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University of Groningen The reactive extrusion of thermoplastic polyurethane Verhoeven, Vincent Wilhelmus Andreas IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2006 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Verhoeven, V. W. A. (2006). The reactive extrusion of thermoplastic polyurethane. s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 13-05-2019

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Page 1: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

University of Groningen

The reactive extrusion of thermoplastic polyurethaneVerhoeven, Vincent Wilhelmus Andreas

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.

Document VersionPublisher's PDF, also known as Version of record

Publication date:2006

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Verhoeven, V. W. A. (2006). The reactive extrusion of thermoplastic polyurethane. s.n.

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.

Download date: 13-05-2019

Page 2: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

The Reactive Extrusion of

Thermoplastic Polyurethane

Vincent Verhoeven

Page 3: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9
Page 4: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 5: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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)

Page 6: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 7: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 8: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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.

Page 9: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

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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.

Page 11: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 12: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 13: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

Page 14: The reactive extrusion of thermoplastic polyurethane · 1 introduction 7 1.1 polyurethane extrusion 7 1.2 scope of the thesis 8 2 an introduction to extrusion and polyurethanes 9

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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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(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;

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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.

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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.

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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

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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

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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.

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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

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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

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[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

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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

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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

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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

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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

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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 plat

order. T

n the ba

peratur

plu

wo heating elements in

ck-plate and one in the

e (Tset

). A thermocouple

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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

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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).

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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)

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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:

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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

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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.

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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

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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

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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

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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.

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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

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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

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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.

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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.

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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

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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

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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

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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

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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

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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.

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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:

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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

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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.

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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.

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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

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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).

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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

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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

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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).

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-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.

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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.

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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.

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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.

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-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.

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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).

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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).

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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

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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

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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

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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.

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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.

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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

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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

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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.

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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

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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

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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:

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( )

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 )

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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

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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

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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.

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( )( )

,...),T(f

,...)(fW

...,WfT

,...t,Tf

NNN

NN

NNN

N,resNN

α=η

η=

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.

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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 )

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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

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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

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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

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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

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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

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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

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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)

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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

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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

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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)

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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

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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

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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

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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.

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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.

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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

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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 -

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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).

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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

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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

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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

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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

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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

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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

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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

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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.

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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).

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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

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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

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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.

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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

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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

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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.

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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

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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).

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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

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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).

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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,

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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

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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.

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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.

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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

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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

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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

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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.

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• 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.

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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

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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

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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.

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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

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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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