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

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1 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): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 The Reactive Extrusion of Thermoplastic Polyurethane Vincent Verhoeven

3

4 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

5 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 ISBN (Electronic version)

6 1 INTRODUCTION POLYURETHANE EXTRUSION SCOPE OF THE THESIS 8 2 AN INTRODUCTION TO EXTRUSION AND POLYURETHANES EXTRUSION THE CLOSELY INTERMESHING COROTATING TWIN-SCREW EXTRUDER POLYURETHANES LIST OF SYMBOLS LIST OF REFERENCES 32 3 RHEO-KINETIC MEASUREMENTS IN A MEASUREMENT KNEADER INTRODUCTION EXPERIMENTAL SECTION THEORY OF MEASUREMENT OF THE KINETICS RESULTS CONCLUSIONS LIST OF SYMBOLS LIST OF REFERENCES 53 4 A COMPARISON OF DIFFERENT MEASUREMENT METHODS FOR THE KINETICS OF POLYURETHANE POLYMERIZATION INTRODUCTION REACTION KINETICS EXPERIMENTAL RESULTS CONCLUSIONS LIST OF SYMBOLS LIST OF REFERENCES 81 5 THE REACTIVE EXTRUSION OF THERMOPLASTIC POLYURETHANE INTRODUCTION THE MODEL EXPERIMENTAL SECTION RESULTS 96

7 5.5 CONCLUSIONS LIST OF SYMBOLS REFERENCES THE EFFECT OF PREMIXING ON THE REACTIVE EXTRUSION OF THERMOPLASTIC POLYURETHANE INTRODUCTION MIXING EXPERIMENTAL SETUP MATERIALS ADIABATIC TEMPERATURE RISE ANALYSIS RESULTS CONCLUSIONS LIST OF SYMBOLS REFERENCES APPENDIX CONCLUSIONS APPENDIX SUMMARY SAMENVATTING LIST OF PUBLICATIONS DANKWOORD 157

8 1 Introduction 1.1 Polyurethane extrusion Polyurethanes are mostly known for their widespread usage as building foam (PURfoam). 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, lowtemperature 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 crosslinked 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.

9 Chapter 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

10 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.

11 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 The closely intermeshing corotating twin-screw extruder 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

12 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

13 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. v barrelwall v b,z z y v b,x x Figure 2.4 The helical flow pattern in a single channel. Near the barrel wall, material flows in the positive x-direction (due to the movement of the wall ) until it meets the upcoming flight. The material is then forced to the bottom of the channel (negative y-direction); at the bottom, the material flows back in the x-direction. This time, the presence of the flight-wall pushes the material upwards (y-direction) and this completes the cycle. Due to the z-component of the barrel wall velocity, the net flow of material is in the downstream direction of the channel; the material therefore follows a helical path. Experiments and 3D-simulations (7) confirm this flow pattern and show that at 2/3th of the channel height a stagnation point exist Energy considerations This helical flow pattern has clear consequences for the temperature gradient in the channel. The material that resides at the center of rotation does not come close to the barrel wall, while other material passes the barrel wall regularly, exchanging heat with the barrel. Therefore, temperature gradients in the channel are inevitable, especially, since viscous dissipation and reaction heat have a dominant effect in the heat balance. This effect is particularly important for larger extruder diameters (D 5 cm). Still, due to the helical flow pattern, the heat transfer is much better than what would be expected for flow between two moving plates. To obtain a first estimate of the effect of reaction, viscous dissipation and heat transfer through the wall on the energy balance, a dimensionless number analysis can be made. Three 12

14 An introduction to extrusion and polyurethanes dimensionless numbers are relevant: Damköhler IV (Da IV ) number, the Brinkmann (Br) number, and the Graez (Gz) number (equation 2.1). Da IV ρ HR Q = λ T D heat of reaction = conductive transport of heat 2 µ N D Br = λ T 2 = viscous dissipation conduction of heat ( 2.1 ) a L Gz = Q conductive heat transfer = convective heat transfer 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 (Da IV / 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) 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): B dp Q = Q drag + Q pressure = A N sinϕ η dl ( 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

