90000
120000
0 4
Time [min]
Mw
(g/m
ol)
8
Figure 3.6 The weight average molecular weight versus time in a measurement kneader.
Tset
= 175°C, 80 RPM.
The reaction rate constant can be derived from the relation between molecular
weight and time by determining the initial slope of the curves (e.g. in figure 3.6 the
average slope between 0 and 4 minutes). As stated earlier, the initial slope gives
the most reliable information on the kinetics. In table 3.2, the different slopes with
their confidence intervals are shown as well as the value for the reaction rate
46
Rheo-kinetic measurements in a measurement kneader
constant k. The reaction rate-constant is calculated using equation 3.7. It increases,
as expected, with increasing temperature. The temperature in table 3.2 is the
measured temperature, Tmeasure
. Since the kneader does not operate completely
isothermally, there is always a temperature range over which the slope is
determined. The mentioned temperature, Tmeasure
, is the average temperature over
which the slope is measured. This temperature range never exceeded 5°C.
Temperature
(°C)
Slope
(MW/min)
Average slope / 1000
(MW/min)
k (kg/mol s)
194.3
42154
47070
44246
44 +/- 6 0.37 +/- 0.06
173.4
17030
17684
18316
17.6 +/- 1.6 0.147 +/- 0.014
149.6
7134
6546
7784
7.2 +/- 1.6 0.060 +/- 0.012
123.3
2172
2416
2332
2.3 +/- 0.4 0.0192 +/- 0.002
Table 3.2 The slopes and the kinetic results obtained from the kneader experiments.
Now, the kinetic constants can be derived from an Arrhenius plot (figure 3.7). The
values obtained for EA and k
0 are respectively 61.3 kJ/mol and 2.18e6 mol/kg K (see
also table 3.1). Three conclusions can be drawn from figure 3.7 and table 3.1. First,
the straight line in the Arrhenius-plot is an extra confirmation that the second order
rate equation holds for the temperature range considered. Secondly, the value of EA
falls within the range reported for TPU-polymerization (30-100 kJ/mol). The scatter
in activation energies reported in the literature are caused by the different catalysts
and chemicals used. Finally, the plot shows that within the experimental
uncertainties that are inevitable for measurement kneader experiments,
quantitative kinetic and rheological results can be obtained.
47
Chapter 3
-5
-4
-3
-2
-1
00.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026
1/T (1/K)
ln(k
) (m
ol/k
g s)
Figure 3.7 The Arrhenius-plot for the kneader experiments.
3.4.3 Evaluation of the kinetic model
Model predictions are compared to experimental data in figure 3.8 in order to
check the correctness of the obtained kinetic parameters. The slopes of the model
prediction and of the experimental results are in good agreement with each other,
which is a confirmation of the data on the kinetics. However, both at the start and
near the end of the reaction, the model and experiment do not coincide. A closer
look at the starting point of the reaction reveals that the initial molecular weight is
much higher than anticipated. For this reason, the model equation (equation 2.15)
is adapted in figure 3.8, to correct for the initial high molecular weight:
[ ] )t])cat[,T(kNCO21(M17000M 0repW ⋅⋅⋅+⋅+=
The value of 17000 for the molecular weight at t=0 is for all temperatures the same,
and is fitted to the experimental curves. This correction is needed, since, at the
start of the measurement, the reaction has already started due the premixing
procedure. However, the molecular weight at the start of the measurement is
unexpectedly high. A calculation learns that, with the kinetic constants obtained in
this research, the molecular weight after the premixing procedure should not
exceed 1500. The difference corresponds to an observation that other authors (16,
17) have also made for TPU-polymerization. The initial low-viscosity part of the
reaction proceeds much faster than the last high-viscosity part of the reaction. This
observation has been verified through ATR-experiments for this system (data not
48
Rheo-kinetic measurements in a measurement kneader
shown). With an initial temperature of 50°C and the same catalyst level as for the
kneader experiments, the reaction reaches a conversion of about 80-90% within 30
seconds.
0
30000
60000
90000
120000
150000
0 4 8
Time [min]
Mw
[g/m
ol]
12
1 7 5 °C
1 2 5 °C
150°C2 0 0 °C
Figure 3.8 The measured and calculated weight average molecular weight versus time.
The explanation of the tremendous decrease in the observed reaction velocity at
higher conversions falls under the term ‘diffusion limitation’. As soon as high
molecular weight material is formed the mobility of the catalyst or the end groups
decreases, which causes a decrease in the observed reaction velocity. The exact
nature of this phenomenon cannot yet be understood due to the limited range of
these experiments. This problem will be the subject of further experimental
research.
At the end of the reaction, the experimental molecular weight levels off to a steady
value. It is improbable that the initial stoichiometric deviation of at most 0.2% is the
cause of this. An imbalance of 0.2% in stoichiometry leads to an equilibrium
molecular weight of 350,000, which is much higher than the maximum molecular
weight reported for this investigation. For the two high temperature runs, it is very
probable that depolymerization has a major impact on the last part of the reaction
and that, therefore, the reverse reaction is the predominant cause of the leveling of
the MW-curve. For the two low temperature runs, the situation is less distinct. Figure
3.8 shows that for the 200°C and 175°C experiments a higher temperature leads to
a lower ‘equilibrium’ molecular weight. This trend is hardly visible for the 150°C run
49
Chapter 3
and not visible at all for the 125°C run, because these runs are not completed
within the time shown. Longer reaction times are here necessary to get to an
equilibrium situation. Unfortunately, the results at long reaction times are less
reproducible. The color of the polymer coming out of the kneader is light
brown/yellow but deepens at longer reaction times. Degradation, therefore,
interferes with experiments that last longer. An obvious indication of allophanate
formation has not been found.
The kinetic model obtained in this research appears to have a limited validity. Still,
an important part of the reaction is captured with this model. The initial, fast
reaction takes only five percent of the total reaction time. Therefore, to predict the
necessary residence time in an extruder the kinetic model obtained in this study is
indispensable. However, an expansion of the model is desirable. At low conversions,
the reaction proceeds much faster than the measured data indicate. On the contrary,
at very high conversions the reaction stops, while the model for the kinetics
predicts a continuous increase of the molecular weight. For the low conversion part,
adiabatic temperature experiments need to be performed to get the kinetic
constants for this part of the reaction. Subsequently, these data can be combined
with the data obtained from the kneader in order to complete the model of the
kinetics. For the very high conversion part of the reaction, depolymerization needs
to be taken into account. Future experimental work will be directed towards
depolymerization and low conversion experiments, to complement the present
results.
50
Rheo-kinetic measurements in a measurement kneader
3.5 Conclusions
Investigations on the kinetic of TPU polymerization, performed in a measurement
kneader, show that quantitative kinetic and rheological data can be obtained using
this method. The method has advantages over other measurement methods since
the reactants are mixed during the experiment, mimicking real processing
conditions. Therefore, for applications where the reaction takes place under mixing
conditions, as is the case for reactive extrusion, the parameters obtained for the
kinetics will be more accurate. Besides, the effect of mixing on the polymerization
reaction can be investigated using this method.
The kinetic data obtained prove that a second order reaction can be used to
describe TPU polymerization. The experiments indicated that a fast initial reaction
is followed by a slower ‘high conversion’ part of the reaction. At the end of the
reaction, the molecular weight levels off due to depolymerization and degradation.
More experiments are necessary to elucidate these effects.
Because of the complex geometrical form of the kneader, the viscosity-value
obtained with a measurement kneader is not very accurate. Therefore, no attempt
has been made to correlate the torque values to viscosity values. Nevertheless, the
activation energy of flow could be established. The activation energy of flow falls
within the range expected for linear polymers, which indicates that the hard
segments are completely dissolved in the soft segments.
51
Chapter 3
3.6 List of symbols
A0 Flow pre-exponential constant N⋅m⋅(mol/g)3.4
A(T) Empirical constant which relates viscosity to MW Pa⋅s⋅(mol/g)3.4
A’(T) Empirical constant which relates torque to MW N⋅m⋅(mol/g)3.4
[Cat] Catalyst concentration mg/g
C, C’ Geometry factor of the kneader m3
D Diameter of barrel m
EA Reaction activation energy J/mol
H Average distance between barrel and paddle m
k0 Reaction pre-exponential constant mol/kg s
Mrep
Average weight of repeating unit g/mol
MW Weight average molecular weight g/mol
n Power law index -
N Rotation speed 1/s
[NCO] Concentration isocyanate groups mol/kg
[NCO]0 Initial concentration isocyanate groups mol/kg
R Gas constant J/mol K
T Temperature K
Tg Glass transition temperature K
Tmeasure
Measured temperature of material in kneader K
Tset
Set temperature of the kneader K
Torque Torque N⋅m
t Time s
UA Flow activation energy J/mol
Vb Barrel velocity m/s
W Width barrel m
Greek symbols
γ& Shear rate 1/s
ηapp
Apparent viscosity Pa⋅s
η0 Consistency Pa·sn
τ Shear stress Pa
52
Rheo-kinetic measurements in a measurement kneader
3.7 List of references
1. P. Cassagnau, F. Mélis, and A. Michel, J. Appl. Polym. Sci., 65, 2395 (1997).
2. A. K. Maity, and S. F. Xavier, Eur. Polym. J., 35, 173 (1999).
3. Y.M. Lee, and L.J. Lee, Intern. Polym. Process., 1, 144 (1987).
4. J.W. Blake, W.P. Yang, R.D. Anderson, and C.W. Macosko, Polym. Eng. Sci., 27, 1236
(1987).
5. D.S. Kim, M.A. Garcia, and C.W. Macosko, Intern. Polym. Process., 13, 162 (1998).
6. X. Sun, J. Toth, and L.J. Lee, Polym. Eng. Sci., 37, 143 (1997).
7. J.M. Castro, C.W. Macosko and S.J. Perry, Polymer. Comm., 25, 82 (1984).
8. R. John, N.T. Neelaqkantan, and N. Subramanian, Thermochim. Acta, 179, 281
(1991).
9. M. Cioffi, K.J. Ganzeveld, A.C. Hoffmann, and L.P.B.M. Janssen, Polym. Eng. Sci., 42,
2383 (2002).
10. A. YA. Malkin, and S. G. Kulichikhin, Rheokinetics, Hüthig & Wepf, Heidelberg,
Germany (1996).
11. S. Schollenberger, K. Dinbergs, and F. D. Stewart, Rub. Chem. Tech., 55, 137 (1981).
12. C. W. Macosko, Rheology, VCH Publishers Inc., New York (1993).
13. J. Brandrup, E. H. Immergut, A. Abe, and D. R. Bloch, Polymer handbook, Wiley, New
York (1999).
14. C. W. Macosko, RIM - Fundamentals of Reaction Injection Molding, Hanser, Munich
(1989).
15. D. W. Van Krevelen, Properties of Polymers, Elsevier, Amsterdam (1990).
16. T. Hentschel, and H. Münstedt, Polymer, 42, 3195 (2001).
17. X. Sun, and C. S. P. Sung, Macromolecules, 29, 3198 (1996).
53
4 A comparison of different measurement methods for
the kinetics of polyurethane polymerization
4.1 Introduction
In the previous chapter a method is described which can be used to measure the
kinetics of polyurethane polymerization for reactive extrusion purposes. Compared
to common methods the method described offers in principle the advantage that
measurements can be performed at high temperatures under mixing conditions,
mimicking extrusion conditions. In the current chapter, this is investigated by
comparing the results of other measurement methods for kinetics with the results
of the kneader experiments.
Technique Conversion range Mixing Temperature
Low
(<98%)
High
(>98%) Yes / No
Low
<60°C
Middle
60-
140°C
High
>140°C
Titration + No +
FT-ir + No + +
ATR + Yes* +
SEC + No + +
NMR + No +
Fluorescence + No +
Rheometry ± + Yes + + * Only premixing
Table 4.1 Different kinetic measurement techniques.
Several techniques have been used for the acquisition of data on kinetics (1, 2, 3, 4).
Commonly used methods are titration, Fourier-transform infrared (FT-IR), adiabatic
temperature rise (ATR) and size exclusion chromatography (SEC). Less common
methods are fluorescence and NMR measurements. Unfortunately, the method
applied often poses limits to the reaction conditions. In general, the reaction should
not be too fast for all of these methods. Therefore, it is often necessary to keep the
temperature and catalyst level low for the measurement of the kinetics. This limits
the predictive window of the investigation, as reactive processing will usually occur
Chapter 4
at high temperature and catalyst loading. In table 4.1, several techniques are
compared. At first, the division of the conversion range in table 4.1 seems a little
peculiar since the transition between ‘low’ and ‘high’ conversion is set at 98%.
However, at this conversion the methods measuring the decrease of reactive groups
become imprecise, while the methods that depend on the size of the molecules
become more accurate above 98% conversion.
If we now look at the extrusion process for polyurethane polymerization, the
monomers are fed to the extruder at a temperature of 60 - 80 °C. The temperature
of the reaction mass increases rapidly in the first part of the extruder, mainly due
to the fast exothermic reaction. Heat transfer through the wall and viscous
dissipation are still of minor importance. For this part of the reaction, the reaction
conditions more or less mimic adiabatic temperature rise measurements, although
no mixing is present during adiabatic temperature rise experiments. However, the
situation changes as soon as high molecular weight material appears. At that
moment, the reaction velocity will have slowed down considerably (due to the
second order nature of the reaction) and relatively little reaction heat will be
generated. Furthermore, the temperature of the reaction mass will be well over
160 °C. In this regime, ATR-experiments will give a poor prediction of the reaction
kinetics since the small heat of reaction will give a large error in the ATR-
measurements. Methods based on molecular weight measurements, such as size
exclusion chromatography or rheology, are more suitable in this situation.
Therefore, two different measurement methods seem necessary to establish the
kinetics for the modeling of the polyurethane polymerization in an extruder. Of
course, this is only the case if a different reaction temperature and different mixing
condition result in a different behavior. In paragraph 4.2, this subject will be
discussed in more detail.
Nevertheless, in the few studies on thermoplastic polyurethane extrusion that are
known in literature (5 - 9) only a single method was used to measure the kinetics.
Either adiabatic temperature rise measurements or size exclusion chromatography
are used in these studies, inevitably leading to the described errors. The
importance of these errors was investigated experimentally; the results are
described in this chapter. The different methods will be compared with respect to
the Arrhenius-behavior, the influence of the catalyst and the effect of mixing. Three
different methods are surveyed: adiabatic temperature rise, size exclusion
chromatography and kneader measurements. Two different thermoplastic
polyurethane systems are investigated in order to further validate the number of
56
A comparison of different kinetic measurement methods
measurement methods that are required to determine the kinetics of polyurethane
polymerization for reactive extrusion purposes.
4.2 Reaction Kinetics
For polyurethane polymerization, a few key phenomena may lead to a change in the
observed activation energy and reaction rate with temperature and mixing:
• Different rate limiting steps may dominate at different temperatures, giving
a change in activation energy and reaction rate. As explained in chapter
2.3.8, the multi-step reaction mechanism for the urethane formation is
often condensed in a second order rate equation. This simplification may
lead to erroneous extrapolation of the kinetics.
• Miscibility of the monomers. Due to the incompatibility of the monomers,
an interfacial reaction will initially take place. If and how this affects the
reaction will be described in paragraph 4.2.1.
• Diffusion limitation at high conversion. The reaction may slow down due to
the appearance of large molecules. To what extent this affects the reaction
will be described in paragraph 4.2.2.
• Phase separation. Phase separation of hard and soft segments (as described
in paragraph 2.2) may give differences in local concentration of reactive
groups. Moreover, the rigid hard segments may slow down the reaction rate
by restricting the mobility of the molecules.
• Depolymerization. When the reverse reaction occurs (paragraph 2.3.4), as is
the case at elevated temperatures, the observed reaction velocity will be
slower. If this is not accounted for, an extrapolation of the result on
kinetics will results in erroneous predictions.
4.2.1 Miscibility of the monomers
Due to incompatibility of isocyanate and alcohol molecules, the reaction will take
place on and near the interface, and interfacial effects will influence the reaction.
These interfacial aspects of polyurethane polymerization have been investigated in
several publications (10 - 12). The starting point of these investigations was to
evaluate the effect of impingement mixing, since many polyurethane products are
made through a reactive injection molding processes where generally impingement
mixing is an important process step. Kolodziej et al. (13) found that impingement
mixing gives a dispersion with droplets that are still quite large (> 100 µm). An
increase of the Reynolds number above 200 did not seem to decrease the droplet
57
Chapter 4
size any further. This droplet diameter is far too high to result in a kinetically
controlled reaction. A second process is necessary to overcome these limitations.
This second (fast) mixing process seems to be related to surface instabilities.
Machuga et al. (14) confirmed the observation of other authors that the polyol
disappears more rapidly into the isocyanate than could be explained by pure
diffusion. They found that the dimers that are formed on the boundary layer of the
isocyanate and the polyol play an important role in this process. Probably, the
urethane groups of these dimers undergo H-bond interactions with the isocyanate
molecules across the border, resulting in strong surface destabilizing forces. It was
found that the initial growth of the interfacial zone was independent of the
monomers used. However, the further growth of this zone appeared to depend on
the viscosities of the species that were present. Rigid oligomer molecules, a fast
reaction, or the use of a crosslinking system limited the growth of the interfacial
zone, which results in a diffusion controlled reaction. The effect of catalyst on the
interfacial process is not clear. Wickert et al. (12) observed a much finer dispersion
with catalyst than without, while Machuga et al. (14) detected no difference between
catalyzed and uncatalyzed experiments.
4.2.2 Concept of functional group reactivity independent of molecule size
Another phenomenon that can have an effect on the polyurethane reaction is the
concept of functional group reactivity independent of molecule size. For
condensation polymerization reactions, it is normally assumed that the reaction
rate constant and the reaction mechanism are constant for the entire reaction (15).
The size of the molecules attached to a reactive group has no influence on the
reaction rate. In other words, possible diffusion limitations will have no effect. To
explain this it is assumed that a reactive group can be in two states: colliding with a
different reactive group, or diffusing to a next reactive group. If a long molecule is
attached to the reactive group, the diffusion time is longer, but the collision time is
also longer. A reactive group will switch many times between these states before it
actually reacts; therefore, the length of a molecule will not have a net effect on the
reaction rate. This hypothesis is applied successfully in many cases. However, the
theory does have a limitation; it does not hold for very long molecules or for very
fast reactions. The theory has been verified with rather slow reacting systems (treaction
> 100 minutes). The polyurethane reaction is much faster, especially at higher
temperatures. Whether this will result in a reaction that is diffusion limited can be
verified experimentally.
58
A comparison of different kinetic measurement methods
4.3 Experimental
4.3.1 Chemicals used
Two different polyurethane systems were used in this investigation. The difference
between both systems is the type of chain extender and the type of isocyanate used.
The two systems were selected on the basis of the difference in compatibility of the
chain extender and the isocyanate. This difference is expected to give a different
behavior upon mixing. Where system 1 is a common TPU system, system 2 is easier
to handle due to the liquid state of the isocyanate at room temperature. Both
systems have the same amount of hard segments (24.0 %) and use the same
catalyst (bismuth octoate). For all experiments, the pre-treatment of the monomers
was as described in paragraph 3.2.2.
System 1:
• A polyester polyol of mono-ethylene glycol, di-ethylene glycol and adipic
acid (MW = 2200 g/mol, f = 2)
• 1,4 butanediol (Mw = 90.1 g/mol, f = 2).
• 4,4 diphenylmethane diisocyanate (4,4-MDI). (Mw = 250.3 g/mol, f = 2).
System 2 (the same system as in chapter 3):
• A polyester polyol of mono-ethylene glycol, di-ethylene glycol and adipic
acid (MW = 2200 g/mol, f = 2).
• Methyl-propane-diol (Mw = 90.1 g/mol, f = 2).
• A eutectic mixture (50/50) of 2,4 diphenylmethane diisocyanate (2,4-MDI)
and 4,4 diphenylmethane diisocyanate (4,4-MDI). (Mw = 250 g/mol, f = 2).
Although the difference is not very large in the chemicals used in both systems, the
differences that do exist may well result in a different reaction pattern. The
following properties are affected:
59
Chapter 4
• The polyol and diol are more compatible for system 2 than for system 1;
therefore, the chain extender will dissolve at a lower temperature in system
2.
• The hard segments in system 1 will crystallize more readily. Both the
differences in chain extender and in isocyanate contribute to that. In
system 2 a methyl group on the chain extender will hinder the formation of
a layered structure of hard segments. In addition, the non-linear 2,4-MDI
that is present in system 2 will also be an obstacle for the crystallization of
the hard segments.
• The compatibility of hard and soft segments in system 2 is also different to
that of system 1. The use of methyl-propane diol as a chain extender in
system 2 may influence the solubility of the hard and soft segments in a
positive way.
• The polymer molecules formed are generally assumed to adapt a different
conformation, depending on the system. While system 1 produces a
completely linear molecule, the polymer molecules in system 2 will adopt a
more staggered/coiled structure, due to presence of non-linear 2,4 MDI.
• The reactivity of the end groups of both systems may differ. We expect that
the isocyanate group of 2,4-MDI that is placed in the ortho position will
have a comparable reactivity to that of an isocyanate group in the para
position. However, the approachability of the isocyanate group in the ortho
position will be less due to steric hindrance. Therefore, the reactivity of the
ortho-positioned isocyanate group may be lower than of the para-
positioned isocyanate group. This difference in reactivity may lead to a
lower overall reaction velocity.
4.3.2 Adiabatic Temperature Rise experiments
Adiabatic temperature rise (ATR) is a common method to measure the kinetics for
polyurethane polymerization. With this method, the polyurethane kinetics at
relatively low conversions and relatively low temperatures can be investigated. Many
authors have described the experimental procedure for ATR measurements (1). The
adiabatic reactor consisted of a paper cup (diameter = 5cm) surrounded by a layer
of urethane foam for insulation. The reactor could be closed with a lid. The lid was
equipped with a thin Copper Constantine thermocouple that stuck in the middle of
the reaction mass when the lid was closed. The reaction mass was stirred with a
turbine stirrer with a diameter of 4 cm. 200 grams (± 1 %) of material was used per
experiment. To start an experiment, the necessary amounts of polyol and diol were
60
A comparison of different kinetic measurement methods
weighed in the reactor and mixed for 60 seconds with a turbine stirrer at 600 RPM.
Care was taken to keep the temperature of the mixture above 60 °C, since demixing
will take place at lower temperatures for both systems. The proper amount of
catalyst was added with a syringe, and the polyol mixture was stirred for another 30
seconds. Finally, the proper amount of isocyanate was added with a syringe, and
the reaction mass was stirred at 1500 RPM for 15 seconds. The cover was put on
top of the reactor and the measurement was started.
Analysis of ATR results
In order to derive kinetic data from the ATR experiments, a simplified heat balance
(equation 4.1) and rate equation (equation 2.12) were solved simultaneously (3, 11).
