Kinetics of Different Methods of Polymerization

Home , Chain termination, Degree of polymerization, Kinetic chain length

Technische Universität Berlin

Institut für Chemie

Polymerization Technology

Karl-Heinz Reichert

Reinhard Schomäcker

Third Edition SS 2017

Preface

This teaching booklet has been written for students attending the Master Program of Polymer Science, established as a joint program by four universities in the cities of Berlin and Potsdam.

This text book focuses on fundamental aspects of polymerization reaction engineering. In the development of a polymerization process the type of reactor and its mode of operation are key factors, which not only affect reactor performance and safety, but also to a large extend the quality of the polymeric product. This is due to the fact that polymers are non uniform materials and the degree of non uniformity is affected by chemistry and reaction engineering conditions as well. I hope that the contents of this text book will be of help to those students who will be envolved in large scale synthesis of polymers in times to come.

I would like to thank my secretary Veronika Schott for writing the manuscript of this booklet and especially for her patience with respect to numerous changes of the text, which I have made all the time. Thanks also go out to Monika Klein, who drew all the figures presented in this book and Scott Kibride who improved the English language.

Finally we would like to thank all my former PhD students and many of our colleagues for some of their scientific results, which we have used in this text book.

Karl Heinz Reichert Berlin in October 2002

Reinhard Schomäcker Berlin in April 2017

TABLE OF CONTENTS

1. Introduction 1 1.1 Classification of Polymers 1 1.2 Types of Polymerization Reactions 2 1.3 Methods of Polymerization 3 1.4 Types of Polymerization Reactors 4 1.5 General References 4 1.6 Tables and Figures 6

2. Kinetics of Polymerization and Molecular Weight of Polymers 9 2.1 Free Radical Polymerization in Solution 9 2.1 Free Radical Polymerization in Emulsion 16 2.3 Free Radical Copolymerization in Solution 23 2.4 Coordination Polymerization in Gas Phase 24 2.5 Coordination Polymerization in Liquid Phase 32 2.6 List of Symbols 34 2.7 References 35 2.8 Tables and Figures 37

3. Viscosity of Reaction Mixture 55 3.1 Introduction 55 3.2 Viscosity of Homogeneous Systems 55 3.3 Viscosity of Heterogeneous Systems 58 3.4 List of Symbols 59 3.5 References 60 3.6 Figures 61

4. Data Acquisition of Polymerization Reactions 66 4.1 Introduction 66 4.2 Reaction Calorimetry/Kinetic and Caloric Data 66 4.3 Reaction Viscosimetry/Rheological Data 70 4.4 Solubility and Diffusivity of Monomer in Polymer 71 4.5 List of Symbols 73 4.6 References 74 4.7 Figures 75

5. Polymerization in Stirred Tank Reactors 83 5.1 Mode of Operation 83 5.2 Mixing of Reaction Mixture 84 5.3 Heat Removal and Safety Aspects 92 5.4 Residence Time Distribution 98 5.5 Reactor Performance 101 5.6 Reactor Selectivity 105 5.7 Reactor Scale-up 109 5.8 List of Symbols 111 5.9 References 113 5.10 Tables and Figures 114

6. Polymerization Processes 139 6.1 General Aspects 139 6.2 Processes for Chain-Growth Polymerization 140 Solution Polymerization/High Density Polyethylene Suspension Polymerization/Poly(vinyl chloride) Emulsion Polymerization/Styrene-Butadiene-Copolymer Slurry Polymerization/High Density Polyethylene Gas Phase Polymerization/High Density Polyethylene 6.3 Processes for Step-Growth Polymerization 146 Condensation Polymerization in Solution/Phenolic Resins Condensation Polymerization in Melt and Solid State/Poly- (ethylene terephthalate) Addition Polymerization in Liquid Phase/Polyurethanes 6.4 References 149 6.5 Tables and Figures 150

1. INTRODUCTION

1.1 Classification of Synthetic Polymers Synthetic polymers can be classified according to their specific properties into thermoplastics, thermosets and elastomers. Examples of major polymers of each kind are listed in Tab. 1.1.

Thermoplastic polymers are organic materials, which consist of linear or branched macromolecules having molecular weights on the order of 100 000 gram per mole. On heating above melting point thermoplastic polymers melt and form highly viscous liquids with a typical flow pattern. On cooling the melt solidifies again. In this way thermoplastic polymers can easily be processed into materials of different shapes. According to the physical structure and chemical composition of the polymers they can be partially crystalline or amorphous materials in the solid state. Amorphous polymers like polyvinyl chloride, polystyrene, and polyesters are transparent materials. Partially crystalline polymers like high density polyethylene and polypropylene are not transparent in the solid state due to their heterophasic structure.

Thermosets are organic materials, which are formed by higly crosslinked macromolecules with extremely high molecular weights. On heating they can not be molten but they do decompose and lose their original properties. Therefore thermosets have to be processed in such a way that synthesis and processing of the polymer material is done at the same time in a given cavity corresponding to the shape of the material which is to be produced. In general, thermosets are filled with glass fibre to improve the mechanical strengh of the materials.

Elastomers are linear or branched macromolecules which are very flexible. The molecules contain double bonds, which can easily react with added crosslinker at elevated temperatures, forming a crosslinked material with rubber-like properties.

Typical properties of organic polymers are low specific weight, low heat and electrical conductivity, and good resistant to corrosion. Feedstocks for major polymers are crude oil, natural gas, salt, air, and water. Organic polymers are produced by a relatively small number of large chemical companies. Approxi- mately seventy percent of all polymers produced are thermoplastics, twenty percent are thermosets, and ten percent are elastomers.

1 1.2 Types of Polymerization Reactions Polymerization reactions can be very complex chemical reactions with many different side reactions. One way of classification of polymerization reactions is to look at the polymer growth reaction, which is essential for polymer formation. By looking at the polymer growth reaction, chainwise and stepwise polymerization reactions can be distinguished. See Tab. 1.2.

In chainwise polymerization reactions the propagation of a molecule happens by the consecutive addition of bifunctional monomer molecules (M) to an active * site ( Pn ) of chain length n. Once the active sites are formed they start a chain of monomer addition reactions until the chain is terminated by a termination reaction. The active sites can be free radicals, organo metallic complexes or anionic or cationic species of very different kinds. Depending on the nature of active sites polymerization reactions can be classified into free radical polymerization, coordination polymerization, and ionic polymerization. If these polymerization reactions do not have any chain termination or chain transfer reaction they are called living polymerization. In case of a living polymerization the life time of active sites are long (at least on the order of total reaction time). The life time of free radicals is in general on the order of seconds. Active sites of organo metallic catalysts can have very different life times. In general they are on the order of seconds or minutes. The concentration of active sites of chainwise polymerization reactions is in general very low and it can be constant or non-constant with conversion of monomer in batchwise reaction. As mentioned before, chainwise polymerization reactions are complex reactions consisting of initiation, propagation, termination and transfer reactions. All of the reactions are running simultaneously. The molecular weight of polymers formed during chainwise polymerization can remain constant or decrease or increse with conversion of monomer. This depends on the contribution of each single reaction. In case of a free radical polymerization run in a batch reactor at constant temperature the molecular weight remains constant with conversion if chain transfer reactions play a dominant role. If not, it will fall with conversion due to decreasing concentration of monomer. The same is true for coordination polymerization. In case of living polymerization the molecular weight of polymer formed is increasing with conversion in any case since no termination and transfer reactions are present in the reacting system. The molar concentration of polymer molecules of chainwise polymerization reactions also depends on the kind of polymerization. It remains constant with conversion for a living polymerization and is increasing for free radical and coordination polymerization since at any time new polymer molecules are formed.

The situation can be quite different in the case of stepwise polymerization reactions. Here the polymer growth reaction takes place by stepwise reactions of bifunctional molecules (Pn and Pm in Tab 1.2). The molecules can be monomers,

2 oligomers, or polymers depending on the degree of conversion. At the beginning of reaction only monomer molecules are present in the reaction mixture. With increasing conversion monomer concentration is rapidly falling and oligomers are formed. High molecular weight polymers are only formed at very high conversion of functional groups (above 99 %). The polymer growth reaction is a typical condensation reaction like the reaction of carboxylic groups with hydroxylic groups; forming ester groups and water. This kind of polycondensation reactions are in general reversible reactions, which have to be shifted to the right side of the equilibrium for high conversions. The active sites are the functional groups of the reacting molecules, with an infinite life time on its own. The concentration of functional groups is decreasing with increasing conversion. In an ideal case there are no other side reactions in stepwise polymerization reactions beside growth reaction. The avarage molecular weight of the condensation products increases with conversion of functional groups. First there is a very slow increase, then at high conversion there is a very strong increase in molecular weight. High molecular weight polycondensates can only be achieved at very high conversions. The molar concentration of polymer molecules decreases with conversion. At a conversion of 100% only one huge macromolecule should be present in the reaction volume.

The most industrially important polymers listed in Tab. 1.1 are produced by free radical polymerization (ethylene, vinylchloride, styrene, butadiene) by coordination polymerization (ethylene, propylene, butadiene) and by condensation or addition polymerization (polyesters, polyurethanes, formaldehyde resins).

1.3 Methods of Polymerization Polymerization reactions are highly exothermic reactions, producing a large amount of heat that has to be removed from the reaction medium. Polymerization reactions are further characterized by a very strong increase of viscosity of the reaction mixture with conversion, which can cause problems with mixing, heat removal, and transport of the reaction mixture. Another characteristic feature of polymerization reactions is the sensitivity of the reaction rate to very small amounts of impurities, such as free radical scavangers or catalyst poisons. These impurities have to be removed by very intensive cleaning of the reactants and solvents before starting the reaction.

Polymerization reactions can be performed in very different ways. In Tab. 1.3 different methods of performing polymerization reactions are listed. The reaction medium can either be a homogeneous or a heterogeneous system. Heterogeneous systems have the great advantage of having a much lower viscosity than the corresponding homogeneous system at equivalent conditions. Due to this advantage mixing, heat removal, and transport is not as much of a problem as it is in the case of homogeneous systems. The decision of which

3 process is to be used for performing a polymerization reaction does not only depend on the engineering aspects named, but also on the properties of the polymer to be produced and the method of polymer processing for manufacturing of the polymeric material. For example polyethylene can be produced by free radical polymerization in bulk phase at super critical conditions (low density polyethylene for films), but also by coordination polymerization in a slurry or gas phase (high density polyethylene for pipes and containers).

1.4. Types of Polymerization Reactors Major polymerization reactors used in industry are represented schematically in Fig. 1.1. The type of reactor used depends mainly on the method of polymerization. Most polymerization reactions are run in liquid phase, with some in gas phase. The most widely used reactor for liquid phase polymerization is the stirred tank reactor. It is used for batch, semibatch and continuous processes. In case of continuous processes the stirred tank reactor is used as a single reactor or as a cascade of stirred tank reactors. A single stirred tank reactor has a very broad residence time distribution while a cascade of stirred tank reactors is characterized by a more narrow residence time distribution. This may affect performance and selectivity of the reactor. In the case of gas phase polymerization reactions the fluidized bed reactor is used in general. It is run continuously and has a very broad residence time distribution. Tubular reactors are used for polymerization in liquid phase. In general they are characterized by a rather narrow residence time distribution. The mode of operation of a reactor or process is determined mainly by the amount of polymer which has to be produced. Commodity polymers are produced in continuous processes. Speci- ality polymers are mostly produced batch- or semibatch-wise.

1.5 General References - "Comprehensive Polymer Science“, 7 Volumes, G. Allen, J. Bevington (Eds.), Pergamon Press, 1989 - “Encyclopedia of Polymer Science and Engineering“, 19 Volumes, H.F. Mark, N.M. Bikales, C.G. Overberger, G. Menges (Eds.), John Wiley and Sons, 1990 - “Ullmann´s Encyclopedia of Industrial Chemistry“, Vol. A 20, A 21, A 22, A 23, VCH, 1992 - A. Rudin: “The Elements of Polymer Science and Engineering“, Academic Press, 1982 - J.A. Biesenberger, D.H. Sebastian: “Principles of Polymerization Enginee- ring“, John Wiley and Sons, 1983

4 - G. Odian: “Principles of Polymerization“, John Wiley and Sons, 1991 - N.A. Dotson, R. Galván, R.L. Laurence, M. Tirrell: “Polymerization Process Modelling“, VCH Publishers, 1996 - K.H. Reichert, H.-U. Moritz: “Polymer Reaction Engineering“, in Compre- hensive Polymer Science, Vol. 3, p. 327, Pergamon Press, 1989 - H.G. Elias: “Plastics, General Survey“, in Ullmanns´s Encyclopedia of Industrial Chemistry, Vol. A 20, p. 543, VCH, 1992 - A. Hamielec, H. Tobita: “Polymerization Processes“, in Ullmann´s Ency- clopedia of Industrial Chemistry, Vol. A 21, p. 305, VCH, 1992

5 1.6 Tables and Figures

Thermoplastics Thermosets Elastomers - Polyethylene - Phenol-Formaldehyde- - Styrene-Butadiene- - Polypropylene Resins Copolymers - Poly(vinyl chloride) - Polyurethanes - Polybutadiene - Polystyrene and Styrenics - Urea-Formaldehyde- - Poly(ethylene terephthalate) Resins Tab. 1.1: Classification and examples of major synthetic polymers

Chainwise Stepwise Polymerization Polymerization   P  P  P  X Polymer growth reaction Pn  M  Pn1 n m nm Free radicals Active sites Organometallics Functional groups Ions Free radical polymerization (FRP) Specific name of Coordination polymeri- Polycondensation or polymerization reaction zation (CP) Polyaddition Living polymerization (LP) Short for FRP and CP Long Life time of active sites Long for LP Low and nearly constant with conversion for FRP According to monomer Concentration of and LP concentration and decrea- active sites Low and non-constant sing with conversion with conversion for CP Initiation (FRP, CP, LP) Other reactions besides Termination (FRP, CP) None (ideal case) growth reaction Transfer reaction (FRP,CP) Nearly constant for FRP Molecular weight and CP Increasing with conversion Increasing for LP

Polymer concentration Constant for LP, increa- Decreasing with conversion sing for FRP and CP Tab. 1.2: Types of polymerization reactions and characteristic features

6 Polymerization of monomer in presence of a Solution Polymerization solvent Homogeneous system

Polymerization of monomer in absence of a Bulk Polymerization solvent (only monomer) Homogeneous or heterogeneous system

Polymerization of liquid monomer droplets dis- Suspension Polymerization persed in a liquid phase (water) using oil soluble initiators and water soluble surfactants

Polymerization of monomer in latex particles Emulsion Polymerization dispersed in a liquid phase (water) using water soluble initiators and surfactants

Polymerization of gaseous monomer in catalyst/ Slurry Polymerization polymer particles dispersed in a liquid phase (gas/solid/liquid system)

Polymerization of gaseous monomer in catalyst/ Gas Phase Polymerization polymer particles dispersed in gas phase

Precipitation Polymerization of monomer in solution and Polymerization precipitation of the polymer formed during polymerization

Tab. 1.3: Methods of polymerization

Fig. 1.1: Schematic representation of major types of polymerization reactors with broad and narrow residence time distribution

8 2. KINETICS OF POLYMERIZATION AND MOLECULAR WEIGHT OF POLYMERS

2.1 Free Radical Polymerization in Solution

Rate and Conversion of Polymerization Free radical polymerization is still the most widely used type of polymerization for polymer production. It can be run in solution, bulk, suspension, and emulsion. The reaction scheme of a typical free radical polymerization reaction is shown in Tab.2.1. The main steps of the reaction are initiation of a chain, propagation of the chain, termination of the chain, and different kinds of transfer reactions. In the initiation reaction the initiator decomposes into two primary radicals which can start a growing chain by addition of a monomer like ethylene, vinyl chloride or styrene. The additon of the first monomer molecule to a primary radical can in general not be distinguished from the addition of the second or third monomer molecule, at least from a kinetic point of view. The initiation reaction is followed by the chain propagation reaction. In this reaction many monomer molecules are added to the growing chain. The number of added monomer molecules is in the order of 1000. Molecules with free radical character are very reactive species which also can react with each other. In this case the chain propagation reaction is terminated. Two different kinds of chain termination reactions have to be considered, with chain termination by recombination being more common than termination by disproportionation. Both ways of termination can happen simultaneously. The result of termination by recombination is the formation of one macromolecule with a much larger chain length than that of the two original molecules. Termination by disproportionation leads to formation of two macromolecules of the same chain length as the original active molecules. One of the two molecules formed has a double bond at the end of the chain and is able to act as a comonomer forming branched macro molecules. Atom abstraction reactions like abstraction of hydrogen or halogen atoms in free radical polymerization reactions are called chain transfer reactions. The atom donor molecule itself (monomer, polymer, solvent, transfer agent) becomes a radical, and the kinetic chain is not terminated if the new radical formed can add further monomer molecules. In this case chain transfer reactions do not affect the kinetics, but only the chain length of the polymer molecules. To control the molecular weight of polymers effective chain transfer agents like mercaptanes are added to the reaction medium.

For a free radical polymerization reaction the following kinetic equations can be derived by making some assumptions. One important assumtion is the quasi- stationary state assumptions for concentration of free radicals.

9 dC R   M  k C1/2 C [ mol /(l  s )] dt I M

1/2  f kd   E  Ed Et k  k p   ; k  A exp  ; E  E p    kt   R T  2 2

The overall rate of polymerization R is first order with respect to monomer concentration CM and one-half order with respect to the initiator concentration CI. The overall rate constant k does not only depend on rate constant of chain propagation, initiator decomposition, and chain termination but also on radical efficiency factor f which is a probability factor for a primary radical to react with monomer rather than to react with other radicals and become inefficient. To express the conversion of monomer as a function of time the differential rate equation has to be integrated. Calling CM,0 and CI,0 the initial monomer and initiator concentration and regarding CI,0 to be constant with time, the result is :

CM 1/2 ln   k CI,0 t CM,0

If conversion of monomer X is of interest the corresponding equations are:

dX  k C1/2 1  X  dt I,0

1/2 X  1  exp  k CI,0 t

If concentration of initiator is not constant with time, and the initiator decomposition is a first order reaction, the following equations have to be considered:

10 dX 1/2  kd   k CI,0 exp  t  1  X  dt  2 

 1/2  2 k CI,0   kd   X  1  exp  exp  t  1        kd   2  

The maximum conversion of monomer which can be achieved depends on the type and concentration of initiator used. If the initiator is decomposing too fast at reaction conditions than the polymerization reaction stops at a conversion smaller than 1. This kind of polymerization is called dead-end polymerization. The maximum conversion of monomer can be calculated by the following equation:

 2 k C1/2  X  1  exp  I,0  max    kd 

For calculation of rate or conversion of free radical polymerization as a function of time the rate constants are needed. In Tab. 2.2 some suggested values of rate constants and corresponding activation energies are given. They can strongly differ and depend on the kind of monomer, initiator, or solvent used. The numerical value of the chain transfer constant cited in Tab. 2.2 refers to transfer reactions of monomer, solvent, or polymer but not of transfer agents. Active transfer agents have much larger rate constants.

In Fig. 2.1 the calculated conversion and rate of a typical free radical polymerization are shown.

Molecular Weight of Polymer

The average molecular weight Mn (number average) of polymers formed by free radical polymerization is given by:

Mn  MM Pn

The average degree of polymerization Pn (number average) does depend on the kinetic chain length .

