PA and ABS
Citation for published version (APA):
Staal, M. P. B. (2005). Synthesis and characterization of compatibilizers for blends of PA and ABS. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR598517
DOI:
10.6100/IR598517
Document status and date: Published: 01/01/2005
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Synthesis and Characterization of
Compatibilizers for Blends of PA and ABS
Synthesis and Characterization of
Compatibilizers for Blends of PA and ABS
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de
Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen
op donderdag 15 december 2005 om 16.00 uur
door
Maarten Pieter Bram Staal
prof.dr. C.E. Koning
Copromotor:
dr.ir. L. Klumperman
CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Staal, Maarten P.B.
Synthesis and characterization of compatibilizers for blends of PA and ABS / by Maarten P.B. Staal. – Eindhoven : Technische Universiteit Eindhoven, 2005.
Proefschrift. – ISBN 90-386-2937-0 NUR 913
Subject headings: polymer blends ; compatibilizers / polymer morphology / impact strength / polyamide ; PA / rubber ; ABS / terpolymers ; SAN-MAh / reaction kinetics
Trefwoorden: polymeermengsels ; compatibilizers / polymeermorfologie / slagvastheid / polyamide ; PA / rubber ; ABS / terpolymeren : SAN-MAh / reactiekinetiek
© 2005, Maarten Staal
Printed by PrintPartners Ipskamp te Enschede
An electronic copy of this thesis is available from the site of the Eindhoven University Library in PDF format (http://w3.tue.nl/nl/diensten/bib).
Chapter 1 Introduction 11
1.1 History of blends 11
1.2 Polymer blends and alloys 12
1.3 PA/ABS blends 13
1.3.1 Reactive compatibilizers 13
1.3.2 Morphology 14
1.3.3 Rubber content 15
1.3.4 Influence of mixing/extruder type 15
1.3.5 Influence of the concentration of functional groups in the
compatibilizer 15
1.4 Objective and outline of this thesis 16
1.5 References 20
Chapter 2 Modeling of reaction kinetics for SAN-MAh
terpolymerizations in a CSTR 23
2.1 Introduction 23
2.2 Free-radical-polymerization kinetics 23
2.3 Copolymerization model 25
2.3.1 Rate of initiation (RI) 26
2.3.2 Propagation rate constant (kp) 29
2.3.3 Chain transfer 33
2.3.4 Termination rate constant (kt) 35
2.4 Predici model 36
2.4.1 Influence of the estimated kinetic parameters on the results of
model calculations 37
2.4.1.1 Propagation rate constants kp, SAA and kp, ASS 37
2.4.1.2 Propagation reactions involving MAh species 38
2.5 Concluding remarks 41
2.6 References 42
Appendix 2A Mayo mechanism of styrene thermal self-initiation in the
presence of maleic anhydride or acrylonitrile 44
Appendix 2B Radical formation steps and values for the rate coefficients as
used in the Predici model 45
Appendix 2C Initiation steps and values for the rate coefficients as used in
the Predici model 46
Appendix 2D Propagation steps and values for the rate coefficients as used
in the Predici model 47
Appendix 2E Chain transfer to ethylbenzene steps and values for the rate
Chapter 3 Molecular characterization of SAN MAh terpolymers 53
3.1 Introduction 53
3.2 Experimental 54
3.2.1 Materials 54
3.2.2 Derivatization of SAN MAh 54
3.2.3 Size-Exclusion Chromatography (SEC) 55
3.2.4 Gradient-Polymer-Elution Chromatography (GPEC) 55
3.2.5 Fourier-Transform InfraRed spectroscopy (FTIR) 55
3.2.6 Elemental analysis 56
3.2.7 Liquid Chromatography – Mass Spectrometry (LC MS) 56
3.2.8 Density-functional-theory (DFT) calculations 57
3.3 Results and discussion 59
3.3.1 Chemical composition 59
3.3.1.1 Maleic anhydride 59
3.3.1.2 Styrene 65
3.3.1.3 Acrylonitrile 66
3.3.2 Inter molecular chemical-composition distribution (CCD) 72
3.3.3 MAh weight fraction as function of the molar mass ( ) 75
3.4 Concluding remarks 77
3.5 References 79
Appendix 3A Peak assignment for the MS spectrum shown in Figure 3.2 81
Appendix 3B SEC calibration line for 4-pyrenebutylamine 82
Chapter 4 Preparation of SAN-MAh terpolymers in a continuously operated stirred tank reactor 85
4.1 Introduction 85 4.2 Experimental 86 4.2.1 Materials 86 4.2.2 Reactor setup 86 4.2.3 Steady-state conditions 88 4.2.4 Startup conditions 89 4.2.5 Gas chromatography 90
4.3 Results and discussion 90
4.3.1 Reaction conditions for reaction CP150-4 91
4.3.2 Copolymer composition 92
4.3.3 Monomer and solvent concentration 96
4.3.4 Molar mass 102
4.3.5 Chemical-composition distribution (CCD) 103
4.3.6 MAh weight fraction in SAN-MAh terpolymers as a function of the
Appendix 4A Reaction conditions and results 140 °C 110
Appendix 4B Reaction conditions and results 150 °C 111
Appendix 4C Reaction conditions and results 170 °C 112
Chapter 5 PA6/ABS blends compatibilized with SAN-MAh terpolymers 115
5.1 Introduction 115
5.2 Experimental 116
5.2.1 Materials 116
5.2.2 Compounding 116
5.2.3 Mechanical testing 117
5.2.4 Melt Volume-flow Rate (MVR) 117
5.2.5 Optical Microscopy 117
5.2.6 Scanning Electron Microscopy (SEM) 117
5.2.7 Transmission Electron Microscopy (TEM) 117
5.3 Results and discussion 118
5.3.1 Influence of compatibilizer on blend morphology 118
5.3.2 Optimum 125
5.3.3 Influence of compatibilizer molar mass on blend impact strength 127 5.3.4 Influence of the weight fraction of the compatibilizer in PA/ABS
blends on the impact strength of the blend 129
5.3.5 Influence of sample orientation on blend impact strength 131
5.3.6 Influence of mixing order 138
5.3.7 Melt Volume-flow Rate (MVR) 139
5.3.8 Influence of (FMAh MMD on blend impact strength ) 141
5.4 Concluding remarks 144
5.5 References 147
Chapter 6 Feasibility study on end-functional reactive compatibilizer precursors for PA/ABS blends 151
6.1 Introduction 151
6.2 Experimental 153
6.2.1 Materials 153
6.2.2 Synthesis of S-dodecyl-S’-(isobutyric acid) trithiocarbonate
(DIBTTC) 154
6.2.3 Synthesis of DIBTTC-S-MAh RAFT agent 154
6.2.4 Synthesis of MAh end-functional SAN (mSAN) 156
6.2.5 NMR spectroscopy 156
6.2.6 Size-Exclusion Chromatography (SEC) 156
6.2.7 Gradient Liquid Chromatography (LC) 157
6.2.8 Compounding 157
6.3.3 PA/ABS blends compatibilized with MAh end-functional SAN
copolymers 166
6.4 Concluding remarks 169
6.5 References 170
Appendix 6A Synthesis of S-dodecyl-S’-(isobutyric acid) trithiocarbonate
(DIBTTC) 171
Appendix 6B Synthesis of DIBTTC-S-MAh RAFT agent 172
Appendix 6C Reaction conditions and results CSTR reactions 173
Chapter 7 Epilogue and technology assessment 175
Summary 179
Samenvatting 183
Acknowledgements 187
Chapter 1 Introduction
1.1 History of blends1
Nowadays, polymers are an integral part of our daily life. Examples are nylon and polyester in clothes, the insulation of electrical wires, computer hardware, car interior and exterior, hair gel, food packaging, Teflon anti-stick pans, paint, capsules for medication; it is hard to imagine daily life without polymers. Although large scale production only started at the beginning of the 20th century, the use of polymers is as old as mankind itself. Natural polymers, such as wood, leather, and fibers have always been used. Bitumen as a sealant (Harappan culture, 4000 BC), shellac for wood varnish (3000 BC), styrene for embalming (Egypt, 3000 BC) and natural rubber (Aztec culture, 1000 BC) have already been used millennia ago to improve the quality of daily life.