For the heat balance, quasi-adiabatic conditions were assumed, since the reactor
was not completely adiabatic for the time period under investigation. Depending on
the reaction time, up to 4 % of the total reaction heat generated during the reaction
was lost to the surroundings. The heat transfer coefficient h* was obtained by fitting
the cooling curves of several experiments, using equation 4.1. We took the density
and the specific heat to be constant over the whole measurement range. Although
both the specific heat and the density are somewhat dependent on the temperature,
the temperature effects of both constants counteract, so that the net effect is
negligible (< 5%). A non-linear regression method (error controlled Runge-Kutta)
was used to solve the differential equations. With a least square routine, the
difference between the model and the measurement was minimized. The
calculations were performed with the software program Scientist.
( )
( )ρ⋅
⋅=−−∆⋅=⋅
−⋅⋅−∆⋅⋅ρ⋅=⋅⋅ρ⋅
VAh
hwithTThHRdtdT
C
orTTAhHRVdtdT
CV
*room
*RNCOp
roomRNCOp
( 4.1 )
[ ]
TRE
m0
TR
E
Uncat,0f
nfCat,NCOUncat,NCONCO
AUncat,A
e]Cat[AeAkwith
]NCO[kRRdt
NCOdR
⋅−
⋅
−
⋅⋅+⋅=
⋅−=+== ( 2.12 )
The fit procedure was as follows. Data obtained from the uncatalyzed runs on EA,Uncat
and A0,Uncat
were used as input parameters for the fit of the catalyzed runs. All the
catalyst dependent runs were fitted simultaneously, giving the values for EA, m and
A0. ∆H
R was taken from the experiment that gave the largest temperature rise.
61
Chapter 4
Representation of the ATR results
Often the results of ATR measurements are plotted straightforwardly as the
temperature versus the time. These plots give a clear view on ∆Tadiabatic
and a global
indication of the reaction velocity. A different method of plotting the results is to
translate the temperature versus time plot into an Arrhenius-plot. Although it is
much harder to visualize ∆Tadiabatic
in such a graph, these plots give more information
on the course of the reaction. The activation energy and the actual reaction velocity
constants are better illustrated. Furthermore, the effect of the catalyst on the
reaction velocity is clearly perceptible in these graphs. For an Arrhenius plot, the
reaction rate constant must be known as a function of temperature. The reaction
rate constant for an n-th order reaction can be calculated from an ATR experiment
according to Richter and Macosko (16):
dtdT
TTTT
]NCO[H
Ck
n
0tad
adn0R
pf ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛−+∆
∆⋅
⋅∆−
⋅ρ=
=
( 4.2 )
To account for the non-adiabatic conditions in our ATR reactor, the temperature
versus time curve that is obtained in an ATR experiment is modified. This modified
curve then serves as the basis for the calculation of the reaction rate constant
(equation 4.2). To modify the curve, the amount of heat lost must be calculated for
every time interval, starting at t = 0 (equation 4.3).
( roomp
*
loss TTtCh
T −⋅∆⋅=∆ ) ( 4.3 )
This temperature loss can be added to the measured temperature at that time
interval. In this way, a modified ATR curve can be constructed.
4.3.3 High temperature measurements
A method to follow the conversion of a polyurethane polymerization at higher
temperatures and conversions is for instance described by Ando et al. (17). In
contrast to ATR experiments, this method is based on isothermal measurements.
Small reaction flasks filled with premixed monomers are kept in a thermostatted
oilbath. The polymer in the flasks is allowed to react for a certain time.
Subsequently, the reaction is quenched and the samples are analyzed using size
exclusion chromatography. The kinetic constants are then derived from a plot of
the number average molecular weight versus time.
62
A comparison of different kinetic measurement methods
Two important conditions must be met in order to get meaningful results from this
method. First, it is important that the reaction flasks reach the oilbath temperature
much faster than the characteristic reaction time. For our experiments, an analysis
based on the Fourier number revealed that this condition is met if the reaction time
is larger than 15 minutes. This analysis does not take into account the reaction heat
generated in the flasks. However, the reaction heat released only helps to reach the
oilbath temperature sooner. Moreover, during the relevant part of the measurement,
hardly any heat is generated.
A second condition that must be met to obtain relevant results is related to the
analytical method. The molecular weight that is measured must represent the real
molecular weight of the sample. Since our SEC equipment is calibrated with
polystyrene samples, this requirement is not obvious. To check for this requirement,
the samples of one experiment have been analyzed on a second SEC system. This
second system was equipped with a triple detection system, so that the real
molecular weight could be determined. A comparison of the results of the two
systems revealed that the polystyrene calibrated system underestimated the weight
average molecular weights ten to twenty percent. The difference in number average
molecular weight was about ten percent. These errors are acceptable, which means
that the results obtained on the polystyrene calibrated column can be used for our
investigations on polyurethane kinetics.
Experimental procedure
The premixing procedure for these experiments was similar to that of the ATR
experiments. However, the premixing time was extended to 40 seconds to ensure
optimal mixing. After premixing, part of the reaction mass was transferred to small
1.5-ml reaction vials using a syringe. Subsequently submerging of the flasks in
liquid nitrogen quenched the reaction temporarily. The total premix, fill and quench
cycle took about two minutes. In the next step the flasks were capped while they
were still frozen, the capping was carried out in a nitrogen atmosphere to prevent
intrusion of moisture. The flasks were then submerged in a heated oilbath to restart
the reaction. After the desired reaction time, a flask was transferred quickly into a
beaker filled with liquid nitrogen. The flasks were broken and the content was
dissolved in a 5% solution of di-butyl-amine in tetrahydrofuran (THF). Subsequently,
the THF was evaporated. The samples obtained in this way were analyzed through
size exclusion chromatography (18). The SEC-procedure used is described in the
previous chapter (section 3.2.3). The experiments for system 1 were performed at
five different temperatures (150, 160, 170, 180, and 200 °C). The effect of catalyst
concentration was investigated at 150 °C. Furthermore, three different catalyst
63
Chapter 4
levels were investigated (0.005, 0.015, 0.05 mg / g). The experiments for system 2
were performed at seven different temperatures (150, 160, 170, 180, 190, 200 and
210 °C). Every experiment was done at least once. The effect of catalyst
concentration was investigated at 180 °C. Three different catalyst levels were
investigated (0.1, 0.17, 0.3 mg / g).
Analysis of the experiments
The result of a high temperature experiment consists of a plot of the number
average molecular weight versus time, an example is shown in figure 4.4. The
number average molecular weight is taken as a measure of the conversion in these
plots, because this average represents the amount of molecules present. For a
second-order step-polymerization reaction, the number average molecular weight
increases linearly in time (19):
( t])cat[,T(k]NCO[1MM f0repN )⋅⋅+⋅= ( 2.15 )
Strictly speaking, equation 2.15 is only valid for step-growth homopolymerizations
with an A-B type of monomer. For the terpolymerization that we investigated, large
deviations of this equation may occur, especially if the reactivities of the chain
extender and the polyol are different (20). However, for the conversion range we
investigated (> 95 %) the differences are negligible and, therefore, equation 2.15 is
still suitable.
To derive the reaction rate constant k from an experiment, the initial slope of the
curve has to be determined. A least square routine is used to establish this slope
for each experiment. As follows from equation 2.15, the initial slope relates to the
reaction rate constant according to:
0rep0rep
Nf ]NCO[M
1slope
]NCO[M1
dtdM
])cat[,T(k⋅
⋅=⋅
⋅= ( 4.4 )
In this way, the reaction rate constants can be obtained at different temperatures.
The initial slope is used to derive the reaction rate constant, since the number
average molecular weight will not increase indefinitely over time.
For each temperature, the equilibrium molecular weight can also be established
with high temperature experiments. This value can be used to calculate the
equilibrium constant and the reverse reaction rate at that temperature (equation
2.17).
64
A comparison of different kinetic measurement methods
( ) TR
E
eq,00
20
0NN2eq
eq
r
feq,A
eA]NCO[M
MMM
]NCO[
]U[
kk
K ⋅⋅=⋅
−⋅=== ( 2.17 )
The experimental graphs (e.g. figure 4.4) show that there is some scatter in the
value for the equilibrium molecular weight. Therefore, an average equilibrium
molecular weight is taken for every temperature. In figure 4.4, the shaded areas
indicate which part of the curve is considered to be in equilibrium.
4.3.4 Kneader experiments
The third method to measure the kinetics of polyurethane polymerizations with a
measurement kneader has been described in chapter 3. Experiments were
performed at four different temperatures (125, 150, 175, 200 °C). The effect of the
catalyst concentration was investigated at 175 °C. Four different catalyst levels were
used (0.25, 0.40, 0.75 and 1.30 mg / g). For system 1 and 2 the same experiments
have been performed. All experiments were repeated three times. The results of
these experiments will be discussed in the result section.
4.4 Results
The result section is split into different parts. The results of each measurement
method are discussed separately, and for each method, the two different urethane
systems are compared. Subsequently, the measurement methods are compared for
every system, in order to see if they really result in different kinetic data.
4.4.1 Adiabatic temperature rise measurements
Typical graph
As discussed in the experimental section, the ATR results are shown in an
Arrhenius plot. Figure 4.1 shows the results of a duplicate experiment for system 1
and 2. The same catalyst level is used for both systems. A second order reaction
rate equation is adopted to construct figure 4.1. This assumption seems to be valid
for both systems. If we compare both graphs, it is clear that system 1 reacts about
one and a half times faster than system 2. As expected, the reaction rate does not
rise to infinity; the reaction slows down considerably at a certain conversion. In
figure 4.1, this is visible at the point where the tangent line deviates from the
measurement points. Surprisingly, the conversion at that point is still quite low, for
both systems between 65 and 70 %. A comparison of all experiments showed that
regardless of the catalyst level, the decrease in reaction velocity starts between 65
65
Chapter 4
and 70 % for both systems. The reaction does proceed after that point, but the
reaction rate constant continues to decrease at higher conversions. The reason for
the decrease of the reaction rate constant is not immediately clear. The decrease is
too large to attribute it to a change in the reaction order.
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
-3
-2.5
-20.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/K)ln
(k) (
kg/m
ol s
)
Figure 4.1 ATR experiments. [Cat] = 0.075 mg/g, ■ / □ system 1, ♦ / ◊ system 2.
As explained in the theoretical section, the reaction may slow down due to diffusion
effects. However, the average degree of substitution at 70 % conversion is about
equal to three, for linear homopolymers this would be too low to give rise to a large
diffusion resistance. Nevertheless, for polyurethanes, phase separation of hard and
soft segments may be the cause of the drop in reaction velocity. Due to the
clustering of the hard segments, the mobility of the molecules decreases
considerably, this can decrease the observed reaction velocity. Blake et al. (21)
showed that for fast ATR experiments, the onset of the phase separation is
dependent on the initial temperature, catalyst level and the hard segment
percentage. They found that phase separation occurred between 66 % and 90 %
conversion, which is in agreement with our observations. However, contrary to
Blake et al. (21), we do not see an effect of the catalyst concentration on the
position of the onset point. This can be explained by the fact that our experiments
are much slower. In that case, the phase separation kinetics will be much faster
than the reaction kinetics, regardless of the catalyst level. In other words, in our
case the phase separation rate does not limit the rate of reaction. Surprisingly, also
the chemical composition seems to have no influence on the onset point, since both
66
A comparison of different kinetic measurement methods
systems show the same effect at the same conversion. Possibly, the structure of the
hard segments does not differ largely for our systems, in spite of the difference in
chain extender and isocyanate.
In many ATR investigations, the effect of phase separation on the reaction velocity
has not been observed. However, these investigations often use a higher hard
segment percentage, which increases the temperature at which the phase
separation takes place (21). Since at higher conversions the reaction becomes
difficult to follow (due to the decrease in heat generation at high conversions) the
effect of phase separation may be less visible, which would explain the lack of data.
In ATR studies using cross-linking polyurethane systems, a decrease in reaction
velocity has been observed at higher conversions (21, 22). Contrary to phase
separating systems, the mobility of the molecules for these systems is limited due
to crosslinking at higher conversions, instead of clustering of the hard segments.
Cross-linking already takes place at a conversion of 70%, this makes the effect
much easier to detect.
-7.5
-6.5
-5.5
-4.5
-3.50.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T
ln (k
) (kg
/ m
ol s
)
0.2000.1500.1000.0760.0500.0380.026uncat
Figure 4.2 ATR experiments. Catalyst dependence of system 2.
Comparison of different catalyst levels
In figure 4.2 and 4.3, the experiments at different catalyst levels are shown. The
zero catalyst experiments are much slower than the runs with the lowest catalyst
level (3 - 6 times for system 1, 2 - 4 times for system 2).
67
Chapter 4
-7
-6
-5
-4
-3
-20.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/K)
ln (k
) (m
ol/k
g s
0.1500.1000.0750.0500.025uncat
Figure 4.3 ATR experiments. Catalyst dependence of system 1.
However, the reaction path of the uncatalyzed runs can hardly be compared with
those of the catalyzed runs. As mentioned in the theory, the isocyanate droplets
may disperse much finer in the presence of catalyst. In case the catalyst is absent,
the then occurring larger droplets will result in a more pronounced diffusion
limitation for the initial part of the reaction. This explains the low initial activation
energy of the uncatalyzed runs (20 kJ/mol for system 1, 35 kJ/mol for system 2).
Nevertheless, at a certain conversion, the oligomers formed are likely to
compatibilize the reaction mass, resulting in a less diffusion-limited reaction and in
a higher activation energy (± 100 kJ/mol mol for system 1, 75 kJ/mol for system 2).
This would explain the sudden increase in activation energy in figures 4.2 and 4.3.
An autocatalytic process might also be responsible for the sudden increase of the
reaction velocity. However, repeated experiments showed that the uncatalyzed runs
were very sensitive to mixing, which supports the mixing hypothesis. A model fit of
the uncatalyzed runs will be imprecise due to this mixing sensitivity, especially
since the activation energy increases suddenly during the reaction. Still a fit of the
uncatalyzed runs was used in this kinetic study, since the uncatalyzed reaction
contributes to some extent to the overall reaction velocity.
Now, if we look at the catalyzed runs, the experiments for system 2 show a
remarkable behavior. Normally, one would expect the reaction velocity to increase
with increasing catalyst level, while the activation energy remains the same.
68
A comparison of different kinetic measurement methods
However, if we look at figure 4.2, it seems that the activation energy decreases with
increasing catalyst level, whereas the initial reaction velocity increases with catalyst
level, as expected. For system 1, this behavior does not occur (figure 4.3).
Therefore, the cause for this phenomenon must be found in the structure of the
monomers of system 2. The 2,4-MDI in system 2 results in staggered oligomer and
polymer molecules (as explained in the theoretical section). Staggered or rigid
molecules hinder the formation of a broad interfacial zone of isocyanate and polyol.
Only if this layer is present the mixing will be so fast that the reaction is kinetically
limited. According to Machuga et al. (16), the initial growth of this zone will be the
same for all catalyst levels. In that case, the reaction velocity depends on the
catalyst concentration in the interfacial zone, resulting in an initial reaction velocity
that is catalyst dependent. However, at higher catalyst levels the growth rate of the
intermaterial zone decreases or even stops, due to the faster formation of large,
viscous molecules. Therefore, the combination of staggered molecules and high
catalyst level may result in incomplete micromixing of the reactants. The resulting
diffusion limitation is observable in an Arrhenius plot as a decrease in activation
energy with increasing catalyst level. In figure 4.2, the activation energy continues
to decrease with higher catalyst concentrations until the maximum in reaction
velocity is reached at high catalyst levels (0.15 and 0.20 mg/g). As a result, two
different sets of kinetic parameters needed to be determined for system 2. The runs
with the lowest four catalyst levels (0.025 – 0.075 mg / g) were used to establish
the kinetic constants for the experiments at a low catalyst level (the fitting
procedure can be found in the experimental section). However, due to the
inconsistency in activation energy of system 2, a second set of parameters was
necessary to model the reaction at high catalyst levels. Therefore, the highest two
catalyst level runs were used to establish a catalyst-independent rate equation,
since these experiments were found to be equally fast, regardless of the catalyst
concentration. The results are shown in table 4.1.
69
Chapter 4
System 1 ATR High Temperature
Experiments
Kneader
Experiments
A0, Uncat (kg/mol s) 169.1
EA, Uncat (kJ/mol) 35.3
A0 (kg/mol⋅s)
⋅(g/mg)m 1.25e6 2.69⋅106 5.13⋅105
m ( - ) 0.61 0.5 0.57
EA (kJ/mol) 50.5 53.6 52.0
System 2
ATR
low
[cat]
ATR
high
[cat]
High Temperature
Experiments
Kneader
Experiments
A0, Uncat (kg/mol⋅s) 5.37e3
EA, Uncat (kJ/mol) 45.8
A0 (kg/mol⋅s)
⋅(g/mg)m 1.09e5 0.208 1.49⋅107 2.18⋅106
m ( - ) 0.92 0 0 0
EA (kJ/mol) 42.5 9.9 71.9 61.3
Table 4.1 The kinetic parameters for system 1 and 2.
In contrast to system 2, the Arrhenius plot for system 1 (figure 4.3) shows a regular
behavior. At a higher catalyst level, the activation energy remains constant whilst
the reaction rate constant increases, indicating that no diffusion limitations occur
unlike system 2. Using figure 4.3, a fit has been made according to the fitting
procedure as described in the experimental section. The resulting model
parameters are also shown in table 4.1.
70
A comparison of different kinetic measurement methods
4.4.2 High conversion experiments
A typical graph for a high conversion experiment is shown in figure 4.4. Two
experiments and their duplicates are shown. System 2 was used for these
experiments. The solid lines represent the model predictions; the model predictions
are based on a fit of all high temperature experiments performed in this research.
The resulting parameters describing the kinetics are shown in table 4.1. As
expected, the molecular weight increases in time. Initially, the increase is linear.
This part of the curve is used to determine the initial slope. At longer reaction times,
the molecular weight levels off due to depolymerization. At both temperatures, the
reproducibility of the experiments is reasonable.
0
10
20
30
40
50
60
70
80
90
0 25 50
Time (min)
Mn
(kg/
mol
)
75
Figure 4.4 M
n versus time for the high temperature experiments for system 2,
experimental results and model prediction. 150 °C, ∆ 150 °C duplicate, ♦
200 °C, ◊ 200 °C duplicate. The points in the grey areas are used to determine
the equilibrium molecular weight.
The procedure to derive the kinetic data is described in the experimental section.
This procedure is used to obtain the forward and reverse reaction rate at every
temperature under investigation.
71
Chapter 4
-5
-4
-3
-2
-1
00.002 0.0021 0.0022 0.0023 0.0024
1/T (1/K)
ln (k
) (kg
/mol
s)
Figure 4.5 The forward reaction rate constant as a function of temperature for high
temperature experiments. ■ system 1, ♦System 2.
In figure 4.5 an Arrhenius plot of the forward reaction rate is shown for all
experiments performed with system 1 and 2. At lower temperatures both systems
exhibit a linear relationship between ln(k) and 1/T, which confirms the second
order rate assumption. However, for system 2 a deviation from linearity turns up at
higher temperatures (200 °C, 210 °C). This is due to the fact that the slopes of these
curves are determined largely during the first 15 minutes of the reaction, when the
flasks are still warming up (as explained in the theoretical section). Therefore, the
effective flasks temperature will be lower than the oilbath temperature, which
explains the downward curvature in figure 4.5. For this reason, the experiments at
200 and 210 °C are not used to determine the Arrhenius-parameters for system 2.
However, the runs at 200 and 210 °C can still be used to determine the kinetics of
the depolymerization reaction.
72
A comparison of different kinetic measurement methods
7
7.5
8
8.5
9
9.5
10
10.5
11
0.002 0.0021 0.0022 0.0023 0.0024
1/T (1/K)
ln(K
) (kg
/mol
)
Figure 4.6 The equilibrium constant as a function of temperature for high temperature
experiments. ■ System 1, ♦ system 2.
The equilibrium molecular weights are determined at reaction times larger than 15
minutes, which makes sure that the flasks have reached the oilbath temperature. In
figure 4.6 the Arrhenius plot for the depolymerization reaction is shown for system
1 and 2.
System 1 System 2
Aeq (kg/mol) 0.0110 0.0393
EA,eq (kJ/mol) 52.7 43.4
Table 4.2 The equilibrium parameters for system 1 and 2.
The equilibrium constant for each temperature is calculated by substituting the
equilibrium molecular weight in equation 2.17. The plot shows that even at 150 °C
the effect of depolymerization is noticeable. The resulting parameters for the
depolymerization reaction are presented in table 4.2. Besides the effect of
depolymerization, the effect of the catalyst concentration was also investigated
through high conversion experiments. For system 2, the catalyst level did not have
an effect on the reaction rate constant, at least not for the relatively high catalyst
levels that were chosen. For system 1, the reaction rate was about proportional to
the square root of the catalyst concentration (table 4.1).
73
Chapter 4
4.4.3 Kneader Experiments
The results of the kneader experiments for system 2 were discussed in a previous
chapter. However, in this chapter only one catalyst level was used. Therefore,
additional experiments were performed to establish the catalyst dependence for
both systems. The resulting plots of reaction rate versus catalyst concentration are
shown in figure 4.7.
-2.5
-2
-1.5
-1
-0.5
0-2 -1.5 -1 -0.5 0 0.5
ln[Cat] (mg/g)
ln(k
) (kg
/mol
s)
Figure 4.7 The dependence of the Arrhenius pre-exponential constant on the catalyst level.
■ System 1, ♦ System 2.
For system 2, the experiments at the highest catalyst level are slightly faster than
the other three experiments, indicating that there is a slight influence of catalyst
concentration on the reaction velocity. This influence is very small, and since the
other three catalyst levels do not show any effect of the catalyst, the reaction
velocity is considered independent of the catalyst concentration. For system 1 the
catalyst dependence is obvious, the dependency factor m in equation 2.12 is equal
to 0.57. More discussion on the effect of catalyst will follow in the next sections.
Furthermore, figure 4.7 shows that system 1 reacts faster than system 2 at all
catalyst levels. As explained in the theoretical section, the 2,4- MDI that is used in
system 2 may cause it to react slower. The effect of the temperature on the reaction
velocity for system 1 is shown in figure 4.8. Analogous to system 2, the model
predictions and the experimental curves are shown, and the kinetic constants are
obtained in a similar way as for system 2 (18).
74
A comparison of different kinetic measurement methods
0
30000
60000
90000
120000
150000
0 4 8 12 16
Time [min]
Mw
[g/m
ol]
175°C
125°C
150°C200°C
Figure 4.8 The Mw versus time for the kneader experiments for system 1. 80RPM. Model
predictions and experimental results.
4.4.4 Comparison of the different measurement methods, System 1
Table 4.1 shows a comparison of all the kinetic parameters obtained for system 1.
Both the catalyst dependence and the activation energy seem to agree fairly well for
all experimental methods. This observation indicates that for all measurement
methods used, the reaction develops identically for system 1. Neither the activation
energy nor the catalyst dependence changes appreciably with the temperature-
range or the conversion-range of the measurement method. The simplified second
order assumption seems to hold for all measurement conditions. If we look at the
catalyzed urethane reaction, the reaction develops through several equilibrium
steps, all related to the catalytic center. Naturally, these equilibriums will shift with
temperature, which may change the reaction order and catalyst dependence.