Pn  for chain termination by disproportionation

Pn  2 for chain termination by recombination

The kinetic chain length for polymerization without any chain transfer reaction can be expresed as:

R k p C  CM k C   p  P  p M 2 Rt 2 k C 2 kt C  t P P

1/2  f k C  with C   d I  P    kt  at steady state the kinetic chain length is given by: k C   p M 1/2 2  f kt kd CI 

With this equation the instanteneous average degree of polymerization is:

k C p M Pn = 1/2 for termination by disproportionation 2  f kt kd CI 

k C p M Pn = 1/2 for termination by recombination  f kt kd CI 

For free radical polymerization with chain transfer to a transfer agent the instanteneous degree of polymerization (number average) is given by:

Rp Pn  Rt  Rtr

Equation of Mayo with P = 1 Rt Rtr 1 Rtr n,0     P = 2 for termination by P R R P R n,0 n p p n,0 p disproportionation and combination

1 2  f k k C 1/2 k C d t I  tr T P = for termination by disproportionation n k p CM k p CM

( f k k C )1/2 k C = t d I  tr T for termination by recombination k C k C p M p M

In Fig. 2.2 the cumulative molecular weights of polymers produced by a free radical polymerization consisting of initiation, propagation, and termination by disproportionation is given. The decay of molecular weight is caused by the decay of monomer concentration with time of reaction.

Gel Effect, Glass Effect and Cage Effect In free radical polymerization effects of autoacceleration can be observed especially in systems with high monomer concentration. In Fig. 2.3 conversion- time plots of methyl methacrylate polymerization in benzene with different monomer concentrations are shown. The temperature was kept constant at 50 0 C. The higher the monomer concentration the stronger the effect of autoacceleration. The same effect can be seen also in other chemical systems. In Fig. 2.4 the rate and instantaneous degree of polymerization (number average) is shown for polymerization of styrene at 50 0C and different initiator concentrations. It can be seen that not only rate of polymerization but also degree of polymerization increases strongly at the onset of the gel effect. The beginning and the intensity of the autoacceleration effect is dependent on the type of monomer, initiator and solvent, but also on temperature and concentration of reactants. Since this kind of effect is observed mainly in systems, which are gel- like the effect is called the gel effect. The gel effect in free radical polymerization is caused by an increase in viscosity of the reaction medium. The viscosity particularly affects the rate of chain termination reaction. The higher the viscosity the lower the rate of termination reaction. The lower the rate of termination reaction the higher the concentration of free radicals, and subsequently the higher the rate of polymerization at steady state. This is due to the fact that in highly viscous systems bimolecular reactions of macromolecules become diffusion controlled. In this case the rate constant of the termination reaction is inversely proportional to viscosity of reaction medium. In literature many models have been published to describe the gel effect of free radical polymerization. One very simple but useful model is that of A.Hamielec. He developed empirical correlations that describe the decay of the rate constant of the chain termination reaction with respect to conversion of

13 monomer. In Tab. 2.3 the correlations of three different monomers are listed. They are valid for bulk polymerization in the temperature range cited. The graphical presentation of the correlations is shown in Fig. 2.5. The decay of termination rate constant with conversion is strongest in the case of methyl methacrylate polymerization and takes place from the very beginning of the polymerization. This strong decrease of the termination rate constant has two effects: it increases the rate of polymerization and the degree of polymerization according to:

1/2  f kd CI  R  k C  C with C    p p P M P    kt 

k C P  p M for termination by recombination and no transfer n 1/2  f kt kd CI  reaction.

With increasing viscosity of the reaction medium not only the rate of termination reaction but also the rate of propagation reaction can be affected. In this case the effect will be smaller since the reaction takes place between a macromolecule and a micromolecule, which is not hindered in diffusion as strongly as a macromolecule. If the reaction mixture becomes solid (glassy state) at a certain conversion, the polymerization reaction stops because monomer molecules can no longer diffuse to the macromolecular radicals and react with them. This effect is called the glass effect. As can be seen in Fig. 2.6 in the case of free radical polymerization of methyl methacrylate in bulk at 22.5 0C the propagation rate constant is beginning to fall at a conversion of about 50% and becomes zero at a conversion of 80%. At this conversion the polymerization stops. It can be started again if the reaction temperature is increased. Thus the temperature of reaction and glass transition temperature of reaction mixture play an important part in the maximum conversion of a reaction. If a conversion of one is to be reached the reaction temperature has to be larger than the glass transition temperature of the polymer to be produced. According to Buche the maximum volume fraction of polymer P,max at a given reaction temperature T can be calculated by using the following equation : 1   P T  Tg,P   ΦP,max  1   for Tg,M  T  Tg,P  M T  Tg,M  P and M are the thermal expansion coefficients of polymer and monomer. Tg,P and Tg,M are the glass transition temperatures of polymer and monomer. The equation is valid for polymerization in bulk, suspension or emulsion. The corresponding maximum conversion of polymerization is:

1 X  max  (T  T )  1  P g ,P M M (T  Tg ,M )P with M and P being the density of monomer and polymer at temperature T.

The correlation of maximum conversion and reaction temperature is shown in Fig. 2.7 in the case of polymerization of styrene in bulk phase.

Not only rate constants can depend on viscosity of reaction medium, but also the radical efficiency factor can be influenced by viscosity. If an initiator molecule is decomposing within a cage of solvent molecules, the primary radicals can diffuse out of the cage and start a polymer chain or they can react with each other and be lost for polymerization reactions. The diffusion of the primary radicals out of the cage will depend on the viscosity of the medium. The higher the viscosity the lower the diffusion coefficient, and subsequently the radical efficiency factor. This effect is called the cage effect. Tefera Shibeshi developed a correlation that describes the effect of conversion on radical efficiency factor in the case of free radical polymerization in bulk phase:

2 f f  0 1  exp g X 

The correlation is shown in Fig. 2.8 for methyl methacrylate polymerization with azo-bis-isobutyronitrile at different temperatures. The fitting factor g is in the order of 0.4.

Effect of Volume Contraction In general polymerization reactions in liquid phase run under volume contraction conditions, because the polymer has a larger density than the monomer. The volume contraction with conversion can be expressed by:

VR  VR,0 1  X 

 with   M  1 P

15 with this correlation the rate of polymerization is:

d X 1/2  kd  1  X  k CI,0 exp  t  d t  2  1   X 1/2

The values of  are on the order of – 0.1 to – 0.3. The effect of volume contraction on rate of polymerization is small and can usually be neglected.

Effect of Inhibitors or Retarders In general chain transfer reactions can be represented by the following reaction steps:  ktr  Pn  T  Pn  T

 kp  T  M  P1

If the numerical value of kp is zero than the transfer agent T is called an inhibitor. If kp is smaller than the propagation rate constant kp than the transfer agent is called a retarder. The effect of inhibitors and retarders on the kinetics of free radical polymerization is shown in Fig. 2.9. Hydroquinone and diphenylamine are chemicals which are effective inhibitors even at concentrations of 10 to 100 ppm. Before a polymerization reaction is started, inhibitors have to be removed from the reaction mixture or an excess of initiator must be used to start the reaction. Dissolved oxygen in a reaction mixture can act as an effective inhibitor and has to be removed carefully by purging with nitrogen or applying vacuum to the system. Variable induction periods can be the result of different concentrations of inhibitor left within the reaction mixture. Retarders are for example nitrobenzene compounds.

2.2 Free Radical Polymerization in Emulsion Emulsion polymerization is one of the most versatile processes of polymerization. For running an emulsion polymerization a suitable surfactant has to be used. The concentration of the surfactant in water must be larger than the critical micell concentration of the surfactant in order to form a large number of micelles, in which the polymerization is takes place. In general the concentration of surfactant is in the order of 0.5 to 5 w% of the amount of monomer. At this concentration the number of micelles is about 1021 micelles per liter of solution. Micelles are in general spherical particles with a diameter of 3 to 5 nm and are formed by 50 to 100 molecules of the surfactant. Next the

16 monomer is added to the solution of surfactant under vigorous stirring, thereby forming spherical monomer droplets with a diameter of 1 to 10 m. The volume ratio of monomer to water is varying from 0,5 to 1. A certain amount of monomer is dissolves into the micells according to the swelling equilibrium of the system. By addition of a water soluble initiator the polymerization is started. 0 For polymerization, at temperatures of 50 to 70 C peroxides like K2S208 are used as initiators. For polymerization at lower temperatures (~ 50C) redox initiators like cumyl hydroperoxide and FeSO4 are added. The amount of initiator added is about 0.1 to 0.5 w% of monomer. The initiator molecules in the water phase decompose into primary radicals, which enter predominantly into micellar particles, where they start the polymerization of the monomer, forming latex particles. At the end of the polymerization reaction a latex is formed containing spherical polymer particles of about 100 nm in diameter and the number of particles per liter of emulsion is approximately 1017. If the polymerization is run batchwise at constant temperature, the rate of reaction is shown in Fig. 2.10. The diagram shown is an idealistic representation. This kind of behaviour can be observed when the monomer is completely insoluble in water phase. If the monomer is slightly soluble bell-shaped curvatures are observed. In any case, three different periods of polymerization can be seen. There is an increase and a decrease in the rate of reaction and in between there is a period of nearly constant rate. Intensive work in modelling the kinetics of emulsion polymerization has been going on since 1940. Pioneers in this field are Fikentscher and Harkins in Europe and Smith and Ewart in USA. According to their fundamental studies the following model has been established:

In period 1 (polymer particle formation) polymer particles are formed by polymerization of monomer within the micellar particles. The formation of polymer particles is going on as long as micellar particles are present in the reaction medium. As soon as concentration of surfactant drops below the critical micell concentration the particle formation period is ending. This period is in general the case at conversions of about 10 %. In period 2 (polymer particle growth) the number of polymer particles and the concentration of monomer and radicals within these particles are constant. This is due to the adjusted equilibria of monomer between the three phases of the system and because of the quasi-steady-state of radical concentration in the particles. Period 2 ends, when no more monomer droplets are present in the reacting system. This happens at a conversion of 30 to 70 %. In period 3 (monomer depletion) the concentration of monomer in the polymer particles is decreasing because it is consumed by polymerization and transportation of monomer into polymer particles does not take place any longer since no monomer particles are present any more in the dispersion. Due to decreasing monomer concentration the rate of reaction falls correspondingly.

The rate of emulsion polymerization is given by :

n Rp  k p CM N in mol /l  s N A

with N being the number of latex particles per liter of emulsion. The number of radicals per latex particle is n. NA is the number of Avogadro.

Monomer concentration in polymer particles The concentration of monomer in polymer particles is determined by the free enthalpy of interfacial tension and by the free enthalpy of swelling of the particles. At equilibrium the following equation (Morton-Kaizerman-Altier) is applicable: 2VM  2   R T [ln1-P  P  P ] rp

3 with VM : Molar volume of monomer [m / mol]  : Interfacial tension [N / m]

rp : Radius of latex particle [m]

P : Volume fraction of polymer

(1-P) : Volume fraction of monomer  : Flory-Huggins interaction parameter

Swelling of polymer particles by monomer is increasing with decreasing interfacial tension, increasing radius of particles and decreasing the interaction parameter, which is equivalent to increasing solubility of polymer in its monomer. In period 2 of emulsion polymerization the interfacial tension and radius of particles are increasing simultaneously. Therefore monomer concentration remains constant as long as monomer droplets are present in the system. In Tab. 2.4 monomer concentration at equilibrium is given for different monomers. The concentration in monomer droplets is on the order of 9 mol/l.

Number of radicals in polymer particles A polymer particle may gain a free radical by absorbing it from the water phase. A particle may lose a radical by desorbing it into the water phase, or radicals inside the particle are lost by radical termination reactions. Taking these three processes (entry, exit, termination) into account, Smith and Ewart developed a

18 radical balance equation of the polymerizing particles. Stockmeyer and O´Toole have solved this balance equation. The result is shown in Fig. 2.11. The average number of radicals per particle depends on the ratios of relative rates of radical entry, radical exit, and radical termination. In general the rate of exit is small compared to the rate of entry and the rate of entry is small compared to the rate of termination. In this case the average number of free radicals per particle is 0.5. On average there is one or no radical inside a particle. But as can be seen from Fig. 2.11 the number of radicals per latex particle can also be larger or smaller than 0.5. Numbers much larger than 0,5 are to be expected if the gel effect is present.

Number of polymer particles Polymer particles can be formed in different ways.

1. By entry of a radical into a micell. The radical startsthe polymerization of the monomer which is present in the micell according to the adjusted swelling equilibrium. 2. A primary radical can start the polymerization of monomer in the water phase since monomer is also present in water to some extent. When the growing oligo-radical reaches a certain chain length it may precipitate from the water phase and form the nucleus for a polymer particle. 3. Primary radicals may also enter into monomer droplets and start polymerization there. Monomer droplets will be transformed into polymer particles.

In the case of an ideal emulsion polymerization the most probable way of forming polymer particles is the entry of primary radicals into micells and polymerization of monomer within micells, which then become polymer particles. For this case of particle formation Smith and Ewart have developed an equation, which makes it possible to calculate the number of polymer particle at the end of the particle formation period:

2 / 5  Rd  3 / 5 3 N  0,53  AS CS  [1/m ]   

3 with Rd  2 f kd CI 1M N A [1/m  s] k   n   p M M [m3/s] 1 M  P N A

2 3 AS CS : Specific interfacial area of surfactant [m /m ]

The end of period 1 is reached when the interfacial area of all polymer particles formed corresponds to the area that can be covered by a monolayer of surfactant molecules. Beyond this point no further polymer particles can be stabilized by surfactant because there is no more free surfactant available in the system. In the case that all primary radicals formed do enter into micells and not into polymer particles, then the rate of particle formation corresponds to rate of free radical formation. This balance leads to the number of polymer particles according to the equation of Smith and Ewart. The rate of radical formation is related to the water phase with a volume fraction of (1-M). M is the volume fraction of monomer. The factor 2f for rate of radical formation should be considered only in the case of initiator decomposition into two radicals. If redox initiators are used for emulsion polymerization then only one primary radical is formed per step of reaction and the factor 2f is not applicable. The rate of volume growth of polymer particles  is considered to be constant since the number of radicals per particle are assumed to be constant and equal to 0.5. M and P are the density of monomer and polymer. The specific interfacial area of surfactant is given by the concentration of surfactant and the specific surface area AS of surfactant. In Fig. 2.12 a schematic of monomer concentration, of number of polymer particles and of free radicals during the three periods of emulsion polymerization can be seen. These parameters determine the rate of polymerization, the molecular weight of polymer and the size of polymer particles.

The rate of polymerization is: n N Rp  k p CM N A

2/5 3/ 5 with N ~ CI CS in period 2 of polymerization

2/5 3/ 5 then Rp ~ CI CS CM

The degree of polymerization is:

N Pn  k p CM   k p CM Rd

2/5 3/ 5 with N ~ CI CS and

5/ 5 Rd ~ CI in period 2 of polymerization

3/ 5 3/ 5 then Pn ~ CI CS CM

The diameter of polymer particle is:

 X 1    6   6 3  1   X  d  3 P  p  N  N

2 / 5 3/ 5 with N ~ CI CS in period 2 of polymerization

3 2 / 5 3/ 5 then d p ~ CI CS

The rate of emulsion polymerization can be influenced by the concentration of surfactant and initiator and by temperature. An increase in concentration and temperature causes an increase in rate.

The molecular weight of the polymer does depend on concentration of initiator and surfactant and on temperature. An increase of initiator concentration and temperature will lower the molecular weight. An increase in surfactant concentration will increase the molecular weight. These dependencies count only for emulsion polymerizations, which are free of transfer reactions. In this case the molecular weight is increasing in period 1, it is constant in period 2 and it is falling in period 3. The degree of polymerization (number average) in the case of an ideal emulsion polymerization corresponds to the kinetic chain length, since termination reactions by recombination of macro radicals do not take places. The predominat mode of termination are recombination reactions between macro and primary radicals, which enter the polymer particles. The average life time of a growing radical chain within a polymer particle is given by the ratio of the number of polymer particles to the rate of radical formation in the water phase. The rate of radical generation is proportional to rate of radical entering into polymer particles. The average life time of a polymerizing radical in a polymer particle is on the order of 10 seconds. If a primary radical is entering a polymer particle it will start a chain. The chain will grow until the next primary radical is entering the particle. The termination reaction happens immediately after entry of the radical. Then a period of no polymerization will follow, which is also in the order of 10 seconds. These successive periods of

21 activity and non-activity of a single polymer particle will take place during the whole course of emulsion polymerization. Since the average life time of a growing radical is much longer in emulsion polymerization than in solution or bulk polymerization the resulting chain length of polymer molecules will also be much larger at comparable conditions and if transfer reactions are not dominant.

The molecular weight distribution in period 1 and 2 of emulsion polymerization is rather narrow since concentration of monomer is constant. In period 3 monomer concentration decreases and molecular weight distribution broadens. Branching and crosslinking reactions increase with increasing polymer concentration. In emulsion polymerization polymer concentration in polymer particles is relatively high from the very beginning of polymerization due to the adjusted swelling equilibrium. This is why in emulsion polymerization the polymers formed are in general more branched or crosslinked than in solution or bulk polymerization. This is also one of the reasons why emulsion polymerization is often terminated at a conversion of about 70% if branched or crosslinked products are not wanted.

The polymer particle size in emulsion polymerization increases in period 2 and 3 since the number of particles is constant and conversion increases. The size of particles can be influenced by the initial concentration of initiator and surfactant. The higher the concentration the smaller the size. The particle size distribution is influenced by the ratio of conversion in period 1 to total conversion. The smaller this ratio the more narrow is the particle size distribution. Monodispersed polymer particles can be produced in emulsion polymerization by avoiding particle formation during reaction. This can be realized by running the polymerization in presence of a seed. The seed is a prepolymerized latex with no micelles present. To avoid agglomeration of particles surfactant has to be added, but its concentration should not exceed critical micell concentration.

In Tab. 2.5 the effect of concentration of initiator and surfactant as well as temperature and volume ratio of monomer to water is shown. These effects can only be seen in the case of an ideal emulsion polymerization. Deviations do occur in the case of emulsion polymerization of monomers with a certain solubility in water and in the case of emulsion polymerization with a gel or glass effect.

2.3 Free Radical Copolymerization in Solution Free radical copolymerization reactions are widely used in industry to produce copolymers with specific properties. If a solution of monomer M1 and M2 is polymerized by means of an initiator, the following reactions have to be considered: Initiation, propagation, termination and transfer reactions. The primary radicals formed may react with either of the two monomers forming   species P1 and P2 , which are radicals with monomer M1 and M2 at the end of the chain. If the reactivity of the radicals does depend only on the type of monomer at the end of the chain, then the following four different chain propagation reactions have to be concidered:

P*  M P* R k C C 1 1 1 p11 p11 P1 M 1 * * P1  M 2 P2 Rp12 k p12 C  CM 2 P 1 P*  M P* R k C C 2 2 2 p22 p22 P 2 M 2 P*  M P* R k C C 2 1 1 p21 p21 P 2 M 1

The rate of polymerization of monomer M1 and M2 is:

 dCM 1 R R ;  dCM 2 R R dt p11 p21 dt p22 p12

At steady state conditions the rate of initiation is equal to rate of termination:

R  2 k C 2  k C 2  k C C i  t11 P1 t22 P 2 t12 P1 P 2 

Of special interest in copolymerization is the cross termination reaction   between two different radicals P1 and P2 . Taking Bodenstein´s rule

Rp12 = Rp21 into account the overall rate of monomer consumption can be expressed by:

dC  C   M 1 M 2  R  R  2 k C C dt p11 p22 p12 P1 M 2

  Replacing radical concentration P1 and P2 by relevant equations, the so called Melville equation of copolymerization reads:

 d( CM 1 CM 2 )  dt  2 2  1 2  r1CM 1 2CM 1CM 2 r 2CM 2  Ri    2 2 2 2 1 2  r  C 2 2r r   C C r  C 2   1 1 M 1 1 2 1 2 M 1 M 2 2 2 M 2 

with 1 / 2 1 / 2 kt11 kt22 k p11 k p22 1  ;  2  ; r 1 ; r2  k p11 k p22 k p12 k p21

k   t12 , R  2 f k C 1/2 i d I 2 kt11 kt22 

The parameter  characterizes the rate constant of cross-termination reaction with respect to the geometric mean value of the rate constants of termination reactions of homopolymerizations. Statistically,  is expected to equal unity. Measured values of  however are frequently greater than one. These devations are ascribed to polar effects, which favor cross-termination over homotermination. The equation of Melville is based on the assumption that termination reactions are not controlled by diffusion processes. This may be correct at low conversion, but not for high conversions and high viscosity media. Furthermore, it was found for some systems, that  is a function of monomer feed composition. This finding was handled by Atherton and North using a single termination rate constant and assuming, that the value of it depends on instantaneous composition of copolymer formed. In Fig. 2.13 the initial rate of copolymerization of styrene and methyl methacrylate is shown as function of mole fraction of styrene f1 in monomer feed. The experimental results (dots) are best fitted with a  value of 13 which in this case does not depend on composition of monomer feed. The  value is much larger than one, indicating a strong tendancy towards alternation copolymerization.