15 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: B dp Q = A N Q ( 2.3 ) L η dl 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): Drag Pressure Q L u = 2 v 0 = u sinϕ cosϕ δ 2 ( D + 2 δ ) ( π ψ) R R P + sinϕ L w + e δ tan ϕ 12η 3 R flight e ( 2.4 ) Due to the small gap size δ R, the pressure driven leakage flow would seem to be a small contribution to the leakage flow. However, for non-newtonian fluids, the 14

16 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: π N D γ& = ( 2.5 ) H so that equation 2.3 becomes: π N D Q = A N H n B k dp sinϕ Q dl L ( 2.3a ) A better estimate of the average shear rate can be obtained through a twodimensional 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

17 Chapter 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

18 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: B dp Q = A N sinϕ Q L Q ( 2.6 ) L,stag η dl 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) 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

19 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: 128 Q η P = L 4 die ( 2.8 ) π ρ d The second parameter that is important for calculating the residence time is the filling degree in the partially filled zones. A general expression gives: Q feed f = ( 2.7 ) Q max Q feed is the feed rate of material. For Q max, 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 Q max changes. 18

20 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 ( 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

21 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 Isocyanates O C N N C O O C N H C H H C H N C O Figure 2.9 Structure of 4,4 -MDI (left) and 2,4 -MDI (right). Only the diisocyanates are of interest for linear urethane polymer manufacturing, and relatively few of these are used commercially. The most important ones in elastomer manufacturing processes are 2,4- and 2,6-toluene diisocyanates (TDI), 4,4 -diphenylmethane diisocyanate (MDI) and its aliphatic analogue 4,4 - dicyclohexylmethane diisocyanate. Also 1,5-naphtalene diisocyanate (NDI) and 1.6 hexamethylene diisocyanate (HDI) are used. The diisocyanates used in this research 20

22 An introduction to extrusion and polyurethanes are 4,4 -diphenylmethane diisocyanate (4,4 -MDI) and a mixture of 50% 4,4 - diphenylmethane diisocyanate (4,4 -MDI) and 50% 2,4 -MDI. The structures of these compounds are shown in figure 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 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 Diols (chain extenders) The flexible (polyol) blocks primarily influence the elastic nature of the product. In addition, they make important contributions towards the hardness, tear strength, and modulus. But chain extenders for example a diol like butanediol particularly 21

23 Chapter 2 affect the modulus, hardness and tear strength, and determine the maximum application temperature by their ability to remain associated at elevated temperatures. Rigid segments are usually formed by the reaction of diisocyanate with a glycol or a diamine. In this research mainly glycol is used as a chain extender, namely methyl-1,3-propanediol Polyurethane chemistry In figure 2.10, the most common reactions that occur when making polyurethanes are shown (25). Figure 2.10 shows overall reaction schemes so no details on the order of the reaction can be concluded. For the production of thermoset polyurethane foam (PUR) reaction 5 is indispensable. For thermoplastic polyurethane (TPU) production, water is excluded, so that only reactions 1, 2, 3 and 4 can take place. For normal condensation polymerization, in which always a small molecule (mostly water) is formed, equilibrium between the forward and the reverse reaction can be prevented by removing this small molecule (e.g. evaporation of water). For all isocyanate reactions, this option is not present; therefore, the reverse reaction can have a substantial impact. For the polyurethane formation reaction (reaction 1), an equilibrium state has been demonstrated. Dissociation of the polyurethane bond has been observed with DSC and rheology (26). In addition, it was shown by Ando (27) that for a bulk system without catalyst and at temperatures between 180 and 220 C the molecular weight decreases with polymerization temperature. Ando (27) attributes this effect to the depolymerization reaction (i.e. the reverse of reaction 1). Which of the reactions shown in figure 2.10 take place during polyurethane production depends on the temperature, and the presence and the type of solvent and catalyst used. Solvent and catalyst can greatly enhance the rate of one (or sometimes more) reactions. Moreover, the temperature affects the reaction rate and the equilibrium of each of the reactions specified. Normally, the type and ratio of monomers and the type of catalyst is chosen in such a way that the polyurethane reaction will dominate. However, even the occurrence of a limited amount of side reactions may interfere with the final material properties. In the literature, some articles have been published that take the side reactions during polyurethane formation into account. However, most of the publications on polyurethane kinetics use the kinetics as input for modeling purposes (e.g. for reactive injection molding), and the side reactions are neglected. Moreover, for these systems the kinetics are very fast which makes a detailed analysis of the reaction difficult. In the next paragraphs, a short overview of the relevant reactions will be presented. 22