Today’s polymer industry traces its beginning to the early modifications of these natural polymers. Rubber vulcanization by sulfur, for example, was rediscovered by Charles Goodyear in 1836. The first known patent on polymer blends was granted to Alexander Parkes in 1846. He discovered the dynamic covulcanization of natural rubber with gutta-percha in the presence of CS2. With this covulcanization he turned
both the brittle gutta-percha and the soft and sticky natural rubber into a material with significantly improved (and controllable) properties.
As from World War II the world production of polymers increased tremendously. Currently, close to 150 million tons of plastics are produced per year and still this market is the fastest growing among all structural materials. Within the polymer market, the polymer blend segment is increasing about three times faster than the whole polymer market.
1.2 Polymer blends and alloys
Blending different polymers is an attractive method to prepare novel polymeric materials. The development time is relatively short, since a large variety of polymers
is commercially available to tune the properties of the new material. Moreover, processing usually takes place in standard industrial equipment, such as twin-screw extruders, which reduces the financial risk inherent in developing novel materials.2-4
However, most polymers are not miscible on a molecular scale. Immiscibility may result in phase-separated blends with a coarse morphology and poor mechanical properties. To overcome problems related to phase separation, compatibilizers can be applied. A compatibilizer acts like an emulsifier in water/oil mixtures; it provides an appropriate degree of dispersion and reduces the rate of coalescence during later stages of mixing and subsequent reaction steps.3 Next to their dispersive
characteristics, compatibilizers also enhance the interfacial adhesion between both blend phases, which is an important factor for the mechanical properties of
immiscible blends5,6. Usually the compatibilizer is a block or graft copolymer
composed of two different blocks that are miscible with the respective blend phases.2,7 These block or graft copolymers can be pre-made and added to the immiscible
polymer blend, or they can be generated in-situ during the blending process. In the latter procedure, known as reactive compatibilization, a polymer is added which is miscible with one blend component and reactive towards functional groups attached to the second blend component. Reactive compatibilization has several advantages over adding pre-made block or graft copolymers2,4:
• the reactive compatibilizer precursor is relatively easy to make
• the block or graft copolymer is only generated where it is needed, i.e. at the interface
• because the precursor is linear and has a relatively low molar mass, its diffusion towards the interface is faster
Polymer blends of which the interface is modified using a compatibilizer are usually called polymer alloys.3 However, in the following text the term polymer blend is used to refer to polymer alloys as well, since only compatibilized blends are discussed in this thesis.
1.3 PA/ABS blends
The advantages of blending PA (polyamide) with ABS (polybutadiene rubber particles grafted to styrene-acrylonitrile copolymer (SAN) matrix) are primarily to reduce moisture sensitivity, to improve toughness and to reduce shrinkage and warpage of the polyamide phase.1 Thanks to ABS, the blend has improved impact strength, even at low temperatures. ABS also reduces the costs of the material compared to pure PA. The polyamide in turn makes the blend highly chemically resistant and heat resistant and provides a good flow behavior. All these properties together make PA/ABS blends interesting as a performance material for various applications such as automotive applications.3 However, polyamide and ABS are
completely immiscible. This means that there is hardly any interfacial adhesion between the two phases, which, consequently, leads to adhesive failure and poor mechanical properties of the blend. Therefore, application of a compatibilizer is necessary to improve the interfacial adhesion and to obtain blends with all the above-mentioned interesting properties.
1.3.1 Reactive compatibilizers
The most frequently used strategy to compatibilize blends of PA and ABS, is to incorporate a polymer into the ABS which is miscible with its poly(styrene-co-acrylonitrile) (SAN) phase and which can react with the polyamide when the two come in contact at the polyamide-ABS interface.2,3,8-25 This reactive compatibilization
strategy can be used thanks to the amine or carboxyl end-groups that are present in the PA phase.
Different reactive compatibilizer precursors are reported in literature. Most of them contain an anhydride functional group that can react with the amine end-groups of the polyamide. Some typical examples of reactive compatibilizer precursors are imidized acrylic (IA) polymers3,10-12,16,17,19,21-23, SAN copolymers containing maleic anhydride functional groups (SAN-MAh)3,8,9,12,14,15,22-25, styrene maleic anhydride copolymers (SMA)16,17, and copolymers of methyl methacrylate with maleic anhydride (MMA-MAh)18. Also, compatibilizer precursors containing functional groups that can react with both the carboxyl and amine end-groups of the PA have been reported, for example SAN with part of the nitrile groups converted to oxazoline groups16,20 and
copolymers of MMA with glycidyl methacrylate (MMA-GMA)13,18, containing an epoxide functionality. However, this type of reactive compatibilizer precursor proved to be less successful in creating a well dispersed blend of PA6 and ABS. Due to their functionality towards both end-groups of PA6, cross-linking reactions can occur, which make it very difficult to achieve well dispersed blends13,18. This cross-linking reaction is also observed when blending polyamides with two amine end-groups, such as PA66, with ABS using an anhydride-functional compatibilizer10.
In the present study the commercially interesting PA6/ABS blend system8,25-27 is investigated. A SAN-MAh type reactive compatibilizer has been used. This study mainly focuses on the toughness of the produced blends. Therefore, in the following sections an overview is given of what knowledge is reported in literature about the factors that influence the impact strength of PA6/ABS blends, produced with SAN-MAh type reactive compatibilizers.
1.3.2 Morphology
To obtain optimal heat and solvent resistance for PA/ABS blends, PA should be the continuous phase. However, to preserve the ABS-generated toughness across a wide range of conditions, the ABS phase should also be continuous. Therefore, a
co-continuous morphology is preferred1. Lacasse et al.9 reported a sharp increase in blend impact strength on changing the morphology from ABS as the dispersed phase
towards a co-continuous morphology for both ABS and PA. This change takes place at an ABS/PA/SAN-MAh composition of 40/56/4 wt%. With higher amounts of ABS in the blend, the impact strength decreases again.
1.3.3 Rubber content
The amount of rubber present in the ABS phase of PA/ABS blends has a large influence on the blend impact strength. For blends of PA6 and ABS, compatibilized with an imidized acrylic polymer (IA), Majundar et al.17 reported a sharp increase in blend toughness if more than 30 wt% of rubber was present in the ABS phase. At about 40 wt% of rubber in the ABS phase, maximum impact strength of the blend was achieved. The blend composition was kept constant at 45/45/10 wt% PA6/ABS/IA.