2.4 Coordination Polymerization in Gas Phase Models of Polymerization of Single Particles For coordination polymerization appropriate catalysts are necessary. Suitable catalysts are Ziegler-, Phillips-, or Metallocene-catalysts. In general, heteroge-

24 neous catalysts are used in industry. They are made by fixation of catalytic active metal complexes onto the surface of certain supports. Coordination polymerization in gas phase is run in fluidized bed reactors by using catalyst particles of less than 100 m in diameter and gaseous monomers. During the course of polymerization the catalyst particles are fragmented by the polymer formed within the pores of the catalyst. The particles grow in size during the course of polymerization and have in general the same shape as the originial catalyst particles if particle agglomeration can be avoided. For modelling the particle growth an appropriate model is necesarry. Many different particle models have been published in literature. The most widely used models are the so called “multigrain model“ and the “polymeric flow model“. Both models are represented schematically in Fig. 2.14. In the case of the multigrain model it is assumed that in the beginning of polymerization there is an extremely fast fragmentation of the catalyst particles and polymerization takes place on the surface of the fragments, forming micro particles with a core of catalyst and a shell of polymer. The thickness of the shell grows during the course of polymerization and thereby also the size of the reacting particle. The polymer particles produced are assumed to be very porous. In the case of the polymeric flow model it is assumed that fragmentation of catalyst particles is also a very fast process, but in this case nonporous particles are formed. It is assumed that the small catalyst fragments are well dispersed within the compact polymer particles, having a concentration gradient from particle center to particle surface. The concentration gradient is caused by the outward oriented flow of polymer, which is continuously formed by polymerization. Both models are frequently used for modelling of polymerization of olefins with heterogeneous catalysts.

Kinetics and Molecular Weight without Effect of Mass Transport In the case of chemical controlled rate of polymerization it is assumed,that mass transport of monomer into reacting particles does not play a major role. In Fig. 2.15 a typical rate-time diagram of coordination polymerization of butadiene with a heterogeneous Ziegler catalyst at constant pressure and temperature is shown. From this figure it can be seen that the kinetic feature of polymerization is characterized by periods of activation and deactivation. For modelling the kinetics of polymerization a simple but realistic scheme of reaction is necessary. For that purpose major information on polymerization reactions and polymer properties is needed. In the present case the following scheme of reaction is postulated based on experimental data:

25 ka  Activation reaction: Me  M  P1

 k p  Polymerization reaction: Pn  M  Pn  1

 kd Deactivation reaction: Pn  Pn  Me

According to this scheme it is postulated that only one type of active site P is formed by reaction of a transition metal complex Me with monomer M. Very often more than one kind of active site has to be considered. This strongly depends on the type of coordination catalyst used. Metallocene catalysts are said to be single site catalysts. Activation reactions can be a very complex process. Very often physical processes like catalyst fragmentation cause activation periods of a reaction. In propagation reactions the active sites add a large number of monomer molecules. It is assumed that rate constant kp does not depend on the length of a growing chain. The life time of active sites can differ strongly depending on type of catalyst used. Active sites of typical Ziegler catalysts have average life times in the order of seconds or minutes. The polymerization reaction as such is also a rather complex reaction and it consists of the following characteristic steps:

1. Controlled coordination of monomer to the catalytic active site. 2. Activation of coordinated monomer by formation of a four-membered ring. 3. Insertion of the activated monomer into the active metal-carbon bond.

As a consequence of these steps of reaction highly stereospecific polymer molecules can be formed. In general active sites of catalyst are deactivated either by typical poisons like water, acids, alcohols, and oxygen or by deactivation reactions of the active sites by themself. In the present reaction scheme a monomolecular self deactivation reaction of active sites is assumed. Very often also bimolecular self deactivation reactions are postulated especially in the case of homogeneous catalyst systems. Deactivation of catalyst can take place also by physical processes like formation of a compact polymer shell around active sites, which prevents the monomer from reaching the active sites. This will be the case if the polymer shell is made by highly crystalline material through which monomer can diffuse only very slowly. For modelling the kinetics of polymerization shown in Fig. 2.15 the material balances of the reactants have to be solved. It is assumed that the concentration of monomer in the polymer particles is constant during the course of polymerization at constant pressure and temperature. This is the case if mass transfer of monomer from the

26 gas phase into the polymer particles is fast compared to the polymerization reaction inside the particles. Monomer concentration in the particles is given by the concentration at equilibrium, which depends on monomer pressure and temperature: CM  CM ,equi  const.

In the case of butadiene/1,4-cis-polybutadiene the solubility diagram shown in Fig. 2.16 was determined by experiments (dots) and calculated (fitted) by the equation of Flory-Huggins (lines):

 p  ln  M   ln   1    1  2   M  M   M   pS,M 

 E  with   0 exp -   R T 

E   4000 J /mol

0  0,105

The correlation between monomer concentration and volume fraction of monomer is given by the following equation:

M M ,L CM  1 M M M

The mass balance of transition metal and active sites should not be expressed in terms of concentration but rather in terms of moles since the volume of reacting particles is increasing with reaction time and causes a decrease of concentration within the particles

d n Transition metal: Me   k C n d t a M Me

nMe  nMe ,0 exp - ka CM t

27 d n P Acitve sites : total  k C n  k n a M Me d P d t total

with these equations and the initial condition n t  0 0 the moles of P total active sites are given by:

k C n n  a M Me ,0  exp - k C t  exp - k t  P a M d total kd  ka CM

The overall rate of polymerization can be defined as:

k C n M p M P M total  g  R    nMe ,0 pM mol  bar  s respectively:

2 3,6 M M ka k p CM  kg  R  exp - ka cM t exp - kd t   pM kd  ka CM  mol  bar  h

This equation was fitted to the experimental results by using the parameters listed in Tab. 2.6. The result can be seen in Fig. 2.15. It should be mentioned that modelling should be done for a large range of reaction conditions (temperature, pressure, catalyst concentration) in order to cheque the quality of the model. For modelling molecular weight distribution of polymers formed commerical simulation programs can be used. One very potential simulation program is “Predici“ developed by M. Wulkow. With this program molecular weight distribution can be simulated if the polymerization scheme and the kinetic parameters are available. Using the postulated reaction scheme and the parameters of gas phase polymerization of butadiene one can see that the experimental molecular weight distribution can not be modeled accurately. The experimental molecular weights are much smaler than the calculated ones. Therefore transfer reactions have to be assumed in the present case of polymerization. One major type of transfer reaction in Ziegler-Natta polymeri-

28 zation is a chain transfer reaction to aluminium organyle, which is present in large excess compared to transition metal compound:

 ktr  Pn  Al  AlPn  P1 -4 -1 With this transfer reaction and a value of 610 s for ktr cAl the experimental molecular weights can be modeled as can be seen in Fig. 2.17. The other parameters are the same as those used for modelling the kinetics of polymerization (Tab. 2.6).

Kinetics and Molecular Weight Distribution with Effect of Mass Transport If the rate of polymerization of reacting particles is faster than rate of mass transport of monomer into the particles then concentration gradients of monomer within the particle will occur. These concentration gradients will effect the kinetics of polymerization and the molecular weight as well as molecular weight distribution of polymer formed. In Fig. 2.18 a schematic diagram of concentration gradients of monomer within and outside of the reacting particle is shown. The concentration gradient in the boundary layer around the particle is in the case of gases in general very small. The thickness of the boundary layer can be influenced by the intensity of mixing of the disperse system. A quick way of testing if concentration gradients are present in reacting particles or not is to vary the particle size of the catalyst or the loading of catalyst particles with active component. If the normalized rate of polymerization does depend on particle size or catalyst loading, then mass transport is affecting the kinetics and molecular weight and its distribution. For modelling kinetics of polymerization or molecular weight distributions of polymers in the case of reacting systems with mass transport effects appropriate material balances of chemical reaction and mass transport have to be considered. In the case of a polymerization scheme like that which was postulated before and with the assumption that the polymerizing particles are non-porous and spherical in shape, the following material balances are adequate:

Monomer : c  2c 2 c  M  D  M  M   R  2  t  r r r  with R  k c c  k c c a M Me p M P total and cM r  rParticle   cM ,equi

Polymer (convective flux): dV 4 r 2 M R P   M d r P

Transition metal:

c V c c M R Me   P Me  Me M  k c c 2 a M Me t 4 r r P

Active sites:

c c c M R P V P P M total   P total  total  k c c  k c 2 a M Me d P  t 4 r r  P total

Of special importance for modelling mass transport is the numerical value of the diffusion coefficient. Since the diffusion coefficient depends on many parameters, it is best determined by experiment at relevant conditions. In case of gas phase polymerization of butadiene the diffusion coefficient was determined by sorption experiments of butadiene in polybutadiene particles at different temperatures and pressures. The results are shown in Fig. 2.19. The polybutadiene particles were made by gas phase polymerization of butadiene and consists of 98% 1,4-cis-polybutadiene. The numerical values of diffusion coefficients measured are an indication that monomer transport may happen by molecular diffusion (D  10-11 m2/s) and by diffusion in micropores with diameter in the order of nanometers (D  10-9 m2/s). Using the set of parameters listed in Tab. 2.7 the experimental results of kinetics and molecular weight distribution can also be modeled very well. This is an indication that mass transport does not have a strong impact on kinetics and molecular weight distributions in the case of gas phase polymerization of butadiene at conditions studied. For reason of comparison of the two models (polymeric flow model with and without consideration of mass transport) the molecular weight distribution of polymer was calculated with the same set of kinetic parameters. The result is shown in Fig. 2.20. The molecular weight distribution is expressed by the polydispersion index, which is the ratio of weight average molecular weight to number average molecular weight. The kinetic parameters used for simulation are listed in Tab. 2.7. As can be seen from Fig. 2.20, the differences in dispersion index are relatively small and will not be seen by experimental studies. However, the effect of mass transport depends strongly on the numerical

30 values of kinetic parameters. In Fig. 2.21 the polydispersion index is shown in the case of a polymeric flow model with and without consideration of mass transport. The data used is listed in Tab. 2.8. In this case larger values of ka, kp and ktr  cAl were used. Large differences of polydispersion indices can be observed. The effect of mass transport is evident. In Fig. 2.22 the kinetics of gas phase polymerization of butadiene is simulated by using three different particle models, but the same set of data. It is evident, that the model used has a very strong effect on the kinetic course of polymerization. The effect of mass transport is increasing from multi grain model to core shell model.

Effect of Heat Transport Polymerizations of olefins are strongly exothermic reactions. Heat of polymerization has to be removed out of the reacting particles. This will happen by heat conductivity through the reacting particles and by heat transfer from the particles to the surrounding gas phase. It has to be checked, which of the two processes is the rate determining step for heat removal. This can be done by looking at the heat conductivitiy of the polymer particle and the gas phase as well as at the characteristic length for heat transport. The conductivity of polymers is in the order of 0.2 W/(mK). The distance for heat transport is the radius of particle. Heat conductivity of monomer gases like olefines or butadiene is in the order of 0.02 W/(mK) and distance is given by the thickness of the boundary layer, which does depend on the relative velocity between particle and gas phase. In the case of non-moving particles, the thickness of the boundary layer will correspond to the radius of the particles. In this case heat transfer at the solid/gas interface will be the rate determining step. The balance of heat transport is then given by:

rP 2 H S  H R 3  r R rdr d T P   0 3 dt P c p,P rP

3 Nu  T  T   Gas P Gas 2 2P c p,P rP

3 T dr  P P rP dt

with Nu = 2 + 0,6 Re0,5 Pr0,33

h d Nu = P Gas

u d  Re = P Gas Gas

 c Pr = Gas p,Gas Gas

The equation of heat balance considers heat formation by polymerization and by monomer absorption. Heat removal is considered by heat transfer from the particle to the gas phase and by heat accumulation within the growing particle. In case of gas phase polymerization of butadiene at 1.6 bar and 50 0C with catalyst particles of 230 m in diameter, the increase of temperature of reacting particles (expressed by the difference between average temperature of particle and gas phase) is shown in Fig. 2.23 for two different Nusselt numbers. A Nusselt number of 2 means that the reacting particle is non-moving while a Nusselt number of 30 corresponds to heat transport within a stirred bed reactor. These simulations show that temperature increase in reacting particles is strongest at the beginning of polymerization and levels off at the end of polymerization. The increase of temperature depends on the size of catalyst particle. The larger the size of catalyst particles the larger the increase in temperature.

2.5 Coordination Polymerization in Liquid Phase Coordination polymerization in suspension is a widely used process for polymerization of ethylene and propylene. The gaseous monomers are dispersed into a liquid phase to form fine bubbles. Catalyst particles are also dispersed within the liquid phase. Monomer has to be transferred from the gas phase into the liquid phase and from liquid phase into solid phase. The solid phase in the beginning of the reaction is the catalyst particles, which in general are porous. The pores of the catalyst particles are filled with liquid phase. During the course of polymerization porous or non-porous polymer particles are formed. They contain the catalyst, which in general is fragmented into very fine particles. These catalyst fragments are distributed within the polymer particles. During polymerization concentration profiles of monomer within the three phase system can be present. Fig. 2.24 shows a schematic concentration profile of monomer

32 within the three phase system gas/liquid/solid. The boundary layers at the interphases are represented by dotted lines. In the present case it is assumed, that mass transport of monomer through a boundary layer on the gas side is fast compared to mass transport through the other two boundary layers of liquid phase. This means that there is no concentration gradient within this boundary layer. During the course of polymerization the solid phase is represented by the polymer particles, which can be porous or non-porous. If the polymerization reaction is faster than mass transport of monomer, concentration gradients of monomer will occur inside the polymer particles as indicated in the present case. Rate of mass transfer and polymerization of monomer can be expressed by the following equations:  Monomer transfer gas/liquid : R  kL a ( cM  cM ,L )

Monomer transfer liquid/solid : R  kS aS (cM ,L  cM ,S )

Polymerization in particles : R  k  f cMe cM ,S

Rates are related to volume of liquid phase (mol/ls).

At steady-state the rates of mass transfer and polymerization can be set equal. By elimination of cM,L and cM,S the following equation results :

c 1 1 1 M    R kL a kS aS k  f cMe

with aS  kcMe

 cM 1 1  1 1       R kL a cMe  kkS k f  

According to this equation the total resistance of the process is given by the sum of the three single resistances. If this model can be applied to coordination polymerization of olefin in suspension, then straight lines should result if  cM / R is plotted versus 1/cMe . This has been tested in case of polymerization of ethylene with a heterogeneous Ziegler catalyst dispersed in a liquid phase. The results are shown in Fig. 2.25. The polymerization was run in a bubble column reactor with a gas flow rate of 4.5 cm/s at different pressures and temperatures. Polymerization was started in presence of polyethylene powder. The concentration was 16 wt%. The rate of absorption of ethylene was measured continuously during reaction. The rate is falling with reaction time. In

33  Fig. 2.25 initial rates are used. cM is the saturation concentration of ethylene in liquid phase at conditions given. From the intercept of the straight lines of Fig. 2.25 the values of kL a can be taken. They are affected little by temperature and pressure, but strongly by flow rate of gas. Mass transfer coefficient kS can be calculated by using Sherwood correlations published in literature. In case of ethylene polymerization in a bubble column reactor the following resistances for mass transport and polymerization reaction were evaluated. The values are listed in Tab. 2.9. They depend as expected on the stage of polymerization. In the beginning of the reaction the resistances are almost the same, but as polymerization goes on the chemical reaction becomes more and more rate determining.

2.6 List of Symbols A Preexponential factor in Arrhenius equation, unit depends on order of reaction 2 AS Area covered by unit weight of surfactant, m / kmol a Specific interface, m2 / m3 C Concentration of chemicals, kmol / m3 cp Specific heat capacity, kJ / (kg  K) D Diffusion coefficient, m2 / s dP Diameter of particle, m E Activation energy, kJ / kmol f Efficiency factor of initiator or catalyst H Enthalpy, kJ / kmol h Heat transfer coefficient, kJ / (s  m2  K) k Rate constant of chemical reaction or mass transport, unit depends on order of reaction, for mass transport unit is m / s

Mn Molecular weight of polymer, number average, kg / kmol

Mw Molecular weight of polymer, weight average, kg / kmol

MM Molecular weight of monomer, kg / kmol N Number of latex particles per unit volume, 1 / m3

NA Number of Avogadro, 1 / kmol n Number of radicals per latex particle or number of moles, kmol

Pn Degree of polymerization of polymer, number average

Pw Degree of polymerization of polymer, weight average p Pressure, bar

34 R Rate of reaction, kmol / (s  m3) r Local position, m rP Radius of particle, m r1,r2 Parameter of copolymerization T Temperature, K

Tg Temperature of glass transition of polymer, K

TP Average temperature of particle, K

Tgas Temperature of gas phase, K t Time, s u Velocity, m / s V Volume, m3 3 VM Molar volume of monomer, m / kmol  3 VP Volumetric flux of polymer, m / s X Conversion of monomer

 Thermal expansion coefficient, 1 /K  Parameter of copolymerization  Volume contraction coefficient or catalyst effectiveness factor  Viscosity, Pa  s  Thermal heat conductivity, kJ / (s  m  K)  Kinetic chain length  Density, kg / m3  Interfacial tension, N / m  Life time, s  Volume fraction or parameter of copolymerization

2.7 References - “Comprehensive Chemical Kinetics“, C.H. Bamford, C.F.H. Tipper (Eds.), Vol. 14 A: Free-radical Polymerization and Vol. 15: Non-radical Poly- merization, Elsevier, 1976 - D.H. Napper, R.G. Gilbert: “Polymerization in Emulsion“, in Comprehensive Polymer Science, Vol. 4, Part II, p. 171, Pergamon Press, 1989 - A.E. Hamielec, I.F. Macgregor, A. Penlidis: “Copolymerization“ in Compre- hensive Polymer Science, Vol. 3, Part I, p. 17, Pergamon Press, 1989

35 - T.F. McKenna, J.B.P. Soares: “Single particle modelling for olefin polymerization on supported catalysts: A review and proposals for future development“, Chem. Eng. Sci., 57, 4131 – 4153 (2001) - R.A. Hutchinson, C.M. Chen, W.H. Ray: “Polymerization of Olefins Through Heterogeneous Catalysis. X. Modelling of Particle Growth and Morphology“, Journal of Applied Polymer Science, 44, 1389-1414 (1992) - S. Floyd, K.Y. Choi, T.W. Taylor, W.H. Ray: “Polymerization of Olefins through Heterogeneous Catalysis. V. Gas-Liquid Mass Transfer Limitations in Liquid Slurry Reactors“, Journal of Applied Polymer Science, 32, 5451- 5479 (1986) - W.R. Schmeal, J.R. Street: “Polymerization in Expanding Catalyst Particles“, Am. Inst. Chem.Eng.Journal, 17, 1188 (1971) - D. Sing, R.P. Merill: “Molecular Weight Distribution of Polyethylene Pro- duced by Ziegler-Natta-Catalyst“, Macromolecules, 4, 599 (1971) - L.H. Peebels: “Molecular Weight Distributions in Polymers“, John Wiley and Sons, 1971 - M. Wulkow: “The Simulation of Molecular Weight Distributions in Poly- reaction Kinetics by Discrete Galerkin Methods“, Macromol. Theory Simul., 5, 393-416 (1996)