Surprisingly, both the reaction order and the catalyst dependence remain constant
for the temperature range under investigation. The order of catalyst dependence (≈
0.5) falls within the limits reported by other authors (0.5 – 1). A possible
explanation for the value of 0.5 for the order of catalyst dependence is given by
Richter et al. (16). They related this value to a simple reaction mechanism. In the
first step of this mechanism, the catalyst dissociates and, in a second step, the
75
Chapter 4
cationic catalytic center forms a complex with an isocyanate group. If both steps
are thermodynamically unfavorable, the reaction order equals 0.5.
-8
-6
-4
-2
050 100 150 200
Temperature (°C)ln
(k) (
kg/m
ol s
)
Figure 4.9 The model reaction rate constant versus the temperature for the different
measurement methods. System 1. The open symbols are extrapolations to areas
where no measurements have been carried out. ■ ATR, ♦ kneader, high
temperature.
The effect of the different measurement methods on the reaction rate constant is
shown in figure 4.9. Figure 4.9 shows that the ATR experiments are as fast as the
high temperature experiments. Within the experimental error, for these two types
of measurements, the method does not seem to have any influence on the observed
reaction rate. A priori, one would expect the kneader experiments to be equally fast,
or even faster than the high temperature experiments. However, the kneader
experiments show reaction rate constants that are 3-4 times slower. No obvious
explanation is available to account for this result. The mysterious drop in reaction
velocity may be attributed to the materials used. The only difference between the
kneader experiments and the other two experiments is the batch of polyol and
chain extender used. The acidity and OH-value, which have an effect on the reaction
rate, may change per batch of polyol. No corrections were made for these changes.
Due to the use of a different polyol batch, no valid comparison can be made
between the kneader experiments and the other two types of experiments. However,
the other two experiments do give important information on the polyurethane
76
A comparison of different kinetic measurement methods
reaction. The observation that the reaction velocity does not depend on the
measurement method deployed implies that the theory of functional group
reactivity independent of chain length is also valid for polyurethanes. Moreover, it
strengthens the belief that for the ATR and high temperature experiments (initial)
diffusion limitations do not occur, since the reaction velocity, the reaction order and
the catalyst dependence is the same for both experiments. For extruder
applications, the result means that the most convenient measurement method can
be chosen to obtain the correct data for the kinetics, at least for this polyurethane
system. The advantage of ATR experiments is the ease of measurement; on the
other hand, the high temperature experiments give essential information on the
depolymerization reaction.
4.4.5 Comparison of the different measurement methods, System 2
Similar to system 1, two batches of materials were used for the experiments of
system 2. The ATR experiments for system 2 were performed with the same batch
of polyol as the ATR experiments and high temperature experiments of system 1.
The kneader and the high temperature experiments were performed with the other
batch of polyol, which is also used for the kneader experiments of system 1. In
table 4.1 the same batches have the same color. Again, possible inconsistency in
batches complicates the comparison of the different experiments. Moreover, the
specific diffusion limitations that were observed for the ATR experiments make
comparison of this method with the other two methods even harder. These
diffusion limitations are specific for the ATR method (and for the polyurethane
system used), and result in a catalyst-independent reaction velocity at higher
catalyst levels, and a lowering of the activation energy. For the high conversion
experiments, the lack of catalyst dependence is also observed at higher catalyst
levels, but the activation energy is much higher for these experiments. Therefore,
the cause of the catalyst independency for these experiments must be different. An
obvious explanation is not available, possibly the functional groups of the polymer
molecules experience a diffusion limitation that is noticeable at higher catalyst
levels. In that case, the catalyst level does not make any difference above a certain
threshold concentration. This explanation is not completely satisfactory. First, this
type of diffusion limitation does not occur for system 1. However, the difference in
monomers for the two systems might give a difference in the polymer structure and
therefore in diffusion behavior. The staggered 2,4-MDI groups in system 2 may
result in a more coiled polymer molecule which subsequently can result in a more
‘entangled’ polymer melt in which diffusion limitations occurs more readily. Still, a
77
Chapter 4
second question remains. The activation energies that are found for the high
conversion experiments are rather high for a diffusion-limited reaction (60 – 70
kJ/mol). The flow activation energy for system 2, which can be considered as the
activation energy of diffusion, is much lower: 43 kJ/mol (18). The reason for this
difference is not clear.
-10
-8
-6
-4
-2
050 100 150 200
Temperature (°C)
ln(k
) (kg
/mol
s)
Figure 4.10 The reaction rate constant versus the temperature for the different
measurement methods. System 2. The open symbols are extrapolations to areas
where no measurements have been carried out. ■ Kneader, • high temperature.
Now, if we look at the difference between the two high conversion methods, mixing
seems to have an influence. Both experiments are performed with the same batch
of polyol; therefore, a comparison can be made. The kneader experiments show a
much higher reaction rate constant than the high temperature experiments (figure
4.10). This observation may support the assumption that the reaction for system 2
is subject to diffusion limitations. Mixing in that case alleviates the diffusion
limitation, resulting in a faster reaction.
78
A comparison of different kinetic measurement methods
4.5 Conclusions
The reaction kinetics of polyurethane polymerization was studied in this chapter. In
particular, the need for different measurement methods for reactive extrusion
purposes was investigated. The study shows that ATR and high temperature
measurements give the same kinetic constants for a commercial polyurethane
system (system 1). Since both methods differ greatly in reaction time, reaction
temperature, and analytical method, it can be concluded that for this system both
measurement methods can be applied. Unfortunately, an extra validation of this
conclusion with a third method (with the measurement kneader) could not be used,
since a different batch of polyol had to be used for these last measurements.
However, the activation energy, catalyst dependence and reaction order was similar
for the kneader experiments, which strengthens the vision that any of the three
measurement methods will yield the same kinetic equation for system 1. Therefore,
it is probable that the reaction is kinetically controlled and that the reaction
proceeds uniformly over a wide range of temperatures and conversions.
For a less common polyurethane system (system 2), a completely different result is
obtained. The three different measurement methods each result in a different
kinetic equation, indicating that for this system a uniform reaction mechanism
cannot be adapted. For extrusion purposes, this means that a single kinetic
measurement method does not suffice. At least two measurement methods seem to
be required; a low temperature, low conversion method as adiabatic temperature
rise experiments and a high temperature high conversion method.
The cause of these inconsistencies may result from the structure of the monomers
used in system 2. As explained in the result section, the presence of 2,4-MDI in
system 2 may hinder the expansion of surface instabilities (which are indispensable
for good micromixing) and therefore prevent a kinetically controlled reaction (14).
However, since this hypothesis is only derived from the kinetic parameters for this
system, a further validation would be necessary; for example by following the
reaction under a microscope.
79
Chapter 4
4.6 List of Symbols
A0 Reaction pre-exponential constant mol/kg s
A Surface area of ATR reactor m2
[Cat] Catalyst concentration mg/g
Cp Heat capacity J/kg·K
EA Reaction activation energy J/mol
∆HR Heat of reaction J/mol
h Heat transfer coefficient J/m2⋅s⋅K
h* Overall heat transfer coefficient J/kg⋅s⋅K
kf Forward reaction rate constant kg/mol⋅s
kr Reverse reaction rate constant 1/s
m Catalyst order -
M0 Average weight of repeating unit g/mol
MN Number average molecular weight g/mol
MW Weight average molecular weight g/mol
n Reaction order -
[NCO] Concentration isocyanate groups mol/kg
[NCO]0 Initial concentration isocyanate groups mol/kg
ρ Density kg/m3
R Gas constant J/mol K
RNCO
Rate of isocyanate conversion mol/kg⋅s
T Temperature K
∆Tad Adiabatic temperature rise K
t Time s
[U] Concentration urethane bonds mol/kg
V Volume ATR reactor m3
Subscripts
Cat Catalyzed
Uncat Uncatalyzed
Eq Equilibrium
80
A comparison of different kinetic measurement methods
4.7 List of References
1. C. W. Macosko, RIM - Fundamentals of Reaction Injection Molding, Hanser, Munich,
(1989).
2. P. Cassagnau, F. Mélis, and A. Michel, J. Appl. Polym. Sci., 65, 2395 (1997).
3. X.D. Sun, and C.S.P. Sung, Macromolecules, 29, 3198, (1996).
4. X. Sun, J. Toth, and L.J. Lee, Polym. Eng. Sci., 37, 143 (1997).
5. P. Cassagnau, T. Nietsch and A. Michel, Intern. Polym. Process., 14, 144 (1999).
6. M.E. Hyun, and S.C. Kim, Polym. Eng. Sci., 28, 743 (1988).
7. A. Bouilloux, C.W. Macosko, and T. Kotnour, Ind. Eng. Chem. Res., 30, 2431 (1991).
8. S. Hoppe, S. Grigis, and F. Pla, Chisa 2002 A53
9. G. Lu, D.M. Kalyon, I. Yilgör, and E. Yilgör, Polym. Eng. Sci., 388 (2003)
10. S.D. Fields, E.L. Thomas, and J.M. Ottino, Polymer, 27, 1423 (1986).
11. S.D. Fields, and J.M. Ottino, AIChE J., 33, 959 (1987).
12. P.D. Wickert, W.E. Ranz, and C.W. Macosko, Polymer, 28, 1105 (1987).
13. O. Kolodziej, C.W. Macosko, and W.E. Ranz, Polym. Eng. Sci., 22, 388 (1982).
14. S.C. Machuga, H.L. Midje, J.S. Peanasky, C.W. Macosko, and W.E. Ranz, AIChE J., 34,
1057 (1988).
15. P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, N.Y.,
(1953).
16. E.B. Richter, and C.W. Macosko, Polym. Eng. Sci., 18, 1012 (1978).
17. T. Ando, Polym. J., 11, 1207 (1993).
18. V.W.A. Verhoeven, M. van Vondel, K.J. Ganzeveld, and L.P.B.M. Janssen, Polym. Eng.
Sci., 44, 1648 (2004)
19. G. Odian, Principles of Polymerization, John Wiley & Sons Inc., New York (1991).
20. F. Lopez-Serrano, J.M. Castro, C.W. Macosko, and M. Tirrell, Polymer, 21, 263 (1980).
21. J.W. Blake, W.P Yang, R.D. Anderson, and C.W. Macosko, Polym. Eng. Sci., 27, 1237
(1987).
22. Y.T. Chen, and C.W. Macosko, J. Appl. Polym. Sci., 62, 567 (1996).
81
5 The Reactive extrusion of thermoplastic polyurethane
5.1 Introduction
The kinetics of the polyurethane reaction has been discussed in the previous two
chapters. Relevant information on the kinetics was obtained under mixing
conditions that also occur during the extrusion process. In the current chapter, we
leave the kinetics behind and shift our emphasis to the extruder. As stated in
chapter 2, extrusion is a relatively expensive process. Comprehension of the
reaction in an extruder, coupled with a rational design of the extruder can therefore
lead to a cost benefit. Improvement of the extruder efficiency and control of the
product quality may be defined as a goal in that perspective. The efficiency of the
extruder operation can simply be expressed as the conversion at the end of the
extruder. The product quality is more difficult to grasp, it is related to the
conversion, the occurrence of side reactions (allophanate formation, oxidation,
crosslinking) and the size and morphology of the hard segments. For the current
study the emphasis lies on understanding how the conversion in an extruder can be
optimized. The use of an extrusion model is essential, because of the complicated
processes that take place in an extruder, and the wide diversity in extruder
configurations that are possible. A model can be useful for the optimization of an
existing process, the implementation of new types of materials, or the conversion
of a batch process into a continuous process.
In the literature, several studies have been directed towards understanding the TPU
production in an extruder (1 - 5), each with their own emphasis. Single screw
extruders (4, 5), counterrotating extruders (1, 2), and corotating extruders (3) have
been studied. A broad range of subjects was covered; predictive modeling (2, 4),
reactive blending (3), mixing efficiency in the extruder (1), and the effect of
extrusion on product quality (5) are described.
However, a missing subject in this survey is the depolymerization reaction. The
depolymerization reaction is inevitably noticeable at temperatures above 150°C (6),
which is a typical extrusion condition. The presence of this reaction may hinder the
extrusion efficiency. In the current study, the effect of the reverse reaction will be
investigated. In addition, the ability of the model to capture the reverse reaction will
be examined.
Chapter 5
5.2 The Model
5.2.1 Introduction
The purpose of the extruder model is twofold: it should increase the understanding
of the complex mechanisms of the reactive extrusion of polyurethane and it should
be suitable to optimize the process. In this way, the number of (expensive)
experimental trials can be minimized when a new process is designed. To meet this
objective, it should be easy to test different extruder configurations and different
operating conditions with the model, and the calculation time should be short. In
that case, a complex computational fluid dynamics model (CFD-model) is not useful.
Therefore, an analytical approach was chosen, which is similar to previous modeling
studies (7 -13). Of course, the flexibility and broad applicability of such an
engineering model comes with a price. Non-incorporated radial temperature
gradients, a simplified approach for the non-Newtonian flow behavior and the
complicated flow in the kneading sections may result in a less accurate model
prediction.
5.2.2 Reaction
As explained in the introductory section, the main output parameter of the model is
the degree of polymerization (α) or the directly related weight average molecular
weight (Mw) at the end of the extruder. The degree of polymerization is governed
by the reaction kinetics of the polyurethane system under investigation. For this
investigation, polyurethane system 2 as described in chapter 4 was chosen. The
kinetics of this polyurethane system can be described by a second order rate
equation:
]NCO[]NCO[]U[and
eA
kk,eA]Cat[kwith
]U[k]NCO[kdt
]NCO[dR
0
TR
E
eq,0
fr
TRE
0m
f
r2
fNCO
eq,A
A
−=
⋅
=⋅⋅=
−==
⋅
−⋅
−
( 2.16 )
To predict the isocyanate conversion α in a reactor, the isocyanate balance is solved
for that specific reactor, taking into account the above rate equation (equation
2.16). To solve the isocyanate balance, knowledge on the residence time
84
The reactive extrusion of thermoplastic polyurethane
distribution of the specific reactor is indispensable. Now, for two extreme cases of
residence time distribution (no (axial) mixing and complete mixing), the isocyanate
balance is solved. Both cases will be used further on in the model.
First, the no-mixing situation is evaluated. Practically, a no-mixing situation is
present in a plug-flow reactor. For a plug-flow reactor, the solution of the
isocyanate balance, using equation 2.16, is as follows:
( )⎟⎠⎞⎜
⎝⎛ ⋅−⋅⋅
−+⋅⋅+=
−
−
Dtf
rDt
rN
N
N
eC1k2
kDeCDk]NCO[ ( 5.1 )
with
Dk]NCO[k2
Dk]NCO[k2Cand]NCO[kk4kD
r1Nf
r1Nf0rf
2d
++
−+=⋅⋅⋅+=
−
− ( 5.2 )
These equations are also applicable for the conversion in an ideally stirred batch
reactor. It is clear from equations 5.1 and 5.2 that the isocyanate concentration is
dependent on the residence time and temperature. The concentration at the end of
the reactor, [NCO]N, is expressed as a function of the residence time t
N and the inlet
isocyanate concentration, [NCO]N-1
.
For the second situation, a completely mixed reactor, the isocyanate balance of a
continuous ideally stirred tank reactor (CISTR) can be solved. Since a polymerization
reaction is under investigation, the micro-mixing situation in such a reactor is best
considered as micro-segregated (14). The conversion in a micro-segregated CISTR is
equal to:
[ ] [ ]∫ ∫∞ ∞ −
⋅⋅=⋅⋅=0 0
tt
batch,tbatch,tN dtet1
NCOdt)t(ENCO]NCO[ ( 5.3 )
[NCO]t,batch
is the isocyanate concentration for a batch reactor with a residence time t,
as can be calculated using equation 5.1 and 5.2. Since no analytical solution is
available, equation 5.3 is solved numerically in the model.
Obviously, the isocyanate concentration for both reactor types is dependent on the
temperature and the residence time. In order to predict the right conversion in the
extruder, these parameters must be known. The residence time in the extruder can
be extracted from the flow model, while the temperature of the reaction mass along
the extruder can be analyzed through the energy balance (which in itself is also
85
Chapter 5
related to the flow model). Furthermore, for every part of the extruder the residence
time distribution must be known. All of these issues will be addressed in the
following paragraphs. In the concluding paragraph, details on the overall extruder
model are given.
5.2.3 Residence time / flow model
In order to be able to predict the residence time, a flow model of the corotating
twin-screw extruder is necessary (paragraph 2.2.5). To model the flow behavior in
the extruder, it should be taken into consideration that different types of screw
elements are used. Most commonly used are the transport elements and the
kneading paddles. To introduce the flow behavior in the model, for both element
types a simplified approach was chosen, based on the flow between two parallel
plates. In this approach, the screw channels are represented as stationary, infinite
screw channels, whereas the barrel moves over the channel (paragraph 2.2.1). This
approach is similar to previous analytical models (7 - 10, 12, 13). Details on the
analysis can be found in these publications. This approach is specifically
appropriate for the most commonly occurring elements, the transport elements. For
kneading elements, a modification is made to this approach. Both types of elements
will be treated separately.
Transport elements
For the transport elements, the filling degree fT of the not fully filled sections is
equal to the ratio of the real throughput (Q) and the maximal obtainable
throughput:
drag,LTmax,,ST QQ
Qf
−= ( 5.4 )
Equation 5.4 is a modified form of equation 2.7. The maximum throughput equals
the maximum conveying capacity (QS,max,T
) minus the leakage flows (QL,drag
) over the
flight The different flows are derived from the parallel plate flow model. Their exact
definitions are described by Michaeli et al. (12). Besides the filling degree of the not
fully-filled zone, the residence time in a transport section is also determined by the
length of the fully filled part. This filled length is a result of the pressure build-up
capacity of the element concerned. In case of a larger pressure build-up capacity
(∆P/∆L), the (filled) length needed to overcome a pressure barrier is shorter. The
pressure build-up capacity in a transport element is calculated according to Michaeli
et al. (12) as well:
86
The reactive extrusion of thermoplastic polyurethane
( )
R0
drag,L
flight
channelT,p3R3
channelT,pdrag,LTmax,,S
cossin2
vuQ
e12
ku
tanew
)(whisin
kQQQ
LP
δ⋅ϕ⋅ϕ⋅=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
η⋅⋅
η⋅⋅⋅δ⋅
ϕ+
+ψ−π⋅⋅⋅⋅ϕ
η⋅⋅−−=
∆∆
( 5.5 )
The pressure build up in a transport element is proportional to the viscosity, and to
the maximum flow rate minus the real throughput and the leakage flow. The
proportionality factor is a function of the channel geometry and a shape factor kP, T
.
The calculation of the maximum conveying capacity (QS,max,T
) takes into account the
effect of the intermeshing zone. The leakage over the flight is taken into
consideration with as well a drag flow dependent (QL,drag
) as a pressure flow
dependent term (integrated in equation 5.5).
The non-Newtonian behavior of a polymer fluid is taken into account indirectly. The
average shear rate in the element is calculated according to Michaeli et al. (10).
Both the shear rates over the flight and in the channel are calculated. In order to
calculate the shear rate in the channel, a two-dimensional flow analysis is made, for
which the actual channel geometry is taken into account. Subsequently, the
apparent viscosities are calculated using the appropriate rheological model and the
calculated shear rates. This apparent viscosity is used in equation 5.5. In this way,
most rheological models can be used.
Kneading paddles
For the kneading paddles, the flow behavior differs considerably from that of a
transport element (paragraph 2.2.4). Still, for the current modeling approach, a
kneading block is considered as a modified transport element, with an extra
leakage flow (QL,k
) due to the staggering of the kneading paddles. The maximal
conveying capacity is lowered due to this leakage flow. Therefore, the equation to
calculate the filling degree of the partially filled zone fk resembles that of the
transport elements:
k,Ldrag,LKmax,,Sk QQQ
Qf
−−= ( 5.6 )
87
Chapter 5
In equation 5.6, QL,k
is a result of the extra leakage flow due to the leakage gaps
that exists between the staggered kneading paddles. The pressure build up (or
consumption) in a kneading section is calculated with (12):
( ))(whi
kQQ
LP
3channelK,PKmax,,S
ψ−π⋅⋅⋅
η⋅⋅−=
∆∆
( 5.7 )
Again, a similarity exists between the equation for the kneading blocks and for the
transport elements. The pressure build up in a kneading element is proportional to
the viscosity, and to the maximum flow rate minus the real throughput. In case of a
kneading element, the extra leakage term due to the staggering of the kneading
paddles is incorporated in the equation for QS,max,K
. For the kneading blocks, the
apparent viscosity is calculated in the same way as for the transport elements.
The approach that is taken in our model for the flow behavior in the kneading
blocks suffices for low staggering angles, since in that case, the similarity with the
transport elements is still present. However, this model is inadequate at higher
staggering angles. In that case, an approach adapted by Verges et al. (13) may give
better results. Still, experimental validation of the pressure build up in kneading
paddles is scarce. This makes a comparison of the different modeling approaches
for the kneading paddles difficult and the present approach sufficient.
5.2.4 Residence time distribution
As explained in the paragraph on the polyurethane reaction, knowledge on the
residence time distribution in the extruder is indispensable to calculate the
appropriate conversion. In the model, a distinction is made between a kneading
block and a transport element, since the flow in a kneading block differs
substantially from the flow in a transport element. Moreover, an extra distinction is
made between flow in partially filled elements and fully filled elements. In a partially
filled element, hardly any axial mixing takes place, because the material is more or
less ‘glued’ to the flank of the screw. Therefore, all the partially filled elements are
considered to operate under plug-flow regime, and the isocyanate balance for a
plug-flow reactor (equations 5.1 and 5.2) can be used to calculate the conversion in
a partially filled zone.
Fully filled transport elements
However, for fully filled elements, the situation differs. In a fully filled transport
element, each particle follows a different (helical) path in the screw channel, which
causes a distribution in the residence time. Pinto and Tadmor (15) developed a
88
The reactive extrusion of thermoplastic polyurethane
residence time distribution model, based on this helical flow pattern in the channels
of a single screw extruder. This model is also applicable for our self-wiping twin-
screw extruder, even though the intermeshing zone will disrupt the flow pattern
somewhat. The RTD analysis of Pinto and Tadmor (15) shows that the flow in the
fully filled transport elements is neither comparable to plug-flow or flow in a pipe.
The actual flow lies somewhere in between. However, as a first approach, the
residence time distribution in the fully filled transport elements will be regarded as
plug-flow in the current model (equations 5.1 and 5.2).
Fully filled kneading paddles
The flow in the kneading paddles differs completely from the flow in a transport
element. In general, in a kneading zone, the circumferential flow rate is much
higher than the axial flow rate (16). Besides, due to the squeezing action of two
paddles in the intermeshing zone, the mixing is much better. Moreover, a
considerable backward flow will be present between two neighboring paddles,
because of a leakage gap between these paddles. For these reasons, the residence
time distribution in a kneading zone will have a similarity to that of a cascade of
continuous ideally stirred reactors. Therefore, this approach is used for the
extruder model (equation 5.3). The kneading blocks are divided in a number of
CISTR´s. Tentative experiments in a Perspex extruder were performed to establish
the length of every reactor; it was found to equal half of the screw diameter. This
length is typically two to four times the width of a kneading paddle.