1.3.4 Influence of mixing/extruder type
Lacasse et al.9 showed that the way of mixing had a large influence on the morphology development in polymer blends. These authors compared the performance of a single- screw and a twin-screw extruder for blending PA6 with ABS, using a SAN-MAh reactive compatibilizer. The particle size of the dispersed phase obtained with the twin-screw extruder turned out to be half of that obtained with the single-screw extruder. Furthermore, with up to 9 wt% of compatibilizer in the blend still no equilibrium morphology was obtained in the single-screw extruder. However, by using a twin-screw extruder 1 wt% of compatibilizer was sufficient to obtain the equilibrium morphology. The explanation given for this difference is that the more-intense mixing in the twin- screw extruder enhances the migration of the compatibilizer to the interface9.
Thanks to the very fast reaction between the anhydride groups in SAN-MAh and the amine end-groups of PA6, extrusion residence times can be relatively short (about one minute). These short residence times prevent extensive degradation of the PA phase28.
1.3.5 Influence of the concentration of functional groups in the compatibilizer
In 1986, Lavengood et al. filed a patent on the reactive extrusion alloying of 50 wt% soft ABS (containing 40 wt% polybutadiene) with 6 wt% SAN-MAh and 44 wt% PA to give alloys with excellent impact strength.8 This discovery led to the
commercialization in 1987 of Triax-1000, a quite successful PA/ABS blend with a co-continuous morphology.1
The patent of Lavengood et al.8 describes the influence of the MAh content in the SAN-MAh compatibilizer precursor on the blend impact strength. With increasing amounts of maleic anhydride in the compatibilizer, higher values for the blend Izod impact strength are reported. This can be explained by an increase in the number of PA grafts per compatibilizer molecule, leading to a higher interfacial adhesion between the ABS and PA phases. However, for compatibilizer precursors containing more than one mole % of MAh groups, the blend toughness decreases again. Several explanations for this behavior can be found in literature. One of the explanations is that upon reaction with PA the anhydride groups in the SAN-MAh terpolymer are
converted into imides, which make the SAN backbone of the compatibilizer immiscible with the SAN phase of the ABS19. However, Majundar et al19 obtained quite good compatibilization for PA/ABS blends using compatibilizers with a composition just outside the miscibility window with the SAN phase of the ABS. In the same article, another explanation is given for the optimum in functional group concentration for the SAN-MAh compatibilizer precursor. With increasing number of PA grafts, the shear stresses transmitted to the compatibilizer molecule by the PA grafts during extrusion, increase as well. At a certain number of PA grafts, those stresses become so large that the compatibilizer is pulled away from the interface, forming micellar domains in the polyamide phase. This mechanism is supported by the work of Steurer et al.29. For PA/SMA blends Steurer et al.29 observed micellar domains in the PA phase formed by ‘over grafted’ SMA chains. Dedecker and coworkers30 reported the same phenomena for blends of PA/PMMA with SMA as reactive compatibilizer.
1.4 Objective and outline of this thesis
The goal of the research work described in this thesis was to gain more insight into the compatibilization mechanism of the SAN-MAh compatibilizer in PA6/ABS blends. The optimum in compatibilization for this system, as described by Lavengood et al.8, depends on the MAh content in the compatibilizer, i.e. on the interaction with the PA phase. More PA grafts lead to a better interfacial adhesion. However, with too many PA grafts, the interaction with the PA phase is so strong that the compatibilizer is pulled away from the interface during the blending process19. To prevent the compatibilizer from moving away from the interface, the interaction with the SAN phase of the ABS should be strengthened. This interaction is based on entanglements between the SAN backbone of the compatibilizer and the SAN chains of the ABS phase. The development of entanglements depends on the molar mass of the polymer chains, i.e. a critical molar mass is necessary for efficient entanglements to occur. The higher the molar mass, the more entanglements can be formed per molecule.
Therefore, in this research, the relation between the optimum in MAh content and the molar mass of the SAN-MAh compatibilizer precursor is investigated.
Two approaches are followed in this research, which are schematically represented in Figure 1.1. The first one is to investigate the distribution of maleic anhydride across the molar-mass distribution of the SAN-MAh compatibilizer precursor and its influence on the properties of the blend. The idea is that a compatibilizer with a high-molar-mass SAN backbone will form more entanglements with the SAN phase of the ABS, see Figure 1.1B. As a consequence, more PA can be grafted onto the SAN-MAh terpolymer before it is pulled away from the interface. However, the higher the molar mass, the slower the reactive compatibilizer diffuses towards the interface during extrusion. To make these high-molar-mass species reach the interface within the residence time in the extruder, low-molar-mass compatibilizer precursors with low MAh contents can be added. These low-molar-mass compatibilizer precursors will diffuse fast to the interface, create a fine dispersion and, hence, reduce the distance to the interface for the high-molar-mass ones30. In this way high-molar-mass species will be able to reach the interface within the residence time of the extruder and, thus, can enhance the interfacial adhesion between the two blend components. To prevent the low-molar-mass compatibilizer from being pulled away from the interface, its MAh content should be lower than 1 wt%. Therefore, it is interesting to prepare
compatibilizers with a distribution of maleic anhydride across the molar-mass distribution: less MAh in the low-molar-mass region and more MAh in the high-molar-mass region.
The second approach is to prepare end-functional compatibilizer precursors. Upon reaction with the PA phase, a di-block copolymer, SAN-b-PA, will be formed instead of a graft copolymer, as shown in Figure 1.1C. Since only the ultimate chain segment is forced to be at the interface, the SAN block can penetrate more deeply into the ABS phase, and, hence, form more efficient entanglements compared to the SAN backbone in SAN-g-PA copolymers shown in Figure 1.1A. Therefore, the interaction with the ABS phase is expected to be greater for SAN-b-PA compatibilizers than for SAN-g-PA compatibilizers.
Figure 1.1 Schematic representation of the compatibilizer conformation at the
PA/ABS interface. = SAN backbone of a SAN-MAh reactive compatibilizer, = MAh group in SAN-MAh, = PA6 grafted onto the compatibilizer and ▬ = entanglement with SAN phase of ABS. In Chapter 2 the polymerization kinetics for the SAN-MAh terpolymerization, carried out in a continuously operated stirred tank reactor (CSTR), are discussed. For a good control of the reaction, a reaction model was developed using Predici, a simulation package for polymerization reactions. All parameters needed for the model are discussed. The assumptions made are evaluated by sensitivity tests using the reaction model.
In Chapter 3 the analytical methods developed for this investigation are discussed. An FTIR method has been developed to determine the copolymer composition of the SAN-MAh terpolymer. With gradient-polymer-elution chromatography (GPEC) the
A
B C
ABS PA
ABS PA
chemical- composition distribution has been measured and a method for the
determination of the MAh distribution across the molar-mass distribution is described. Chapter 4 describes the SAN-MAh terpolymerizations carried out in the CSTR.
Terpolymers with different molar masses and MAh contents have been prepared in the CSTR. Experimentally observed conversions and polymer properties, e.g. molar mass and chemical composition, are compared with the results of Predici model calculations.
In Chapter 5 PA6/ABS blends made with the different compatibilizer precursors, as described in Chapter 4, are discussed. The toughness, measured with different impact test methods, and the morphology of the different blends are discussed with respect to the differences between the compatibilizers applied.
Chapter 6 describes the preparation of a maleic anhydride end-functional
compatibilizer using Reversible Addition-Fragmentation chain Transfer (RAFT) polymerization. Also, the results of the blend trials with this compatibilizer are shown here.
Concluding remarks, a technology assessment and recommendations for further research are given in Chapter 7.
1.5 References
(1) Utracki, L. A. Commercial polymer blends; Chapman & Hall: London, 1998. (2) Koning, C.; van Duin, M.; Pagnoulle, C.; Jerome, R., Prog.Polym.Sci., 1998,
23, 707.