2.8 Tables and Figures

Initiation

Initiator decomposition k I d  2R Initiation  k i  R  M  P1

 k p  P 1  M  P2

  Propagation P 2 M P3

  P n M Pn +1

Termination

Combination   kt,c Pn  Pm  Pnm Disproportionation   kt,d Pn  Pm  Pn Pm

Transfer Reactions

Monomer  ktr,m  Pn  M  Pn  M Polymer  ktr,p  Pn  Pm  Pn Pm Solvent  ktr,s  Transfer agent Pn  S  Pn  S

 ktr,t  Pn  T  Pn T

Tab. 2.1: Reaction scheme of free radical polymerization

5 kd  10 1/ s Ed  120 kJ / mol 3 k p  10 l /mol  s Ep  20 kJ / mol 7 kt  10 l /mol  s Et  10 kJ / mol 2 ktr  10 l /mol  s Etr  70 kJ / mol f  0.5

Tab. 2.2: Guide values of rate constants of free radical polymerization at 50 0C and activation energies 

Monomer Correlation Coefficients Valid for  k  2 B  41.54 0.1082TK Methyl Meth- t X  1 2  0  exp BX  CX  C  23.46 0.0785TK 40-90 C acrylate k 1 X   t  X 0  B  2.57 5.05 103 TK  kt  2 2 0 X  exp  BX  CX 2 DX 3 C  9.56 1.76 10 TK 50-200 C Styrene k 3  t  X 0 D  3.03 7.85 10 TK   B   0.4407  kt  0 Vinyl Acetate X  exp BX  CX 2 DX 3 C   6.7530 50 C k  t  X 0 D   0.3495  Tab. 2.3: Empirical correlations for modelling the gel effect in bulk polymerization of different monomers 

Monomer concentration mol/l Monomer polymer particle water Styrene 5.4 0.005 Butadiene 6.5 0.015 Vinyl chloride 6.0 0.11 Methyl methacrylate 7.0 0.15 Vinyl acetate 7.6 0.3

Tab. 2.4: Monomer concentration in latex particles and water phase at equilibrium and 500C

Effect on Number Rate Molecular Particle Particle

of of weight size size particles polymerization distribution Increase of

Concentration increase increase increase decrease broadening of surfactant

Concentration increase increase decrease decrease narrowing of initiator

Temperature increase increase decrease decrease narrowing

Volume ratio of monomer to no effect no effect no effect increase narrowing water  no transfer reactions present

Tab. 2.5: Effect of concentration, temperature and phase ratio on different parameters of emulsion polymerization

50 0C E / J  mol-1 -1 -1 -4 ka / lmol ·s 8.16  10 100 000 -1 -1 kp / lmol ·s 7.83 20 000 -1 -5 kd / s 6.46  10 25 000

Tab. 2.6 Rate constants for simulation of butadiene gas phase polymerization without mass transport effect. See Fig. 2.15

50 °C E / J  mol-1  0.46 -4000 D / ms-1 3.6  10 –10 17430 -1 -1 –4 ka / lmol ·s 9  10 100000 -1 -1 kp / lmol ·s 10 25000 -1 –5 kd / s 7  10 20000 -1 -4 ktr  cAl / s 610

Tab. 2.7: Data for simulation of butadiene gas phase polymerization with mass transport effect. See Fig.2.15

50 °C  0.46 D / ms-1 3.6  10 -10 -1 -1 ka / lmol ·s 105.5 -1 -1 kp / lmol ·s 105.5 -1 -5 kd / s 7.3110 -1 -3 ktr  cAl / s 610

Tab: 2.8: Data for simulation of polydispersion index of gas phase polybutadiene. See Fig. 2.21

1 1 1

kL  a kS  as k  f   cMe

At beginning 20 s 31 s 33 s of polymerization After 1 h of 20 s 0.1 s 33 s polymerization

Tab. 2.9: Different resistances of mass transfer and chemical reaction of ethylene polymerization in slurry

Fig. 2.1: Calculated conversion and rate of free radical polymerization as function of reaction time 0.5 0.5 –4 Data: k = 0.002 l /(mol  s), kd = 2.610 1/s, CI,0 = 0.04 mol/l

 Fig. 2.2: Calculated cumulative molecular weight of polymer (weight and number average Mw and Mn) during the course of free radical polymerization. Simulation with Predici program. –5 3 Data: CM,0 = 9 mol/l, CI,0 = 0.02 mol/l, kd = 10 1/s, kp = 10 l/(mols), 7 kt,d = 10 l/(mol s), f = 0.5

Fig. 2.3: Effect of monomer concentration (w %) on kinetics of free radical polymerization of methyl methacrylate at 500C

Fig. 2.4: Rate of styrene polymerization and degree of polymerization at 500C and different initiator concentrations: a: 0.02, b: 0. 06, c: 0.28 mol/l

Fig. 2.5: Decay of termination rate constant with conversion. Bulk polymerization of o a: Vinyl acetate, b: Styrene, c: Methyl methacrylate at 50 C.

Fig. 2.6: Effect of conversion on rate and propagation rate constant of bulk 0 polymerization of methyl methacrylate at 22.5 C (unit of kp in l/(mol s))

Fig. 2.7: Correlation of maximum conversion of styrene bulk polymerization and polymerization temperature

Fig. 2.8: Effect of conversion of methyl methacrylate polymerization in bulk on radical efficiency factor of initiator

Fig. 2.9: Effect of retarder and inhibitor on temporal course of free radical polymerization a: no inhibitor or retarder present b: only retarder present c: only inhibitor present

Fig. 2.10: Kinetic profile of ideal emulsion polymerization

Fig. 2.11: Average number of radicals per particle as function of relative rates of  and m

Fig. 2.12: Monomer concentration CM, number of latex particles N and number of radicals n during the three periods of emulsion polymerization

Fig. 2.13: Initial rate of copolymerization of styrene and methyl methacrylate as function of mole fraction of styrene in feed. Dots: experiment. Line: modelling with  = 13

Fig. 2.14: Particle growth models

Fig.2.15: Rate of gas phase polymerization of butadiene at 500C and 1.6 bar monomer pressure

Fig. 2.16: Equilibrium concentration of 1,3-butadiene in 1,4-cis-polybutadiene as function of pressure of butadiene and temperature

Fig. 2.17: Molecular weight (number and weight average) of polybutadiene as function of reaction time. Dots: experiment. Lines: simulation

Fig. 2.18: Schematic diagram of concentration profiles of monomer within particle and gas phase

Fig. 2.19: Diffusion coefficients of butadiene in polybutadiene particles at different pressure of butadiene and temperature

Fig. 2.20: Polydispersion index of molecular weight distribution of polybutadiene. Simulation with and without effect of mass transport. Polymerization at 1.6 bar and 500C. Simulation data in Tab. 2.6 and 2.7

Fig. 2.21: Polydispersion index of molecular weight distribution of polybutadiene. Simulation with and without effect of mass transport. Polymerization at 1.6 bar and 500C. Simulation data in Tab. 2.8

Fig. 2.22: Kinetic diagram of gas phase polymerization of butadiene simulated with three different particle models with the same set of kinetic data

Fig. 2.23: Simulated temperature increase of polymerizing particles in gas phase polymerization of butadiene for two different Nusselt numbers.

Fig. 2.24: Concentration profile of monomer in slurry polymerization of ethylene

Fig. 2.25: Effect of catalyst concentration on rate of polymerization. Experimental results of ethylene polymerization in a bubble column reactor at different temperatures and pressures

54 3. VISCOSITY OF REACTION MIXTURE

3.1 Introduction During polymerization of monomer the viscosity of the reaction mixture increases very sharply. This sharp increase in viscosity can have an effect on:

- kinetics of polymerization (gel-, glass-, cage-effect) - removal of heat from reaction mixture - generation of heat by stirring of reaction mixture - degree of mixing of reaction mixture (micro or macro mixing) - flow pattern of reaction mixture in continuous reactors (residence time distribution)

Viscosity therefore has a strong influence on reactor performance, reactor selectivity, and reactor safety. In Fig. 3.1 a schematic of the increase in viscosity of a reaction mixture of different methods of polymerization is shown. The strongest increase in viscosity takes place in homogeneous bulk polymerization. In suspension polymerization, on the other hand, there is almost no increase in the viscosity of a reaction mixture so long as the volume fraction of the disperse phase remains constant during the reaction.

3.2 Viscosity of Homogeneous Systems The viscosity of homogeneous reaction mixtures, either polymer melts or polymer solutions, is a complex function of many parameters. The following parameters have an effect on viscosity: - Molecular weight, molecular weight distribution, chemical and physical structure of polymer - Concentration of polymer - Temperature and pressure - Shear rate or shear stress - Type of solvent

In Fig. 3.2 the effect of shear rate on the viscosity of a polymer solution is shown. The viscosity of the solvent is not dependent on shear rate. The polymer solution however shows the phenomenon of shear thinning at higher shear rates. This phenomenon can be explained by disentanglement processes of polymer molecules at higher shear rates. One very often used correlation to calculate viscosity of pseudoplastic liquids is that of Ostwald-deWaele. Pseudoplastic liquids can therefore have different effective viscosities in stirred tank reactors. At the tip of stirrer the effictive viscosity of pseudoplastic liquids will be much

55 smaller than at the wall of reactor due to different local shear rates. This has to be considered in the case of heat removal and mixing in stirred tank reactors.

Effect of Molecular Weight of Polymer In Fig. 3.3 the effect of molecular weight on viscosity of polystyrene-toluene solutions is shown. The concentration of polymer is 3 wt % and the temperature is 250C. The region of Newtonian flow behaviour is decreases the higher the molecular weight of the polymer. At very high molecular weights only non- Newtonian flow behaviour is observed even at very low shear rates. All lines end up in a single line with a slope of – 0.83. The slope is a measure for the degree of pseudoplastic behaviour of the polymer solution. Fig. 3.3 shows that polymer solutions of the same concentration but different molecular weights can have the same effective viscosity at a given shear rate. The effect of molecular weight of polymer on zero shear viscosity can be represented by the following empirical correlations:

 0 = K M with 2.5    1 for M < Mcr

3.4 0 = K´ M for M > Mcr

K, and K´ depend on polymer/solvent system. The transition from one correlation to the other occurs in a relative narrow range of molecular weight. The critical value of molecular weight is obtained by the intersection of straight lines representing the two regions of the same log-log plot. The transition behaviour at certain critical molecular weights is attributed to the onset of chain entanglement of polymer molecules. The critical molecular weight depends on polymer/solvent systems and varies from 2,000 to 60,000 g/mol.

Effect of Polymer Concentration The effect of polymer concentration on viscosity can be seen in Fig. 3.4. At relatively high concentration of polymer no Newtonian regime is present. The following correlations of zero shear rate viscosity with resprect to concentration are reported in literature:

 0 = K CP with 6.3    3.4 for M > Mcr

 0 = K CP with 4.4  ´  0.5 for M < Mcr

Also in this case there is a critical molecular weight beyond which entanglement of the polymer molecules will occur and will cause change in flow behavior. The effect of molecular weight and concentration of polymer on entanglement

56 respectively flow properties can be seen schematically from Fig. 3.5. In practice the concentration of the reaction mixture is in general larger than 10 weight percent and the molecular weight is larger than 100,000 g/mol. At these reaction conditions entangled macromolecules will be present in the reacting system. Knowledge on the increase of viscosity of a reaction mixture in polymerization reactors is of interest for the design and control of reactors. One suitable empirical correlation to calculate the viscosity increase of polymerizing systems is that of Lyons and Tobolsky. It correlates the zero shear rate viscosity of a reaction mixture with the viscosity of the solvent, polymer concentration, and molecular weight of the polymer expressed by intrinsic viscosity []. kH is the Huggins constant, which does depend on solvent quality. b is an adjustable parameter.

  kH [ η] CP   0  S 1  CP [ ] exp     1  b CP  with X CM,0 M M 3 CP  [ g/cm ] 103 (1  ε X )

 3 [ ]  KMH M [cm /g]

Fig. 3.6 shows an example of the application of Lyons and Tobolsky correlation. The corresponding parameters of the equation of Lyons and Tobolsky are shown in Fig. 3.7. Application of the equation of Lyons and Tobolsky on reacting systems with changing polymer concentration, molecular weight, and average shear rate should be done with caution.

Effect of Temperature One widely used empirical correlation to consider the effect of temperature on the viscosity of liquids is the WLF-equation by William, Landel, and Ferry:

c1 (T  Tref ) log η (T )  log η (Tref ) c2  (T  Tref )

c  17.44 and c  51.6 if T  T with 1 2 ref g c  8.86 and c  101.6 if T T ~ 43 K or 1 2 ref g

 57  This equation holds for a range of temperature from Tg to about Tg +100 K for many polymers.

3.3 Viscosity of Heterogeneous Systems The increase in viscosity of a reaction mixture with conversion in suspension polymerization can be neglected. In case of emulsion polymerization the increase is moderate. In case of precipitation polymerization the increase can be significant. This is due to different effects of different parameters on the viscosity of heterogeneous systems. The viscosity of a dispersion in the liquid phase depends on following parameters:

- Viscosity of continuous liquid phase - Volume fraction of disperse phase - Particle size, particle size distribution, particle shape and surface properties of particles - Temperature and pressure - Shear rate or shear stress

In Fig. 3.8 the effect of shear stress on the viscosity of a polymer latex with an average particle size of 200 nm is shown for different volume fractions of disperse phase. From this figure the effect of shear thinning and shear thickening can be seen, especially in the case of lattices with high solid content. The effect of shear thinning is attributed to an orientation of latex particles in stream lines. Shear thickening is attributed to agglomeration effects of latex particles. In Fig. 3.8 another phenomenon can be seen. Concentrated lattices start to flow only if a certain shear stress is reached.

Effect of Volume Fraction of Particles One very useful empirical correlation for modelling the viscosity of dispersions with high solid content is that of Eilers, which is based on the equation of Einstein.  2 1.25 P rel  1  1  ( /  )  P P,max 

This equation was originally derived for narrowly distributed spherical particles with a maximum volume fraction close to the theoretical value of 0.74. It can be  used, however, also for non-spherical polymer particles like polyethylene dispersions with much lower maximum volume fractions of solid. Fig. 3.9 shows a plot of relative viscosity of polyethylene suspensions versus volume fraction of solid. The five polyethylene samples used have different maximum

58 volume fractions from 0.2 to 0.5. The maximum volume fraction of the polyethylene samples can be determined from the density of the polymer bed and the density of polyethylene (P,max=bed/PE). Large deviations between experiment and calculation can be seen only for sample number 5 with the smallest maximum volume fraction of 0.2. The other 4 samples with maximum volume fractions of 0.3 to 0.5 can be modeled very well with the equation of Eilers.

Effect of Particle Size Experimental studies with dispersions of spherical particles with diameters larger than 1 m indicate no or only slight effects of particle size on the viscosity of a suspension. Below 1 m stronger effects are observed. This is expected since for dispersions of equal solid content, since the distance between particles will become smaller and the specific interface larger if particles are getting smaller. The interactions between particles will increase with decreasing particle size. For dispersions with rough, irregular particles this effect can be seen even at larger particle diameter. Polydispersity of particle size may also effect the viscosity of a dispersion. For small particles, effects of surface nature and electric surface charge are become more pronounced. In this case the volume fraction must be corrected for the thickness of adsorbed surface layers of surfactant. If the surfactant is a polymer, the thickness of the surface layer represents an appreciable fraction of the particle diameter and has to be considered according to :

3  2δ  P,eff  P 1    dP 

With  being the thickness of the layer of surfactant. In Fig. 3.10 the effect of effective volume fraction on viscosity of dispersions with different particle size is shown. In this case a strong effect of particle size on viscosity can be observed at higher volume fractions. The large variety of dispersions and the large number of parameters affecting the rheological behaviour of dispersions makes it difficult to formulate a general correlation for viscosity of dispersions.

3.4 List of Symbols dP Diameter of particle, m M Molecular weight of polymer, kg / kmol (cr: critical, M: monomer, : viscosity average, w: weight average)

59 T Temperature, K (ref: reference, g: glass transition) X Conversion of monomer  Shear rate, 1 / s  Thickness of surfactant layer, m  Viscosity, Pas (o: zero shear rate, s: solvent, rel: relative, []: intrinsic viscosity)

P Volume fraction of polymer

3.5 References - R.B. Bird, R.C. Armstrong, O.Hassager: “Dynamics of Polymeric Liquids“, John Wiley and Sons, 1977 - C.W. Macosko: “Rheology, Principles, Measurements and Applications“, VCH, Publishers, 1994 - H.-U. Moritz: “Increase in Viscosity and its Influence on Polymerization Process“, Chem.Eng.Technol., 12, 71-87 (1989)

60 3.6 Figures

Fig. 3.1.: Schematic representation of viscosity increase of reaction mixture with conversion for different methods of polymerization

Fig. 3.2.: Effect of shear rate on viscosity of polymer solution at constant temperature

Fig. 3.3: Effect of molecular weight (Mw in g/mol) on viscosity of polystyrene/ toluene solutions

Fig. 3.4: Effect of polymer concentration on viscosity of polystyrene/toluene solutions

Fig. 3.5: Molecular weight-concentration diagram of polybutadiene in a good solvent. Domains of entanglement and no entanglement of polymer molecules

Fig. 3.6: Zero shear rate viscosity of polydimethyl siloxane of different molecular weight (viscosity average in g/mol)in siloxane solvent at 30oC. Dots: experiment, lines: simulation

Fig. 3.7 Effect of molecular weight (viscosity average) on parameters of equation of Lyons and Tobolsky

Fig. 3.8: Viscosity of polymer latex with different volume fractions of disperse phase as function of shear stress

Fig. 3.9: Relative zero shear rate viscosity of polyethylene dispersions as function of volume fraction of polyethylene. Maximum volume fraction of sample 1 to 5: 0.474 / 0.373 / 0.336 /0.339 / 0.195.

Fig. 3.10: Effect of volume fraction and size of particles on viscosity of dispersions

65 4. DATA ACQUISITION OF POLYMERIZATION REACTIONS

4.1 Introduction For the design of a polymerization reactor, reliable data of polymerization reactions and polymer properties are necessary. Most important is data on the kinetics and thermodynamics of the polymerization reaction. But important also is data on the rheology of the reaction mixture and polymer properties. Very often this kind of data is not available in literature or is very difficult to find and not consolidated to one source. In this case data has to be determined by experimentation. The scale of experimentation depends on data needed. In general first experiments are run in laboratory scale. The most widely used technique of polymerization is polymerization in liquid phase. In this case the most oft used type of reactor is the stirred tank reactor. In laboratory scale stirred tank reactors with reaction volumes of 1 to 5 liters are used. In Fig. 4.1 the schematic configuration of a stirred tank reactor for data acquisition of polymerization reactions in liquid phase is given. The unit consists of the reactor itself, a dynamic thermostat for temperature control, sensors for acquisition of data, and finally a computer for data mining, modelling and control of the reactor. Sensors for measuring temperature, pressure, and stirring speed are available at moderate costs but sensors for measuring viscosity of the reaction mixture, concentration of reactants or particle size, and molecular weight distributions of polymer are relatively expensive. A very versatile technique for on line monitoring of kinetic and caloric data is the method of reaction calorimetry which has been developed originally in chemical industry for safety studies.

4.2 Reaction Calorimetry / Kinetic and Caloric Data Reaction calorimetry is a useful method by which caloric data of chemical reactions or physical processes can be determined. In the case of polymerization reactions the rate and conversion can be measured directly if the heat balance of the system can be solved. Reaction enthalpy and heat transfer coefficient of the reactor can be determined as well if certain parameters are known. One has to consider that by reaction calorimetry the total heat production within a reactor is measured. For exact determination of caloric data one has to know how many heat producing or heat consuming processes are running in parallel. The parallel or consecutive processes can be of chemical or physical nature. Therefore the precise evaluation of caloric experiments is in no way a simple procedure. Reaction calorimeters can be classified into adiabatic, isoperibolic and isothermal calorimeters.