5.2.5 Energy
The temperature is the last essential factor that is needed for calculating the
conversion in an extruder. The temperature can be derived from the energy balance.
In our model, the energy balance for the extruder or for a part of the extruder is:
( ) ( )
[ ] ( ) FC1NN0R
NWallwall1NNp
WWNCOHQ
TTAhTTQC
&& ++α−α∆⋅
−−⋅=−⋅⋅
−
− ( 5.8 )
The temperature rise in (a part of the) extruder (TN-T
N-1) is a result of the heat
transfer through the wall, of the exothermic reaction and of the viscous dissipation
in the channel (WC), and over the flight (W
F).
The energy balance considers the extruder or a part of the extruder to be a
continuous ideally stirred reactor (CISTR). Obviously, a more complicated flow
situation exists in the extruder, which will result in radial and axial temperature
89
Chapter 5
gradients. The latter can be resolved through applying equation 5.8 on short axial
sections of the extruder. Nevertheless, the radial temperature gradient can result in
a deviation of the measured and predicted temperature in an extruder.
The heat transfer coefficient in the energy balance is adapted from Todd et al. (17).
As for the average shear rate in the channel, the viscous dissipation in the channel
is calculated using a two-dimensional flow analysis (10). Since the viscous
dissipation over the flight is substantial (7), it is integrated in the heat balance
according to an equation by Michaeli et al. (10):
Lsin
ei
vW
R
20
flightF ∆⋅ϕ
⋅⋅δ
⋅η=& ( 5.9 )
5.2.6 Modeling approach
A general modeling scheme has been developed to calculate the conversion in the
extruder. For this calculation, the extruder is split up in segments of a quarter of
the diameter of the extruder. The output of the first segment is the input of the
second segment and so on. The sectioning is necessary due to the large
temperature and conversion gradient in the axial direction. The size that is chosen
for the segment is a compromise between accuracy and calculation time.
The sectioning strategy is not compatible with the continuous laminar flow profile
that is present in an extruder. For the sectioning approach, a continuous flow is
divided into segments that have closed-closed boundary conditions. For example, in
case a fully filled transport zone is divided into segments, the residence time
distribution over the whole section can be calculated with the approach of Pinto and
Tadmor (15). However, to do so for every segment and applying closed boundary
conditions will give an erroneous result. To prevent this error, a plug-flow approach
is chosen for the transport zones. A plug-flow reactor can be divided in segments
without any problems.
Segmental iteration
For a segment N, the temperature TN, conversion α
N, viscous dissipation W
N, average
shear rate γN and the viscosity η
N are calculated. The equations used for every
parameter are described in the previous paragraph. However, it is not possible to
solve these equations sequentially; looking at equation 5.10 it is clear that the
equations are interrelated.
90
The reactive extrusion of thermoplastic polyurethane
( )( )
,...),T(f
,...)(fW
...,WfT
,...t,Tf
NNN
NN
NNN
N,resNN
α=η
η=
α=
=α
&
& ( 5.10 )
Therefore, a dichotomy routine is used to solve equation 5.10 for every segment.
The convergence criterion for this routine is the viscosity, since the viscosity is the
most sensitive parameter in equation 5.10. In general, the dichotomy routine
converged within five steps.
Extruder iteration
Having calculated all variables in segment N, the output of this segment is the input
of the next one, segment N+1. However, in an extruder, the situation of this next
segment can influence the filling degree of the previous segment. At the start of the
´extruder iteration´, all segments are considered partially filled. Both the die and
reverse or neutral screw elements raise a pressure barrier. This pressure barrier
needs to be overcome by the previous segment, which fills ‘itself’ for that reason. A
similar mechanism is present in the model (figure 5.1).
Pres
sure
Pres
sure
0
N-2 N-1 N N-2 N-1 N
0
Figure 5.1 The calculation of the filled length in front of a reverse element.
In case a negatively conveying segment (N) is encountered, the upstream segment
(segment N-1) is ´filled´ and recalculated using the segmental iteration.
Subsequently, the usual calculation order is followed, so the next (in this case the
negatively conveying) segment (N) is calculated. In case the pressure at the end of
this segment is still below zero, another upstream segment is filled (N-2) and so on,
until the pressure at the end of segment N is zero. For the die, a similar routine is
followed. The calculation ends if the pressure at the outlet of the die is atmospheric.
91
Chapter 5
5.3 Experimental section
Several types of experiments were performed to validate the extruder model: cold-
flow extrusion experiments, non-reactive extrusion experiments and reactive
extrusion experiments. In the experimental section, every type of experiment is
addressed separately. Two types of extruders have been used for the validation
study: a Perspex extruder (D = 50mm, Cl = 39mm, δR = 1mm, L/D = 25) and an APV-
Baker MPF50 twin-screw extruder (D = 50mm, Cl = 39mm, δR = 0.8mm, L/D = 24).
Both extruders can be equipped with different types of transport elements or with
kneading paddles (width = 0.25⋅D) with staggering angles of 30, 45, 60, 90, 120,
135 and 150°. For the APV-baker extruder, the temperature of the barrel wall can be
regulated through ten independent heating/cooling zones (electric heating, water
cooling).
5.3.1 Cold-flow extruder experiments
For the cold-flow experiments, the Perspex extruder was equipped with two-lobed
50/50 (diameter/pitch) transport elements. A calibrated pressure gauge was placed
in front of the die and at 22 D. Glucose syrup and a 1.5 % solution of hydroxy-ethyl
cellulose (HEC) in water were used for the experiments. Both liquids were
rheologically characterized with a constant strain rheometer (TA Instruments, AR
1000-N Rheometer) using a cone and plate geometry. Glucose syrup showed a
Newtonian behavior (η = 10 Pa⋅s) while the shear dependency of the HEC viscosity
obeyed a power-law equation (η0 = 76.1 Pa⋅s, n = 0.25). A gear pump (Maag) was
used as a feed pump for the extruder. The throughput was set to 7.5 kg/hour and
the rotation speed of the extruder was varied between 12.5 and 100 RPM.
5.3.2 Non reactive validation
Polypropylene (Stamylan PP, DSM) was used for the non-reactive validation. The
rheological behavior of the polypropylene was established on the same rheometer
as for the cold flow experiments, the rheometer was operated in the oscillatory
mode. The temperature dependency of the viscosity could be described with a
Williams-Landel-Ferry (WLF) equation:
)TT(C)TT(C
)T()T(
logr2
r1
r −+−
−=⎟⎟⎠
⎞⎜⎜⎝
⎛ηη ( 5.11 )
92
The reactive extrusion of thermoplastic polyurethane
With C1 = 2.66, C
2 = 305.6, and T
r = 493 K. The shear rate dependency was
accounted for using the Williamson model:
K493at)001214.0(1
1.322625.0app
γ⋅+=η ( 5.12 )
The extruder was equipped with one -45/8/100 kneading zone (stagger
angle/number of kneading paddles/ length kneading zone) to ensure complete
melting of the polypropylene. The kneading zone was placed 20 cm downstream of
the inlet zone. The pressure is measured at three locations for establishing the
pressure gradient in the fully filled zone. The temperature is measured in two
places along the fully filled zone with non-protruding thermocouples. No significant
difference in temperature was observed along the fully filled zone, indicating an
isothermal fully filled zone. Five different rotation speeds and five different wall
temperatures were investigated. For every experiment, the die diameter was
adapted to obtain a sufficiently long fully filled zone. The polypropylene is added to
the extruder with a hopper (K-tron T-20). A constant feed rate of 15 kg/hour was
maintained.
5.3.4 Reactive validation
Equipment
The extruder layout for the reactive experiments is shown in figure 5.2. One
kneading zone (45/8/100) is placed three diameters from the inlet. Only half of the
extruder is used for these experiments to prevent an excessive long residence time.
Two feed streams are added to the extruder. These streams come together above
the feed pocket of the extruder. To premix both streams, a static mixer of the
Kenics type of variable length can be placed in the joint feed line. The first stream
consists of the premixed chain extender and polyol; the second stream is formed
by the isocyanate. A solution of the catalyst in dioctyl-phtalate is added
continuously to the polyol feed line using an HPLC-pump. The static mixer of 32
elements is placed after the catalyst injection point to mix the catalyst evenly in the
polyol. The isocyanate supply vessel is kept at 25 °C while the polyol supply vessel
and feed lines are kept at 80 °C. The flows of both streams are controlled in the
same way. A gear pump (Maag TX 22/6) is combined with a flow sensor (VSE, VS-
0.04-E) which sends its signal to a PI controller/flow computer (Contrec 802-A).
Through a frequency deformer (Danfoss VLT 2010), the PI controller controls the
93
Chapter 5
gear pump. A throughput of 12.5 kg/hour is maintained for most of the
experiments.
Polyol + diol + catalyst
MDI
P1 P2 P3
Figure 5.2 The extruder layout for the reactive validation experiments.
Rheo-kinetics
System 2 as described in chapter 4 was used for the reactive extrusion experiments.
This system consists of:
• A polyester polyol of mono-ethylene glycol, di-ethylene glycol and adipic
acid (MW = 2200 g/mol, f = 2).
• Methyl-propane-diol (Mw = 90.1 g/mol, f = 2).
• A eutectic mixture (50/50) of 2,4 diphenylmethane diisocyanate (2,4-MDI)
and 4,4 diphenylmethane diisocyanate (4,4-MDI). (Mw = 250 g/mol, f = 2).
A0, Uncat (kg/mol s) 7.4⋅104
EA, Uncat (kJ/mol) 52.4
A0 (kg/mol⋅s) ⋅(g/mg)m 4.53⋅107
m ( - ) 2.25
EA (kJ/mol) 45.18
Table 5.1 The kinetic parameters used for the reactive extrusion model.
Adiabatic temperature rise experiments were used to obtain the kinetic parameters,
according to paragraph 6.6.4. For these experiments, the monomers were premixed
94
The reactive extrusion of thermoplastic polyurethane
with the static mixer as shown in figure 5.2. The resulting kinetic parameters are
shown in table 5.1.
As discussed in chapter 4, the reaction rate slows down considerably at high
conversions for this polyurethane. Mixing seems to have an effect a high
conversions (paragraph 4.4.5), moreover, hardly any catalyst dependence is present
(paragraph 4.4.3). Both factors are caused by diffusion limitations. However, the
conversion and temperature at which the reaction slows down has not been
established. For the extrusion model, a pragmatic approach was chosen to consider
the high conversion effects. Above a conversion of 98% (Mn > 31000) the kinetics
found with the kneader experiment (table 4.1) were applied.
The relationship between viscosity, temperature, and molecular weight has been
obtained from the extruder experiments by applying equation 5.13 and 5.14 to the
experimental data.
nn
3
QC
R
)n/13(QRL
2
Pk
⎟⎟⎠
⎞⎜⎜⎝
⎛ρ
⋅+⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅π⋅ρ
+⋅⎟
⎠
⎞⎜⎝
⎛ ⋅
= ( 5.13 )
and
TRU
flow,04.3
A
eAMwk ⋅⋅⋅= ( 5.14 )
In equation 5.14, the consistency of a power-law liquid is given as a function of the
molecular weight and temperature (19). Equation 5.13 shows the relationship
between the consistency of a power-law liquid k and the pressure drop over the die,
with a factor C added for entrance losses. Equation 5.13 can be substituted in
equation 5.14. For all different experimental conditions, the pressure drop over the
die, the molecular weight, and the temperature of the material coming out of the
extruder was measured. In addition, the power law index n of the polyurethane was
determined experimentally on a capillary rheometer (Göttfert Rheograph 2003) and
found to be equal to 0.61. With these data, a least square fit was performed using a
substituted version of equations 5.13 and 5.14, in order to obtain the parameters
UA, A
0,flow, and C.
95
Chapter 5
5.4 Results
In the result section, a validation study of the extrusion model is presented.
Moreover, the effect of several extrusion parameters on the polyurethane extrusion
will be discussed and compared with the model. The result section is split into
several parts. First, a limited validation study is presented on the pressure build-up
capacity of the screw elements. As stated in the theoretical section, a correct
prediction of the pressure build-up capacity will contribute substantially to a correct
prediction of the residence time and therefore of the end conversion. Moreover, the
validity of the approach for the flow model can be tested by checking the pressure
build-up capacity. Subsequently the extruder model will be compared to an
experimental study on polyurethane extrusion. Measurements on the conversion,
temperature, and pressure will be compared with the model predictions. The effect
of several extrusion parameters will be discussed and special emphasis will be put
on the depolymerization reaction.
5.4.1 Validation of the transport elements, a literature check
As stated in paragraph 2.2.3, the pressure build-up capacity of the transport
elements is often expressed as (20):
dLdPB
NAQorB1
)QNA(dLdP
⋅η
−⋅=η−⋅= ( 2.2 )
At first sight, a comparison of equation 2.2 with our pressure build up description
(equation 5.5) seems troublesome. However, a closer look reveals that the factor B
in equation 2.2 is equal to the denominator divided by the k-factor in equation 5.5,
while (QS,max
-Ql,drag
)/N is equal to the A factor. A few experimental studies (21, 22)
have been directed to experimental determination of the A and B factors for
Newtonian fluids.
96
The reactive extrusion of thermoplastic polyurethane
D
(cm)
Cl
(cm) Pitch (cm)
δR
(mm) A (cm3) B (cm4) k (-)
5 3.85 5 0.4 36 / 40.8* 0.12 / 0.118* 27
5 3.85 1.67 0.4 12.8 / 12.4* 0.017 / 0.021* 27
3.07 2.62 2 0.25 4.9 / 4.6# 0.0038 / 0.0045# 27
3.07 2.62 4.2 0.25 9.5 / 11.5# 0.015 / 0.013# 27
Table 5.2 A and B factors for transport elements (bold face current model, * (21), # (22)).
In table 5.2, the results of these studies for transport elements are compared with
our model. The resemblance is good, considering the engineering purposes of the
model. Strictly speaking, equation 2.2 is only valid for Newtonian fluids. Model
calculations show that for non-Newtonian fluids the deviation can be considerable
(23), however, no supporting experimental data exists for twin-screw extruders. In
literature, some experimental results are shown for which the pressure is plotted
versus extruder length for non-Newtonian fluids. We compared one of these studies
(8) with our model; the comparison shows a satisfactory agreement (table 5.3).
D=30mm, 28/28 dP/dL (bar/mm)
100 rpm
dP/dL (bar/mm)
200 rpm
dP/dL (bar/mm)
300 rpm
Polystyrene 1.30 / 1.08 1.67 / 1.59 1.88 / 2.0
HDPE 0.78 / 0.65 1.26 / 1.42 1.60 / 1.9
Table 5.3 Pressure build up comparison for non-Newtonian fluids (bold face current
model, regular face according to (8))
5.4.2 Validation of the transport elements, an experimental check
As an addition to the literature validation, experiments were performed on a
Perspex extruder. In this extruder, the filled length together with the pressure
along the filled length can be measured. Sugar syrup was used as a Newtonian
experimental fluid. A viscosity of 10 Pa⋅s was chosen, in order to prevent
gravitational effects to be dominant over the viscous forces (24). In addition, a non-
Newtonian fluid was tested, which consisted of a 1.5% solution of hydroxy-ethyl
cellulose (HEC) in water.
97
Chapter 5
0
0.1
0.2
0.3
0.4
0 20 40 60 80 10
Rotation speed (RPM)
(dP/
dL)*
0
Figure 5.3 The pressure build up capacity as a function of rotation speed. (dP/dL)*=(dP/dL)
/ (η0⋅γ(n-1)) D = 5 cm, Cl = 3.85 cm, pitch = 5 cm, δ = 0.02⋅D, Hydroxy-ethyl
cellulose, ♦Sugar syrup.
For both liquids, the experimental and model pressure build up capacity of 50/50
transport elements is shown as a function of rotation speed (figure 5.3). The
agreement between model and measurement for the HEC is good, while the
pressure build-up for the sugar syrup is overestimated at higher rotation speeds.
Air bubbles were inevitably present at higher rotation speeds for the sugar syrup
experiments, which may cause a deviation of the flow behavior. The pressure build
up capacity (expressed as (dP/dL) / ηapp
) for the sugar syrup is considerably higher
than for the hydroxy-ethyl cellulose solution, which is according to expectations.
For a non-Newtonian fluid, the apparent viscosity over the flight decreases
considerably due to shear thinning. The pressure-driven leakage over the flight is
therefore substantially higher than for a Newtonian fluid. Therefore, the pressure
build up divided by the apparent viscosity is much lower for HEC than for sugar
syrup. These experiments emphasize the importance of the leakage flow over the
flight.
98
The reactive extrusion of thermoplastic polyurethane
50
100
0
r/m
150
250
300
Tem
ptu
re (°
C)
15
)dP
/dL
(ba
200
era
00 50 100 150 200
Rotation Speed (RPM)
100
Figure 5.4 The pressure build up and temperature for the polypropylene extruder
experiments (barrel wall temperature: 190°C, ♦205°C, ■220°C, •240°C, closed
symbols: pressure build up, open symbols: measured temperature).
To test the pressure build up capacity for a non-Newtonian polymeric material,
experiments were performed with polypropylene in an APV-Baker twin-screw
extruder. The material was rheologically characterized with a cone and plate
rheometer. The results of the extruder experiments are plotted in figure 5.4. The
pressure build-up capacity is predicted accurately, except for the 190°C experiment.
The temperature of the melt seems to be over predicted for all of the experiments.
However, the temperature was measured using a wall thermocouple, which tends to
underestimate the melt temperature. Since the pressure prediction is correct for
these experiments, we can assume the temperature to be predicted correctly. This
observation indicates that the energy balance of the model approaches the actual
situation.
Considering the validation studies above, the flow in the transport elements is
su
elements and
.4.3 Validation of the kneading elements
described fficiently well using the model, at least for the types of transport
the extruder diameters that were investigated.
5
Concerning the pressure characteristics of the kneading paddles, less information is
present in literature. In an experimental study by Todd (21) the pressure build up
characteristics for kneading paddles are expressed in the same A and B factors that
are used in equation 2.2. In order to compare these factors with our model,
equation 5.7 can be rewritten in a similar manner as was done for the transport
99
Chapter 5
elements. The factor B in equation 2.2 is equal to the denominator in equation 5.7
divided by the k-factor, while (Q
S,max)/N is equal to the A factor. A comparison
between the experiments of Todd (21) and our model is shown in figure 5.5.
0
20
40
60
80
100
120
0.4
0.65
0 0.1 0.2 0.3 0.4 0.5 0.6
Paddle Width (Width/D)
A-fa
ctor
(cm
^3)
-0.35
-0.1
0.15
B-fa
ctor
(cm
^4)
Figure 5.5 A and B-factors for a kneading block as a function of paddle width and
staggering angle (D = 5 cm, Cl = 3.85 cm, δ = 0.008⋅D, open symbols B-factor,
closed symbols A-factor. Stagger angle: squares 30°, triangles 45°, circles 60°).
The lines represent the model simulations, the symbols are the measured values.
simplicity of
model is rem s largely
nderestimated. Due to the nature of the modeling approach for the kneading
In this figure, the paddle width and stagger angle is varied. Considering the
the modeling approach, the agreement between experiments and
arkable. Only for the 60° kneading paddles, the B-factor i
u
paddles, this deviation is understandable. In the modeling approach, a kneading
block is considered as a modified transport element. For larger staggering angles,
this approach deviates largely from the actual situation.
For non-Newtonian fluids, hardly any experimental data are present for the
kneading elements. With the flow model currently used, Michaeli et al. (12) show a
reasonable prediction of the pressure characteristics of the kneading paddles for
non-Newtonian fluids. A comparison of the dimensionless pressure build up
capacity with a 2-D non-Newtonian model (25) shows an acceptable agreement
(figure 5.6). Only for a right-handed 60°-stagger angle element, the pressure
consumption is overestimated.
100
The reactive extrusion of thermoplastic polyurethane
20
40
60
-100
-80
-60
-40
-20
-90 -60 -30 0 30 60 90
Staggering Angle (°)
(dP/
d
0
)* (-
)z
* nFigure 5.6 Dimensionless pressure gradient (dP/dz) = (∆P/∆L)⋅R / (η0⋅(2⋅π⋅N) ) as a function
of staggering angle. The dimensionless throughput Q* = Q/(2⋅π⋅R3⋅N) is equal to
0.05. (solid line = model Noé, dashed line = this chapter).
5.4.4 Polyurethane extrusion
A reactive validation study has been carried out on an APV-Baker MPV-50 extruder.
The experimental details of this study are described in a previous section.
Obviously, for every experimental setting, a model simulation is generated in order
to compare the model prediction with the experiment. Figure 5.7 shows such a
simulation for one specific situation. In this figure, the development of the
conversion, temperature, pressure, and filling degree along the extruder is shown.
Of course, the reaction proceeds mainly in the fully filled sections, due to the
longer residence time in these sections. Furthermore, the reaction a roaches an
slows down
area, a dyna
eaction are e
pp
equilibrium situation before leaving the extruder; the increase in molecular weight
considerably in the last fifteen centimeters upstream of the die. In this
mic equilibrium is approached for which the forward and the reverse
qually fast. Due to the link between the flow, energy and the reaction, r
the equilibrium is specific for this particular operation condition and extruder
geometry.
101
Chapter 5
0
50
100
150
200
250
erat
ure
(°C
),Fi
lling
deg
ree
(%)
20
30
40
Pres
sure
(bar
)
0 0.2 0.4 0.6
Length (m)
Tem
p
0
10
Mw
(kg/
mol
),
Figure 5.7 An example of the pressure, Mn, temperature and filling degree along the
extruder. The number average molecular weight ( ), pressure (■) and melt
temperature (•) at 150 RPM, 12.5 kg/hour, Tbarrel
= 185 °C , [cat] = 30ppm, and
ddie
= 4 mm.
A model simulation as shown in figure 5.7 has been carried out for all operating
conditions that were experimentally tested. In order to compare the odel with the
xperiments, the temperature and conversion are preferably measured at different
locations lo
can be obtain rison can be made
between the model and the experiments. However, in an extruder, the
and conversion is notoriously unreliable. The
Mn T
P
Filling degree
m
e
a ng the screw. In this way, a complete view of the extruder performance
ed. Furthermore, with these data, a detailed compa
measurement of the temperature
temperature of the melt can only be measured using protruding thermocouples,
which affects the flow situation considerably (26). Sampling ports are sometimes
used for conversion and temperature measurements but they are vulnerable to
clogging; moreover, the sampling procedure can take too long for a reliable
measurement. To overcome these problems, an inventive and promising sampling
port design has been described by Carneiro et al. (27). Unfortunately, such
geometry could not be adapted to our extruder. Therefore, our validation study
takes into account the conversion and temperature at the end of the extruder. In
addition, the pressure development along the extruder is followed by three
pressure sensors. The temperature is measured by inserting a thermocouple in the
melt coming out of the extruder. The conversion is measured by a size exclusion
chromatography method. Material coming out of the extruder is immediately
102
The reactive extrusion of thermoplastic polyurethane
quenched in liquid nitrogen. Subsequently the molecular weight of the sample is
determined as described in chapter 3.
figure 5.7, the outcome of one extruder experiment is compared with the model.