(3) Weber, M., Macromol.Symp., 2002, 181, 189.
(4) Majumdar, B.; Paul, D. R. Reactive compatibilization; In Polymer Blends; Paul, D. R.; Bucknall, C. B., eds. John Wiley & Sons: New York, 2000; pp 539-574.
(5) Creton, C.; Kramer, E. J.; Hadziioannou, G., Macromolecules, 1991, 24, 1846. (6) Brown, H. R., Macromolecules, 1191, 24, 2752.
(7) Eastwood, E. A.; Dadmun, M. D., Macromolecules, 2003, 35, 5069. (8) Lavengood, R. E.; Harris, A. F.; Padwa, A. R., EP 0202214 A2, 1986. (9) Lacasse, C.; Favis, B. D., Advances in Polymer Technology, 1999, 18, 255. (10) Majumdar, B.; Keskkula, H.; Paul, D. R., Polymer, 1994, 35, 5468.
(11) Kudva, R. A.; Keskkula, H.; Paul, D. R., Polymer, 2000, 41, 335. (12) Kudva, R. A.; Keskkula, H.; Paul, D. R., Polymer, 2000, 41, 239. (13) Kudva, R. A.; Keskkula, H.; Paul, D. R., Polymer, 1998, 39, 2447.
(14) Nair, S. V.; Wong, S.-C.; Goettler, L. A., Journal of Materials Science, 1997,
32, 5335.
(15) Grmela, V.; Konecny, D., International Polymer Science and Technology,
1994, 22, 368.
(16) Triacca, V. J.; Ziaee, S.; Barlow, J. W.; Keskkula, H.; Paul, D. R., Polymer,
1991, 32, 1401.
(18) Araujo, E. M.; Hage Jr., E.; Carvalho, A. J. F., Journal of Polymer Science,
2002, 87, 842.
(19) Majumdar, B.; Keskkula, H.; Paul, D. R.; Harvey, N. G., Polymer, 1994, 35, 4263.
(20) Liu, X.; Mantia, F. L.; Scaffaro, R., Journal of Applied Polymer Science,
2002, 86, 449.
(21) Pressly, T. G.; Keskkula, H.; Paul, D. R., Polymer, 2001, 42, 3043. (22) Kitayama, N.; Keskkula, H.; Paul, D. R., Polymer, 2000, 41, 8041. (23) Kitayama, N.; Keskkula, H.; Paul, D. R., Polymer, 2000, 41, 8053.
(24) Jafari, S. H.; Potschke, P.; Stephan, M.; Pompe, G.; Warth, H.; Alberts, H.,
Journal of Applied Polymer Science, 2002, 84, 2753.
(25) Lavengood, R. E.; Padwa, A. R.; Patel, R., EP 220155, 1986. (26) Aoki, Y.; Watanabe, M., EP0402528, 1989.
(27) Lin, J. L.; Kao, H. C.; Lee, M. S.; Hsu, J. P.; Wu, T. K., US 5248726, 1993. (28) Duin, M. v.; Machado, A. V.; Covas, J., Macromol.Symp., 2001, 170, 29. (29) Steurer, A.; Hellmann, G. P., Polym.Adv.Technol., 1998, 9, 297.
Chapter 2 Modeling of reaction kinetics for SAN-MAh
terpolymerizations in a CSTR
2.1 Introduction
For the preparation of the SAN-MAh type reactive compatibilizer, a 1.5 L continuously operated stirred tank reactor (CSTR) has been used. The reactor, equipped with a flash evaporation unit, facilitated the production of large batches of terpolymer, enough to compatibilize five kilograms of PA/ABS blend. To obtain well defined SAN-MAh terpolymers, the reaction kinetics have been modeled using the commercially available program Predici. In this chapter the theoretical background, the reaction steps, and the kinetic parameters used to develop the Predici model are discussed. The influence of some major assumptions, regarding kinetic-parameter values, on the performance of the model is tested as well. The validation of the model calculations with experimental results is described in Chapter 4.
2.2 Free-radical-polymerization kinetics
The reactions carried out in the CSTR are free-radical solution polymerizations of styrene (S), acrylonitrile (AN) and maleic anhydride (MAh) (Scheme 2.1). The obtained polymer is a statistical poly(styrene-co-acrylonitrile-co-maleic anhydride) terpolymer (SAN-MAh). Equation (2.1) gives the mass balance for each monomer i over the reactor:
, , ,
, , ,
M i M i M i
mol in mol out p i r
dN
R V
dt =φ −φ − (2.1)
where dNM,i/dt, Rp,i, Vr, i , M
mol in
φ and Mi ,
mol out
φ stand for the change in amount of
monomer i as a function of time (mol s-1), the rate of polymerization for monomer i
(mol L-1 s-1), the reaction volume (L), the flow rate of monomer i into the reactor (mol
CH CH2 CH2 CH C N CH CH C O C O O b c a CH CH2 CH2 CH C N CH CH C O C O O T > 100 oC
Scheme 2.1 Polymerization reaction of SAN-MAh terpolymers.
For a perfectly mixed reactor at steady state conditions Equation (2.1) simplifies to:
, [ ] , [ ] , 0
V in Mi in V out Mi out R Vp i r
φ ⋅ −φ ⋅ − = (2.2)
where φV in, , φV out, and [Mi] stand for the volumetric flow rate of the feed (L s
-1), the
volumetric flow rate of the effluent (L s-1) and the concentration of monomer i (mol L-1).
The conversion of monomer i, Xi, at steady state can be obtained from Equation (2.2):
, , , , , [ ] [ ] [ ] [ ] p i r V in i in V out i out i V in i in V in i in R V M M X M M φ φ φ φ − = = (2.3)
To predict the conversion at steady state for a given monomer feed (φV in, [Mi]in) and constant reaction volume (Vr), Rp,i needs to be calculated. For homopolymerizations
Rp,i can be expressed as shown in Equation (2.4):
, ,[ ] 2 I p i p i i t R R k M k = (2.4)
where kp, [Mi], RI and kt stand for the propagation rate constant (L mol-1 s-1), the concentration of monomer i in the reactor (mol L-1), the rate of initiation (mol L-1 s-1) and the termination rate constant (L mol-1 s-1), respectively.
However, in case of copolymerization reactions, also cross propagation between the different monomers takes place. The number of propagation steps used to describe the rate of polymerization for each monomer depends on the model used to describe the copolymerization kinetics. For that reason a copolymerization model is introduced in the next section and expressions for RI, kt and kp are discussed in terms of the model of choice.
2.3 Copolymerization model
For the description of copolymerization reaction kinetics, different statistical models can be used, such as Bernoulian1, terminal (Mayo-Lewis)2, penultimate (Merz-Alfrey-Goldfinger)3, or third-order Markov statistics4. In the Bernoulian model, equal
reactivity is assumed for chain-ends, regardless of their chemical nature. This simple representation of the copolymerization process, however, fails to describe the
copolymerization of many comonomer pairs. The most widely used model in
literature5 is the terminal model, where the reactivity depends on the chemical nature of both the chain-end and the adding monomer. More complex models take the last two (penultimate) or even the last three (third-order Markovian) monomer residues of the growing polymer chains into account. These complex models are often avoided due to the practical limitation of a number of unknown variables and the complexity of the analytical equations.