66 Adiabatic reaction calorimeter In this type of calorimeter there is no heat exchange between reaction mixture and its surrounding. All the heat set free during reaction is accumulated within the reaction mixture. The temperature of the reaction mixture is increasing with time and is running into a constant value. In Fig. 4.2 a typical temperature-time profile is shown. The heat balance is very simple if the temperature increase is caused by a chemical reaction only. In this case the heat flux by chemistry is equal to heat flux by accumulation:

  Qchem  Qaccu

If only one chemical reaction takes place the temperature of the reaction mixture is directly proportional to the conversion of this reaction. Adiabatic calorimeters are relatively simple in construction, they can be used for very fast reactions, and they are suitable for safety studies. One has to consider that the course of the reaction may be affected by temperature increase. Side reactions may take place at elevated temperatures. Effects of temperature and concentration of reactants on the kinetics of reaction can only be separated by simulation procedures.

Isoperibolic reaction calorimeter In this case the jacket temperature of calorimeter is kept constant during the run of reaction. See Fig. 4.3. Part of heat of reaction is transferred to the cooling agent in the jacket, and the rest is absorbed by the reaction mixture itself. This can be seen by the temperature increase of the reaction mixture in the beginning of the reaction. At the end of the reaction temperature of the reaction mixture is running again into a stationary state. The heat balance of an ideal isoperibolic reaction calorimeter is given by:

   Qchem  Qcond  Qaccu

The heat flux of chemical reaction is equal to the sum of heat flux by conduction and heat flux by accumulation. Isoperibolic reaction calorimeters are also very simple calorimeters. They can be run either in an adiabatic way or at sufficient cooling capacity nearly isothermal. The kinetics of reaction is also affected by temperature changes. These changes are however relatively small compared to adiabatic operation procedures. Nevertheless, also in this case the effects of

67 temperature and concentration of reactants on kinetics can only be separated by simulation procedures.

Isothermal reaction calorimeter In Fig. 4.4 the temperature profiles of an ideal isothermal reaction calorimeter are shown. Reaction temperature is constant with time. Jacket temperature is changing with time depending on the kinetic characteristic of the chemical reaction. The heat balance is given by:

   Qchem  Qcond  Qaccu

One advantage of an isothermal reaction calorimeter is that chemical heat flux is directly proportional to the rate of chemical reaction. Isothermal reaction calorimetry is one of the very few methods by which rate of reaction can be measured on-line during the run of reaction if heat is produced by chemistry only. Another advantage is that this mode of operation is very often used in industry. In special cases the heat transfer coefficient of the reactor can also be determined. On the other hand isothermal reaction calorimeters are extensive devices, which are rather expensive. Temperatures have to be measured with high precision. The same is true for measurement of volumetric or gravimetric fluxes of cooling agent. In practise one has to distinguish between two different types of isothermal reaction calorimeters. In the case of a so-called heat flux reaction calorimeter the conductive heat flux through the reactor wall is determined by measuring the temperatures of reaction mixture T and cooling agent Tj according to:  Qcond U A(T  Tj )

 For calculation of conductive heat flux Qcond the value of UA is necessary. This value depends on many parameters. One parameter is the viscosity of the reaction mixture at the wall of the reactor, but also fouling on the wall of the reactor has a strong input on the heat transfer coefficient U. In the case of polymerization reactions with a volume contraction of the reaction mixture the effective cooling area A of reactor will decrease with increasing conversion of reaction. If using a heat flux reaction calorimeter one has to know the exact value of UA but also possible changes during the course of reaction. Values of UA are in general determined by calibration before and after the chemical reaction. In the case of changes of UA appropriate interpolation operations have to be done. One way is to correlate UA with the viscosity of the reaction mixture, which however must be measured during reaction.

68 The other type of isothermal reaction calorimeter is called a heat balance calorimeter. In this case the convective heat flux of the cooling agent is measured by measuring the temperatures of the cooling agent at the inlet and outlet of the jacket of reactor. Furthermore, the gravimetric flux of the cooling agent also has to be measured with high precision. The convective heat flux is given by:

 Qconv  m cp (Tj,ex  Tj,in )

The advantage of a heat balance calorimeter is that viscosity, fouling of reactor walls, and volume contraction will have no impact on caloric measurements. Both types of reaction calorimeters need the complete heat balance in order to determine the chemical heat flux necessary for calculation of rate or conversion of reaction. As an example the heat balance of a heat flow calorimeter shown schematically in Fig. 4.5 will be discussed. The heat balance reads:

    Qchem  P  Qcond  Qlos  Qaccu

 Qchem = V R j (  H R, j ) Heat flux by exothermic chemical reaction j

3 5 P = Ne N d  = 2  N MT Heat flux by stirring

 Qcond = U A (T - Tj ) Heat flux by conduction through reactor wall

 Qlos = h A (T - Ts ) Heat flux from reactor to surroundings

dT Q = C Heat flux by accumulation accu R dt

In order to determine the other four heat fluxes need to be known very precisely. Problematic is the determination of . It is done by using an  electric heater inside the reactor with a well known heating power Qel . Power input by stirring and heat loss to surroundings is considered by correction of the base line of the temperature profile. For the calibration of the calorimeter determination of the heat transfer coefficient is done by used of the following equation:

69 Q UA  el (T  T j )el  (T  T j )

The term (T – Tj ) takes into consideration heat loss to surroundings and heat input by stirring. Calibration is done by measuring first T and Tj without having the electrical heater in operation, then the heater is turned on and T and Tj are measured at thermal equilibrium of the reactor. This is done before and after the chemical reaction. In the case of significant deviations of UA values average  values or interpolations have to be used for calculation of Qchem . With the rate and conversion of a reaction can be calculated if only one reaction is taking place:

t  Qchem dt Q  R  chem and X  0  V (  H R ) Qchem, total

If reaction enthalpy is not known it can be determined by calorimetry according to: t  Qchem dt 0  H R  V X(t)CM,0

As an example of a polymerization reaction run in an isothermal heat flux calorimeter, the measured temperature profiles are given in Fig. 4.6. For calibration of the calorimeter an electrical heat flux of 58 W was introduced into the reaction mixture for 10 minutes. It can be seen that the temperatures of jacket are pulled down immediately after turning on the electrical heater and they go back to original level again after heater is turned off. After 40 minutes the polymerization reaction is started by injection of the initiator into the reactor. Again the jacket temperatures are pulled down strongly due to heat production by polymerization. With decreasing rate of polymerization the temperatures of jacket are increasing simultaneously. After the end of the polymerization another calibration was run by introducing again 58 W into reaction mixture. The response of tempertures is almost the same as that of first calibration. This is an indication that heat transfer coefficient has not changed during polymerization reaction. From this diagram and the heat balance of the calorimeter

70 the rate and conversion of the reaction can be calculated as a function of reaction time.

4.3 Reaction Viscosimetry/Rheological Data Viscosity of a reaction mixture is a very important parameter in polymerization reaction engineering. It can affect reactor performance and safety, but also product quality. A very useful procedure to measure viscosity of a reaction mixture in a stirred tank reactor is illustrated in Fig. 4.7. If stirring speed N and torque of stirrer MT are known the power input of stirrer P can be calculated. With this parameter the Newton number can be determined. For further procedure the power input characteristic of the stirred tank reactor must be known. This characteristic diagram can be measured by mesuring the power input of the stirrer at different stirring speeds or different viscosities of a Newtonian liquid and plotting the Newton number versus Reynolds number in a log-log-plot. A typical power input diagram of a given stirred tank reactor is shown in Fig. 4.8. From this diagram the corresponding Reynolds number can be taken if the Newton number is known. With this Reynolds number the effective viscosity can be calculated. It is evident that this procedure will work only if the flow pattern of the liquid is within the laminar region. In the turbulent region the Newton number is constant and viscosity will have no effect on power input. An important point of this procedure is the precise measurement of power input. This can be done best by using stirrers with magnetic coupling to the stirring motor. In this case the friction of the stirrer shaft is minimized. Reaction viscosimetry was applied to the polymerization of a monomer in solution using a stirred tank reactor with a helical type of stirrer without baffels. The corresponding power input diagram is given in Fig.4.8. It was measured by using sugar solutions of different sugar concentration. Stirring speed was also changed in order to cover a broad region of Reynolds numbers. From this diagram and with the data of torque and stirring speed the effective viscosity of a reaction mixture was determined during the course of polymerization. In Fig. 4.9 the increase of viscosity is shown for three different initial concentrations of monomer.

4.4 Solubility and Diffusivity of Monomer in Polymer For modelling of kinetics or molecular weight distribution in multiphase systems monomer concentration at the local position of active sites has to be known. It is surprising to see that this kind of data is difficult to find in literature. Very often experimental studies are the only way of getting information on solubility and diffusivity of monomers in heterogeneous systems. Solubility and diffusivity of gases in polymers can be determined by measuring the sorption of gas in polymer at different pressures and temperatures. These measurements can be done by using a suitable micro balance. The polymer sample can be used as a

71 film or as a pellet. For determination of correct values of solubility the buoyancy force has to be taken into account. In Fig. 4.10 the sorption diagram of 1,3- butadiene in 1,4-cis-polybutadiene is given. Polymer particles of 1.5 mm diameter were used. Plotted is the solubility of monomer in weight fraction versus time at 250C and different pressures of butadiene. Equilibrium is reached between 20 and 40 minutes. Equilibrium concentration of butadiene in polybutadiene is plotted versus pressure of butadiene at different temperatures in Fig. 4.11. Dots are experimental results. Lines are calculated by using the equation of Flory-Huggins:

 p   M  2 ln    ln M  1 M   1 M   pM ,L 

 E     with   0 exp    R T 

M M ,L and cM  1  M M M

The equation of Flory-Huggins has to be solved by iteration. The temperature dependence of Flory-Huggins coefficient  can be seen in Fig. 4.12. It can be described by an equation according to Arrhenius:

 E       0 exp    R T 

with 0 = 0.105 and E = - 4000 J/mol in case of butadiene/polybutadiene.

There are many ways to determine diffusion coefficient from sorption measurement. In the present case with spherical polymer particles with narrow particle size distribution, Fick’s diffusion equation was used as an analytical solution: m (t ) 6  exp( Dn2 2 / r 2 ) M  1  P 2  2 mM ,eq  n1 n

The result for one experiment is shown in Fig. 4.13. The diffusion coefficients are, as expected, dependent on temperature, but it was found that they are also slightly dependent on pressure. This can be seen in Fig. 4.14. The dependence on temperature can be described according to Arrhenius:

 ED  D  D0 exp    R T  7 2 with D0  2.4 10 m /s and ED  17 400 J / mol in case of butadiene/polybutadiene.

 Things get more complicated in three phase systems, like for example in the case of polymerization of propylene in a slurry. Here propylene is first dissolved in the liquid phase and then in the solid polymeric phase. Hutchinson and Ray have shown a method for calculation of monomer concentration in the polymer phase. They were using the theory of Krigbaum-Carpenter. According to this theory the concentration of propylene in polypropylene is smaller than the concentration of propylene in solution at partial pressures of propylene between 1 and 10 bars and temperatures between 40 and 70 0C. These results are shown in Fig. 4.15.

4.5 List of Symbols A Area, m2 3 CM Monomer concentration, kmol / m

cp specific heat capacity, kJ / (kg  K)

CR Heat capacity of reaction mixture, kJ / K D Diffusion coefficient, m2 / s d Diameter of stirrer, m E Activation energy, kJ / kmol

 HR Enthalpy of reaction, kJ / kmol h Heat transfer coefficient, kJ / (m2  K  s)

MM Molecular weight of monomer, kg / kmol

MT Torque of stirrer, N  m

mM Mass of monomer, kg m Mass flow, kg / s N Stirring speed, 1 / s Ne Newton number P Power input of stirrer, kJ / s

pM Partial pressure of monomer, bar

pM ,L Vapor pressure of liquid monomer, bar Q Heat flux, kJ / s

73 R Rate of reaction, kmol / (m3  s) Re Reynolds number rP Radius of particle, m T Temperature, K U Overall heat transfer coefficient, kJ / (m2  K  s) V Volume of reaction mixture, m3 X Conversion of monomer  Viscosity, Pa  s  Density, kg / m3

M Volume fraction of monomer  Flory-Huggins parameter

4.6 References - J. Brandrup, E.H. Immergut: “Polymer Handbook“, John Wiley and Sons, 1989 - D.W. Van Krevelen: “Properties of Polymers“, Elsevier, 1997 - D.C.H. Chien, A. Penlidis: “On-Line Sensors for Polymerization Reactors“, JMS-Rev. Macromol. Chem. Phys., C 30 (1), 1-42 (1990), Marcel Dekker

- W. Regenass: “The Development of Stirred Tank Heat Flow Calorimetry as a Tool for Process Optimization and Process Safety“, Chimia 51 (1997) 189- 200 - F. Rieger, N. Novak: “Power Consumption Scale-up in Agitating Non- Newtonian Fluids“, Chem. Eng. Sci., 1974, Vol. 29, pp. 2229-2234 - R.A. Hutchinson, W.H. Ray: “Polymerization of Olefins through Heterogeneous Catalysis. VIII. Monomer Sorption Effects“, J. Appl. Polym. Sci., 41 (1990), 51 - T.F. McKenna, J. Dupuy, R. Spitz: “Modelling of Transfer Phenomena on Heterogeneous Ziegler Catalysts. Differences Between Theory and Experiment in Olefin Polymerization (An Introduction), J. Appl. Polym. Sci., 57 (1995) 371 - J. Crank, G.S. Park: “Diffusion in Polymers“, Academica Press, 1968

74 4.7 Figures

Fig. 4.1: Configuration of stirred tank reactor for data acqusition of isothermal batch polymerization in liquid phase

Fig. 4.2: Ideal temperature-time profile of reaction mixture of an adiabatic calorimeter

Fig. 4.3: Ideal temperature-time profile of reaction mixture (T) and jacket temperature of reactor (Tj) of an isoperibolic calorimeter

Fig. 4.4: Ideal temperature-time profile of reaction mixture (T) and jacket temperature of reactor (Tj) of an isothermal calorimeter

Fig. 4.5: Scheme of heat flow calorimeter for isothermal reaction

Fig. 4.6: Temperature profiles of isothermal reaction calorimeter during period of calibration and polymerization

Fig. 4.7: Procedure for determination of effective viscosity in a stirred tank reactor by measurement of stirring speed and torque of stirrer

Fig. 4.8: Power input diagram of stirred tank reactor with a helical type of stirrer without baffels

Fig. 4.9: Increase in viscosity of reaction mixture during polymerization in solution at three different monomer concentrations

Fig. 4.10: Absorption diagram of 1,3-butadiene in 1,4-cis-polybutadiene at 250C and different pressures of butadiene

Fig. 4.11: Equilibrium concentration of 1,3-butadiene in 1,4-cis-polybutadiene as function of butadiene pressure and temperature. Dots: experiment, lines: Flory-Huggins equation

Fig. 4.12: Flory-Huggins coefficient of the system butadiene/polybutadiene as function of temperature. Dots: experiment with range of error, line: Arrhenius equation

Fig. 4.13: Butadiene absorbed in polybutadiene as function of time. Line: experiment, dots: calculation

Fig. 4.14: Diffusion coefficient of butadiene in polybutadiene as function of pressure and temperature. Dots: fitting to experiment, lines: regression

Fig. 4.15: Equilibrium concentration of propylene in polypropylene as function of concentration of propylene in n-hexane

82 5. POLYMERIZATION IN STIRRED TANK REACTORS

5.1 Mode of Operation The most widely used type of reactor in polymer production is the stirred tank reactor. It is used as single reactor or as a cascade of stirred tank reactors. In the case of a cascade, three to five rectors are in general connected in series. A stirred tank reactor can be run batchwise, semi-batchwise, or in a continuous way. Advantages and disadvantages are listed in Tab. 5.1. Batch reactors are used in general for small scale production of polymers. It can be used for production of different types of polymers in short periods of time. A major disadvantage of a batch reactor is its relatively large cycle time necessary for filling, heating, cooling, emptying, and cleaning of the reactor as well as for running of the reaction. Since the reactor is filled at the beginning of reaction with a large amount of monomer thermal run away phenomena may happen in the case of failure of cooling. This may lead to thermal explosions of the reactor. In order to reduce the risk of thermal run away phenomena the semi-batch operation of a stirred tank reactor can be applied. In this case certain reactants are not filled into the reactor at the beginning of reaction but they are introduced into the reactor in a time controlled way. This procedure is applied especially in the case of production of uniform copolymers when monomers of different reactivity are used. In this case the less reactive monomer is filled into the reactor first and the more reactive monomer is pumped into the reactor in such a way that the ratio of concentration of both monomers is kept constant during the entire course of copolymerization. Semi-batch operation is also applied in the case of condensation polymerizations in order to achieve polymers with high molecular weight. In this case the low molecular weight byproduct of the condensation reaction is removed permanetly from the reactor in order to shift the chemical equilibrium reaction to the side of high molecular weight products.

Continuous stirred tank reactors are used for production of large amounts of polymers with constant quality. In general more than one stirred tank reactor is used. In a train of stirred tank reactors higher conversions of monomer can be achieved within a given period of time in comparison to the single continuous stirred tank reactor. Continuous processes have in general a larger polymer production performance than batch or semi-batch processes. This is due to the absence of operation time for filling and emptying of the reactor in case of batch and semi-batch processes. In general stirred tank reactors are run isothermal but also non-isothermal operations are known. The volume of stirred tank reactors can differ very strongly. Reactors with volumes of 100 m3 and more are used in polymer industry.

83 5.2 Mixing of Reaction Mixture Types of stirrers and power input characteristic Mixing of reactants in stirred tank reactors is especially important if reactants are fed separately into the reactor, or if the polymerization process is run continuously. In the case of mixing, three characteristic times have to be considered. Mixing time, time constant of polymerization reaction, and mean residence time of reaction mixture in case of a continuous process. Mixing time is the time which is necessary to achieve a certain degree of homogeneity in a reaction mixture. Time constant of reaction is defined as the ratio of initial monomer concentration to initial rate of reaction. The mean residence time of an ideally mixed continuous stirred tank reactor is given by the ratio of reaction volume to volumetric flow rate of the reaction mixture. For achieving high reactor performance and selectivity it is logical that mixing time should be much smaller than characteristic time constant of polymerization reaction and mean residence time of reactor. In practise mixing time should be at most 10 % of time constant of reaction or residence time. For good mixing an appropriate stirrer must be used. Many different types of stirrers are available. They can be classified according to the resulting flow pattern of the flowing liquid and according to the viscosity range of liquids which have to be mixed. Some major types of stirrers used in stirred tank reactors are given in Fig. 5.1. The corresponding flow pattern indicated by arrows are shown in Fig. 5.2. The task of mixing can be very different. We have to distinguish between homogenization of miscible liquids, emulsification of one liquid into another immsicible liquid, sparging of gas into a liquid phase, or dispersing solid particles into liquids by stirring. These different mixing tasks will need different types of stirrers. In Tab. 5.2 a few suitable stirrers for different methods of polymerization are given. Turbine and propeller agitators are fast running stirrers used for emulsification of liquids and dispersing of fine solids into liquids. Blade stirrer is in general used for homogenization of liquids. The intermig stirrer  is a very efficient stirrer used for many tasks but especially for mixing of disperse systems (gas/solid/liquid). Helical type of stirrers are used for mixing of highly viscous systems as in case of bulk polymerization of liquid monomers. For characterization of individual stirrers the power input diagram is used. The power input characteristic of different stirrers is shown in Fig. 5.3. The power input of a stirrer is given by:

P  Ne N 3d 5 

It can be measured by measuring the torque of the stirring shaft MT :

P  2 N MT

84 Knowing P, the Newton number Ne can be determined if stirring speed N, diameter of stirrer d, and density of liquid phase  is known. This dimensionless Newton number is plotted in a logarithmic diagram versus dimensionless Reynolds number of stirrer. From this power input diagram different flow regions can be characterized.

Laminar region (Ne  Re = constant):

P  C N 2 d 3 

with C  Ne at Re  1

Turbulent region (Ne = constant) :

P  Ne N 3 d 5 

From the power input diagram the following information can be taken:

- Determination of power input in a given liquid for a given stirrer at given stirring conditions. First the Reynolds number is calculated than the Newton number is taken from the diagram. With this Newton number the power input is calculated. - Comparison of different stirrers with respect to power input at given Reynolds number. - The effect of baffles on power input at given Reynolds number.