24 An introduction to extrusion and polyurethanes Possibly catalyzed (1) Urethane Formation: N C O + OH N C H O O O (2) Isocyanurate Formation: 3 N C O O C N C N C N O (3) Allophanate Formation: N C H O O + N C O H N O C N C O O (4) Uretidione Formation: 2 N C O N O C C O N (5) Urea Formation: H 2 O + N C O N C H OH O H N C O H N N C O H N H + CO 2 Figure 2.10 The most commonly occurring isocyanate reactions Reaction 2: Isocyanurate formation At lower temperatures (up to 50 C) and with N,N,N -pentamethyl dipropylene triamine (PMPT) as a catalyst, it was shown that up to 30% isocyanurate can be formed (28). HPLC measurements showed that allophanate appears as an intermediate during this reaction. A second publication of these authors (29) shows that the type of tertiary amino catalyst determines if and at what speed isocyanurate is formed. A mechanism for isocyanurate formation is proposed by Kresta et al. (30). A catalyst-isocyanate complex is formed in an equilibrium step; 23

25 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 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 (k 2 ) = / R T. 24

26 An introduction to extrusion and polyurethanes The short list of publications on allophanate formation indicates that there is limited knowledge on this subject. Based on the publications as presented above, allophanate formation does not take place below 120 C, but above this temperature, the formation rate can be substantial. For polyurethane extrusion, allophanate formation may therefore interfere with the polyurethane reaction. Allophanate formation interferes with the stoichiometric ratio of alcohol and isocyanate, resulting in a lower final molecular weight. Moreover, allophanate will give branched polymer chains at low concentrations and at high concentrations, even a cross-linked polymer network would result. In fact, for polyurethane production at high temperatures (> 150 C, for example during extrusion), a constant amount of isocyanate will be present due to the reverse reaction. These free isocyanate groups can choose between a relatively low concentration of alcohol groups and a relatively high concentration of urethane groups. Depending on the reaction rate constants and the equilibrium constants of the urethane and the allophanate reaction, a gradual increase of allophanate groups may therefore occur when keeping polyurethane at a high temperature for a longer time. Hentschel and all showed this effect indirectly by rheological experiments (26) 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 Polyurethane kinetics Reaction mechanism O H N C O + OH -OH N C O.. : k1.. N.. C O.. : k2 O O H H k3 H N C O + O OH Figure 2.11 Lewis base catalysis for urethane formation. 25

27 Chapter 2 Several studies have been conducted on polyurethane kinetics. Two reaction mechanisms are used as the basis for a kinetic equation: A Lewis acid catalyzed reaction and a Lewis base catalyzed reaction. Actually, uncatalyzed reactions do not exist for polyurethane formation, since the alcohol group itself works as a Lewisbase 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 Lewisacid catalysis is shown in figure 2.12 (35). H k 1.. N C O +HA H... ROH [ N C O.. : A] N C O + HA k 2 k 3 O 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: [ ] d NCO dt [ ] d NCO dt [ ] d NCO dt [ ] d NCO dt = k = k = k = k f f f f [ Cat] [ OH] [ Cat] [ NCO] [ [ Cat] [ NCO] [ OH] OH 0.5 [ Cat] [ NCO] [ OH] ] ( 2.10 ) Which equation prevails depends on the degree of dissociation of the metalcomplex 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