In a similar manner, a wider model validation study has been carried out. For the
model validation, t e, rotation speed and
throughput is inve ly in the discussion
below.
5.4.5 The effect
In figure 5.8, the e l on the extruder performance is shown
for a barrel wall temperature of 185°C and a rotation speed of 150 RPM. The model
predictions and measurements agree reasonably well on the end pressure, outlet
melt temperature, and the molecular weight. Due to viscous dissipation, the
temperature of the melt exceeds the wall temperature considerably.
In
he effect of catalyst level, barrel temperatur
stigated. Every variable is discussed short
of the catalyst
ffect of the catalyst leve
150
200 20
r)
0
50
100
0 100 200 300 400 500
Catalyst Concentration (ppm)
Mw
(kg/
mol
)
0
5
10Pr
ess
250
, Tem
pera
ture
(°C
)
15
25
ure
(ba
Figure 5.8 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of catalyst level. (150 RPM, 12.5 kg/hour, Tbarrel
= 185°C, ddie
= 4 mm)
In figure 5.8, a surprising trend is visible; the molecular weight of both the model
simulations and the measurements does not show any catalyst dependence. For all
catalyst levels, the end conversion and temperature is more or less the same. This
observation is not in agreement with earlier kinetic experiments that were
performed with this polyurethane (6). In these experiments, a catalyst dependence
103
Chapter 5
was observed. An explanation for the extrusion results may be that the reaction
reaches a depolymerization equilibrium before leaving the extruder. In that case,
the catalyst concentration has no effect on the end conversion. To test this
hypothesis, a more discriminative working zone was tried. The barrel wall
temperature was lowered to reduce the effect of the depolymerization reaction.
Moreover, we chose a larger die diameter to decrease the residence time in the
extruder. The results of these adjustments are shown in figure 5.9.
0
200
ure
50
100
150
Mw
(kg/
mol
), Te
mpe
ra
0
10
20
Pres
sure
(bar
250
0 100 200 300 400
Catalyst Concentration (ppm)
t (°
C)
-10
30
40
)
Figure 5.9 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of catalyst level. (100 RPM, 12.5 kg/hour, Tbarrel
= 160°C, ddie
= 5 mm)
Clearly, a more profound effect of the catalyst concentration is present for both
model and experiment. The agreement between the model predictions and
experimental results is reasonable, although a somewhat strange and inexplicable
deviation exists at 90 ppm. Nevertheless, the upward trend of molecular weight as
a function of catalyst concentration is predicted sufficiently by the model.
Remarkably, the catalyst level seems to need a threshold value before having an
h
5.4.6 The the barrel wall temperature
n increase in the barrel wall temperature is a critical test for the extruder model.
effect, whic can be observed both in the model and experimentally.
effect of
A
Changing the barrel wall temperature has a large influence on the reaction in the
extruder, the rheological properties of the polymer and on the heat transfer to the
104
The reactive extrusion of thermoplastic polyurethane
melt. At a higher temperature, the reaction velocity will increase and the
depolymerization reaction will gain importance. Viscous dissipation will have a
lesser influence due to a decrease of the viscosity.
0
50
100
150
200
250
Tem
pera
ture
(°C
)
5
10
15
20
sure
(bar
)
150 160 170 180 190 200 210 220
Barrel temperature (°C)
Mw
(kg/
mol
),
-10
-5
0 Pres
Figure 5.10 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of barrel temperature. (solid line: 150 RPM, 12.5 kg/hour,
[cat] = 30 ppm, ddie
= 4 mm, dashed line (open symbols): 150 RPM, 12.5 kg/hour,
[cat] = 30 ppm, ddie
= 5 mm)
The effect of the barrel wall temperature was investigated at two different die
diameters. The results are shown in figure 5.10. As can been seen in this gure, the
rd
conditions, in
viscous dissi not present. The latter is clear if we look at the temperature
f the melt, which is about the same as the barrel wall temperature. In contrast, at
gure 5.10, the
effect of a longer residence time is considerable at lower temperatures. With a
smaller die diameter, the end conversion and temperature of the melt are much
fi
reaction ha ly develops at 160 °C and 180 °C for the larger die diameter. At these
the molecular weight at the end of the extruder rema s low and
pation is
o
210 °C, the molecular weight is much higher and approaches its equilibrium value.
The combination of residence time and temperature is insufficient to reach a high
conversion at lower temperatures. A prolonged residence time or a higher catalyst
level will give a better result. The first idea is tested experimentally by decreasing
the die diameter. For the current extruder configuration, most of the residence time
is generated in the last part of the screw. Therefore, the residence time increases
considerably by decreasing the die diameter. As can been seen in fi
105
Chapter 5
higher at 160°C. This effect lessens at a higher temperature. The decline of the
y, due to the depolymerization
action.
This paragraph started by stating that an increase in barrel wall temperature is an
interesting test for the extruder model. If we now look at figure 5.10, and compare
the model and the experiments, the agreement for the small die diameter is
reasonably sound. For the larger die diameter, the model prediction does not follow
the experiment well at 180 °C. However, the trend going from a low to a high
temperature is clearly captured.
5.4.7 The effect of the rotation speed
An increase of the rotation speed has both an influence on the residence time and
on the viscous dissipation in an extruder. Due to an increase in the rotation speed,
the melt temperature will rise and the residence time will shorten; these effects
have an opposite influence on the conversion. Which effect prevails depends on the
extruder geometry and the polyurethane under consideration.
effect of a prolonged residence time at higher temperatures can be attributed to the
depolymerization reaction. The depolymerization reaction limits the conversion at
higher temperatures. In that case, an increase in residence time does not lead to a
higher conversion so that the final conversion for both die diameters is about the
same. If this situation were translated to a commercial situation, it would mean that
expensive extruder volume is not utilized efficientl
re
0
200
250
e (°
Cat
ur)
30
0
5
10
15
Pres
sure
(ba20
25
r)
50
100
150
50 100 150 200 250 300
Rotation Speed (RPM)
Mw
(g/m
ol),
Tem
per
Figure 5.11 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of rotation speed. ([cat] = 30 ppm, 12.5 kg/hour, Tbarrel
=
185°C, ddie
= 4 mm)
106
The reactive extrusion of thermoplastic polyurethane
From figures 5.11 and 5.12, it seems that both effects keep each other in
equilibrium for this system. In both figures, the rotation speed does not seem to
affect the molecular weight to a large extent. As expected, the temperature rises in
both situations slightly with increasing rotation speed. However, this effect is not
very spectacular and is obviously counterbalanced by a shorter residence time,
since the conversion remains approximately the same, independent of the rotation
speed. In contrast, the effect of the rotation speed on the end pressure is more
obvious. The end pressure decreases with increasing rotation speed. Presumably,
the decrease of the end pressure is caused by the combined effect of an increase in
temperature and a somewhat lower molecular weight. Both effects lower the melt
viscosity and therefore the pressure drop over the die.
If we compare the model with the measurements (figures 5.11 and 5.12), the model
follows the experiments well for different rotation speeds. A change in rotation
speed gives a change in viscous dissipation and therefore a different equilibrium
situation in the energy balance. This means that for the current extruder
configuration the viscous dissipation is described sufficiently well.
0
200
50
100
150
(kg/
mol
), Te
mpe
ratu
r
75 100 125 150 175 200 225
Rotation Speed (RPM)
Mw
-5
-2.5
5
e (°
C)
0
2.5Pr
essu
re (b
ar)
Figure 5.12 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of rotation speed. ([cat] = 30 ppm, 12.5 kg/hour, Tbarrel
=
160°C, ddie
= 5 mm)
5.4.8 Effect of the throughput
In figure 5.13, the effect of a change in the throughput is shown. Both model and
measurement show little effect of the throughput on the molecular weight. A higher
throughput will give a higher pressure-drop over the die, which wi increase the ll
107
Chapter 5
filled length in the extruder. However, in this case this increase in reactor volume
d to a higher conversion, due to a higher throughput to volume ratio in
. Therefore, the re
does not lea
the extruder sidence time remains more or less constant, giving
n equal conversion for all three the throughputs. Figure 5.13 shows that the model a
prediction for the temperature and conversion is accurate; however, the pressure at
the end of the extruder is over-estimated.
09 10 11 12 13 14 15 16
Throughput (kg/hour)
Mw
0
50
100
150
200
250
(kg/
mol
), Te
mpe
ratu
re (°
C)
10
15
20
25
Pres
sure
(bar
)
5
Figure 5.13 Weight average molecular weight ( ), pressure (♦) and melt temperature (■) at
the die as a function of the throughput. ([cat] = 30 ppm, 150 RPM, Tbarrel
= 160°C,
ddie
= 5 mm)
5.4.9 Depolymerization
Obviously, for all extrusion circumstances, the depolymerization reaction has a
severe impact on the extruder performance. Model simulations show that in case
the reverse reaction is not incorporated, the simulated molecular weight is a factor
ten higher than in case the reverse reaction is incorporated. Likewise, the
temperature of the melt is much higher without depolymerization. Of course, for
the experiments, the depolymerization reaction cannot be suppressed; the effects
of the reverse reaction are always present. In case an experimental parameter is
adjusted, the change in molecular weight is dampened by the depolymerization
reaction. This effect is very clear for the experiment with different cataly levels at
h
because th e
experiments weight at the die is within five percent of the
equilibrium molecular weight at the outlet temperature.
st
185°C. In t is case, an increase of the catalyst level does not have any impact,
e reverse reaction limits the maximum conversion. For th se
, the molecular
108
The reactive extrusion of thermoplastic polyurethane
If we focus on this situation, it is somewhat surprising that the conversion reaches
Figure 5.14 Build up of the weight average molecular weight and pressure in front of the
die.
If we look at the model, this effect may be explained by the way the filling degree in
front of the die is calculated. As described in the theoretical section, the pressure
drop over the die must be overcome by the filled length in front of the die. Through
an iteration procedure, the filled length is extended from zone to zone until the
pressure at the end of the die is atmospheric. If we look at a non uilibrium
of the cataly ys
In figure 5.14, ptual (isothermal) drawing of this situation is shown. If a
reverse reaction is introduced, the situation changes in figure 5.14. In that case, the
y, for example, the dashed line in figure 5.14. This
almost the same limiting value for every catalyst level. Both model and experiments
show this behavior, and for both the model and the experiments, the filled length
decreases with a higher catalyst level.
0
20
40
60
0,3 0,4 0,5 0,6
Extruder Length (m)
-eq
second order reaction, the filled length remains more or less the same, independent
st level, only the conversion increases with an increased catal t level1.
a conce
molecular weight is limited b
means that for the low catalyst run, the situation does not change, regardless of the
reverse reaction. However, for the high catalyst experiment, the molecular weight in
1 For a simplified isothermal situation, the pressure build-up capacity in the filled zones is a function of
Mw3.4, and the pressure drop over the die is a function of Mw3.4. In case the Mw in the filled zone increases
(for example due to a higher catalyst concentration), the pressure build up capacity increases. However, the
pressure drop over the die rises proportionally, giving an equal filled length. Therefore, for this situation,
the reaction velocity does not influence the filled length in front to the die.
80
100
120
140
160
Mw
(kD
a)
0
50
100
0,3 0,4 0,5 0,6
Extruder Length (m)
Pr
150
200
essu
re (b
ar)
109
Chapter 5
the last part of the extruder will not exceed the equilibrium molecular weight. This
limitation will result in a lower molecular weight at the die, giving a lower pressure
drop over the die. A lower pressure drop will give a shorter filled length upstream
of the die and therefore a shorter residence time in the reactor. The result is that
experiments at 160°C (figure 5.8). For these
xperiments, the conversion clearly increases with the catalyst level. Presumably,
the conversion for these experiments is lower than the equilibrium molecular
weight. In that case, more ‘normal’ catalyst dependence is observable, which is
comparable to the lower curve in figure 5.14. A comparison of the measured weight
average molecular weight with the equilibrium molecular weight at the outlet
temperature endorses this assumption for the experiments at 160°C. The
depolymerization reaction has several important consequences:
• Firstly, the reaction is not finished after a reactive extrusion process. For
commercial applications, the polyurethane is pelletized at the die. Due to
the equilibrium reaction, the remaining pellets still contain a considerable
react ay continue from hours to days.
• Secondly, the continuous presence in the extruder of reactive isocyanate
obtained extruder stability has a price. Due to the depolymerization
reaction, the extruder volume is not used efficiently. Hardly any reaction
of throughput and die
onfiguration, the currently developed model can be of use. In addition, the
the molecular weight is more or less independent of the catalyst level for this
situation. Only the filled length changes with the catalyst concentration. Exactly this
behavior is observed for the experiments with different catalyst levels at 185°C. The
behavior is somewhat different for the
e
amount of reactive groups and they will continue to react in the bag. Th
ion m
is
groups in a pool of urethane bonds may also lead to undesired allophanate
formation.
• Thirdly, the depolymerization reaction has a stabilizing influence on the
extrusion process. In case the depolymerization reaction governs the
extrusion performance, as in the example above, small variations in the
process parameters will hardly affect the end conversion. The reaction near
the die is very slow, and therefore a small disturbance at the entrance of
the extruder will not affect the output to a great extent. However, the
takes place in the last part of the extruder.
To improve this situation, the throughput can be increased, in combination with a
larger die diameter. To evaluate the best combination
c
110
The reactive extrusion of thermoplastic polyurethane
temperature profile of the extruder may be modified. For example, if the
temperature of the zones near the die is lowered, the reaction may proceed to a
higher conversion, because the depolymerization reaction is slowed down.
Nevertheless, for larger extruders, which operate almost adiabatically, such a
measure may not be very effective. Also for this situation, an extrusion model can
be helpful to evaluate the net effect.
5.4.10 Pressure build up
For all experiments, the pressure build up characteristics have been measured in
the last part of the extruder through three pressure sensors (figure 5.2). The
pressure build up capacity in front of the die can be monitored in this way;
furthermore, the filling degree in front of the die can be estimated. For reasons of
brevity, these data were left out in the foregoing comparison. However, if we
compare these data with the model predictions, a clear trend is visible; the model
seems to overestimate the pressure build-up capacity in all cases (figure 5.15).
300
200
Mod
el
100
dP/d
L (b
ar/m
),
00 100 200
dP/dL (bar/m), Experiment
Figu
Several pla
assess t
sufficien
the extr
exact reas
used in e
pressure non-reactive validation studies
re 5.15 Calculated versus measured pressure build up capacity in front of the die.
usible reasons can be formulated for this phenomenon. However, to
he exact cause of the overestimation of the pressure drop, it is not
t to have only data on the pressure drop. Preferably, the conversion along
uder should also be known. Since the latter could not be determined, the
on of the discrepancy cannot be established. Possibly, the k-factor that is
quation 5.5 is too high, which will result in an over prediction of the
build up capacity. On the other hand, the
111
Chapter 5
did not show an inaccurate prediction of the pressure build-up. Another explanation
ore, in a fully filled section, the pressure flow
will almost equal the forward flow, which will lead to considerable back mixing.
in our extruder is relatively large, which will also
n
e channels of a single screw extruder may be of help. This model is also
applicable for a self-wiping twin-screw extruder, even though the intermeshing
zone will disrupt the flow pattern somewhat. The residence time distribution (RTD)
analysis of Pinto and Tadmor (15) shows that the flow in the fully filled conveying
elements falls within plug-flow and flow in a pipe. This observation of coincides
with the correction factor noticed in the previous paragraph.
In case the RTD approach of Pinto and Tadmor is used in the current extrusion
model, it must be incorporated in the ´segmental structure´. The plug flow
assumption for transport elements used in the current model prevents difficulties
that arise when a continuous laminar flow (as is the case for a screw channel) is
subdivided in segments (as is he case for the current extrusion model). In that case,
going from segment to segment, closed-closed boundary conditions are unsuitable.
In a later stage, this problem will be tackled. To do so, the inc ing flow can be
ly
ed conveying zone, every batch reactor will follow a specific continuous path, and
for the discrepancy between model and measurement may lie in the approach for
the residence time distribution. The elements in front of the die are considered as
plug flow reactors. A plug flow reactor will give a much higher conversion than a
well-mixed reactor for the same residence time (14). Therefore, the filled length
needed to reach a certain conversion is much shorter for such a reactor. For our
specific extruder configuration, it might be expected that the flow behavior in the
filled section in front of the die comes closer to a well-mixed reactor than to a plug
flow reactor. The extruder is operated at a low throughput in comparison to its
maximum throughput capacity. Theref
Moreover, the leakage gap
contribute to considerable mixing of the material. Both factors contribute to a much
higher mixing degree than for a plug flow situation. This will give a lower
conversion per centimeter extruder length. Consequently, the experimentally
observed pressure drop per length unit is lower than anticipated from the model
predictions. A correction factor of 1.3 is applicable in this case.
To improve the residence distribution modeling, a residence time distribution
model formulated by Pinto and Tadmor (15), based on the helical flow pattern i
th
om
divided in a group of small batch reactors that flow through the extruder. In a ful
fill
have a specific residence time, according to the RTD-function. Going from segment
to segment, the flow-lines are not disturbed, so that a batch reactor will have an
equal residence time in every segment. For every segment, the conversion of all
112
The reactive extrusion of thermoplastic polyurethane
batch reactors can be calculated and averaged, to give the average conversion in a
segment.
5.4.11 The effect of the residence time distribution on conversion
For a second order reaction, a plug flow reactor is a far more efficient reactor (1.5
to 2 times). In fact, for all nth-order reactions with n > 1, a plug flow reactor is more
efficient. If only the residence time distribution was important for reactive extrusion,
the screw layout should be designed to approach as plug-flow as well as possible.
Generally, transport elements are regarded as the screw elements that come closest
to plug-flow. The reason that so many other types of elements are used lies in the
fact that in an extruder different processes are combined, which require different
type of elements.
In process technology, a plug flow reactor is often approached with a cascade of
continuous ideally stirred reactors. A similar analogy can be made for extrusion. A
study performed by Todd (28) demonstrated that an extruder only filled with
kneading elements showed mixing behavior that came closer to a plug flow reactor
than an extruder filled with transport elements. However, the forward transport
capacity and the energy consumption (and the related temperature rise) with a
surplus of kneading paddles may be undesirable. Possibly new types of radial
mixing elements (29) may benefit a narrow residence time distribution and improve
the efficiency of a reactive extrusion process.
113
Chapter 5
5.5 Conclusions
A comparison of the experimental data with the model predictions demonstrates
that the present model describes the polyurethane polymerization reaction in the
extruder satisfactory, especially considering the engineering approach chosen for
the model. The reverse reaction is also captured adequately in the model.
The de lymerization reaction has a profound impact on the extruder performance
lymerization
of side reactions (e.g. allophanate formation).
po
by limiting the maximum conversion. At the same time, the depo
reaction may stabilize the extruder performance due to the considerable decrease
of the reaction velocity near the die. Small disturbances at the inlet will be wiped
out at the fully filled reaction zone near the die. From an extruder performance
point of view, this stagnant zone is an inefficient use of expensive reactor volume.
In addition, the consequence of the reverse reaction is that polyurethane that exits
the extruder may continue to react in the bag. A prolonged presence of a
polymerization-depolymerization equilibrium may be disadvantageous due to the
possible occurrence
The depolymerization reaction is an extra complicating factor for understanding
polyurethane extrusion. An extruder model is therefore a helpful tool for
optimizing the polyurethane extruder.
The current approach for the residence time distribution in the model is coarse. For
example, at the relative high pressure to drag flow ratio that is present in the
current extruder configuration, the residence time distribution in the filled
transport elements comes closer to ideally stirred than to plug flow, while the latter
approach is used in the model. However, a correction factor can be used in this
case.
114
The reactive extrusion of thermoplastic polyurethane
5.6 List of symbols
A0 Reaction pre-exponential constant mol/kg·s
A0,flow
Flow pre-exponential constant Pa·sn
Awall
Surface of the barrel wall m2
-
-
Shape factor for kneading elements -
kr Reverse reaction rate constant 1/s
L Length of the die m
m Catalyst order -
MW Weight average molecular weight g/mol
n Reaction order -
n Power law index -
N Rotation speed 1/s
[NCO] Concentration isocyanate groups mol/kg
[NCO]0 Initial concentration isocyanate groups mol/kg
[NCO]N Isocyanate concentration at the outlet of a reactor mol/kg
[NCO]N-1
Isocyanate concentration at the inlet of a reactor mol/kg
∆P/∆L Pressure gradient in the axial direction of the extruder Pa/m
C Correction for entrance losses at the die 1/m3·n
Cp Heat capacity J/kg·K
[Cat] Catalyst concentration mg/g
e Flight land width m
EA Reaction activation energy J/mol
EA,eq
Equilibrium reaction activation energy J/mol
E(t) Exit age function -
f Functionality -
ft Filling degree of a not fully filled transport element -
fk Filling degree of a not fully filled kneading element
h Height of the screw channel m
h Heat transfer coefficient J/s·m2·K
i Number of channels
k Power law consistency Pa·sn
k0 Forward reaction rate constant, catalyst independent mol/kg·s
keq Equilibrium reaction rate constant mol/kg
kf Forward reaction rate constant, catalyst dependent kg/mol·s
kp,t
Shape factor for transport elements -
kp,k
115
Chapter 5
Q Throughput kg/s
ing capacity, transport elements kg/s
S,max,K Maximum conveying capacity, kneading elements kg/s
]
3
QS,max,T
Maximum convey
Q
QL, drag
Drag term of leakage flow over the flight kg/s
QL, k
Leakage flow between the kneading paddles kg/s
R Gas constant J/mol K
R Radius of the die m
RNCO
Rate of isocyanate conversion mol/kg⋅s
t Time s
T Temperature K
u Circumference of the eight-shaped barrel m
[U Concentration urethane bonds mol/kg
UA Flow activation energy J/mol
v0 Circumferential velocity of the screw m/s
V Volume ATR reactor m
w Width of the screw channel m
CW& Viscous dissipation in the channel J/s
FW& Viscous dissipation over the flight J/s
eek symbols Gr
α Conversion (1 - [NCO] / [NCO]0) -
δR Clearance between barrel and flight tip m
γ& Shear rate 1/s
ηchan
Viscosity in the channel Panel
η
·s
flight
ψ Intermeshing angle -
Viscosity over the flight Pa·s
ϕ Pitch angle -
116
The reactive extrusion of thermoplastic polyurethane
5.7 References
1. K eveld, and L.P.B.M. Janssen, .J. Ganz Polym. Eng. Sci., 32, 457 (1992).
illo m. Res.2. A. Bou ux, C.W Macosko and T. Kotnour, Ind. Eng. Che ,3 (19910, 2431 ).