However, in a comprehensive review article, Coote and Davis6 conclude from a diverse range of published studies that the terminal model cannot adequately describe copolymerization reactions. Furthermore, Klumperman et al. reported a close
agreement between experimental data and the penultimate-unit model for
copolymerizations resulting in SMA7 and SAN8. Therefore, despite the complexity of the model, the penultimate-unit-model approach is used in the present study.
In the following sections the expressions for the rate of initiation (RI), the propagation rate constant (kp), and the termination rate constant (kt) will be discussed in terms of the penultimate-unit model. Chain transfer to solvent is taken into account as well.
2.3.1 Rate of initiation (RI)
The thermal self-initiation of styrene is used to initiate the SAN-MAh polymerization reaction. The mechanism and kinetics of this initiation mechanism were described previously by Mayo9 and by Hui and Hamielec10 (Scheme 2.2). The reaction starts with a Diels-Alder cycloaddition of two styrene molecules to produce a styrene dimer. In the next step the styrene dimer undergoes an electron transfer reaction with another styrene molecule to form two radicals, M* and D*. The Diels-Alder addition can also occur between styrene and another vinyl monomer, as was described by Sato and co-workers11 for the copolymerization of styrene and maleic anhydride and by Liu et al.12 for the copolymerization of styrene and acrylonitrile. The resulting Diels-Alder adducts for the thermal self initiation of styrene in the presence of acrylonitrile and/or maleic anhydride are shown in Appendix 2A. The thus obtained radicals initiate the polymerization reaction as follows:
* i bd, * b d bd k D +M ⎯⎯⎯→P (2.5) * i ce, * c e ce k M +M ⎯⎯⎯→P (2.6)
where ki, D*, M*, M and P* stand for the initiation rate constant, a Diels-Alder adduct radical, a monomer radical, monomer, and a macro radical, respectively. The
subscripts denote the different monomers that take part in the reaction: b, c, d and e can be styrene, acrylonitrile or maleic anhydride. Since homopolymerization of maleic anhydride is unlikely to occur at the polymerization conditions used in the present work13, the following condition holds: if b = MAh then d ≠ MAh and if c = MAh then e ≠ MAh.
H H k1,b k2,b k3,bc Db Db MS Mb Mc Mc* Db*
Scheme 2.2 Mayo mechanism of styrene thermal self-initiation for the
terpolymerization of SAN-MAh, where M, D, M* and D* stand for monomer, the Alder adduct, a monomer radical and a Diels-Alder adduct radical, respectively. The subscripts S, b and c denote the different monomers that take part in the thermal self-initiation of styrene; S is styrene, b and c can be styrene, acrylonitrile or maleic anhydride with the restriction: if b = MAh then c ≠ MAh. The molecular structures illustrate the situation where b = c = styrene. Several kinetic studies10,14 have shown that the rate of radical formation for the
thermal self-initiation of styrene is apparently third order with respect to the monomer concentration. Assuming pseudo steady states for the reaction-intermediate Diels-Alder adducts, the initiation rate RI for the terpolymerization can be expressed as shown in Equation (2.7):
[ ][ ][ ]
, I ith bc S b c R =∑
k M M M (2.7) with 1, , 3, 2, 2 b ith bc bc b k k k k = (2.8)where [M], kith and k1, k2, k3 stand for the monomer concentration, the apparent and the real thermal self-initiation rate constants, respectively; S stands for styrene, b and
c stand for styrene or acrylonitrile or maleic anhydride, with the restriction: if b =
MAh then c ≠ MAh.
Table 2.1 Values for the rate of radical formation by the thermal self-initiation of
styrene. All radical formation steps are listed in Appendix 2B. kith value at different temperatures
[10-10 L2 mol-2 s-1] kith A0 [L2 mol-2 s-1] E/R [K] 140 oC 150 oC 170 oC Ref. kith,SSS 4.14 × 104 12278 51.4 104 384 15 kith,SSA 2.03 × 10-6 3231 8.15 9.8 13.8 15 kith,SAS 2.03 × 10-6 3231 8.15 9.8 13.8 15 kith,SAA 1.14 × 107 14164 147.2 331 1499 15 kith,SMS 4.51 × 101 8230 1007 1612 3878 16 kith,SSM 4.51 × 10 1 8230 1007 1612 3878 16
The values for kith that are reported in literature are listed in Table 2.1. In Table 2.1, as well as in the following text, rate constants are denoted with a subscript containing three capitals. These three capitals represent the monomer units that play a role in the reaction step: S, A and M stand for styrene, acrylonitrile and maleic anhydride, respectively. In case of radical-formation rate constants, the first two capitals
represent the two monomer units which have formed the Diels-Alder adduct. For rate constants describing propagation and chain-transfer reactions, the first two capitals represent the penultimate and terminal unit of the macroradical, respectively. The third capital represents the monomer that takes part in the reaction. To account for the temperature dependence, all rate constants are expressed as an Arrhenius equation:
0exp E RT k A ⎛− ⎞ ⎜ ⎟ ⎝ ⎠ = (2.9)
where k, A0, E, R and T are the rate constant, frequency factor, activation energy (J mol-1), gas constant (J mol-1 K-1) and temperature (K), respectively.
The corresponding values for the rate constants at the different reaction temperatures used in the present study are listed as well.
For values of kith,SAM and kith,SMA, which are not available in literature, the following assumption has been made. Maleic anhydride and acrylonitrile are both electron acceptor species and therefore the propagation rate for the reaction of maleic
anhydride and acrylonitrile species is assumed to be equal to the propagation rate for the reaction in which two acrylonitrile species are involved:
kith,SAM = kith,SMA = kith,SAA (2.10)
2.3.2 Propagation rate constant (kp)
According to the penultimate-unit model, 22 reactions, see Appendix 2D, describe the propagation for the terpolymerization reaction of SAN-MAh:
* p abc, *
ab c bc
k
P +M ⎯⎯⎯→P (2.11)
where P* is a macroradical, M is monomer, k
p the propagation rate constant and a, b and c can be styrene, acrylonitrile or maleic anhydride (MAh) with the restriction: if b = MAh, then a ≠ MAh and c ≠ MAh.
Values for the propagation rate constants reported in literature are collected in Table 2.2.
Table 2.2 Propagation rate constants for the homopolymerizations of styrene and
acrylonitrile and for the copolymerization of SMA.
kp value at different temperatures
[L mol-1 s-1] kp A0 [L mol-1 s-1] E/R [K] 140 oC 150 oC 170 oC Ref. kp, SSS 1.10 × 107 3548 2049 2510 3665 17 kp, AAA 1.05 × 108 3663 14816 18269 27001 18 kp, MSS 3.20 × 106 3139 1604 1919 2683 16
For copolymerizations, a lot of data have been reported in literature on ratios of propagation rate constants, so called reactivity ratios. Reactivity ratios are defined as:
, , p abb ab p abc k r k = (2.12)
where a, b and c are one of both monomers participating in the copolymerization reaction and b ≠ c.