In the case of non-Newtonian homogeneous liquids like polymer solutions the power input characteristic is similar to Newtonian liquids if Reynolds number is 2 determined by using the effective viscosity of liquid phase (Reeff = N d  / eff). The effective viscosity of the non-Newtonian liquid at a given stirring speed can be determined by measuring first the viscosity as a function of shear rate in a rotational viscosimeter. Then the correlation between shear rate and rotation frequency of the stirrer is necessary. For this purpose correlations of Metzner and Otto can be taken which are only valid for laminar region. Correlations of Metzner and Otto have the form   K N with K = 10 for propeller, K = 12 for turbine and K = 30 for helical ribbon agitator. For gas/liquid or gas/solid/liquid dispersions one has to take into account that the Newton number is a function of gas throughput. It decreases with increasing flow rate of gas.

85 Mixing of miscible liquids

Homogenization of miscible liquids is one of the most often used unit operations in chemical engineering. The homogenization process of liquids in stirred tank reactors can be regarded as a two step process. In the first step mixing will take place by convection of the liquid phase. In the case of turbulent mixing small volume elements of liquid will be formed. The smallest volume elements which will be formed can be expressed by the theory of Kolmogorov. The micro scale of turbulence  [m] depends on the specific energy input of stirring  [W/kg or m2/s3] and on the viscosity of the liquid  [m2/s] and is given by:

1 / 4  3          

In the case of water with a viscosity of 10-6 m2/s and an energy input of 1 W/kg, the diameter of segregated volume elements is 32 m. In the case of glycerine with a viscosity of 10-3 m2/s and the same energy input the scale of volume elements is already 5.6 mm. This shows that viscous liquids like polymerization mixtures are always to some extent segregated systems. Power input of stirring has only a small effect on micro scale of turbulence (   -0.25). In the second step of turbulent mixing the interior of the micro scale volume elements is mixed by diffusion. This kind of mixing is called micro mixing and takes place on a molecular scale. The mixing time by diffusion is given by:

2   D

With the diffusion coefficient on the order of D = 10 –9 m2/s, which is typical for liquids, the micro mixing time is 1 second for water and 30 seconds for glycerine. This result shows, that micro mixing is fast compared to macro mixing by convection. Macro mixing does depend on the scale of the reactor. Micro mixing is scale independent. Mixing times of liquids in reactors are in general determined by experiment since many parameters may affect the numerical values. In practise, physical and chemical methods are applied. A mixing time has to be connected with a degree of mixing. In Fig. 5.4 the mixing characteristics of different types of stirrers with and without baffles are given. Mixing time  refers to perfect mixing (micro mixing). For mixing of highly viscous liquids the helical ribbon stirrer is an effective type of stirrer. It is used for mixing in the laminar flow regime. Mixing time is affected by stirring speed. In case of blade stirrers one can classify two regimes of mixing:

86 1. Re = 10 to 10 2 : N   1/Re :    / (Nd)2

2. Re  10 3 : N   const :   1 / N

In the laminar regime time of mixing does depend on viscosity and strongly on stirring speed and the diameter of the stirrer. In the turbulent regime time of mixing is independent on viscosity and the scale of the stirrer. It is affected only by stirring speed. In polymerization reactors very often liquids with differences in density and viscosity have to be mixed. Furthermore, a reaction mixture may have non- Newtonian flow properties. In this case mixing characteristic becomes more complex and mixing number N  is not only dependent on the Reynolds number but also on the Archimedes number, which is defined as:

d 3 g   Ar   2 

Mixing time will depend on average density and viscosity but also on gravity and the density difference of the two liquids. Non-Newtonian mixtures are homogenized much slower than Newtonian liquids at same mixing conditions in the laminar and transient regimes of flow. This is due to the fact that there is a shear rate gradient in the reactor which causes large viscosity differences. The viscosity of reaction mixture is increasing from stirrer to reactor wall. Opara studied the mixing behavior of non-Newtonian liquids in stirred tanks in transient regimes of flow and noticed the formation of non-mixed zones in the form of vortex rings which rotate around the stirrer. Mixing within these rings is slow compared to mixing in the well mixed part of reactor. In this case two different mixing times have to be considered. Mixing by convection is fast whereas mixing by diffusion in the stagnant rings is a slow process. Total mixing time of non-Newtonian liquids can be about 10 times larger than for Newtonian liquids if mixing is done in the laminar regime. In turbulent regimes the differences become less and less.

Mixing of non-miscible liquids In emulsion and suspension polymerization liquid monomers are dispersed by stirring into the surfactant-containing water phase. In suspension polymerization water soluble polymers are used as surfactants. The average particle size of monomer droplets in this case is determined by parameters like:

- Physical properties of the two liquids (viscosity, interfacial tension, density)

87 - Geometry of the stirred tank (type, number and position of stirrer and baffle, ratio of hight to diameter of reactor, ratio of stirrer diameter to reactor diameter - Operation conditions (stirring speed, time of stirring and polymerization, volume ratio of phases, degree of filling of reactor, temperature, batchwise or continuous operation)

In the case of turbulent mixing the following type of equation is proposed in literature for calculation of the mean diameter of monomer droplets:

d 32  C We 3 / 5 1  C   d 1 2 M

3  ni di (Sauter mean diameter of with d  i 32 2 monomer droplets)  ni di i

d 3 N 2  We  C (Weber number) 

The constants C1 and C2 depend on the chemical and physical system used. This correlation must be used with caution since at larger Weber numbers deviations are reported in literature. If the factor 1  C2 M  is neglected, the following correlation between droplet diameter and power input by stirring is obtained:

0,4 d32  C3 

P with   C V

These kind of correlations have also been reported for average diameter of polymer particles produced in suspension polymerization at high concentration of surfactants. The constant C3 is determined mainly by the physical properties of the two phase system and by the energy distribution of stirring within the reactor volume.

88 In the case of vinyl chloride polymerization in suspension, the effect of Weber number (i.e stirring speed) on the average diameter of polymer particles is shown in Fig. 5.5. It can be seen that at Weber numbers larger than 3105 the particle size is no longer decreasing with increasing Weber number, but becomes independent of Weber number and at very large Weber numbers it is even increasing. The three zones of Weber numbers are explained by different interaction between processes of particle break-up, particle coalescence, and re- agglomeration of particles.

Mixing of gas in liquid phase In slurry polymerization of ethylene or propylene in stirred tank reactors the gas phase is dispersed into an organic liquid (low boiling hydrocarbon). The rate of mass transfer of monomer from gas to liquid phase is given by:

R  kL a CM

A with a  (specific interface) V

 CM  CM  CM ,L (see Fig. 2.24)

k L = D/

 The saturation concentration of monomer in liquid phase CM does depend on the kind of monomer and liquid, partial pressure of the monomer and temperature. The concentration of monomer in liquid phase CM,L depends on the rate of mass transport and rate of polymerization. The liquid-side mass transfer coefficient kL is defined according to “two film“- theory as the ratio of diffusion coefficient of transfer component D to thickness of liquid-side boundry layer . Effective sparging of liquid phase with gas can be done with a turbine agitator. The gas phase is introduced into liquid phase through a pipe placed below the stirrer. The kLa value is affected by gas flow rate. Gas flow rate may affect also power input of stirring. With increasing gas flow rate the relative gas hold up of liquid phase is increasing and density of disperse system is decreasing. This will lead to a decay in power input by stirring. In Fig. 5.6 the decay in Newton number with increasing gas flow rate is shown in the case of a 6 blade turbine stirrer with gas inlet below the stirrer. The gas flow rate is expressed by a dimensionless gas flow number Q. This correlation is valid within certain limitations. At larger gas flow numbers the gas dispersing efficiency of stirrer will be lost completely because beyond certain flow rates the stirrer will be surrounded completely by gas phase. The numerical

89 values of kLa depend on many parameters like physical properties of disperse systems, geometry of the stirred tank and operation conditions of stirring. The average diameter of gas bubbles dispersed in pure liquids of low viscosity is around 3 to 5 mm and not affected strongly by stirring conditions. In the case of mixtures of homogeneous liquids, the diameter of bubbles is in the order of 0.3 to 0.5 mm at the same stirring conditions. This is due to the fact that the process of bubble coalescence is surpressed in mixtures of different liquids or in presence of dissolved salts. On the other side there are chemicals like nonionic surfactants which strongly enhance coalescence of gas bubbles an thereby reduce kLa values drastically. Process oriented parameters which affect kLa values strongly are the power input of stirrer and the flow rate of gas. The following correlations are named in literature:

2 0.4 0.5 kL a  2.6 10 (P /V) u0 (for non coalescing systems)

3 0.7 0.2 kL a  2.0 10 (P /V) u0 (for coalescing systems)  -1 3 with kL a in s , P/V in W/m and u0 in m/s. Gas flow rate u0 is related to the empty reactor (superficial gas velocity). In Fig. 5.7 the effect of power input on the liquid side mass transfer coefficient of ethylene is shown in the case of a bubble column reactor filled with n-heptane or Exsol D 200/240 (a mixture of hydro carbons). The liquid phase contained 16 wt % of polyethylene powder. It can be assumed that power input primarily affects the specific interface and not mass transfer parameter as such.

Mixing of solid particles in liquid phase Mixing of solid particles in a liquid phase is an important process in suspension and slurry polymerization, especially if the process is run continuously. The degree of mixing in a stirred tank reactor can be expressed by the standard deviation of particle distribution within the vessel :

2 n     2  1   1 n    1   with  = Volume fraction of solid at measuring point  = Average volume fraction of solid at ideal mixing (arithmetical set point) n = Number of measuring points

90 In Fig. 5.8 the distribution of glass beads within a stirred tank reactor at different stirring speeds is shown. The reactor has a diameter of 365 mm. The diameter ratio of propeller stirrer to reactor is 0.315. The position of the stirrer within the reactor is marked with hS. The glass beads have a diameter of 200 m. The volume fraction of glass beads is 0.1. Water was used as liquid with a viscosity of 10-3 kg/ (ms). The relative density difference of the dispersion is 1.87. As can be seen from Fig. 5.8, the homogeneity of the suspension is improves with increasing stirring speed. A perfectly mixed suspension would have a relative solid content of 1 and a standard deviation of 0 at any position within the reactor volume. At a standard deviation of 0.25 the glass particles are totally distributed within the reactor volume, although not evenly. In practise this standard deviation is the upper limit from an energetic and mechanical stand point. In the case of slurry polymerization of olefins the relative density difference of the two phases is smaller and a distribution of solid particles within the total reactor volume may be reached at higher standard deviations ( 0.5). The effectiveness of stirrers for mixing of solid particles into liquids can be quite different. In Fig. 5.9 the standard deviation of mixing versus power input of the stirrer is plotted for different stirrers at the same mixing conditions. As can be seen, the so called intermig stirrer has the best mixing effectiveness at the lowest power input. The rate of mass transfer of monomer from liquid to solid phase is given by:

R  kS a CM

A with a  (specific interface) V

CM  CM ,L  CM ,S (See Fig. 2.24)

The mass transfer coefficient kS for a single sphere of diameter dP at rest within a large volume of stagnant fluid is given by kS = 2 D/dP. D is the diffusion coefficient of monomer in the liquid phase. Any motion of the spherical particle relative to the liquid phase will increase the numerical value of kS. The following dimensionless correlation is proposed for mass transfer of flow past single spherical particles covering the entire range of hydrodynamics with respect to the Reynolds number.

Sh  2,0  0,76 Re1 / 2 Sc1 / 3

with Sh  kS dP / D

91 Re  u dP / Sc  / D In slurries of small particles in a gently stirred liquid the relative velocity of the two phases is low and roughly that of free fall of a particle due to gravity. The terminal velocity of small spheres in a stagnant liquid is given by the law of Stokes: g d 2  u  P 18

Using the Sherwood equation and Stoke’s law, kS as a function of dp can be calculated. The correlations are plotted in Fig. 5.10 for suspensions of different density differences. Slurries of catalyst particles suspended in a liquid are agitated vigorously to keep the particles well dispersed and to promote absorption of the monomer gas. The resulting turbulence in the slurry phase promotes mass transfer and the actual mass transfer coefficient will be larger than that taken from Fig. 5.10. As a first approximation the actual mass transfer coefficient may be twice the value taken from Fig. 5.10 based on Sherwood numbers with termal velocity of particle in free fall. One of the best ways of estimating kS is correlations for mass transfer in agitated slurries based on power input of stirrer, provided that power input is wellknown. Calderbank and Moo Young for example have published the following equation:

2 / 3 1 / 4 kS Sc  0,13 (  )

Ne N 3 d 5 with   V

The exponent of the Schmidt number has to be taken with caution since other lower values have also been published.

5.3 Heat Removal and Safety Aspects Heat removal and heat formation Heat can be removed from stirred tank reactor in different ways. See Fig. 5.11. The following methods of heat removal are used: - Indirect cooling by jacket of reactor, by internal cooling coils or by external heat exchanger - Direct cooling by feed of reaction mixture or by evaporation of monomer or solvent

92 A common problem of heat removal from polymerization reactors is the tendency of reaction mixtures to form polymer films on the wall of cooling areas.

These films can reduce the heat exchange capacity of heat exchangers very strongly. If external heat exchangers are applied then the reaction mixture has to be pumped through the heat exchanger and this may cause strong pressure drops, especially if the reaction mixture is highly viscous. In the case of heat removal by evaporation of a liquid phase inside the reactor, the formation of foam may happen. The foam may rise into an external heat exchanger and block the piping. Remixing of a condensed liquid with viscous reactor content may also be difficult. Indirect cooling takes place by conduction of heat through the walls of heat exchangers whereas direct cooling happens by convection of heat by flowing liquids or vapors.

Heat formation inside a polymerization reactor can happen by chemical reaction, by stirring or by physical processes like in-situ crystallization. Polymerization reactions are in general exothermic reactions with very different reaction enthalpies. Heat formation by stirring has to be considered when highly viscous liquids are stirred. The heat balance of a continuous stirred tank reactor can be expressed by the following equation:

     Qaccu  Qchem  P  Qcond  Qconv  Qevap

dT with Q  m c (heat flow by accumulation) accu p dt  Qchem  R  HR V (heat flow by chemical reaction) 3 5 P  Ne N d  (heat flow by stirring)  Qcond U A T TJ  (heat flow by conduction)  Qconv  m cp T  T0  (heat flow by convection)  Qevap  n  Hevap  (heat flow by evaporation)

The previous heat balance does not consider heat losses of the reactor to surroundings nor heat formation by physical processes like crystallization of polymer formed.

93 In the case of heat flow by accumulation one has to keep in mind that heat is not only absorbed or generated by the reaction mixture but also by the reactor itself.

Heat formation by polymerization reaction does depend on the rate of monomer polymerization. This rate can be constant with time as in the case of continuous processes at stationary state, or it can change with time as in the case of batch processes. In general it will fall with increasing conversion of monomer. In auto- catalytic polymerization reactions it will first increase with time and then decrease during the course of reaction. Monomers like styrene, butadiene, vinyl chloride, propylene, and ethylene have reaction enthalpies in the range of -70 to -100 kJ/mol. Condensation polymerization reactions have much lower reaction enthalpies. The reaction enthalpy of poly(ethylene terephtalate) synthesis is about -10 kJ/mol. Addition polymerization reactions like polyurethane synthesis are strongly exothermic reactions with enthalpies of about -200 kJ/mol. The catalytic synthesis of resins like phenol/formaldehyde and urea/formaldehyde are also very exothermic reactions.

Heat formation by stirring has to be considered, especially if highly viscous reaction mixtures are to be mixed by stirring. Viscous liquids are mixed in laminar regimes of flow. Here the Newton number is inversely proportional to the Reynolds number and power input by stirring is proportional to viscosity of liquid and proportional to the second order of stirring speed.

Most important in heat removal of polymerization reactors is heat transport by conduction. The heat transfer coefficient U is affected by the geometry of the reactor, by physical properties of reaction mixture (viscosity, thermal conductivity, specific heat capacity), and by operation conditions of mixing (stirring speed, temperature). The heat transfer coefficient of a stirred tank reactor with clean walls can be expressed according to Peclet as:

1 1 d 1   w  U hr w h j

The total resistance of heat transfer is given by the addition of three single resistances, namely the resistance of heat transfer from reaction mixture to reactor wall, the resistance of heat transfer through the wall of reactor with thickness dw and thermal heat conductivity w, and finally the resistance of heat transfer from reactor wall to cooling agent within the jacket of the reactor. The single heat transfer coefficients hr and hj are given by the ratio of thermal heat conductivity of the corresponding liquid and the thickness of boundry layer of liquid. The thermal heat conductivity of steel is in the range of 15 to 20, of polymer 0.2 to 0.3, of organic liquids 0.1 and of water 0.6 W/(mK). The

94 thickness of the boundary layer does depend on physical properties of the liquid phase and stirring conditions. In general the main resistance of heat transfer is the resistance of heat transfer from the reaction mixture to the reactor wall if the wall is not covered by a thick film of polymer. In this case so called Nusselt correlations can be used to determine the numerical values of hr and subsequently U. For homogeneous Newtonian liquids the following Nusselt equation can be used for turbulent region of mixing (Re>200) :

Nu  const. Re2/3 Pr1/3 Vis0.14

h D N d 2  with Nu  r r ; Re    

c p   (T ) Pr  ; Vis    (T j )

The constant of heat transfer characteristic has numerical values from 0.3 to 0.8 for fast rotating agitators and up to 10 for slowly rotating agitators. The exponent of the viscosity number depends on heat flow direction. For cooling it is smaller than 1 and for heating it is larger than 1. In the laminar regime of flow the effect of Reynolds number on heat transfer becomes less. For a helical ribbon agitator the following correlation is given:

Nu  4.2 (Re Pr)1/3 Vis0.2

This correlation should be valid for Newtonian and non Newtonian liquids as well, if effective viscosities are used. It has to be remembered, however, that the heat transfer coefficient of a polymerization reactor can change strongly during the course of a polymerization reaction. In Fig. 5.12 the change of heat transfer coefficient of a 2 liter steel reactor with helical ribbon agitator at 160 rotation per minute is shown for solution polymerization of methyl methacrylate with an initial concentration of 55 weight percent. The decrease of heat transfer coefficient with increasing conversion of monomer is caused by the increase of viscosity of reaction mixture. The previous correlations of heat transfer are valid for homogeneous reaction mixtures. In the case of heterogeneous reaction mixtures the same correlations can be used if average values of physical properties of dispersions are taken into account. If the reaction mixture is a sparged liquid than additional parameters like superficial gas velocity and gravity have to be considered. The heat transfer correlation has, in this case, a different form:

95 2 a St  const (Re Pr Fr )

hr u0 d  with St  ; Re  ;  c p u0 

 c u Pr  p ; Fr  0  d g Heat removal by convection can only be applied in the case of continuous or semi-batch reactors. The heat flow by convection is mainly determined by mass flow of feed and by the difference of temperatures between inlet and outlet. The specific heat capacities of organic liquids are about 2 kJ/(kgK). Water has a heat capacity of about 4 kJ/(kgK). One industrial example of direct cooling by feed of reaction mixture is the process of free radical ethylene polymerization at high pressure and temperature. Due to reactors with thick walls only a small amount of heat can be removed by indirect cooling via the jacket. The rest of the heat is removed by direct cooling via convection. Another example is the gas phase polymerization in fluidized bed reactors with heat removal mainly by convection. Heat removal by evaporation is used if polymerization can be run at the boiling temperature of the monomer or solvent at the conditions given. The heat flow by evaporation is given by the molar flow of monomer or solvent and by the enthalpy of evaporation. The molar flow is controlled by the area of evaporation. The heat of evaporation depends on the type of monomer or solvent. The numerical values are in the range of 15 to 40 kJ/mol. Cooling by evaporation is used in production of resins of phenol and formaldehyde in water as solvent. The reaction temperature is kept constant at 95oC by this method of cooling. The cooling capacity of a stirred tank reactor is defined as the difference between heat removal by conduction and heat production by stirring. The difference should be as large as possible. The maximum value of cooling capacity is connected to an optimum value of rotation of the agitator. This can be seen in Fig. 5.13, which shows the effect of stirring speed on the cooling capacity of the reactor. The dotted lines in Fig. 5.13 show the effect of stirring speed on heat removal by conduction and on heat production by stirring. In the laminar regime of flow heat generation by stirring is proportional to the second power of stirring speed, whereas heat removal by cooling via jacket is only proportional to the square root of stirring speed. That is why the cooling capacity of a reactor runs through a flat maximum of about 30 kW in the case of Fig. 5.13, and the optimum rotation number of the stirrer is about 20 rotations per minute. Very often stirring speed will not be fixed by cooling capacity of reactor but rather by the degree of mixing of the reaction mixture. The quality of mixing is in general more important since it can affect polymer quality to a great extent.