28 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: R T R [ ] K C1 e [ Cat] [ OH] [ = dt 1+ K [ OH] dnco EC 1 1 T C2 NCO ] ( 2.11 ) The main assumption Steinle et al. (41) make is that E A of k 2 is equal to E A of k 3. The rate equation of Steinle et al. (41) is both used for uncatalyzed reactions and reactions with tertiary amines as a catalyst. No decisive evidence has been presented on the exact reaction mechanisms during the polyurethane bond formation. The developed kinetic equations are therefore quite general, without any deep knowledge on which intermediate steps are rate limiting, and what the activation energy of each step is. In practice, this knowledge does not seem to be necessary to describe reactive injection molding processes. However, with reactive extrusion, the experiments on the kinetics are performed at different temperatures than the reactive extrusion process is operated, which may give an incorrect extrapolation of the reaction rate constant. Most authors report that up to 50 % conversion, the kinetics follow a second order trend but at higher conversions different effects are observed. Both acceleration and deceleration of the reaction velocity have been reported. Acceleration is mostly ascribed to the autocatalytic effect of the polyurethane bond. However, this autocatalytic effect has never been quantified. Deceleration is attributed to diffusion effects which may become important (especially in bulk systems) at higher conversions. In case of diffusion limitation, the idea that the reactivity of a functional group is independent of the chain length is no longer valid. For relatively short chain lengths, Król (42) has shown that a higher molecular weight causes a slower reaction rate, but this effect is only observable up to a carbon backbone of five units. The slowing-down of the reaction at high conversions is therefore not explained by his findings. However, the findings of Król (42) could mean that for polyurethane polymerization the chain extender reacts faster than the polyol. This difference in reaction rate is hardly ever taken into account for bulk polyurethane polymerization. The underlying reason is that the experimental difficulties related to the tracking of the two species (chain extender - OH and polyol -OH) in a fast reacting high-temperature bulk process are hard to 27

29 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: R NCO with k f [ ] dnco = dt = A = R 0,Uncat NCO, Uncat e E A,Uncat R T + R + A NCO, Cat 0 [cat] = k m e f E A R T [NCO] n ( 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: 1 1 n 1 [ NCO] ( 1+ k (n 1) [NCO] ) n [ NCO] 0 f 0 t = ( 2.13 ) Often a second order rate equation is found to be valid for polyurethane polymerization, which gives for the isocyanate concentration: [ NCO] [NCO] = 1+ k [NCO] t ( 2.14 ) f 0 0 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): M N = M rep ( 1+ [NCO] k (T,[cat]) t) MW = Mrep ( f [ NCO] k(t,[cat]) t) ( 2.15 ) In this equation M rep is the molecular weight of a repeating unit and [NCO] 0 is the initial isocyanate concentration. 28

30 An introduction to extrusion and polyurethanes As explained in paragraph 2.3.4, the reverse reaction of polyurethane formation occurs at higher temperatures. To incorporate the reverse reaction, the rate equation (equation 2.12) changes: R NCO d[nco] = = k f [NCO] dt 2 k r [U] with k f = [Cat] m A 0 e E A R T, k r = A 0,eq k f E e A,eq R T ( 2.16 ) and [U] = [NCO] 0 [NCO] 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): K k [U] M EA,eq ( MN Mrep ) R T f eq N = = = = A 2 2 0,eq e ( 2.17 ) kr [NCO] eq Mrep [NCO] 0 This equation can be used to calculate the effect of the reverse reaction. 29

31 Chapter List of Symbols a Thermal diffusivity m 2 /s A Geometrical constant kg A 0 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 E A Reaction activation energy J/mol f Filling degree of a not fully filled element - H Height of the screw channel m H R Heat of reaction J/mol k Power law consistency Pa s n k f Forward reaction rate constant kg/mol s k r 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 - M N Number average molecular weight g/mol M rep Average weight of repeating unit g/mol M W 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 R NCO Rate of isocyanate conversion mol/kg s t Time s T Temperature K T Temperature difference K u Circumference of the eight-shaped barrel m 30

32 An introduction to extrusion and polyurethanes [U] Concentration urethane bonds mol/kg v Velocity m/s v 0 Circumferential velocity of the screw m/s w Width of the screw channel m Greek symbols δ R 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 m 2 /s ρ Density kg/m 3 ψ Intermeshing angle - Subscripts b Cat Die Eq L Uncat Barrel wall Catalyzed Die Equilibrium Leakage Uncatalyzed 31