Table 2.3 Reactivity ratios reported in literature for the copolymerizations of
SAN and AN-MA.
r value Reference rSS (SAN) 0.242 8 rSA (SAN) 0.119 8 rAS (SAN) 0.559 8 rAA (SAN) 0.108 8 rAA (AN-MA) 6 19
Reactivity ratios reported in literature for the copolymerizations of styrene-acrylonitrile (SAN) and styrene-acrylonitrile-maleic anhydride (AN-MA) are collected in Table 2.3. The reactivity ratios collected in Table 2.3 have been determined at 60 °C and to the author’s best knowledge no data are available on the influence of
temperature. In work of O’Driscoll20 it was reported that the effect of temperature only becomes significant for reactivity ratios which are ≥ 10 or ≤ 0.1 at 60 °C. Therefore, rSS (SAN), rAS (SAN) and rAA (AN-MA) may be considered independent of temperature. Since no data are available on the relation of rSA (SAN) and rAA (SAN) with temperature, these r values were assumed to be independent of temperature as well. With this assumption, the following kp values can be calculated using the reactivity ratios from Table 2.3, according to:
kp, SSA = kp, SSS/rSS (SAN) (2.13)
kp, SAS = kp, SAA/rSA (SAN) (2.14)
kp, ASA = kp, ASS/rAS (SAN) (2.15)
kp, AAS = kp, AAA/rAA (SAN) (2.16)
kp, AAM = kp, AAA/rAA (AN-MA) (2.17)
Reactivity ratios reported in literature for the copolymerization of styrene-maleic anhydride (SMA) are listed in Table 2.4. The reported temperature dependence of rSS
(SMA) and rMS(SMA) is in accordance with the work of O’Driscoll20. Both rSS (SMA) and
rMS(SMA) obey the criterion ≤ 0.1 at 60 °C. The following kp values can be calculated
using the reactivity ratios listed in Table 2.4, according to:
kp, SSM = kp, SSS/rSS (SMA) (2.18)
kp, MSM = kp, MSS/rMS (SMA) (2.19)
Unfortunately, to the author’s best knowledge, hardly any data have been reported in literature on the reaction of acrylonitrile and maleic anhydride nor on the
terpolymerization of styrene with acrylonitrile and maleic anhydride. Therefore, some propagation rate constants have to be estimated. This is discussed in the following text.
Table 2.4 Reactivity ratios reported in literature for the copolymerization of
SMA
r value at different temperatures [L mol-1 s-1] r A0 [L mol-1 s-1] E/R [K] 60 oC 140 oC 170 oC Ref. rSS (SMA) 0.79 1119 0.028 0.053 0.063 16 rMS (SMA) 126.5 2357 0.107 0.421 0.619 16
In ab initio quantum theoretical calculations, Heuts et al.21 represent the transition state of the propagation reaction by three hindered rotors. This representation indicates that hindrances of the internal rotations are influenced by the penultimate unit. Based on their calculations, Heuts et al.21 conclude that the penultimate unit
could affect the value of kp by a factor of approximately 2. Therefore the following propagation rate constants are assumed to be twice as low as their respective homopropagation rate constants:
, , 0.5 p SAA p AAA k k ≅ (2.20) , , 0.5 p ASS p SSS k k ≅ (2.21)
Coote et. al.22 have reported that the penultimate unit effect is likely to be polar in
origin. Maleic anhydride and acrylonitrile are both polar monomers, as compared to styrene. Therefore, for the following pairs of propagation rate constants, the
penultimate-unit effects of maleic anhydride and acrylonitrile are assumed to be not significantly different. Hence, the corresponding propagation rate constants are set equal: kp, MAS = kp, AAS (2.22) kp, MAA = kp, AAA (2.23) kp, MSA = kp, ASA (2.24) kp, MAM = kp, AAM (2.25) kp, ASM = kp, MSM (2.26)
Florjanczyk and Krawiec23 demonstrated that, for the terpolymerization of styrene-acrylonitrile-maleic anhydride, the addition of acrylonitrile to a MAh-ended
macroradical is slower than the addition to a styrene-ended macroradical. Therefore, in the present work the ratio of kp,AMA and kp,SAA is set to 0.1:
, , 0.1 p AMA p SSA k k ≅ (2.27)
The addition of MAh to a styrene-ended macroradical has been reported24 to be faster than the addition of styrene to a MAh-ended macroradical. Therefore, in the present work kp, SMS is assumed to be a factor 10 lower than kp, SSM :
, , 0.1 p SMS p SSM k k ≅ (2.28)
For the next assumptions the difference in penultimate-unit effect of acrylonitrile and styrene was assumed to be negligible in view of the high reactivity of the MAh-ended macroradical and MAh monomer:
kp, AMS = kp, SMS (2.29)
kp, SMA = kp, AMA (2.30)
kp, SAM = kp, AAM (2.31)
2.3.3 Chain transfer
Chain-transfer reactions have been taken into account as well. Severini et al.25 have reported that for styrene homo-polymerization in the presence of EPDM rubber, transfer to polymer takes place. However, in the simultaneous presence of ethylbenzene, transfer to EPDM polymer is suppressed and mainly transfer to ethylbenzene occurs. Reported values for chain transfer to monomer in bulk polymerization of styrene26, are a factor of 30 lower than values reported for chain transfer to ethylbenzene in styrene solution polymerizations27. Since ethylbenzene is used as solvent for the terpolymerizations described in the present work, chain transfer to polymer and to monomer have been assumed negligible. Only chain transfer to the solvent ethylbenzene has been taken into account, see Appendix 2E:
* tr ab, *
ab
k
P +EB⎯⎯⎯→ +P S (2.32)
where P*, EB, P, S* and k
tr stand for a macroradical, ethylbenzene, a terminated polymer chain, a styrene radical and the chain-transfer rate constant; a and b can be styrene, acrylonitrile or maleic anhydride with the restriction: if a = MAh then b ≠ MAh.
To the author’s best knowledge, hardly any data has been reported in literature on the temperature dependence of rate constants for chain-transfer to ethylbenzene. Only for the solution homo-polymerization of styrene, rate coefficients for transfer to
ethylbenzene have been reported at different temperatures28. These reported chain-transfer constants were used to determine the frequency factor and activation energy for the chain transfer reaction between styrene and ethylbenzene, see Table 2.5.
Table 2.5 Value for the chain-transfer rate constant to solvent for the solution
polymerization of styrene in ethylbenzene.
ktr value at different temperatures
[L mol-1 s-1] ktr A0 [L mol-1 s-1] E/R [K] 140 oC 150 oC 170 oC Ref. ktr, SS 1.79 × 107 6850 1.13 1.67 3.48 29
For all other chain-transfer reactions to ethylbenzene, based on preliminary experiments the chain-transfer rate constant at 170 oC is assumed to be two times larger than the chain-transfer rate constant at 140 oC. For chain-transfer reactions at 60 oC, the acrylonitrile chain-transfer rate constant (ktr,AA) to ethylbenzene is 90 times higher than the one for styrene (ktr, SS)30. Assuming equal activation energies for ktr, AA and ktr, SS, the ratio between both chain-transfer constants becomes temperature independent, hence: , , 90 tr AA tr SS k k = (2.33)
Due to the close similarity between ethylbenzene and styrene, the assumptions made for the propagation reactions of a macroradical with styrene (as discussed in the previous section) were considered to hold for the chain-transfer reaction of the same macroradical with ethylbenzene as well. Assuming a not significantly different penultimate-unit effect for acrylonitrile and maleic anhydride leads to the following equalities:
ktr, MA = ktr, AA (2.34)
ktr, MS = ktr, AS (2.35)
Assuming a penultimate-unit effect of a factor of two21 for acrylonitrile and styrene:
, , 0.5 tr AS tr SS k k ≅ (2.36) , , 0.5 tr SA tr AA k k ≅ (2.37)
To obtain values for the chain-transfer rate of the SM and AM macroradicals with ethylbenzene, a comparison is made with their propagation rate towards styrene species, kp, SMS and kp, AMS, respectively. As discussed in Section 2.3.2, kp, SMS and kp, AMS have been assumed to be not significantly different, so the difference between ktr, AM and ktr, SM is assumed to be negligible as well:
ktr, AM = ktr, SM (2.38)
The assumptions described in Section 2.3.2 lead to a value for the propagation rate constant kp, SMS which is a factor of two higher than kp, SSS. Analogous to this assumption, the ratio of ktr,SM and ktr,SS is set to 0.5:
, , 0.5 tr SM tr SS k k ≅ (2.39)
2.3.4 Termination rate constant (kt)
For all terpolymerization reactions described in the present thesis the monomer feed contains over 50 mole % of styrene. Therefore, styrene being the major reactant, the termination rate constant of styrene has been chosen as input for the model. Similar to the termination mechanism for the styrene polymerization31, the termination
mechanism for the terpolymerization reactions has been assumed to occur by combination only:
* * t
ab cd
k
P +P ⎯⎯→P (2.40)
where P, P* and k
t stand for a terminated polymer chain, a macroradical and the termination rate constant; a, b, c and d can be styrene, acrylonitrile or maleic anhydride.