Thermal stability of the continuous stirred tank reactor Safe operation of a reactor means that it should not burst or leak. Bursting of a reactor can be caused by uncontrolled temperature increase beyond certain limits. In order to understand how fast the temperature of a reactor will increase and to what upper level it will rise in the case of a disturbance in cooling, simulation studies of thermal stability of the reactor should be done. P. Wittner and others have studied thermal runaway phenomena in the thermal polymerization of styrene in bulk phase in a continuous stirred tank reactor. First order reaction kinetics were used for modelling the polymerization reaction. The following heat and mass balance was used:

d T 1  1 T     n0 k (1  X )(  H R )  q (T  T j )   c p d T d t c p     T0 

 E  with cp  cp,0   T ; k  k0 exp    R T 

U A V  q  ;   V  m

n0 : Feed concentration of monomer [mol/kg]

d X X  k (1  X )  d t 

X At stationary state:   st k (1  X st )

Data used for simulation: 9 k0 = 1,410 1/min cp,0 = 0,4 kJ/(kgK) E = 89 kJ/mol  = 4.310-3 kJ/(kgK)

(- HR) = 74 kJ/mol T0 = 288 K -3 q = 12.310 kJ/(kgKmin) T j = 358 K

Results of simulation: In Fig. 5.14 the rate of heat generation and heat removal is plotted versus temperature of reaction at a constant mean residence time of 388 minutes. Heat generation is a complex exponential function and heat removal is a linear equation. The two curves cross each other in three points which represent potential operating points of reactor. The lowest crossing point represents virtually no reaction. The polymerization reaction has not initiated. Whereas crossing points P1 and P2 are realistic operating point with high conversion of monomer at conditions given. Inspection of these two points P1 and P2 reveals that P1 is a non stable operating point whereas P2 is a thermally stable point. At point P1 a small rise in temperature would produce a greater generation of heat than removal. Hence temperature would tend to increase further until operating point P2 is reached. Similarly, a drop in temperature would induce a greater drop in temperature and temperature will fall till the lowest operating point is reached. This phenomena does not apply to operating point P2 which is thermally stable. Fig. 5.14 does not reveal how fast these transitions from one operating point to the other will take place. In this case the transition characteristic of the process has to be simulated by simultaneous solution of both differential equations. In Fig. 5.15 the transition of operating point P1 (at 0 0 130 C and 60% conversion) to operating point P2 (at 170 C and 95 % conversion) is shown, when cooling temperature of the jacket increases by two degrees. It takes about 600 minutes until the new operating point is reached. One of the worst cases is the total break-down of cooling and feeding of the reactor. This causes an adiabatic runaway of reactor temperature. The result of a simulation is shown in Fig. 5.16. Temperature is rising within 50 minutes to a maximum value of nearly 260 0C. The adiabatic temperature increase is given by:

CM ,O (  H R )  Tad  c p 

5.4 Residence Time Distribution

If molecules or elements of a fluid are taking different routes through the volume of a continuous operated reactor, they will spend different times within such a reactor. The distribution of these holding times is called the residence time distribution (RTD) of the fluid. The RTD can affect the performance of a reactor and may also have a strong input on the selectivity of a chemical reaction. In the case of polymerization reactions the RTD can have an effect on the molecular weight distribution of the

98 polymer formed. This will mainly be the case when the mean life time of the active species of the polymerization reaction is in the same order of magnitude like the mean residence time of the reactor. In this case polymers with a narrow molecular weight distribution can only be produced in a reactor with narrow RTD. The RTD in the case of polymerization reactions can also play a major role if the reaction mixture is a segregated system. Segregation in the reaction mixture can easily occur if the reaction mixture is of high viscosity or a heterogeneous nature, with elements that act as individual micro reactors without an exchange of mass. The RTD of a polymerization reactor is therefore an important parameter which may affect the performance of the reactor and also the properties of the polymer formed.

Experimental methods for determination of RTD

Most important for determination of the RTD of a reactor is the application of a suitable tracer. A suitable tracer should be easy to detect and the total amount of injected tracer should be detectable at the exit of reactor. The most important methods for the determination of the RTD are the so called pulse and step experiments. They are easy to perform and interpret. a) The pulse experiments

In this case a certain amount of a tracer is added pulse-wise to the fluid entering the reactor and the concentration-time relation of the tracer at the exit of reactor is recorded. This is shown schematically in Fig. 5.17. From the balance of material for the reactor the mean time of the concentration-time distribution can be found.



tCdt tiCi ti 0 i Mean time (holding time): t    [s] Ci ti Cdt i 0

To find the RTD, which is also called the exit age distribution E, concentration- time distribution has to be normalized in such a way that the area under the distribution curve is unity. For doing this the concentration readings have to be divided by the area under the concentration curve. This is shown in Fig. 5.18. The relationship between C and E curves only holds exactly for reactors with so called closed boundary conditions. This means that the fluid only enters and only leaves the reactor one time. No adsorption of tracer at the walls of the reactor should happen. Very often it is convenient to use a dimensionless Eθ curve for reasons of comparison of reactors. In this case time is measured in terms of mean residence time   t / t . Then E  t  E .

99 b) The step experiment

In this case the tracer is not introduced pulse wise into the fluid entering the reactor but is introduced in a continuous way by injecting a constant side stream of tracer to the fluid entering the reactor and measuring the outlet tracer concentration C versus time as shown in Fig. 5.19. The mean residence time is given by following equation:

Cmax tdC  Cmax 0 1 t  C  tdC max C  dC max 0 0

The dimensionless form of the concentration curve is called the F curve or transition function. Here the tracer concentration is rising from zero to unity with time (see Fig. 5.20).

RTD of mixed flow reactors with ideal flow pattern

Fig. 5.21 shows the residence time distribution of a cascade of N equal size well mixed stirred tank reactors which are connected to each other in series. The most narrow distribution is shown by the cascade of stirred tank reactors with an infinite number of vessels. The broadest RTD results in case of a single stirred tank reactor. The RTD of equal sized stirred tank reactors with mixed flow is given by the following equations:

N 1 Nt 1 t  N N  E    e t t  t  N  1!

with t  N ti (N : number of reactors and ti : mean time of single reactor)

Nt 2 N 1   Nt 1  Nt  1  Nt   F  1 e t 1     ...     t 2!  t  N  1)! t  

RTD of mixed flow reactors with non-ideal flow pattern

In reality the flow pattern of reactors deviate from ideal mixed flow pattern. This is especially the case for polymerization reactors in which a polymer solution or dispersion with high viscosity is flowing through the volume of the reactor, causing a non-ideal flow pattern. Non-ideal flow patterns can result for example

100 if the reactor volume contains so called dead or stagnant regions or if bypass or recycle flow is present next to the active flow through reactor regions of mixed flow. If these non-ideal flow patterns are present in a given reactor they can be seen easily by looking at the corresponding experimental RTD. The following models can be used to describe the measured RTD of real reactors with deviation from ideal flow:

 Compartment Model  Dispersion Model  Tanks-In-Series Model  Convection Model (for laminar flow in pipes)

In Fig. 5.22 compartment flow models are given for a stirred tank reactor which is characterized by the presence of dead zones and bypass. The corresponding RTD of the two compartment models are shown in Fig. 5.23. The dispersion and tanks-in-series model is used in general when small deviations from plug flow are expected. They are one parameter models. A dispersion number is used in the case of the dispersion model whereas the number of stirred tanks is used in case of the tanks-in-series model.

The convection model is used if a viscous liquid is pumped through a tubular reactor. In general the flow is of a laminar characteristic with a parabolic velocity profile. Thus the spread in residence times is caused only by velocity variations. The velocity profile of a laminar flow is shown together with the corresponding RTD in Fig. 5.24.

5.5 Reactor Performance Conversion, reaction volume and reactor capacity Reactor performance of a given stirred tank reactor depends on the mode of operation. In Tab. 5.3 correlations of conversion and reaction volume are given for different types of stirred tank reactors (batch reactor, homogeneous continuous stirred tank reactor, cascade of equal sized stirred tank reactors). The correlations are valid for polymerization reactions of first order at constant temperature, volume of reaction and initiator concentration. The Damköhler number is defined as: Da = k t or k  in the case of a continuous process. In Fig. 5.25 conversion–Damköhler correlations are represented in a graphical way. From this graph it can be seen that a batch reactor is the most effective reactor with respect to conversion achieved within a certain period of reaction time. It is followed by the cascade of reactors. The effectiveness is increasing with increasing number of reactors. The single continuous stirred tank reactor needs the longest time of reaction for a given conversion of monomer. The same result

101 can be seen in Fig. 5.26. Here reactor capacity, which is determined by rate of reaction, is plotted versus time or conversion. Differences in reactor capacity are largest at higher conversions. At very low and very high conversions there is nearly no difference in capacity of different types of reactors. The reason for different reactor performance is the different rate of reaction in different reactors. This can best be seen in a qualitative way from Fig. 5.27. Here the profiles of monomer concentration is given during the course of polymerization for different types of reactor. In batch reactors there is an exponential decay of monomer concentration with time in the case of first order reactions. In continuous stirred tank reactors at steady state the monomer concentration is constant. The level of concentration depends on the rate of reaction and mean residence time of the reactor. So if we compare for a given conversion the average monomer concentration in the three different reactors we see the highest average monomer concentration in batch reactors and the lowest in single continuous reactors. The cascade reactor is in between and the average monomer concentration depends on the number of reactors. A cascade with an infinite number of reactors corresponds in reactor performance to a batch reactor of the same reaction volume. Things look different if the reactor performance of different stirred tank reactors is compared in the case of zero order polymerization reactions. In this case no differences will be seen since reaction rate is not depending on monomer concentration. Another point of interest is the reactor performance of a batch reactor related to the total time of reactor operation. Batch reactors have to be filled, warmed up, cooled down, emptied and cleaned. This so called dead time can be larger than the time of reaction. Due to the effect of dead time the performance of a batch reactor is in general lower than that of a continuous reactor of same size. The performance of a reactor depends also on its size. The reaction volume can be calculated from the mass balance of a reactor according to equations given in Tab. 5.3. The volume of a reactor depends on the rate of polymer production, conversion of reaction, and initial monomer concentration. In the case of a batch reactor the dead time has to be considered. In the case of a cascade the number of reactors is affects its volume.

Effect of segregation on conversion In polymerization reactions mixing of reactants can have a large effect on reactor performance as well as on polymer quality. Think of a continuous polymerization in solution in a stirred tank reactor. In this case a low viscous monomer solution must be mixed with a high viscous polymer solution inside the reactor. Mixing of the two solutions down to a molecular level will not be an easy task. On the contrary, the two miscible solutions may easily form a segregated system consisting of monomer solution distributed within the viscous polymer solution. Mixing to a molecular level will take a certain amount of time and this time will depend primarily on energy

102 input of stirring and diffusivity of the monomer (and solvent), which is strongly affected by the viscosity of the medium. Segregation effects can be even stronger in heterogeneous systems. For example in the case of continuous slurry polymerization of olefins in stirred tank reactors or fluidized bed reactors small catalyst particles are injected into the reactor. These catalyst particles form polymer particles which behave like micro reactors with an individual residence time within the macro reactor. These kinds of segregation phenomena can have an effect on reactor performance in case of non first order polymerization reactions. In Fig. 5.28 conversion plots of completely segregated and non-segregated reacting systems are shown for zero- and first-order reactions. For zero-order reactions the perfectly mixed reactor (HCSTR) will have higher conversions than the completely segregated reactor (SCSTR) at Damköhler numbers larger than 0.3. The corresponding conversion equations are listed in Tab. 5.4. The performance equation of a completely segregated system in a continuous stirred tank reactor is given by the following equation: t  X   X batch E dt t 0 with Xbatch being the conversion-time correlation of a batch reactor and E dt the exit age distribution of the mixed stirred tank reactor. The exit age distribution of segregated and non-segregated systems in stirred tank reactors are the same. Segregation can not be seen by the residence time distribution. The residence time distribution of a continuous well mixed stirred tank reactor is given by:

1  t  E dt  exp   dt    

With conversion-time correlations of batch reactors for zero- and first-order reactions the performance equations of a segregated continuous stirred tank reactor can be calculated. Segregation lowers conversion of continuous stirred tank reactors if the order of reaction is smaller than 1, and segregation increases conversion if the order of reaction is larger than 1. For first-order reactions there is no difference in reactor performance of segregated or non-segregated systems, because conversion does not depend on monomer concentration. In practise reaction mixtures of polymerizing systems are in general partially segregated and the question is how can the degree of segregation be determined. Baumann, for example, has published a characteristic segregation number for identification of the degree of segregation of a given system:

 N  seg 

103 2 with  = (micro mixing time) D V  = (mean residence time) V  3 / 4  = (diameter of segregated department)If water with a  1 / 4 viscosity of 10-6 m2/s is mixed in a stirred tank reactor with a specific power input of 1 W/kg, the size of segregated elements is about 30 m in diameter. These elements of 30 m diameter lose their identity by action of molecular diffusion. The diffusion coefficient in water is on the order of 10-9 m2/s. Thus segregated elements of water 30 m in size lose their identity in approximately 0.9 seconds, which is a very short time. The segregation number of a continuous process with a mean residence time of 1 hour is in this case 2.510-4. This is a very small segregation number, indicating that the system is to be regarded as mixed on a molecular level (micro mixed). Things become different for polymerizing systems. Assuming the viscosity of a reaction mixture is 10-3 m2/s, then the micro scale of fluid elements is in the order of 5.6 mm if power input remains constant. With a diffusion coefficient of about 10-10 m2/s the micro mixing time becomes very large (87 hours) and the segregation number is also very large (87). In practice the volume of continuous stirred tank reactor is in some cases not totally well mixed, and so called dead or stagnant regions may be present within the vessel. The remaining active volume of reactor may have zones of mixed flow or plug flow. This depends on the geometry of the reactor and stirrer and also on feed inlet and outlet. Further effects are those of the operation conditions of the reactor (stirring speed, throughput, temperature) and properties of the reaction mixture, like viscosity. For calculation of conversion in such reactors with dead zones and regions of mixed and plug flow, so called compartment models can be used. In Fig. 5.29 a compartment model of a continuous stirred tank reactor with volume elements of dead water (Vd), and mixed and plug flow (Vm and VP), is given. The corresponding residence time distribution differs according from that of a homogeneous continuous stirred tank reactor. The mean conversion of the reactor not well mixed is given by the segregation model in the case of a first-order polymerization reaction as:

   V  V  V  X  1  exp  Da   exp    P  d   V V  V   O  m  m  

104 V  V  exp  Da P  Vm  V   1    V Da  Vm

The effect of volume fraction of dead water and plug flow on relative conversion of the reactor is shown in Fig. 5.30 for two different reference conversions of 0.2 and 0.8. The result is that volume elements of plug flow increase conversion whereas volume elements of dead water lower conversion of a first order reaction as expected. In summary the following can be said: reactor performance is a complex function of polymerization kinetics, type of reactor and its residence time distribution, as well as of degree of segregation of reaction mixture and earliness or lateness of mixing of reactants.

5.6 Reactor Selectivity Molecular Weight Distribution of Polymers One of the most important parameters for the characterization of polymers is the molecular weight distribution and its mean values, like weight and number average of molecular weight. Mechanical and rheological properties of polymers are especially affected by molecular weight and its distribution. Molecular weight and distribution are determined by:

- Chemical mechanism of polymerization reaction - Method of polymerization - Reactor used and operation conditions

Thus chemistry and engineering play a major role in determining the chain length distribution of polymers. The complex interactions of different parameters can best be demonstrated by looking first at a very simple kind of free radical polymerization reaction consisting of initiation, propagation, and termination by disproportionation. We further assume that the rate of initiation is constant and the reaction is not affected by gel-, glass- or cage-effects. The reaction is run in three different stirred tank reactors such as a batch reactor (BR), homogeneous continuous stirred tank reactor (HCSTR), and segregated continuous stirred tank reactor (SCSTR). The BR is equivalent to a cascade of stirred tank reactors with an infinite number of vessels. When the polymerization reaction is run in a BR at constant temperature the concentration of monomer decreases with conversion andtime of reaction. In the case of free radical polymerization the average life time of active sites is very

105 short (seconds) compared to the time of reaction for high conversion (hours). Thus during the course of polymerization the average chain length of macromolecules become smaller and smaller with increasing conversion. This is shown in Fig. 5.31. The instantaneous number average degree of polymerization is given by:

k C 1 P  p M  n 1 / 2 2 ( f kd kt,d CI ) (1  ) and the instantaneous weight chain length distribution of polymer is given by the Schulz-Flory distribution, or most probable distribution:

W ( P )  (1  )2 P  P1 ~ (1  )2 P exp  (1 ) P

R k C with   p  p M 1 / 2 Rp  Rt,d k p CM  2 ( f kd kt,d CI )

The breadth of the distribution is described by the dispersion index D= Pw/Pn. Pw is given by Pw=2/(1-). Dispersion index is two in the case of termination by disproportionation. When termination is exclusively by combination the dispersion index is 1.5. In Fig. 5.32 the weight chain length distribution of instanteously formed polymer at five different conversions is shown. A set of Schulz-Flory distributions results in decreasing degrees of polymerization at increasing conversion of monomer. The dispersion index for all distributions shown in Fig. 5.32 is equal to 2. Integration of the distributions with appropriate weight factors gives the chain length distribution of the final polymer product at the end of the batch process. The cumulative distributions broaden with increasing conversion. This is shown in Fig. 5.33. Here the dispersion index is plotted versus conversion of polymerization for different reactors and for termination by disproportionation and combination. In BRs molecular weight distribution increases strongly at high conversion due to the decay of monomer concentration and short life time of active species. In the case of SCSTRs the molecular weight distribution broadens even more with increasing conversion. This is caused by the broad residence time distribution of the SCSTR. In this case we have very many individual batch reactors, each with an individual residence time. The broad residence time distribution which is given by 1  t  E(t )  exp      

106 leads to a very broad molecular weight distribution. The dispersion of the distribution strongly increases with increasing conversion. In contrary to BR and SCSTR, the HCSTR produces polymers with narrow molecular weight distributions even at high conversion. The reason for this is the constant monomer concentration at stationary state and the very short life time of active sites. In this case residence time distribution does not affect the molecular weight distribution of polymers. These simulations of a given polymerization reaction run in different reactors have shown that the molecular weight distribution of polymers formed can be very different from each other depending on conversion of reaction. However it must be mentioned that the effect of the reactor on the molecular weight distribution of polymers is not always the same, but does depend on the mechanism of the polymerization reaction. When chain transfer reactions play a significant role completely different results may be seen with respect to the molecular weight distribtution of polymers produced in a different reactor. This has to be checked from case to case. The next example is a condensation polymerization forming only linear chains. If this type of polymerization reaction is run in a BR the conversion of functional groups is defined as the fraction of functional groups that have reacted at a given time:

N  N p  0 N0 and the degrees of polymerization are given by:

N 1 P  0  n N (1  p )

1  p P  w 1  p

The chain length distribution is given by:

W( P ) (1  p )2 P pP1 and is again the Schulz-Flory distribution with a polydispersion index of two at complete conversion of functional groups (D= Pw/Pn = 1+p). Fig. 5.34 shows the increase of number average degree of polycondensation with conversion of functional groups. Polymers of technical use with a degree of polymerization on

107 the order of 100 can only be produced at very high conversions. This can only be done in an economical way in a BR or in continuous reactors with a plug flow profile. In Fig. 5.35 the weight distribution of chain lengths is shown at various conversions. Since in polycondensation reactions conversion can vary from 0 to 1 the dispersion index varies from 1 to 2. This is different from free radical polymerization. Here the dispersion index is always 2 because the probability of propagation is always very close to unity. In single continuous stirred tank reactors much broader molecular weight distributions do result as shown in Fig. 5.36. This is due to the effect of the broad residence time distribution. In polycondensation reactions the life time of growing chains is extremely large and therefore the chain length distribution is affected by the residence time distribution of the reactor. However these results are purely theoretical results since HCSTR and SCSTR are not adequate reactors for running polycondensation reactions at very high conversion, and on the other hand many condensation and addition polyreactions are accompanied by side reactions, which cause the formation of polymers with a Schulz-Flory distribution.