P. Cassag3. nau, T. Nietch and A. Michel, Int. Polym. Process.,1 ). 4, 144 (1999
4. M.E.Hyun and S.C. Kim, Polym. Eng. Sci., 28, 743 (1988).
5. G. Lu , D.M. Kalyon, I. Yilgör and E. Yilgör, Polym. Eng. Sci., 43, 1863 (2003).
6. V.W.A. Verhoeven, A.D. Padsalgikar, K.J. Ganzeveld and L.P.B.M. Janssen, J. Appl.
Polym. Sci. , accepted for publication
7. H.E. Meijer and P.H.M.Elemans, Polym. Eng. Sci., 28, 275 (1988).
8. H. Potente, J. Ansahl and R. Wittemeier, Int. Polym. Process., 3, 208 (1990).
9. H e, J. Ansahl and B. Klarholz, . Potent Int. Polym. Process., 9, 11 (1994).
10. W. Michaeli, A. Grefenstein and U. Berghaus, Polym. Eng. Sci., 35, 1485 (1995).
11. H.Kye and J.L. White, Int. Polym. Process., 11, 129 (1996).
12. W eli, and A. Grefenstein, . Micha Int. Polym. Process., 11 21 (19 6). , 1 9
13. B. Vergnes, G. Della Valle and L. Delamare, Polym. Eng. Sci., 38, 1781 (1998).
14. K terterp, W.P.M. Van Swaaij an eenacke s, ical R .R. Wes d A.A.C.M. B r Chem eactor
D d Operationesign an , John Wiley & Son w er, s, Ne York, Brisbane, Chichest Toronto
15. . Pinto
(1984).
G and Z. Tadmor, Polym. Eng. Sci., 10, 279 ). (1970
H. Potente, Untersuchung der Schweissbarkeit Thermoplastischer Kunststoffe mit 16.
Ultraschall, Aachen (1971).
d, SPE ANTEC Tech. Papers17. D.B. Tod , 34, 54 (1988).
.W.A. V . 18. V erhoeven, M.P.Y. Van Vondel, K.J. Ganzeveld, L.P.B.M. Janssen, Polym. Eng
Sci., 44, 1648 (2004).
19. D. W. Van Krevelen, Properties of Polymers, Elsevier, Amsterdam (1990).
20. L.P.B.M. Janssen, Reactive Extrusion Systems, Marcel Dekker Inc., New York, Basel,
(2004).
21 D.B. Todd, . Int. Polym. Process., 6, 143 (1991).
22. T. Brouwer, D.B. Todd and L.P.B.M. Janssen, Intern. Polym. Process.,17, 26 (2002)
23. Z. Tadmor, G. Gogos, Principles of Polymer Processing, John Wiley & Sons, New York,
Brisbane, Chichester, Toronto (1979).
4. R.A. De Graaf, D.J. Woldringh, and L.P.B.M. Janssen, Adv. Polym. Tech.2 , 18, 295
(1999).
5. J. Noé, Etude des écoulements de polymères dans une extrudeuse bivis corotative.,2
Phd-Thesis, Ecole des Mines Paris (1992).
6. M.V. Karwe and S. Godavarti, J. Food Sci.2 , 62, 367 (1997).
27. O.S. Carneiro, J.A. Covas and B. Vergnes, J. Appl. Polym. Sci., 78, 1419 (2000).
28. D.B. Todd, Chem. Eng. Prog., 69, p. 84 (1969).
29. D.B. Todd, Plastic compounding, Hanser, Munich (1998).
117
6 The effect of premixing on the reactive extrusion of
thermoplastic polyurethane
6.1 Introduction
For the reactive extrusion of polyurethane, the extruder performance may be
improved by premixing of the monomers. The polyurethane monomers (di-
isocyanate and the di-alcohols) are immiscible. Therefore, mixing is required to
attain a kinetically controlled reaction. Obviously, mixing takes place in the
extruder. However, valuable extruder length may be saved by premixing, since in
that case the reaction starts earlier. Moreover, the polymer formed may be more
homogeneous in composition, since a better defined reaction mass enters the
reactor. To validate these assumptions, the effect of premixing is investigated in
the current chapter. The approach that is taken to measure the effect of premixing
is straightforward. The conversion in the extruder is measured with and without
premixing. Moreover, the effect of the degree of premixing is established with
batch experiments. By measuring the reaction rate at different degrees of
premixing, the effect of premixing is established. Adiabatic temperature rise (ATR)
experiments are used to measure the reaction rate.
For premixing, both static mixers and dynamic mixers (e.g. a high-speed rotating
blade mixer) are used in practice. Due to its superior dispersive mixing action, at
first glance a dynamic mixer seems to be a better choice for the current application.
However, such a mixer is sensitive to clogging, especially at the inlet points of the
monomers. A static mixer is less sensitive to congestion. Moreover, if a static mixer
is clogged, it is much easier, faster, and cheaper to replace. Therefore, in the
current investigation, a static mixer is used to premix the monomers.
After premixing of the monomers, a dispersion of isocyanate drops in a continuous
di-alcohol matrix is formed. To have a completely kinetically controlled reaction, the
droplet diameter must be small enough so that the diffusion time is shorter than
the reaction time. In several publications on reactive injection molding (RIM) of
polyurethane, it was found that the reaction rate and the maximum conversion
increase with the mixing intensity, up to a certain maximum (kinetically controlled)
regime (1-3). Increasing the catalyst level increased the reaction velocity and the
necessary mixing to reach a kinetically controlled regime. Most of these
experiments were performed with cross-linking systems and impingement mixing.
Cross-linking systems are more susceptible to diffusion limitations due to the lower
Chapter 6
mobility of the reactive groups near and beyond the gel point. Impingement mixing
g a
experiments with (pre and Lee et al. (4, 5).
Similar results were obtained as with the impingement mixers.
ives much higher shear rate than present in our static mixer. Batch ATR
-) stirring were performed by Fields et al.
6.2 Mixing
As stated in the introduction, the isocyanate droplets must be small enough to
obtain a kinetically controlled reaction. The Fourier number, which compares the
reaction time (treaction
) with the diffusion time (d2 / ID), applies for this situation:
2reaction
d
tIDFo
⋅= ( 6.1 )
The Fourier number should be larger than one for a kinetically controlled reaction.
An estimation for the current system shows that the droplets must be smaller than
20 µm in that case (ID = 10-11 m2/s, treaction
= 60 s, Fo > 2).
The minimum droplet diameter that can be obtained in the static mixer can also be
estimated through an analysis of a dimensionless number. The droplet diameter is
governed by the Capillary number, which is the ratio between the force applied on a
droplet (η· γ& ) and the interfacial forces (σ / d) that keep the droplets together:
σ⋅γ⋅η
=d
Ca&
( 6.2 )
As long as the capillary number is much larger than unity, the droplets size can still
be reduced. At Ca ≈ 1 (6), the minimum droplet size is reached. For the static mixer
used in this investigation, the minimum droplet diameter that can be reached is
estimated at about 250 µm (Cacr =1, σ = 0.01 N/m, γ& = 160 s-1, η = 0.25 Pa·s). In
practice, the droplet diameter may be somewhat smaller, since elongational forces
are also present in Kenics-type static mixers.
If we compare the two droplet diameters, it seems that a kinetically controlled
reaction can never be reached in a static mixer alone. For a polymerization reaction,
this is particularly troublesome, since high molecular weight barriers will appear at
the interface, due to a rapid reaction on the isocyanate-polyol surface (7),
preventing completion of the reaction. However, it was established by Machuga et
al. (8) and Macosko (1) that the isocyanate polyol interface is unstable. The unstable
120
The effect of premixing on the reactive extrusion of polyurethane
surface results in an interfacial reaction zone that may stretch out to 100 µm within
a second, depending on the monomers used. In this zone, the di-isocyanates and
the di-alcohols are mixed. The calculation of the minimum droplet diameter, based
on the capillary number is therefore a worst-case approach. During the passage
through the static mixer, the interfacial tension between di-isocyanate and di-
stantially reduced due to the interfacial reaction zone. This
e c ard,
ince reaction, diffusion, and mixing for the polymerization reaction interact. A
short analysis of the dynamics of the mixing process in a static mixer may help to
estimate the effic
.2.1 Mixing dynamics
tatic retched and broken down
fo tatic
mixer (9). Taking into account this exponential decay, the thread diameter will have
ached the critical diameter within three elements (dintial
= 2 mm, dcrit
= 0.25 mm).
Break-up is th
alcohol fraction is sub
will give a much smaller droplet diameter. It is even conceivable that at the end of
the mixer a single phase will appear.
Nonetheless, th alculation of the final droplet diameter is not straightforw
s
iency of extra mixing elements.
6
The mixing action of a static mixer is both dispersive and distributive. The
isocyanate thread that enters the s mixer will be st
plets will binto small droplets, and these dro e distributed evenly over the polyol
phase with a narrow droplet size distribution. Far from the equilibrium diameter (Ca
>> 1), the diameter of the thread that enters the mixer decreases exponentially, due
to affine de rmation and the ´bakers transformations´ that take place in the s
re
en not immediate; the relevant time scale for breaking up is (9):
σ
=−t upbreak ( 6.3 )
For the premixing in this investigation, the break-up time is about 0.01 second,
which means that the thread is broken into droplets within one mixing element (the
residence time for one mixing element = 0.05 seconds).
According to the above dimensional analys
⋅η d
is, the complete dispersive mixing
process should be completed within about four mixing elements. Distributive
mixing continues, but since the droplet diameter cannot be reduced further, the
reaction velocity will only increase slightly by distributing the droplets evenly.
However, the effect of the interfacial reaction zone must also be taken into account.
In that case, it is conceivable that the interfacial reaction zone mixes continuously
121
Chapter 6
with the bulk through the static mixing action. In that case, also distributive mixing
will improve the reaction considerably.
A possible approach to estimate the effect of the interfacial zone is to look at the
diffusion velocity of the interfacial zone. This diffusion velocity may be rate limiting.
To estimate this effect, the penetration theory for non-stationary mass transport
can be used. According to the penetration theory, the penetration depth is
proportional to (ID⋅π⋅tresidence
)1/2. Since tresidence
, the residence time, is proportional to the
number of mixing elements, the penetration depth of the interfacial zone is
one that is formed will be rapidly
mixed in the bulk. Distributive mixing in the static mixer may therefore increase
gure 6.1 The extruder layout for the premixing experiments.
truder can be found in
element
proportional to N1/2. The striation thickness, which can be seen as a measure of the
distributive mixing action, is inversely proportional to 2N in a Kenics-type static
mixer. If we compare these two dependencies, it is clear that the interfacial
diffusion velocity is rate limiting; the interfacial z
with N1/2.
6.3 Experimental setup
Polyol + diol + catalyst
P1 P2 P3
MDI
Fi
Figure 6.1 shows a detailed picture of the static mixer and the extruder. The
configuration is the same as for the extrusion experiments described in chapter 5.
The description of the feeding equipment and the ex
paragraph 5.3.4. For the ATR experiments, a throughput of 15 kg/hour is
maintained for all of the ATR experiments, for the extrusion experiments the
throughput is 12.5 kg/hour.
At the inlet of a static mixer, the isocyanate is inserted at the middle of the polyol
stream through a small nozzle (d = 2 mm). The static mixer (Mixpac MC 06-32)
consists of 32 mixing elements (D = 6.35 mm, L/D = 1). The number of mixing
122
The effect of premixing on the reactive extrusion of polyurethane
elements can easily be reduced. The static mixer outlet is placed near the extruder
inlet. If an ATR experiment is performed, the ATR reactor is placed under the outlet
d
ia atic reactor consisted of a disposable cup (diameter = 4cm) surrounded
ion. The reactor could be closed with a lid.
opper Constantine thermocouple sticking in
th tion mass. At the start of an experiment, the reactor is filled
with a continuous flow of reaction mass. The temperature of the entering material
is ured. The time to fill the reactor at 15 kg/hour was 25 seconds, giving a
final content of about 100 gram.
For the lowest catalyst level, the filling time is not relevant. Ho ver, at t high st
catalyst levels, the filling time of the reactor is relatively long compared to the
reaction time (treaction
= 80 seconds at 100 ppm; 120 seconds at 75 ppm). This makes
the analysis of the reaction at the highest catalyst level not as straightforward as
with the ´regular´ ATR experiments. On the other hand, the measurement is not
or th or an evaluation of the
ffect of premixing. The first consequence of the relatively long filling time is that
ct, every experiment is performed in triplicate. In case
e fi
reaction times in the reaction mass. The first part of the reaction mass has reacted
of the static mixer.
6.4 Materials
System 2, as described in chapter 4, was used for the premixing experiments. The
system consists of a liqui form of diphenylmethane diisocyanate (an eutectic
mixture of 2,4-MDI and 4,4-MDI), methyl-propane-diol and a polyester polyol (Mw =
2200, functionality =2). The treatment of the chemicals before usage is described in
in chapter 2. The percentage of hard segments (isocyanate + methyl-propane-diol)
was 24%. The reaction was catalyzed using bismuth octoate.
6.5 Adiabatic temperature rise analysis
The ad b
by a layer of urethane foam for insulat
The reactor was equipped with a thin C
e middle of the reac
meas
we he e
intended f e determination of kinetic constants but f
e
temperature gradients over the reaction mass may occur (Damkohler IV > 1):
Material that enters the reactor initially will have reached a higher temperature than
the last part of the material entering the reactor, since it has already reacted for 25
seconds. Combined with the fact that in the ATR reactor, the macromixing of the
colder and warmer material is not perfect, no uniform reactor temperature may be
reached. To estimate this effe
large temperature gradients occur, the triplicate measurements should show large
deviations.
A second consequence of the larg lling time is the presence of a distribution in
123
Chapter 6
for 25 seconds at the time the last part enters the reactor. The isocyanate
concentration follows a similar distribution in the reactor, due to the poor micro
mixing properties of the reacting polymer system. A micro segregated reaction
mass with a variable isocyanate concentration is the result. This may bias the fitting
high catalyst concentrations. In case an isocyanate
ic error was ignored.
In order to derive kinetic data from the ATR experiments, a simplified heat balance
tion lved simultaneously.
procedure, especially at
distribution is present, for a given ATR-curve, a standard ATR analysis will
underestimate the activation energy and overestimate the reaction velocity (when a
second order kinetic equation applies). A coarse approach was taken to investigate
this effect (appendix 6.1). It was found that the activation energy and the reaction
rate constant were slightly affected by micro segregation (< 3 % at the highest
catalyst level). Considering the size of the effect, this systemat
(equa 4.1) and rate equation (equation 2.12) were so
( )ρ⋅
⋅=−−∆⋅=⋅
VAh
hwithTThHRdtdT
C *room
*RNCOp
( 4.1 )
[ ] nTRE
0NCO ]NCO[eAdt
NCOdR
A
⋅⋅−== ⋅−
( 2.12 )
For the heat balance, quasi-adiabatic conditions were assumed, since the reactor
order to determine the maximum temperature rise, the complete ATR
was not completely adiabatic for the time under investigation. Depending on the
reaction time, up to 4 % of the total reaction heat generated during the reaction was
lost to the surroundings. The heat transfer coefficient h* was obtained by fitting the
cooling curves of several experiments, using equation 4.1. We took the density and
the specific heat to be constant over the whole measurement range. Although both
the specific heat and the density are somewhat dependent on the temperature, the
temperature effects of both constants counteract, so that the net effect is negligible
(< 5%). ∆HR was taken from the experiment that gave the largest temperature rise. A
non-linear regression method (error controlled Runge-Kutta) was used to solve the
differential equations. With a least square routine, the difference between the
model and the measurement was minimized. The calculations were performed with
the software program Scientist. For the model fit, only the first part of the ATR
curve was utilized, up to a conversion of about 75 %. As described in chapter 4, at a
higher conversion the reaction slows down due to phase separation of hard and soft
segments. In
curve was fitted.
124
The effect of premixing on the reactive extrusion of polyurethane
6.6 Results
In figure 6.2, typical adiabatic temperature rise curves are shown. As the figure
shows, a substantial part of the reaction occurs during filling of the reactor. After
25 seconds, the filling of the reactor has ended and the three temperature curves
coincide, indicating a good reproducibility. The model fit is performed on the area
between the two dotted lines. The low limit is of course related to the filling time of
the reactor, while the upper limit is derived from an Arrhenius representation of the
ATR curves (chapter 4). The upper limit represents the point at which the Arrhenius
plot (not shown) deviates from a straight line. The reaction slows down at this point,
due to the separation of the hard and soft segments (chapter 4), or more generally
due to the crossing of the glass temperature of the material.
320
340
360
380
400
0 50 100 150 200
Time (s)
Tem
pera
ture
(K)
Figure 6.2 Typical adiabatic temperature rise curves, a triplicate experiment (16 mixing
elements, [Cat] = 75 ppm).
6.6.1 The effect of premixing on the reaction velocity
The effect of catalyst level and number of mixers on the apparent reaction rate
constant is shown in figure 6.3. The error bars in this figure represent the standard
deviation based on three experiments. For the experiments most susceptible to
diffusion limitations, the high catalyst experiments, the reaction rate increases with
the mixing intensity, clearly indicating a diffusion controlled reaction at low mixing
intensity. The reaction seems to approach the kinetically controlled regime at 32
elements. These results are contradictory to the analysis of the dimensionless
numbers that was discussed in the theoretical section. In this analysis, no effect of
mixing is expected with more than four mixing elements. Moreover, the effect of
125
Chapter 6
mixing should follow an exponential pattern, instead of the slow increase of the
reaction velocity with the number of mixing elements as found in figure 6.3.
0
0.01
0.02
0.03
0.04
0.05
k (k
g/m
ol s
)
0 8 16 24 32
N (-)
Figure 6.3 The effect of the number of mixing elements (N) on the reaction rate constant
for different catalyst levels (♦ = uncat, ■ = 50 ppm, = 75 ppm, • = 100 ppm).
Evidently, the analysis of dimensionless numbers in the theoretical section is based
on best estimates of the physical constants, and the analysis may therefore give a
deviation from the actual situation. However, the general conclusion of the analysis
of dimensionless numbers that the minimum droplet diameter is in the range of 50
to 200 µm diameter is supported by experimental results of Kolodziej et al. (3).
Therefore, the difference in the analysis of dimensionless numbers and the
experimental results must have a different origin than a faulty estima .
re
typical for polyurethanes: the presence of an interfacial reaction zone. On the
of the di-alcohols in the
te
In the theo tical section, a possible scenario is sketched based on an effect that is
boundary layer of isocyanate and di-alcohol, rapid diffusion
isocyanate droplets occurs, forming an interfacial reaction zone. This instable
boundary layer will be continuously mixed in the bulk due to the distributive mixing
effect of the static mixer. For this scenario, the reaction velocity increases with N1/2,
in case the reaction is diffusion limited.
126
The effect of premixing on the reactive extrusion of polyurethane
0
0.02
0.04
1 2 3 4 5 6
(N)^0.5 (-)
k (k
g/m
ol s
)
Figure 6.4 The effect of the square root of the number of mixing elements (N) on the
reaction rate constant for different catalyst levels (♦ = uncat, ■ = 50 ppm, =
75 ppm, • = 100 ppm).
To test this
e theoretical approach is valid, the reaction rate of the reaction with the highest
scenario, figure 6.4 shows a plot of the reaction velocity versus N1/2. If
th
catalyst level should rise linearly with N1/2. This seems not to be the case. The
simplified theoretical approach therefore does not describe the measurements. The
exact mixing mechanism must relate to a different mechanism.
0
0.02
0 0.1
k (k
g/m
ol s
)
0.04
0.2 0.3
1 / N (-)
481632
Figure 6.5 The effect of the inverse of the number of mixing elements (N) on the reaction
rate constant for different catalyst levels (♦ = uncat, ■ = 50 ppm, = 75 ppm,
• = 100 ppm).
127
Chapter 6
A least square fit of the reaction velocity of the highest catalyst level versus Nx
shows that for x ≈ -1 a linear plot is obtained. The obvious effect of the decreasing
efficiency of an extra mixing element is shown in figure 6.5. Looking at this figure,
it seems that for the highest catalyst level, the reaction does not reach a kinetically
controlled regime within 32 elements. For the 75 ppm experiments, a similar rise of
the reaction rate with the number of mixing elements is visible, but for this catalyst
level the kinetically controlled regime is reached at 16 mixing elements. The lowest
catalyst level and uncatalyzed experiments do not seem to be bothered by any
diffusion limitations. These observations agree with the idea that the faster the
reaction, the more prone a reaction is to diffusion limitations. Moreover, a higher
degree of mixing is necessary to reach a kinetically controlled regime for a faster
6.6.2 The n the adiabatic temperature rise
he adiabatic temperature rise is related to the initial mixing efficiency. In case the
reaction.
effect of premixing o
T
initial (micro-) mixing is insufficient, high molecular weight diffusion barriers may
appear, which prevent the reaction to come to a full completion, giving a lower
∆TAdiabatic
. Both dispersive and distributive mixing are important in this case.
60
65
70
75
0 10 20 30 40
N (-)
Adi
abat
ic te
mpe
ratu
re ri
se (°
C)
Figure 6.6 The effect of the number of mixing elements (N) on the adiabatic temperature
rise for different catalyst levels (♦ = uncat, ■ = 50 ppm, = 75 ppm, • = 100
In figure 6.6, the number of mixing elements and the catalyst level on
e adiabatic temperature rise is shown. The difference between the uncatalyzed
and catalyzed series is striking. The adiabatic temperature rise for the uncatalyzed
ppm).
the effect of
th
128
The effect of premixing on the reactive extrusion of polyurethane
reaction is unaffected by the number of mixing elements, while the catalyzed
reactions show a steady increase of ∆Tadiabatic
with the number of mixing elements.
The effect for the uncatalyzed experiments is probably related to the time after
which an experiment was stopped. As stated before, the reaction slows down
considerably at high conversions. As expected, the difference in ∆Tad as a function
of mixing degree is generated in this last part. Unfortunately, the temperature was
monitored for too short a time to capture the complete tail of the uncatalyzed
reactions.
For the catalyzed reactions, it seems that the catalyst concentration has no
significant effect on ∆Tadiabatic
, at least not within the experimental error of the
current experiments. This observation is in agreement with a study on the
interfacial activity, which does not see an effect of catalyst or the catalyst level on
the initial formation velocity of an interfacial layer (8). As soon as catalyst is present,
cadiabatic
endent of the the mi ro mixing efficiency (expressed as ∆T ) increases, indep
catalyst concentration. This catalyst independence implies that both the droplet
diameter and the interfacial zone at the end of the static mixer are of equal size for
all catalyst levels, or more general, the degree of mixing is similar for all catalyst
levels and only dependent on the number of mixing elements.
60
65
70
75
0 0.1 0.2 0.3
1 / N (-)
Adi
abat
ic te
mpe
ratu
re ri
se (°
C) 481632
Figure 6.7 The effect of the inverse of the number of mixing elements (N) on the adiabatic
temperature rise for different catalyst levels (♦ = uncat, ■ = 50 ppm, = 75
ppm, • = 100 ppm).
In analogy with the reaction velocity, the adiabatic temperature rise is plotted
versus the inverse of the number of mixing elements (figure 6.7). Although the
significance level is not optimal, it seems that even with 32 elements no ´ideally
129
Chapter 6
micro mixed´ situation exists. This is in agreement with the high catalyst level
experiments, which show that even wi 32 elements the reaction is diffusion
limited for the fastest reaction. However, for the low catalyst levels the reaction
seems kinetically controlled for all mixing levels according to figure 6.5. This does
not seem to agree with the adiabatic temperature rise data (figure 6.7), which show
the opposite effect. Since the differences in adiabatic temperature rise (∆T
th
ixing only bothers the low catalyst experiments for the last part of the
ce m
adiabatic) for
the different mixing levels are made at the end of the reaction, it may be so that
imperfect m
reaction. The kinetic data is obtained at lower conversions, before the reaction
slows down. This differen ay be the origin of the inconsistency.