The termination rate constant is assumed to be the same for all growing polymer chains and is listed in Table 2.6. All termination reactions, as used in the Predici model, are listed in Appendix 2F.
Table 2.6 Termination rate constant of styrene, used to describe the termination
reaction in the terpolymerization of SAN-MAh.
kt value at different temperatures
[108 L mol-1 s-1] kt A0 [L mol-1 s-1] E/R [K] 140 oC 150 oC 170 oC Ref. kt 1.255 × 109 849 1.61 1.69 1.85 32 2.4 Predici model
To calculate the conversion at steady state, all fundamental steps described in section 2.3 need to be solved simultaneously. To perform these calculations, the
commercially available software package Predici® has been used.
All fundamental steps and corresponding rate coefficients for the SAN-MAh
terpolymerization, as described in section 2.3, were entered into the Prediciprogram. For a given reactor type (and size), reaction time, monomer feed and temperature, the Predici program calculates the course of the reaction using all the kinetic coefficients as entered.
2.4.1 Influence of the estimated kinetic parameters on the results of model calculations
To get insight into the influence of the assumptions, discussed in section 2.3, on the outcome of the Predici calculations, a sensitivity test has been performed. A reaction temperature of 140 °C and a recipe, representative for most of the reactions performed in the present study, see Table 2.7, has been used as input for the Predici model. Values of rate constants have been varied within reasonable boundaries. The influence of these variations of the rate coefficients on the calculated steady state values for molar mass, monomer conversion and monomer, polymer and solvent concentration have been investigated.
Table 2.7 Feed recipe used as input for Predici model calculations. The total
reaction time was 546 minutes.
Feed component Amount (g)
styrene 2820 acrylonitrile 509
maleic anhydride 1.81
ethylbenzene 1542
2.4.1.1 Propagation rate constants kp, SAA and kp, ASS
The validity of the assumptions that kp, SAA and kp, ASS are twice as small as kp, AAA and
kp,SSS, respectively has been tested by changing the values for kp, SAA and kp, ASS by a
factor of 2, 4 and 0.2. As demonstrated by the results in Figure 2.1, these changes affect the calculated values for all properties of the reaction product at steady state. Since changes in kp, SAA and kp, ASS have a significant influence on the outcome of the Predici calculations, small deviations from the assumed values can be used to fit the model to the experimental data.
Mn Mw 0 20 40 60 80 100 120 140 160 molar mass (kg/ m o l)
polymer AN EB MAh (*0.01) STY 0 50 100 150 200 250 300 350 concent rat ion (mg/ ml ) AN MAh Sty 0 10 20 30 40 50 60 70 80 90 conver sion (%)
Figure 2.1 Influence of kp, SAA and kp, ASS on steady-state values for the molar mass, monomer, solvent and polymer concentration and monomer conversion as calculated by the Predici program model. To visualize changes in MAh concentration, its value has been multiplied by a factor of 100.
: kp, SAA = 7408 L mol-1 s-1 and kp, ASS = 1025 L mol-1 s-1, : kp
multiplied by 2, : kp multiplied by 4, : kp multiplied by 0.2. Values for all other coefficients used in the model are listed in Appendix 2D.
2.4.1.2 Propagation reactions involving MAh species
All other estimated propagation rate constants are related to reactions in which always maleic anhydride species are involved. To investigate the influence of these
propagation rate constants on the model predictions, a division into two groups has been made: reactions in which the macroradical reacts with a maleic anhydride
monomer and reactions where maleic anhydride is involved only as the penultimate or the terminal unit.
The influence of the rate of propagation on the model predictions, for reactions with maleic anhydride as terminal or penultimate unit, is shown in Figure 2.2. Hardly any difference in the properties of the reaction product can be observed when these propagation rate constants are increased by a factor of 100. The small effect of a 100 times increase in propagation rate of macroradicals with an MAh terminal or
penultimate unit on the outcome of the reaction model can be explained by the low amount of maleic anhydride used in the recipe. In all reactions performed in the
present study less than 4 mole % of MAh has been used in the monomer feed. Therefore, the fraction of
Mn Mw 0 20 40 60 80 100 120 140 molar mass (kg/ m o l)
polymer AN EB MAh (*0.01) STY 0 50 100 150 200 250 300 350 concent rat ion (mg/ ml ) AN MAh Sty 0 10 20 30 40 50 60 70 80 conver sion (%)
Figure 2.2 Influence of propagation rate constants, related to reactions where
maleic anhydride is the terminal or penultimate unit, on steady-state values for molar mass, monomer, solvent and polymer concentration and monomer conversion as calculated by the Predici model. To visualize changes in MAh concentration, its value has been multiplied by a factor of 100. : kp,MAS = 1367, kp,MAA = 147.7, kp,MSA = 18.33,
kp,MAM = 24.69, kp,AMA = 0.848, kp,SMS = 36.59, kp,AMS = 36.59 and kp,SMA
= 0.848 (values for kp are in 102 L mol-1 s-1), : kp multiplied by 100, : kp devided by 10, : kp devided by 100. Values for all other coefficients used in the model are listed in Appendix 2D.
macroradicals containing a MAh molecule as the terminal or penultimate unit will be low. As long as these macroradicals propagate, their concentration is too low to have a significant influence on the total monomer concentration and conversion.
Lowering the propagation rate constants by a factor of 10 or 100, however, does result in a lower monomer conversion and a decrease in the degree of polymerization. This implies that, if the rate of propagation is lower than the estimated values,
macroradicals containing a MAh molecule at the terminal or penultimate unit would significantly slow down the whole polymerization reaction. However, for the reaction of styrene and maleic anhydride, addition of MAh has been reported only to increase the mean propagation rate constant of the reaction16. Therefore, the estimated values
for the propagation rate constants of macroradicals containing a MAh molecule at the terminal or penultimate unit seem to be in the right order of magnitude.
Only two reactions, in which the macroradical reacts with maleic anhydride
monomer, needed assumptions for the propagation rate constants: kp, SAM and kp, ASM. The effect of the values of kp, SAM and kp, ASM on the results of the Predici model calculations is shown in Figure 2.3. Increasing or decreasing the values for kp, SAM and
kp, ASM by a factor of 100 shows that kp, SAM and kp, ASM have no significant influence on
the results of model predictions for total conversion, concentration and degree of polymerization. However, increasing the values for kp, SAM and kp, ASM significantly affects the MAh concentration and the MAh conversion.