33 Chapter 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

34 An introduction to extrusion and polyurethanes 35. J.H. Saunders and K.C. Frisch, Polyurethanes chemistry and technology. Part 1, Chemistry, Interscience publishers (1962). 36. K. Jöhnson, and P. Flodin, Brit. Polym. J., 23, 71 (1990). 37. O. Imawaga, F. Ishimaru, Y. Kurahashi and T. Yamada, Polym. React. Eng., 4, 47 (1996). 38. K.J. Dorozhkin, V.J. Kimelblat, and J.A. Kirpikznikov, Vysokomol. Soed. A., 23, 1119 (1981). 39. A. Petrus, Int. Chem. Eng., 11, 314 (1971). 40. E.B. Richter, and C.W. Macosko, Polym. Eng. Sci., 18, 1012 (1978). 41. E.C. Steinle, F.E. Critchfield, and C.W. Macosko, J. Appl. Polym. Sci., 25, 2317 (1980). 42. P. Król, J. Appl. Polym. Sci., 57, 739 (1995). 43. G. Odian, Principles of Polymerization, John Wiley & Sons Inc., New York (1991). 33

35

36 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 microstoichiometry 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

37 Chapter 3 this sampling procedure superfluous. Unfortunately, no obvious method is available. An adiabatic method as applied by Lee et al. (3) or Blake et al. (4) is not apt, due to the lack of heat production at higher conversions. A combination of rheology with a spectroscopic method, for example with fiber optic IR or Raman spectroscopy, has not been reported yet for polyurethanes. The accuracy at high conversion is not sufficient, and a stagnant polymer layer may form on the measurement cell. If we return to the comparison between a rheometer and a kneader, a rheometer seems more suitable for measurement of the rheo-kinetics, since, in a rheometer, the viscosity can be measured directly. Nevertheless, a measurement kneader is preferred in this research. The reasons for this are: The mixing behavior in a kneader resembles the mixing behavior in an extruder more closely, with both dispersive and distributive mixing action and both simple shear and elongational flow. Highly viscous material can be processed more accurately in a kneader, because in a rheometer, constant shear experiments at shear rates that are comparable to those occurring in an extruder are sensitive to edge failure and demand a high torque. Sampling of a small amount of material does not disturb the measurements in a kneader, whereas rheology measurements are gravely affected by taking (several) samples. Temperature control in a kneader is straightforward. In a rheometer, temperature control becomes complicated at temperatures above 150 C since both cone and plate must be heated in that case. There are several studies known in which the kinetics of TPU polymerization is measured under mixing conditions (3-8). All of these measurements were performed at relatively low temperatures (<90 C) and mostly on cross-linking systems. Therefore, no high conversions could be reached, since the gellation temperature was reached reasonably early in the reaction (around 70% conversion). Methods for measuring the kinetics that do reach high conversions are largely zero-shear methods. As is the case for radical polymerization (9), little attention has been paid to the interaction between mixing and reaction in step polymerization. Often it is expected for step polymerization that shear does not have a major impact on the reaction velocity due to the relatively high mobility of the reactive end groups of a polymer chain. Malkin et al. (10), for instance, state 36

38 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 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. back plate kneading paddles front plate plug Figure 3.1 The Brabender measurement kneader. The kneader is driven by a Brabender 650-E Plasticorder. Two heating elements in combination with two control thermocouples (one in the back-plate and one in the kneader section) keep the kneader on the set temperature (T set ). A thermocouple 37

39 Chapter 3 sticking in the non-intermeshing zone of the kneading chamber is used for the measurement of the temperature of the melt (T measure ). The torque and temperature development in the kneader can be followed by means of a data acquisition system 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 = 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 Size Exclusion Chromatography (SEC) Samples were analyzed for their molecular weight distribution by size exclusion chromatography (Polystyrene calibrated). The chromatography system consisted of 38

40 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) Rheology η (M) η (t) Figure 3.2 The rheokinetic scheme (10). 39

41 Chapter 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 V b. The shear stress (τ) at the wall is then equal to: NπD τ = ηapp γ& = ηapp M (3.1) H 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 (η app ), 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. Torque = (Area Shear Stress) Lever Arm = ( πdw τ) (D / 2) (3.2) For two paddles, this equals: 2 3 Mπ D W Torque = N ηapp = C N ηapp (3.3) H 40