6.6.3 The effect of premixing on the extruder performance
Rotation
speed
(RPM)
Residence
time (s)
Mw
premixed
Mw
non-
premixed
PDI
premixed
PDI
non-
premixed
100 114 76 70.1 2.1 2.2
100 110 72.3 69.6 2.2 2.3
150 117 68.4 67.1 2.1 2.1
200 193 70.8 67.7 2.0 2.1
Table 6.1 The process parameters and results for the extrusion experiments (PDI =
polydispersity index).
Extrusion experiments were carried with and without premixing (table 6.1). The
mixing intensity and residence time in the extruder was varied to evaluate the
effect of mixing in the extruder versus the effect of premixing. Model simulations
(chapter 5) were performed to calculate the residence time. In table 6.1, the
extrusion parameters are listed including the residence time model simulations.
130
The effect of premixing on the reactive extrusion of polyurethane
55
65
75
Mw
(kg/
mol
)
2
2.2
2.4
2.6
Poly
disp
ersi
ty (-
)
0.5 1.5 2.5 3.5 4.5
RPM x Time (-)
200150100 RPM
Fi Weight average molecular weight (♦) and without (■) premixin the
p ith d without ixing ( ) as tion of the train
in er.
In f 6.8, olecula eight a e polydi ity of the med
poly ane (wi d witho mixing otted ve the produ the
rota peed a e resid me. Th er is a cru easure of total
stra reactio has e tered d processin due to mo less
onstant time and viscosity, the total strain coincides with the maximum shear
s
scale for bot ersive mixing. The catalyst level was varied in the
se
in conversion due to premixing is independent of the mixing degree in the extruder.
The premixing benefit may be caused by a faster initial reaction velocity in the
extruder due to premixing of the reaction mass. Then again, a higher degree of
initial mixing may also lead to a higher final conversion, as for example the batch
experiments show. In the latter case, high molecular weight ´diffusion barriers´
that occur due to the poor initial mixing are prevented by premixing. These barriers
may be difficult to break, even in the flow field of the extruder, due to their high
gure 6.8 with g and
olydispersity w
the extrud
(◊) an prem a func total s
igure the m r w nd th spers for
ureth th an ut pre ) are pl rsus ct of
tion s nd th ence ti e latt de m the
in the n mass ncoun uring g. If, re or
c
stress, as i the case in figure 6.8, the x-axis can been seen as a combined mixing
h distributive as disp
above experiments, to obtain a more or less similar conversion for all experiments.
As can been seen in figure 6.8, premixing has a slight effect on the final conversion.
The weight average molecular weight is 5 tot 10 % higher for the premixed
experiments. Since for condensation polymerization, the molecular weight is
linearly dependent on the reaction time, 5 to 10% of reaction time (or extruder
length) is saved by premixing the reaction mass. Figure 6.8 shows that the increa
131
Chapter 6
viscosity and small size. The reduction in reaction velocity at the end of the reaction
is prevented and the reaction will carry on to a higher conversion.
For all experiments the polydispersity decreases when the reaction mass is
premixed. This observation reflects that a better defined reaction mass gives a
polymer with a narrower molecular weight distribution. The mixing applied in the
extruder does not seem to change that, even at a high mixing degree the difference
in polydispersity remains between the premixed and non-premixed experiments.
On the other hand, figure 6.8 shows also that the polydispersity decreases with the
amount of mixing the extruder. This indicates that mixing in the extruder must
have some beneficial effect on the homogeneity of the reaction mass.
6.6.4 A comparison of the results with the results of chapter 4
In chapter 4, different types of kinetic experiments were performe with the
sensitive to mi
d
chemical system currently under investigation. The system was found to be very
xing. Several findings led to this conclusion:
• For the ATR experiments, the activation energy decreased at higher catalyst
levels and the reaction velocity seemed to reach a maximum value at higher
catalyst levels.
• For the kneader and high temperature experiments, the experiments
without mixing proceeded at a lower reaction velocity.
If we look at the current experiments, the mixing sensitivity is also clearly present.
However, it is interesting to compare the batch ATR results as presented in chapter
4 with the current ´continuous´ ATR results. For the batch experiments the
reaction mass is premixed with a turbine stirrer, while a static mixer is used for the
continuous experiments. In fact when comparing the two methods, superior
dispersive mixing (turbine stirrer) is compared with superior distributive mixing. In
table 6.2, the reaction rate constant of the uncatalyzed experiments and three
catalyst levels are compared.
For all catalyst levels, the experiments with the static premixing are faster than the
dynamically premixed experiments. Moreover, with increasing catalyst level, the
dynamically premixed experiments become relatively slower. Apparently, for this
polyurethane, premixing with a static mixer is more efficient than with a turbine
stirrer. Hence, the spatial distribution of the monomers must be imperfect for the
dynamically premixed experiments, causing the observed diffusion limitations. The
132
The effect of premixing on the reactive extrusion of polyurethane
better dispersive mixing action of a turbine stirrer does not seem to be decisive in
this case.
uncat 50 ppm 75 ppm 100 ppm
static mixer 0.003 0.009 0.024 0.041
turbine stirrer 0.002 0.007 0.012 0.016
ratio 1.4 1.3 2.0 2.6
Table 6.2 The reaction rate constant (kg / mol⋅s) at 100°C for the batch and continuous
ATR experiments (using 32 mixing elements).
em, a fit of the
kinetically controlled.
owever, the effect of diffusion limitation is moderate, so that the kinetic constants
will rd
6.7
For
the con ixing results in a
arrower molecular weight distribution, giving improved material properties.
al risks.
In light of the extrusion experiments performed with the current syst
dynamically premixed experiments (with 32 elements) is appropriate as an input for
the extruder model. According to the analysis of the results of this chapter, only
with 100 ppm catalyst, the reaction is not completely
H
ha ly be affected.
Conclusions
the polyurethane under investigation, premixing has a small beneficial effect on
version at the end of the extruder. Moreover, prem
n
Although the effect of premixing for this system is not substantial, it will increase
with faster reacting monomers. For faster reactions, diffusion barriers at the start of
the reaction are more dominant and premixing will help to level them. The
investment costs for implementing (static) premixing are low, but whether to
implement premixing depends on the clogging sensitivity of the static mixer, and
the effect of a jam on the functioning of the feeding system. The benefit of
premixing for the current polyurethane is not so great that the benefits always
outweigh the added operation
Looking at the effect of the degree of premixing, it is clear that for the currently
investigated polyurethane, the reaction velocity and the final conversion are
affected by the degree of premixing. At low catalyst levels, the reaction velocity is
independent on the degree of premixing, while at higher catalyst level premixing
has a positive effect on the (apparent) reaction velocity.
133
Chapter 6
6.8 List of symbols
Surface area of ATR reactor m2
A0 Reaction pre- nt nt mol/kg s
Cl C e dis m
Cp ity J/kg⋅K
d Diameter m
Diffusion coefficient m2/s
A
h J/m2⋅s⋅K * Overall heat transfer coefficient J/kg⋅s⋅K
0oncentration isocyanate groups mol/kg
ge molecular weight g/mol
A
expone ial consta
enterlin tance
Heat capac
ID
E Reaction activation energy J/mol
Heat transfer coefficient
h
∆HR Heat of reaction J/mol
L Length m
n Reaction order -
N Number of mixing elements -
[NCO] Concentration isocyanate groups mol/kg
[NCO] Initial c
MW Weight avera
t Time s
R Gas constant J/mol K
RNCO
Rate of isocyanate conversion mol/kg⋅s
T Temperature K
V Volume ATR reactor m3
Greek symbols
δ Clearance between barrel and flight tip m
γ& Shear rate 1/s
η Viscosity Pa⋅s
ρ Density kg/m3
σ Surface tension N/m
134
The effect of premixing on the reactive extrusion of polyurethane
6.9 References
1. C. W. Macosko, RIM - Fundamentals of Reaction Injection Molding, Hanser, Munich,
1989.
2. L.J. Lee, J.M. Ottino, W.E. Ranz, C.W. Macosko, Polym. Eng. Sci., 20, 868 (1980).
3. Kolodziej, C.W. Macosko, and W.E. Ranz, Polym. Eng. Sci., 22, 388 (1982).
4. S.D. Fields, and J.M. Ottino, AIChE J., 33, 157 (1987).
5. Y.M. Lee, and L.J. Lee, Intern. Polym. Process., 1, 144 (1987).
6. H.P. Grace, Chem. Eng. Commun., 14, 225 (1982).
7. S.D. Fields, and J.M. Ottino, AIChE J., 33, 959 (1987).
8. S.C. Machuga, H.L. Midje, J.S. Peanasky, C.W. Macosko, and W.E. Ranz, AIChE J., 34,
1057 (1988).
9. J.M.H. Janssen, Ph. D. Thesis, Eindhoven University of technology (1993).
10. V.W.A. Verhoeven, M. van Vondel, K.J. Ganzeveld, and L.P.B.M. Janssen, Polym. Eng.
Sci., 44, 1648 (2004).
135
Chapter 6
6.10 Appendix 1
The average isocyanate concentration in the reactor just after filling is calculated by
ting thsubtrac e measured inlet temperature from the measured temperature just
er fillaft ing.
( )RH∆
[NCO]
[NCO] t=0
p0t25t CTTN[ ]CO
⋅ρ⋅−= ( 6.4 )
sequ
Figure 6.9 T
r
The ATR fit st
reactors, each
concentration
reactors toget
reactor just a
simultaneousl
regular ATR f
catalyst level i
==
Sub ently, a concentration distribution as should be present just after filling is
drawn up, assuming a zero-order isothermal reaction (figure 6.9).
0
4
1
heoretica
eactor.
arts at t
with the
accordin
her is eq
fter fillin
y solved
its. In t
s shown
2
l isocyanate conc
his point. The A
same temperat
g to figure 6.9.
ual to the avera
g. For the mod
together with
able 6.2, the re
.
Time
3
entration
TR react
ure but e
The ave
ge isocy
el fit, th
the over
sult for
136
5
distribution during filling of the ATR
or is modeled as five different batch
ach with a different initial isocyanate
rage concentration of the five batch
anate concentration in the complete
e mass balance for every reactor is
all heat balance, as is done for the
an ATR experiment at the highest
25
The effect of premixing on the reactive extrusion of polyurethane
137
EA (kJ/mol) A
0 (kg/mol·s) k at 80°C (kg/mol·s)
Regular fit 33.9 1.89 0.0206
With isocyanate distribution 34.8 (3.2 %) 2.48 0.0201 (2.5 %)
Table 6.2 Fitted reaction rate constants with and without an isocyanate concentration
distribution ([Cat] = 100 ppm).
7 Conclusions
In case an engineer is asked to optimize or to develop a new reactive extrusion
process, for example for polyurethane manufacturing, she or he can choose several
ways to do the job. Most straightforward is to start doing small-scale extrusion
experiments on a lab or pilot scale extruder. The experimental approach can be
preceded by batch experiments. Through batch experiments, the feasibility of the
process can be tested. The engineer can get an estimate if the process will work on
the extruder, and if the desired product properties can be obtained. For the
extruder experiments that follow, the targeted objective can be reached through a
process in which iterative experiments are combined with previously gained
knowledge. When phenomena are encountered that contradict expectations, or
when the target is found to be difficult to reach, this engineer will look for
background knowledge to understand what is happening or to get a clue where to
go. For a reactive extrusion process, this will sometimes lead to inexplicable
phenomena, because the response of the system is not always linear. Several
processes interact: the reaction and the related change in viscosity, the flow in the
extruder, and the heat transfer and generation. Moreover, when scaling up the
extruder, ´surprises´ might appear.
An approach that can be useful in addition to the experimental approach is to make
use of an experimental design. With an experimental design, the number of
experiments can be optimized and a statistical model can be built. Since the
extruder is not a complete black box, the engineer can combine the obtained
results with his or her knowledge to reach the targeted objective. Nonetheless, the
interplay between experimental design and previous knowledge is a challenging
undertaking.
A different approach the engineer can take is to make use of a model that is based
on the processes that take place in the extruder. The model can be used as a
complete substitution of the experimental work or as an addition to experimental
work. Complex phenomena may become better understandable with the use of
such a model; moreover, extrapolation to other process conditions can be done
with more confidence with the use of a model. Also before doing experimental work,
model simulations can help to narrow the experimental window. The benefits of a
model are clearly present; however, the applicability of such a model is hampered
by several factors. First, for every polyurethane under investigation, rheo-kinetic
data must be obtained. For every change in hard segment percentage, catalyst type,
Chapter 7
change in chain extender etcetera, new data must be generated, which is a
cumbersome task. The benef d cost may not be that
s presented for measuring the polyurethane
inetics, based on measurement kneader measurements. The method was
. Besides, the effect of mixing on the polymerization reaction can be
it of a model concerning time an
large due to this necessary experimental work. Second, no exact prediction can be
obtained with the model. As discussed in paragraph 5.2.1, the status of extruder
modeling is such that the results still are in between indicative and predictive. Last,
the objective of the study must be expressible in a model parameter.
The current thesis is aimed at reactive extrusion of thermoplastic polyurethane. To
assist the above engineer, both ´background knowledge´ as well as better
understanding of the process through a reactive model is presented. Three subjects
were covered specifically:
1. The effect of the measurement method on the kinetic results, especially
tailored for reactive extrusion.
2. The modeling of the extruder and the effect of the depolymerization
reaction on the extruder performance.
3. The effect of premixing on the extruder performance.
In chapter three, a new method wa
k
validated; it was found that quantitative kinetic and rheological data could be
obtained using this method. The method has advantages over other kinetic
measurement methods since the reactants are mixed during an experiment, and
the temperature is close to extrusion circumstances; mimicking real processing
circumstances. Therefore, for applications where the reaction takes place under
mixing conditions, as for reactive extrusion, the kinetic parameters obtained will be
more accurate
investigated with this method.
In chapter 4 the necessity of such a method was investigated for two different
polyurethanes. It was found that for a typical thermoplastic polyurethane (system 1),
the measurement method did not seem to matter. Also relatively low conversion
adiabatic temperature rise experiments (no mixing) as high temperature
experiments (with mixing) give the same result. Apparently, the reaction is uniform
and kinetically controlled over a large range of temperatures and conversions.
Adiabatic temperature rise experiments seem therefore the preferred choice for
characterizing polyurethane polymerization. These types of experiments are easy to
perform and to analyze. However, when analyzing the experiments, care must be
140
Conclusions
taken. It was found that diffusion limitations due to phase separation of soft and
hard segments appear already at 70% conversion (depending on the temperature). If
this is not noticed, the obtained kinetic constants will underestimate the real
reaction velocity (4.4.1). For extrusion purposes, the kinetics of the reverse reaction
must also be known. Unfortunately, a second kinetic measurement is necessary to
establish the reverse kinetics. In paragraph 4.4.2, a method based on high
mperature batch experiments is worked out. Reproducible results on the
hat was investigated showed a more complicated kinetic
ehavior. The ATR experiments showed a decrease of activation energy and a
max
reaction ation of a broad interfacial reaction zone
on
of the is indispensable for a kinetically
con l tation, it was found
rough high conversions that mixing did have an influence on the reaction velocity.
scribes the polyurethane polymerization reaction in
te
depolymerization reaction were obtained. Depending on the reaction velocity, the
kinetic constants of the forward reaction can also be established, but the method is
more cumbersome than performing adiabatic temperature rise experiments.
The second polyurethane t
b
imum in reaction velocity at higher catalyst levels, indicating a diffusion limited
. For this polyurethane, the form
the polyol-isocyanate surface may be hindered, due to the spatial conformation
oligomers. This interfacial reaction zone
trol ed reaction. As a confirmation on this diffusion limi
th
For reactive extrusion modeling of this particular polyurethane, two kinetic
measurement methods seem necessary, adiabatic temperature rise experiments for
low conversions and kneader experiments for high conversions.
The latter polyurethane was used for extrusion experiments. A reactive extrusion
model was built to evaluate the results (chapter 5). The model was based on one-
dimensional equations. This type of model was chosen to have optimal flexibility
and calculation speed. The model was validated with non-reactive data from own
experiments and literature, and showed a satisfactory agreement.
A comparison of the reactive experimental data with the model predictions
demonstrates that the model de
the extruder satisfactory, especially considering the engineering approach chosen
for the model. For model verification the rotation speed, the barrel wall temperature,
the catalyst concentration, and the throughput were varied. The difference between
the predicted molecular weight and the measured molecular weight was on average
no more than 20 percent. More importantly, the response of the extrusion process
towards changing process parameters was captured adequately. Therefore, the
extrusion model seems a good tool for evaluating an extrusion process. However,
an evaluation of the model with different polyurethanes and different extruder
diameters would help to further validate the model.
141
Chapter 7
The reverse reaction was an important factor for the performed experiments. The
presence of this reaction smoothens some effects, for example the effect of
changing the catalyst concentration. Moreover, as explained in paragraph 5.4.9, the
reverse reaction has several effects on the reactive extrusion process:
• The reverse reaction causes further reaction in the extruded material after
extrusion
• The reverse reaction can give extra allophanate formation
• The reverse reaction stabilizes the extrusion process
For the extrusion model, a simple approach was chosen for the residence time
distribution. An analysis showed (paragraph 5.4.10) that in some cases, such as for
the transport elements, the approach oversimplifies the real situation. For the
transport elements, the plug-flow assumption underestimates the spread in
residence time. As is shown in paragraph 5.4.10, in case a section shows more
ideally stirred behavior, the efficiency of that section drops (the efficiency
expressed as conversion per meter extruder length). Therefore, for reactive
polyurethane extrusion, screw elements that give a plug-flow behavior should
prevail. In general, transport elements are considered closest to plug-flow. However,
since a group of kneading paddles resembles a cascade of stirred reactors, the
spread in residence time may be smaller than that of transport elements. Although
many investigations have been conducted towards residence time distribution in
extruders, the coupling with an extrusion model based on flow equations is still not
completely developed. A start has been made by Poulesquen et al. (reference 20,
chapter 2). Further development in this area will help to improve the choice for the
optimal screw layout.
The efficiency of the extruder may be improved by premixing of the monomers.
Through premixing, valuable extruder length may be saved since the reaction gets
a ´head-start´. Moreover, the product may be more homogeneous in composition.
The effect of premixing was investigated in chapter 6. It was concluded that
premixing has a small positive contribution to the conversion at the end of the
extruder, and that the final product has a narrower molecular weight distribution.
Although in this investigation the effect of premixing may be dampened by the
reverse reaction, the effect of premixing is rather small. For every situation, a
careful consideration must be made if the risk of premixing (clogged equipment) is
worth the improved extrusion performance and product quality.
142
8 Appendix
8.1 Summary
Thermoplastic polyurethane (TPU) is a widely used polymer that is used in
auto o
changin osition, the rubber-like material can be optimized for a specific
app t e thermoplastic
poly et nes are very stiff.
hermoplastic polyurethane is often produced in an extruder. A typical process
er. Moreover, local minima or maxima can be missed in this
were evaluated in
chapter 3 and 4 of the thesis. The effect of mixing and reaction temperature on the
m tive products, electronics, glazing, footwear and for industrial machinery. By
g the comp
lica ion. The range of material properties is therefore large; som
ur hanes may be very elastic while other uretha
T
consists of feeding the monomers to the extruder, formation of the polymer in the
extruder, and cutting the final polymer in small pellets at the exit of the extruder.
The pellets can be processed to its final application in a later stage.
Reactive extrusion of polyurethane is a relative expensive and a not very well
understood process. The lack of understanding is caused by the complicated flow
patterns in the extruder, and because the processes that occur in the extruder are
difficult to measure. In industry, reactive extrusion is therefore often approached in
a pragmatic way. However, improved knowledge could lead to cost benefits. Both
the daily practice and the development or scale-up of new processes would benefit,
leading to a more efficient extrusion process.
An engineer working on the extrusion of polyurethane has several choices to reach
his or hear goal. Firstly, available knowledge can be combined with batch or
extrusion experiments. As an addition, the engineer can use experimental design
techniques to optimize the data collection process. However, the knowledge build-
up in this way is difficult to extrapolate, due to the non-linear character of the
processes in an extrud
way. Another option for the engineer is to build an extrusion model. A reactive
extrusion model is better able to describe the non-linear effects. Moreover, a model
can be used to scan a whole range of parameters within a short time period, among
which the effect of the screw profile (which is a cumbersome task when doing
experiments). A disadvantage of a model is that for each polyurethane a new set of
kinetic parameters must be obtained.
In this thesis, a model was built and the predictive power was evaluated through a
validation study. For such a model, the input parameters are equally important as
the model itself. Especially, accurate kinetic parameters are indispensable.
Therefore, different methods for obtaining the kinetic parameters
Chapter 8
kinetic data was established. Because of the immiscibility of the monomers, mixing
was supposed to have an impa velocity and on the final
conversion.
od was developed (chapter 3) to establish the effect of
flow activation
e percentage hard segments (24%).
ct on the apparent reaction
A new measurement meth
mixing on the kinetics at higher temperatures (150 – 200°C); in a measurement
kneader the torque and the molecular weight development were followed for a
polyurethane polymerization reaction. In this way, extrusion conditions are
mimicked and relevant kinetics data can be obtained. The kinetics were determined
for a system consisting of a polyester polyol, methyl-propane-diol and a 50/50
mixture of 2,4’- and 4,4’-diphenylmethane diisocyanate (MDI). The reaction
proceeded according to a second order reaction for which the activation energy was
found to be equal to 61.3 kJ/mol, and the pre-exponential factor was equal to
2.18e6 mol/kg K. For the temperature range under investigation the
energy was equal to 42.7 kJ/mol, which is comparable to that of a linear polymer.
This indicates that the hard and soft segments are completely mixed at the
temperatures investigated.
The results obtained with the kneader were compared with other kinetic
measurement methods in chapter 4. Two different polyurethane systems were
investigated. Both polyurethane systems had the same large chain polyol (a
polyester polyol, Mw = 2200) and the sam
However, system 1 contained 4,4’-diphenylmethane diisocyanate (4,4-MDI) and
butane diol, while system 2 contained a 50/50 mixture of 2,4’- and 4,4’-
diphenylmethane diisocyanate and methyl-propane-diol. System 2 was used in the
kneader experiments as described above. The monomers of system 2 are better
compatible, which should lead to less diffusion limitations during the reaction.
Three different kinetic methods were compared: adiabatic temperature rise,
measurement kneader and isothermal high temperature measurements. For the less
miscible polyurethane system (system 1), the reaction conditions did not seem to
depend on the measurement temperature and the mixing conditions, implicating
for all reaction conditions a kinetically controlled reaction. The reaction was second
order in isocyanate concentration, 0.5-th order in catalyst concentration and had an
activation energy of 52 kJ/mol.