Mn Mw 0 20 40 60 80 100 120 140 molar mass (kg/ m o l)
polymer AN EB MAh (*0.01) STY 0 50 100 150 200 250 300 concent rat ion (mg/ ml ) AN MAh Sty 0 10 20 30 40 50 60 70 80 90 conver sion (%)
Figure 2.3 Influence of kp, SAM and kp, ASM on steady-state values for the molar mass, monomer, solvent and polymer concentration and monomer conversion as calculated by the Predici program model. To visualize changes in MAh concentration, its value has been multiplied by a factor of 100. : kp, SAM = 2469 L mol-1 s-1 and kp, ASM = 3335 L mol-1 s-1
: kp multiplied by 10, : kp devided by 10, : kp devided by 100. Values for all other coefficients used in the model are listed in Appendix 2D.
2.5 Concluding remarks
The fundamental reaction steps involved in the terpolymerization of styrene,
acrylonitrile and maleic anhydride have been discussed. For all fundamental steps the rate coefficients were looked up in literature and reasonable assumptions were made if values were, to the best of our knowledge, not available in literature. All these
fundamental steps were introduced into the Predici program. Predici calculates the steady-state performance of the CSTR in terms of molar mass, monomer conversion and monomer, polymer and solvent concentration. The approach to steady-state for molar mass, monomer conversion and monomer, polymer and solvent concentration can also be calculated by Predici. A sensitivity test was performed to investigate the influence of the assumptions, made for the kinetic parameter values which were not reported in literature, on the outcome of the Predici calculations.
From the sensitivity test of the Predici model we can conclude that most of the estimated propagation rate constants, related to reactions in which MAh species are involved, have no significant effect on the outcome of the model. This is mainly due to the low amount of MAh used in the reactions. Therefore, the probability that a reaction, in which MAh is involved, takes place is low and, hence, a change in propagation rate constant for such a reaction does not significantly influence the results of the model calculations. The only exceptions are kp, SAA and kp, ASS. These two propagation rate constants, for which no values are reported in literature, have a significant effect on the results of the model calculations. kp, SAA and kp, ASS are therefore used as fit parameters.
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Appendix 2A Mayo mechanism of styrene thermal self-initiation in the presence of maleic anhydride or acrylonitrile
k1,M k2,M k3,MS H O O O H O O O O O O O O O
Scheme 2.3 Mayo mechanism of styrene thermal self-initiation in the presence of
maleic anhydride. H C N C N C N H C N k1,A k2,A k3,AA C N C N
Scheme 2.4 Mayo mechanism of styrene thermal self-initiation in the presence of
Appendix 2B Radical formation steps and values for the rate coefficients as used in the Predici model
ki,th value at different
temperatures [10-10 L2 mol-2 s-1] Radical fomation step A0
[L2 mol-2 s-1] E/R [K] 140 oC 150 oC 170 oC , , i th SSS k S+ + ⎯⎯⎯⎯S S →SS⋅ + ⋅ S 4.14 × 104 12278 51.4 104 384 , , i th SSA k S+ + ⎯⎯⎯⎯S A →SS⋅ + ⋅ A 2.03 × 10-6 3231 8.15 9.8 13.8 , , i th SSM k S+ +S M ⎯⎯⎯⎯→SS⋅ + ⋅ M 4.51 × 101 8230 1007 1612 3878 , , i th SAS k S+ + ⎯⎯⎯⎯A S →SA⋅ + ⋅ S 2.03 × 10-6 3231 8.15 9.8 13.8 , , i th SAA k S+ + ⎯⎯⎯⎯A A →SA⋅ + ⋅ A 1.14 × 107 14164 147.2 331 1499 , , i th SAM k S+ +A M ⎯⎯⎯⎯→SA⋅ + ⋅ M 2.03 × 10-6 3231 8.15 9.8 13.8 , , i th SMS k S+M + ⎯⎯⎯⎯→S SM⋅ + ⋅ S 4.51 × 101 8230 1007 1612 3878 , , i th SMA k S+M + ⎯⎯⎯⎯→A SM⋅ + ⋅ A 2.03 × 10-6 3231 8.15 9.8 13.8
Appendix 2C Initiation steps and values for the rate coefficients as used in the Predici model
Initiation step ki value [1010 L mol-1 s-1] , i SSS SS k SS⋅ + ⎯⎯⎯→S P ⋅ 1 , i SSA SA k SS⋅ + ⎯⎯⎯→A P ⋅ 1 , i SSM SM k SS⋅ +M ⎯⎯⎯→P ⋅ 1 , i SS SS k S⋅ + ⎯⎯⎯→S P ⋅ 1 , i SA SA k S⋅ + ⎯⎯⎯→A P ⋅ 1 , i SM SM k S⋅ +M ⎯⎯⎯→P ⋅ 1 , i SAS AS k SA⋅ + ⎯⎯⎯→S P ⋅ 1 , i SAA AA k SA⋅ + ⎯⎯⎯→A P ⋅ 1 , i SAM AM k SA⋅ +M ⎯⎯⎯⎯→P ⋅ 1 , i AS AS k A⋅ + ⎯⎯⎯→S P ⋅ 1 , i AA AA k A⋅ + ⎯⎯⎯→A P ⋅ 1 , i AM AM k A⋅ +M ⎯⎯⎯→P ⋅ 1 , i SMS MS k SM⋅ + ⎯⎯⎯→S P ⋅ 1 , i SMA MA k SM⋅ + ⎯⎯⎯→A P ⋅ 1 , i SSM SM k SM⋅ +M ⎯⎯⎯→P ⋅ 1
Appendix 2D Propagation steps and values for the rate coefficients as used in the Predici model
kp value at different temperatures
[L mol-1 s-1] Propagation step A0 [104 L mol-1 s-1] E/R [K] 140 oC 150 oC 170 oC , p SSS SS SS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 1100 3548 2049 2510 3665 , p SSA SS SA k P ⋅ + ⎯⎯⎯⎯A →P ⋅ 4545 3548 8467 10373 15144 , p SSM SS SM k P ⋅ +M ⎯⎯⎯⎯→P ⋅ 1392 2430 38885 44683 57900 , p SAS SA AS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 4.21 580 10345 10695 11377 , p SAA SA AA k P ⋅ + ⎯⎯⎯⎯A →P ⋅ 5235 3663 7387 9108 13462 , p SAM SA AM k P ⋅ +M ⎯⎯⎯⎯→P ⋅ 1745 3663 2462 3036 4487 , p SMS SM MS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 139 2430 3889 4468 5790 , p SMA SM MA k P ⋅ + ⎯⎯⎯⎯A →P ⋅ 455 3548 847 1037 1514 , p ASS AS SS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 367 3548 683 837 1222 , p ASA AS SA k P ⋅+ ⎯⎯⎯⎯A →P ⋅ 656 3548 1222 1497 2185 , p ASM AS SM k P ⋅ +M ⎯⎯⎯⎯→P ⋅ 2.53 782 3813 3987 4334 , p AAS AA AS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 9.29 580 22798 23568 25072 , p AAA AA AA k P ⋅ + ⎯⎯⎯⎯A →P ⋅ 10470 3663 14773 18217 26924 , p AAM AA AM k P ⋅ +M ⎯⎯⎯⎯→P ⋅ 1745 3663 2462 3036 4487 , p AMS AM MS k P ⋅ + ⎯⎯⎯⎯S →P ⋅ 139 2430 3889 4468 5790