For the second (miscible) system (system 2), each of the three measurement
methods showed a different behavior. Only at a low catalyst concentration, the
adiabatic temperature rise experiments demonstrated a catalyst dependence, at a
higher catalyst levels and for the other two measurement methods no catalyst
dependency was present. Furthermore, the adiabatic temperature rise experiments
144
Appendix
showed a much higher reaction velocity in comparison to the other two methods.
For this system, the rapid diffusion of the monomers and the oligomers through the
interface between the species is probably hindered due to the presence of bulky
the viscous dissipation were calculated on basis of a
zation reaction is of importance at temperatures
oligomer molecules. The result is a diffusion-limited reaction at low conversions
and an inhomogeneous distribution of species at higher conversions. The presumed
better miscibility for system 2 was therefore not demonstrated. Contrary to system
1, the isocyanate and chain extender of system 2 are hardly used for commercial
applications. For more regularly occurring systems based on 4,4-MDI, it seems
probable (based on the results of system 1) that any kinetic measurement method
is appropriate to establish the kinetics for reactive extrusion modeling.
In chapter 5, the extrusion model is described. For the model, a one-dimensional
approach was chosen. For this approach, the extruder was divided in zones with a
length of 0.25•D. For every zone the temperature, conversion, viscous dissipation,
average shear rate, and the viscosity were calculated. The actual channel geometry
and the effect of the intermeshing zone were incorporated in the flow equations.
The average shear rate and
two-dimensional analysis. The leakage over the flight was taken into account for
calculating the viscous dissipation, the pressure build up and the conveying
capacity. In the model, a distinction was made between transport elements and
kneading elements. For each element type, different flow equations were used. In
addition, the residence time distribution was considered differently for each type of
element. The reaction mass was considered to be micro-segregated for both type of
elements, but the kneading zones were assumed to be ideally mixed, while the
transport zones were considered as plug-flow reactors.
The extrusion model was validated with literature data and through non-reactive
extrusion experiments. Both validations showed a satisfactory agreement. Moreover,
a reactive validation study was carried out with polyurethane system 2. The kinetics
obtained in chapter 4 and 6 were used as input parameters. In the reactive
validation study the catalyst level, throughput, rotation speed and the barrel wall
temperature was varied. A comparison of the experiments with the model showed
that the model predicted the polyurethane extrusion well. In chapter 4, it was
established that the depolymeri
higher than 150°C. Since the extrusion conditions are generally above this
temperature, the depolymerization reaction in polyurethanes extrusion is a relevant
but often neglected phenomenon. In chapter 5 it was found that the extruder
operation is strongly affected by the depolymerization reaction: the
depolymerization reaction limits the maximal obtainable conversion, increases the
145
Chapter 8
amount of allophanate bindings that are formed, stabilizes the extruder operation,
and causes undesired post-extrusion curing of the polyurethane.
In the last regular chapter of this thesis (chapter 6), the effect of premixing the
monomers (before extrusion) was investigated. To do so, a static mixer was placed
at the feed port of the extruder. Extrusion trials were performed with and without
premixing; the effect of premixing was evaluated through the final molecular
weight and polydispersity of the product. For the polyurethane under investigation
(system 2), it was found that premixing had a small beneficiary effect on the
conversion at the end of the extruder. Moreover, premixing resulted in a narrower
molecular weight distribution, giving improved material properties. However, the
difference in behavior was
benefit of premixing is for the current polyurethane not of such extend that the
benefit always outweighs the added operational risks (clogging of equipment). Still,
although the effect of premixing for this system was not substantial, the
implementation of pre-mixing is cheap and straightforward. Moreover, the
beneficiary effect of premixing will increase with faster reacting monomers.
The effect of the degree of premixing on the reaction is also described in chapter 6.
The effect of the number of static mixer elements on adiabatic temperature rise
experiments was established. A difference was found in the reaction velocity and
adiabatic temperature rise as a function of the catalyst level and number of mixer
elements. At low catalyst levels, the reaction velocity was independent of the degree
of premixing, while at higher catalyst level an increased degree of premixing had a
positive effect on the (apparent) reaction velocity. The adiabatic temperature rise
showed a different behavior and was independent of the catalyst level but
dependent on the number of mixing elements. This
attributed to the part of the reaction that is represented by the two parameters. The
reaction velocity is related to the initial and middle part of the reaction, while the
adiabatic temperature rise is related to the end of the reaction.
The objective of this thesis was to increase the understanding of the reactive
extrusion of thermoplastic polyurethane. Overall, several issues were identified:
• Using a relative simple extrusion model, the reactive extrusion process can
be described. This model can be used to further investigate and optimize
the reactive extrusion of thermoplastic polyurethane.
• Premixing has a small beneficiary effect on the efficiency of the extrusion
process and the quality of the product formed.
146
Appendix
• The depolymerization reaction has a large influence on the extrusion
process
• For a regular polyurethane, the temperature and the mixing conditions do
not affect the kinetic parameters over a wide temperature range.
147
Appendix
8.2 Samenvatting
Thermoplastisch polyurethaan is een veelgebruikt polymeer dat onder andere wordt
toegepast in schoenzolen, sportuitrustingen, aandrijfriemen, oormerken voor vee
en auto-onderdelen. Door de samenstelling van de grondstoffen te wijzigen kan het
rubberachtige materiaal voor elke specifieke toepassing geoptimaliseerd worden;
zo kan zijn dat het ene thermoplastische polyurethaan zeer elastisch is terwijl een
ander thermoplastisch polyurethaan zeer stijf is. Thermoplastisch polyurethaan
wordt vaak in een extruder geproduceerd, waarbij in de extruder de monomeren
reageren tot het polymeer. Op het moment dat het polymeer uit de extruder komt
wordt het versneden in korrels, die later verder verwerkt kunnen worden in de
uiteindelijke toepassing.
Reactieve extrusie van thermoplastisch polyurethaan is een relatief duur en
onbegrepen proces. De onvolledige begripsvorming wordt veroorzaakt door de
aanwezigheid van een ingewikkeld stromingsprofiel in de extruder, gecombineerd
met het feit dat de processen die in de extruder plaatsvinden nauwelijks meetbaar
zijn. In de industrie wordt reactieve extrusie om die reden vaak pragmatisch
benaderd. Meer begrip van de processen die in de extruder plaatsvinden zou echter
een kostenvoordeel kunnen opleveren. Zowel de dagelijkse praktijk als het
ontwikkelen of opschalen van nieuwe processen kan dan met meer efficiency
bedreven worden.
Een ingenieur die aan extrusie van polyurethaan gaat werken heeft diverse keuzes
om tot zijn of haar doel te komen. Aanwezige kennis kan gecombineerd worden
met extra batch experimenten of extrusie experimenten. Hierbij kan eventueel
gebruik gemaakt worden van ‘experimental design’ technieken. De resultaten
hiervan zijn echter lastig te extrapoleren, doordat niet-lineaire effecten
onvermijdelijk aanwezig zijn in een extruder. Een ander optie is om gebruik te
maken van een extrudermodel. Een reactief extrusiemodel kan de niet-lineaire
effecten beter ondervangen. Bovendien kan met een model binnen een kort
tijdsbestek een hele range aan parameters getest worden, waaronder het effect van
het schroefprofiel (wat bij een experiment zeer tijdrovend is). Een nadeel van een
model is dat voor elk verschillend type polyurethaan de kinetische parameters
moeten worden vastgesteld.
In dit proefschrift is een reactief extrusiemodel ontwikkeld en de betrouwbaarheid
van het model is getest met een validatiestudie. Het model geeft meer inzicht in het
proces en kan bovendien gebruikt worden om het proces te verbeteren. Voor een
dergelijk reactief model zijn de ingebrachte parameters minstens zo belangrijk als
149
Chapter 8
het model zelf. In het bijzonder spelen de kinetische parameters een belangrijke rol.
n 4 van het proefschrift verschillende kinetische
mengsel van 2,4´- en 4,4´-difenylmethaan diisocyanaat
erste systeem was hetzelfde polyurethaan waarmee de batch
sch gelimiteerd was. De reactie verliep volgens een
Daarom zijn in hoofdstuk 3 e
methodes bekeken en met elkaar vergeleken. Het effect van de reactietemperatuur
en menging is hierbij vastgesteld. Omdat de monomeren niet mengbaar zijn, was
de verwachting dat menging een invloed op de reactie zou kunnen hebben.
In hoofdstuk 3 is een nieuwe methode ontwikkeld om bij hogere temperaturen (150
– 200°C) het effect van mengen op de kinetiek vast te stellen. Bij deze methode
wordt het moment en het molecuulgewicht in een batch kneder in de tijd gevolgd.
Op deze manier worden extrusie-omstandigheden nagebootst. Het bleek dat met
deze methode relevante kinetische parameters gemeten konden worden. De
kinetiek is bepaald voor een systeem dat bestond uit een polyester polyol, methyl-
propaan-diol en een 50/50
(MDI). De reactie verliep volgens een tweede orde reactievergelijking. De
activeringsenergie was daarbij 61.3 kJ/mol en de pre-exponentiele factor was
2.18e6 mol/kg K. Binnen het onderzochte temperatuursgebied was de
activeringsenergie 42.7 kJ/mol, wat overeen komt met een lineair polymeer. Dit
betekent waarschijnlijk dat alle harde segmenten en zachte volledig gemengd zijn;
de fasescheiding tussen deze twee onderdelen is opgeheven.
In hoofdstuk 4 is een vergelijking gemaakt tussen de batch kneder metingen en
andere kinetische meetmethodes. Twee verschillende polyurethanen zijn daarbij
onderzocht. Het e
kneder experimenten zijn uitgevoerd. Omdat dit systeem een minder gangbaar
polyurethaan is, is dit systeem aangeduid als systeem 2. Het andere systeem,
systeem 1, had hetzelfde polyester polyol als systeem 2 en hetzelfde harde
segmenten percentage (24%). Daarnaast bevatte systeem 1 butaan-diol en 4,4´-
difenylmethaan diisocyanaat (MDI). De monomeren van systeem 1 zijn minder goed
mengbaar. Dit zou tot meer diffusie effecten moeten leiden gedurende de reactie.
Drie verschillende kinetische methodes zijn met elkaar vergeleken in hoofdstuk 4:
adiabatische temperatuur stijging experimenten, batch kneder metingen en
isothermische hoge temperatuur metingen. Het bleek dat voor systeem 1 de
reactieomstandigheden (temperatuur en menging) geen effect hadden op de
gevonden kinetische parameters. Dit betekent dat over een groot temperatuur- en
mengbereik de reactie kineti
tweede orde reactie met een activeringsenergie van 52 kJ/mol. De reactiesnelheid
was recht evenredig met de wortel uit de katalysatorconcentratie.
Voor systeem 2 gaven elk van de drie meetmethodes een ander resultaat. Alleen bij
lage katalysatorconcentraties vertoonden de adiabatische temperatuurstijging
150
Appendix
experimenten een katalysatorafhankelijkheid. Bij hogere katalysatorconcentraties
en voor de andere twee meetmethodes had de katalysatorconcentratie geen effect.
Daarnaast was de reactiesnelheid bij de adiabatische temperatuurstijging
experimenten veel hoger dan bij de andere experimenten. Deze waarnemingen
duiden op ‘diffusie limitaties’. Meer specifiek was voor dit systeem de snelle
erd daarbij verdeeld
aarden kwamen
oppervlaktediffusie die polyurethaanreacties kenmerkt (het polyol-isocynaat
oppervlak is instabiel waardoor beide fases veel sneller met elkaar mengen dan bij
een star oppervlak) waarschijnlijk gehinderd door de aanwezigheid van
diffusiebeperkende oligomeermoleculen. Dit resulteerde in een diffusielimitatie bij
lagere conversies en een inhomogeen verdeelde reactiemassa bij hoge conversies.
De veronderstelde betere mengbaarheid van systeem 2 is daarom niet aangetoond,
eerder het tegenovergestelde. In tegenstelling tot systeem 1 wordt het isocyanaat
(en de ketenverlenger) van systeem 2 zelden gebruikt voor commerciële
toepassingen. Daarom lijkt het waarschijnlijk dat voor polyurethanen gebaseerd op
4,4-MDI elke meetmethode geschikt is om de kinetiek te bepalen voor reactieve
extrusie.
In hoofdstuk 5 staat het ontwikkelde extrusiemodel beschreven. Bij dit model is
voor een eendimensionale benadering gekozen. De extruder w
in zones met een lengte van 0.25·D. Voor elke zone werd de temperatuur,
conversie, viskeuze dissipatie, gemiddelde afschuifsnelheid en viscositeit berekend
als functie van de vorige zone en de omstandigheden in de betreffende zone. De
feitelijke kanaalgeometrie en het effect van de ‘intermeshing’ zone zijn in de
stromingvergelijkingen gebruikt. De gemiddelde afschuifsnelheid en de viskeuze
dissipatie zijn berekend door middel van een tweedimensionale analyse. In de
vergelijkingen voor de viskeuze dissipatie en voor de drukopbouw in de extruder is
rekening gehouden met lekstroming over de flank van de schroef. In het model is
onderscheid is gemaakt tussen transportelementen en kneedelementen. Voor elk
elementtype zijn verschillende stromingsvergelijkingen gebruikt. Ook is voor elk
elementtype een andere benadering gekozen voor de verblijftijdspreiding. Voor
beide elementtypes is de reactiemassa als ‘micro-segregated’ beschouwd. De
kneedelementen zijn daarbij beschouwd als een serie van ideaal gemengde
reactoren, terwijl de transportelementen als propstromingreactoren zijn
gemodelleerd.
Het extrusiemodel is gevalideerd met behulp van literatuurgegevens en niet-
reactieve extrusie-experimenten; het model en de gevonden meetw
daarbij goed overeen. Daarnaast is een reactieve validatie studie uitgevoerd met
systeem 2. De kinetiek die in hoofdstuk 3, 4, en 6 gemeten was is daarbij gebruikt.
151
Chapter 8
In de reactieve validatiestudie is de katalysatorconcentratie, de doorzet, het
toerental en de wandtemperatuur gevarieerd. Een vergelijking van de experimenten
met het model toonde aan dat het model een goed voorspellend vermogen had; de
meetresultaten en de modelsimulaties verschilden niet meer dan 20 %.
In hoofdstuk 4 is vastgesteld dat de depolymerisatiereactie merkbaar aanwezig is
boven een temperatuur van 150°C. Doordat de reactieve extrusie van polyurethaan
over het algemeen boven deze temperatuur plaatsvindt, is het effect van de
depolymerisatie reactie op polyurethaan extrusie ook onderzocht in hoofdstuk 5.
Daarbij is gevonden dat de depolymerisatiereactie een groot effect heeft op de
polyurethaanextrusie: de depolymerisatie reactie limiteert de maximaal haalbare
conversie, veroorzaakt mogelijk ongewenste allophanaat vorming, stabiliseert het
extrusieproces en veroorzaakt ongewenst doorreageren na extrusie.
In het laatste reguliere hoofdstuk van dit proefschrift, hoofdstuk 6, is het effect van
voormenging van de monomeren onderzocht. Met voormenging wordt bedoeld dat
de monomeren gemengd worden voordat ze aan de extruder worden gedoseerd.
Voormenging zou kostbare extruder lengte kunnen besparen en een beter
peratuurstijgingexperimenten. Daarbij is een verschil gevonden in
gedefinieerd polymeer kunnen geven. Om dit te kunnen onderzoeken is een
statische menger bij de invoerpoort van de extruder geplaatst. Vervolgens zijn
extrusie experimenten mét en zonder voormenging uitgevoerd (met systeem 2).
Het effect van voormenging werd daarbij geëvalueerd door het molecuulgewicht en
polydispersiteit van het gereageerde product bij de spuitkop van de extruder te
meten. Voor het onderzochte polyurethaan is gevonden dat voormenging een klein
positief effect had op de conversie aan het einde van de extruder. Bovendien gaf
voormenging een lagere polydispersiteit, wat een positief effect heeft op de
materiaaleigenschappen. Daarbij moet gezegd worden dat effect klein was en
mogelijk niet opweegt tegen het voornaamste risico dat met voormenging gepaard
gaat: verstoppen van de apparatuur. De afweging om wel of niet voor te mengen zal
daarom uit een kosten en risico analyse moeten volgen. Het effect van voormenging
is waarschijnlijk groter bij sneller reagerende monomeren. Dit betekent dat het
effect van voormenging voor andere polyurethanen groter kan zijn.
Het effect van de mate van voormenging is ook onderzocht in hoofdstuk 6. Hierbij
is het aantal statische mengelementen gevarieerd en is de reactie gevolgd met
adiabatische tem
de reactiesnelheid en de adiabatische temperatuurstijging als functie van de
katalysator concentratie en het aantal mengelementen. Bij lage
katalysatorconcentraties was de reactiesnelheid onafhankelijk van het aantal
mengelementen, maar bij hogere katalysator concentraties had extra voormenging
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een positief effect op de schijnbare reactiesnelheid. De adiabatische
temperatuurstijging liet een ander beeld zien; deze stijging was onafhankelijk van
de katalysator concentratie maar afhankelijk van het aantal mengelementen. Het
verschil in gedrag is toegeschreven aan het deel van de reactie die
vertegenwoordigd wordt door de twee parameters. De reactiesnelheid is gerelateerd
aan het begin en het middelgedeelte van de reactie, terwijl de adiabatische
temperatuurstijging gerelateerd is aan het einde van de reactie.
Het doel van dit proefschrift was om meer begrip over reactieve extrusie van
thermoplastisch polyurethaan te verkrijgen. Een aantal zaken is daarbij aan het licht
gekomen:
• Voormenging heeft een gering positief effect op de eindconversie en
polydispersiteit van het gevormde polyurethaan
• De depolymerisatie reactie heeft een groot effect op de extrusieprestatie
• Voor een gangbaar polyurethaan is de kinetische meetmethode van
ondergeschikt belang voor de bepaling van relevante kinetische parameter
Daarnaast is een extrusiemodel ontwikkeld en gevalideerd dat zowel in de
dagelijkse praktijk als bij het ontwikkelen of opschalen van nieuwe processen
gebruikt kan worden.
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Appendix
8.3 List of publications
igh temperature solution polymerization of butyl acrylate/methyl methacrylate:
reactivity ratio estimation. M. Hakim, V. Verhoeven, N.T. Mcmanus, M.A. Dubé, A.
Penlidis, J. Appl. Polym. Sci.
H
, 77, 602 (2000).
Rheo-kinetic Measurement of Thermoplastic Polyurethane Polymerization in a
Measurement Kneader. V.W.A. Verhoeven, M. van Vondel, K.J. Ganzeveld and
L.P.B.M. Janssen, Polym. Eng. Sci., 44, 1648 (2004).
Method for producing a shaped cheese product, the cheese product obtained and
an apparatus for continuously performing the method. V. Verhoeven, T. Jongsma
and R. Fransen, EP 01520481A1
A Kinetic Investigation of Polyurethane Polymerization for Reactive Extrusion
Purposes., V.W.A. Verhoeven, A.D. Padsalgikar, K.J. Ganzeveld and L.P.B.M. Janssen,
J. Appl. Polym. Sci., accepted for publication
The Reactive Extrusion of Thermoplastic Polyurethane and the Effect of the
Depolymerization Reaction. V.W.A. Verhoeven, A.D. Padsalgikar, K.J. Ganzeveld and
L.P.B.M. Janssen, Int. Polym. Process., accepted for publication
The effect of premixing on the reactive extrusion of thermoplastic polyurethane.
V.W.A. Verhoeven, A.D. Padsalgikar, K.J. Ganzeveld and L.P.B.M. Janssen, Polym. Eng.
Sci., send in for publication
155
Appendix
8.4 Dankwoord
Dit proefschrift is met de bijdrage van vele mensen tot stand gekomen. Ik ben
dankbaar dat ik de afgelopen jaren zoveel inhoudelijke, praktische en morele steun
heb mogen ontvangen.
Voor de inhoudelijke bijdrage wil ik ten eerste Léon bedanken, die mij de
gelegenheid heeft geboden om dit onderzoek te starten en me de ruimte heeft
gegeven om er zelf richting aan te geven. Daarbij heeft je positieve houding mij
gesteund in het afronden van het proefschrift. Ineke, je bent iets later bij het
project betrokken geraakt, maar je me daarna volle kracht geholpen met je kritische
blik en je heldere visie op ‘de grote lijn’. Zelfs nadat je een nieuwe baan begonnen
bent heb je nog heel wat versies doorgelezen. Ajay, thank you for all the support
and guidance you gave during the project and for helping to find my way through
the Huntsman organization. In addition, I received valuable help form Huntsman
Polyurethanes, especially from Wim Vignero, Koen De Roovere, John Hobdell
Valentina Gizzi, John Kendrick and Willem-Jan Leenslag.
De leden van de leescommissie, Ton Broekhuis, Arend-Jan Schouten en Stephen
Picken wil ik bedanken voor de tijd en aandacht die ze aan dit proefschrift hebben
gegeven.
Mijn afstudeerders die gekozen hebben om het TPU-avontuur in te stappen wil ik
ook graag bedanken. Bas, Maarten Mariëlle en Bernard, jullie werk is een
waardevolle bijdrage gebleken voor dit proefschrift.
Alle mensen die me vanuit de vakgroep hebben ondersteund wil ik graag ook
noemen. Laurens, Marcel, Erwin en Anne, bedankt voor alle ondersteuning in de
breedste zin om polyurethaan te kunnen extruderen en onderzoeken. Mijn dank
gaat uit naar Jan-Henk voor de SEC en Gert voor de rheologische metingen. Marya,
bedankt voor alle assistentie op afstand.
Tijdens mijn periode aan de Nijenborgh 4 heb ik frustratie, euforie en vriendschap
mogen delen met mijn mede-promovendi. Ten eerste met mijn kamergenoot en
eeuwige collega Mario, met wie ik ondanks mijn introductie toch nog on speaking
terms ben geraakt. Daarnaast met Jasper, Francesca, Cedric, Vincent, Marga en
Mook, met wie ik gedurende 4 jaar veel vriendschap en broodjes van de maand heb
gedeeld. Ook de overige vakgroepsgenoten, Erik Heeres, Sameer, Poppy, Iris, Josée,
Gerald, Anette en Anant hebben mijn jaren aan de Nijenborgh 4 kleur gegeven.
Mijn collega’s bij Friesland Foods Cheeeezzze wil ik bedanken voor de zachte
dwang en interesse in mijn proefschrift.
Erik en Martijn, bedankt dat jullie mij op de dag zelf willen bijstaan als paranimfen.
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Chapter 8
De afgelopen jaren ben ik in staat geweest mijn spaarzame vrije tijd gedoseerd in te
iten. Alle Spicemen en fietsvrienden van Tandje Hoger,
r, Rogier, Eduard, Gerko en Hinko danken voor hun
zetten voor andere activite
bedankt voor de vele uurtjes ontspanning, inspanning en gezelligheid die heel
belangrijk zijn geweest om dit proefschrift te kunnen afronden. Daarnaast wil ik
speciaal Martijn, Sande
vriendschap.
Het slotwoord van deze onderneming is voor mijn ouder en voor Ellen. Pap, mam,
zonder jullie was ik nooit zover gekomen.
Als laatste lieve Ellen, bedankt dat je er altijd voor me was.
.
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