Composition Distribution of Copolymers Most of the polymers used are copolymers and not homopolymers. An exception is poly(vinyl chloride), polystyrene and low density polyethylene. The advantages of copolymers are the specific properties, which can be adjusted by the monomers used and by the composition of copolymer and its distribution. We have to distinguish between random, alternating, block, and graft copolymers. Of special interest are random copolymers produced by free radical or coordination polymerization. Since very often the reactivity of monomers can be very different, special polymerization procedures have to be used in order to produce copolymers with an equal distribution of monomers from chain to chain and within a single chain. Chemically uniform copolymers can be produced in batch or plug flow reactors at high conversions only in the case of binary systems with copolymerization parameters being equal and close to unity (r1=r2=1), or in the case of copolymerization with an azeotropic point. This can be seen in Fig. 5.37. It shows for three different binary systems the composition of copolymer formed (expressed by the mole fraction F1 of monomer 1 in copolymer) in a batch reactor as a function of monomer composition of charge f1 and of conversion. The resulting distribution of copolymer composition can be seen in Fig. 5.38. In general the copolymer composition distribution will be very broad in batch reactors, since most of the industrially important copolymers are not systems with r1 = r2=1, or with an azeotropic point at a certain composition of monomer. The majority of comonomers have rather a very different reactivity of copolymerization, and the result is a strong change of composition of monomer

108 mixture during the course of reaction in a batch or plug flow reactor, leading to formation of very non-uniform copolymers with increasing conversion. Copolymers of uniform composition can be produced in the case of monomers with different reactivity by using the semi-batch technique, or running the copolymerization in a mixed flow reactor. In the case of semi-batch copolymerization the less active monomer is introduced completely into the reactor and the more reactive monomer is than added in such a way that the ratio of monomer concentration is kept constant during polymerization. For this purpose analytical sensors or reliable computer programs are necessary. More convenient is the copolymerization in mixed flow reactors like the homogeneous continuous stirred tank reactor. In a HCSTR operating at steady state monomer concentration is constant in space and time. The result is therefore a chemically uniform copolymer. The instantaneous copolymer equation

r f 2  f f F  1 1 1 2 1 2 2 r1 f1  2 f1 f2  r2 f2

cM ,1 with f1   1  f2 cM ,1  cM ,2

nM ,1 and F1   1  F2 nM ,1  nM ,2 can be used for calculation of mole fraction of monomer 1 in the copolymer. cM,1 and cM,2 are the monomer concentrations in the exit stream of the reactor. In Fig. 5.39 the change in steady state copolymer composition is shown for the system of styrene and acrylonitrile as a function of conversion. A copolymer with a certain composition can be made either by varying the composition of feed at a fixed conversion or by varying the extent of conversion at a given composition of monomer feed. However perfect mixing on a molecular scale cannot be realized in practise as envisioned by the concept of a homogeneous continuous stirred tank reactor. Most industrial reactors are not micro mixed, and the reaction mixture is partially or fully segregated, especially at high viscosities. In the case of a segregated continuous stirred tank reactor the copolymer composition distribution will be much broader than in case of a HCSTR, and will broaden with increasing conversion. It will be even broader than distributions of copolymers produced in a BR. This again is the effect of the broad residence time distribution of the SCSTR.

109 5.7 Reactor Scale-up In general polymerization reactions are first run in lab scale reactors at certain reaction conditions. If polymer properties fulfill the demand the same reaction is then run in a larger scale reactor to produce more polymer for more intensive testing. Scale-up of a reactor should be done by using reactors of the same geometry. Geometric similarity means that all pertinent dimensions of reactors should have a common constant ratio. For example the ratio of tank diameter to stirrer diameter should be constant (see Fig. 5.40). Next step in scale-up of polymerization reactors is the definition of parameters that must be kept constant. Of special interest are parameters like :

- Mixing time for homogenization of miscible liquids - Droplet diameter or specific interface of emulsions - Distribution of polymer or catalyst particles within the reactor volume - Mass transfer coefficient in heterogeneous systems - Heat transfer coefficient of a reactor These parameters may affect important polymer properties like particle size and particle size distribution but also molecular weight and molecular weight distribution. If the most important parameter is identified, then an appropriate scale-up criterion has to be chosen. One of the oldest and most often applied scale-up criterion is that of Büche, which says that the specific power input of stirring should be kept constant during polymerization. Penney used different scale-up criteria and plotted them in a diagram which is shown in Fig. 5.41 In this logarithmic diagram the ratio of specific power input of stirring is plotted versus the volumetric scale-up factor of a reactor. From this diagram it can be seen that with the scale-up criterion of P/V = constant most of the named process parameters can be kept constant. If for example the particle size of monomer droplets (d32 ) should be the same in reactors of different size, then the specific power input by stirring should be the same in each reactor. In the case of mixing of liquids of low viscosity in the turbulent regime of flow, constant mixing times can only be realized in the scale-up of reactors when stirring speed is kept constant. This however means that specific power input by stirring must be increased strongly with increasing volume of the reactor, and for economical reasons this not the right thing to do. Thus, a somewhat larger time of mixing has to be accepted in large scale reactors at constant specific power input.

The functional correlation of specific power input and volume of a reactor shown in the Penney diagram shall be demonstrated in the case of mixing of liquids. If mixing in stirred tank reactors is performed in the laminar regime of flow, then the following correlations are valid:

110 P  const. N 2 d 3  and N   const. in the case of a helical ribbon.

If N is substituted by 1/ and d 3 by V the following equation results when the reaction mixture is the same in both reactors:

2 P / V L  L     P / V S  S 

From this equation one can see that mixing time  will be the same in both reactors if the specific power input of stirring will be equal in both cases. If mixing, however, is performed in the turbulent regime of flow a different correlation results. In this case P  Ne N 3 d 5  and N   constant for all types of stirrers

Again substitution of N by 1/ and with V~d3~D3 in the case of reactors of geometric similarity one gets the following correlation:

3 2 P / V L  L   DL       P / V S  S   DS 

In this case the specific power input of stirring has to be increased according to the second power of the ratio of reactor diameters if mixing time shall be equal in both reactors.

5.8 List of Symbols A Area, m2 Ar Archimedes number, Ar  d 3  g   /( r2   ) C Concentration of chemicals, kmol/m3 D Diffusion coefficient, m2/s, or Dispersion index of polymers n1 Da Damköhler number, Da  k  C0 Dr Diameter of reactor, m

111 d Diameter of agitator, m dP Diameter of particle, m d32 Sauter diameter of particle, m dw Thickness of reactor wall, m E Residence time distribution function, 1/s, or Activation energy of reaction, J/mol F Mol fraction of monomer in copolymer f Mol fraction of monomer in monomer mixture, or Efficiency factor of initiator Fr Froude number, Fr = u0 /(dg) g Standard gravity, m/s2 h Heat transfer coefficient, W/(m2K) H Enthalpy, J/mol k Rate constant of chemical reactions and mass transport processes MM Molecular weight of monomer, kg/k mol MT Torque acting on stirrer shaft, Nm m Weight, kg m Weight flux, kg/s N Number of revolutions of stirrer, 1/s, or Number of functional groups, or Number of reactors in a cascade Ne Newton number, Ne  P /( N 3  d 5   )

Nu Nusselt number, Nu  h  Dr /  Nseg Number of segregation, n Molar flux, mol/s P Power input of stirrer, W Pn Degree of polymerization, number average Pw Degree of polymerization, weight average Pr Prandtl number, Pr  cp  /  p Degree of conversion in condensation polymerization Q Heat flux, W Q Gas flow number, Q  g /( N  d 3 ) g Gas flow rate, m3/s R Rate of reaction, kmol/(m3s) R Gas constant, J/(molK) r Copolymerization parameter Re Reynolds number, Re  N  d 2   / Sc Scmidt number, Sc=/D Sh Sherwood number, Sh  ks  dP / D T Temperature, K or 0C

112 t Time, s U Overall heat transfer coefficient, W/(m2K) u Linear velocity, m/s u0 Superficial gas velocity, m/s V Volume, m3 V Volumetric flux, m3/s X Conversion

 Probability factor  Shear rate, 1/s  Thickness of layer, m  Specific energy input, W/kg or m2/s3  Dynamic viscosity, Pa s or kg/(ms)  Mixing time, s  Thermal heat conductivity parameter, W/(mK) or micro scale of turbulence, m  Kinematic viscosity, m2/s  Density, kg/m3  Interfacial tension, N/m or J/m2  Average residence time, s  Volume fraction,

5.9 References - S. Nagata: „Mixing, Principles and applications“, Halsted Press, John Wiley and Sons, 1975 - J.Y. Oldshue: „Fluid Mixing Technology“, McGraw-Hill Publications, 1983 - F.A. Holland and F.S. Chapman: „Liquid Mixing and Processing in Stirred Tanks“, Reinhold Publishing, 1966 - L.M. Rose: „Chemical Reactor Design in Practice“, Elsevier, 1981 - H.S. Fogler: „Elements of Chemical Reaction Engineering“, Prentice-Hall International, 1999 - T. Grewer: „Thermal Hazards of Chemical Reactions“, Elsevier, 1994 - K.H. Reichert and H.U. Moritz: „Polymer Reaction Engineering, in Comprehensive Polymer Science, Vol. 3, Part I, page 327, Pergamon Press, 1989 - M. Zlokarnik: „Dimensional Analysis and Scale-up in Chemical Engineering, Springer, 1991

113

5.10 Tables and Figures

Advantage: ideal for small-scale production, very flexible, multi purpose application, high conversion obtainable.

Batchwise Disadvantage: large cycle time, dangerous process, concentration gradients may affect polymer quality, temperature control can be difficult with fast exotermic reactions.

Advantage: good control of reaction rate and product quality (copolymer composition), relative safe process, high yield by shifting the chemical equilibrium Semi-batchwise (polycondensation), stationary concentration of

reactants. Disadvange: lower performance than batch reactor, extra devices for pumping and controlling.

Advantage: ideal for large quantities of polymers with constant quality, high degree of automation, relative safe process, high reactor performance. Continuous Disadvantage: process is not flexible, expensive instru-

mentation (pumps, sensors, controllers), high costs for maintenance.

Tab. 5.1: Mode of operation of stirred tank reactor

114

Agitator Diameter Baffles Tip Speed Polymerization Ratio (m/s) Method

Turbine  0.3 yes 3 – 12 Emulsion Propeller  0.3 yes 3 – 12 Suspension

Blade  0.5 yes/no 1 – 10 Solution Intermig  0.7 yes/no 1 – 10 Suspension, (Ekato) Slurry, Solution

Helical Ribbon  0.9 no 0.5 – 2 Solution ( > ) Helical Screw  0.9 no 0.5 – 2 Bulk (>> )

Tab. 5.2: Agitators used for different methods of polymerization. Agitator/Reactor

Reactor Conversion Reaction Volume

m P t  tdead  BR X  1  exp Da V  M M CM ,0 X

1 m HCSTR X  1  V  P 1  Da k M M CM ,0 1  X 

1 1/ N X  1  m P N[ 1  X   1] Cascade N V   Da  1   k M M CM ,0 X  N 

Tab. 5.3: Conversion and reaction volume of different stirred tank reactors. Correlations refer to polymerization reaction of first order

115 Reaction HCSTR SCSTR

 1  O. Order X  Da X  Da  Da exp  (Da = k / CM,0)  Da 

1 1 1. Order X  1  X  1 (Da = k) 1  Da 1 Da

Tab. 5.4: Conversion equations of segregated (SCSTR) and non-segregated (HCSTR) reaction systems of zero- and first-order reactions

116

Fig. 5.1: Some major types of agitators and viscosity ranges of application

Fig. 5.2: Axial and radial flow patterns in stirred tank reactors equiped with baffles

117

Fig. 5.3: Power input characteristic of different stirrers with and without baffles for homogeneous Newtonian liquids

Fig. 5.4: Mixing time characteristic of different types of agitators for Newtonian liquids of similar density and viscosity

118

Fig.5.5: Sauter mean diameter of polymer particles produced by suspension polymerization at different Weber numbers, stirring speeds and surfactant concentrations (1 : 0.11 %, 2 : 0.13 %, 3 : 0.17 %)

Fig. 5.6: Effect of gas flow number Q on Newton number Ne in stirred reactor Ne = P/(N 3 d 5), Q = q/(Nd 3), q=V/t

119

Fig. 5.7: Effect of specific power input on liquid-side mass transfer coefficient in bubble column reactor filled with different liquids containing polyethylene particles

Fig. 5.8: Distribution of glass beads in stirred tank reactor at different stirring speeds

120

Fig. 5.9: Comparison of mixing effectiveness of different agitators at different power input

Fig. 5.10: Calculated mass transfer coefficient for spherical particles of different size settling at terminal velocity in a liquid

121

Fig. 5.11: Different methods of heat removal from stirred tank reactor

Fig. 5.12: Decrease of heat transfer coefficient and increase of viscosity with conversion of solution polymerization in a stirred tank reactor (helical ribbon agitator, 160 rotations per minute)

122

Fig. 5.13: Effect of stirring speed on cooling capacity of stirred tank reactor

123

Fig. 5.14: Stability diagram of reactor at stationary state with  = 388 min Curve a: heat production Curve b: heat removal

Fig. 5.15: Transition characteristic of operating point at an increase of jacket temperature from 85 to 870C at time zero

124

Fig. 5.16: Temperature run away phenomena at different failures of operation a : monomer feed and cooling fail completely b : monomer feed stops but cooling by jacket works

Fig. 5.17 Tracer concentration-time correlation of a pulse experiment

125

Fig. 5.18: Transforming the experimental concentration curve into the exit age curve E

Fig. 5.19: Tracer concentration-time correlation of a step experiment

v F  C M

Fig. 5.20: Transforming the experimental tracer concentration curve into the F curve (transition function)

126

E



Fig. 5.21: RTD of a cascade of equal sized stirred tank reactors (with N=1, 5 and )

127

v v Vm V va

V vb d

Fig. 5.22: Compartment models for stirred tank reactors with dead zone (left) and bypass (right)

128

Fig. 5.24: Parabolic flow velocity profile and residence time distribution of laminar flow in pipe

129

Fig. 5.25: Dimensionless conversion-time correlations of different stirred tank reactors for 1. order polymerization reaction with k = 10-4 s-1

Fig. 5.26: Reactor capacity of different stirred tank reactors as function of time and -4 -1 conversion. First order polymerization with CM,0 = 5 mol/l and k=10 s

130

Fig. 5.27: Concentration profiles and residence time distribution of different stirred tank reactors

Fig. 5.28: Effect of segregation on conversion. Polymerization reaction of 0. and 1. order

131

Fig. 5.29: Compartment model of a continuous stirred tank reactor and the correspondinng residence time distribution (CSTR)

Fig. 5.30: Effect of volume fraction of dead water and plug flow on relative conversion of stirred tank reactor at two different reference conversions (0.2 and 0.8)

132

Fig. 5.31: Relative cumulative degree of polymerization (weight and number average) as function of conversion of free radical polymerization without chain transfer reactions

Fig. 5.32: Weight distribution of chain length of instantaneously formed polymer by free radical polymerization in batch reactor at small conversion increments

133

Fig.5.33: Dispersion index (D=Pw / Pn) of polymers produced by free radical polymerization in different stirred tank reactors as function of conversion (dotted line: termination by disproportionation, solid line: termination by combination)

Fig.5.34: Cumulative degree of polymerization as function of conversion of condensation polymerization

134

Fig.5.35: Molecular weight distribution of polymer formed by condensation polymerization in a batch reactor

Fig. 5.36: Dispersion index D =PW/PN as a function of degree of condensation polymerization in different reactors

135

Fig.5.37: Composition of the copolymer produced in a batch reactor as function of monomer composition of charge as well as conversion First column: instantaneous composition; second column: instantaneous compositions, starting with cM,1:cM,2=1:3, 1:1 and 3:1; third column: cumulative compositions based on the same starting ratios

Fig. 5.38: Copolymer composition distributions of different pairs of monomers. Complete polymerization in a batch reactor for three different molar ratios of monomer (CM,1 : CM,2 = 1 : 3 (first column) 1 : 1 (second column) and 3 : 1 (third column) F1 : mol fraction of monomer 1 in the copolymer)

136

Fig.5.39: Continuous copolymerization in a stirred tank reactor of styrene (f1=0.4) and acrylonitrile(f2=0.6). Composition of accumulated copolymer F1 and F2 as a function of conversion

Fig. 5.40: Scale-up of stirred tank reactor

137

Fig. 5.41: Penney diagram with different scale-up criteria

138 6. POLYMERIZATION PROCESSES

6.1 General Aspects Chainwise polymerization reactions are characterized by the following features: - Strong increase in viscosity of a reaction mixture during the entire course of polymerization - Kinetics of reaction can be very sensitive with respect to small amounts of impurities like free radical scavangers or catalyst poisons - Non-uniform polymers are formed due to the mechanism of polymerization - Polymerization reactions are strongly exothermic and in general non reversible at reaction conditions

Stepwise polymerization reactions are in general reversible reactions. The viscosity of the reaction mixture increases strongly only at very high conversion of functional groups. Typical condensation reactions are relatively slow running reactions with low reaction enthalpies. They have to be run at high conversion in order to get polymers with high molecular weight. Another important parameter which also affects molecular weight is the exact stoichiometry of functional groups. The stoichiometry of reactants must be carefully controlled.

Industrial polymerization processes are in general continuous processes run at constant temperature and pressure. The structure of a typical polymerization process is characterized by physical and chemical treatment steps (see Fig. 6.1). The materials entering the polymerization process undergo first a number of physical treatments like purification, mixing, heating, or cooling. Then the monomers are polymerized in a suitable reactor at certain reaction conditions. After chemical reaction the reaction mixture is again treated in physical ways in order to recover the polymer in such a form and quality as demanded by customers. Purification of monomers and solvents for chainwise polymerization focuses on the removal of traces of free radical scavangers and catalyst poisons. In general separation processes like distillation and adsorption are used for this purpose. In the case of stepwise polymerization the complete removal of monofunctional monomers is of interest, otherwise no polymers with high molecular weight can be produced. Purification of polymers at the end of a polymerization process deals with the removal of unreacted monomer from the polymer. The effective removal of monomer from the polymer is a demanding task. Heating, evaporation, and effective mixing of polymer are the appropriate procedures of purification. Effective compounding of polymers with property improving additives at the end of a polymerization process is also an important polymer treatment step. In general extruders are used for this purpose.

139 The development of a new polymerization process starts with the choice of the chemical polymerization reaction for synthesis of a wanted polymer product. Today especially coordination and condensation or addition polymerization reactions are of special interest. These reactions allow the synthesis of polymers with a special architecture or special chemical composition. The next step in process development is the choice of a suitable polymerization procedure. Polymerization in heterogeneous systems can have some advantages in comparison to homogeneous systems, like better mixing of a reaction mixture or better heat removal due to lower viscosities. From a commercial point of view the bulk phase polymerization is a suitable process since no solvent or diluent has to be used. Mixing and heat removal however can cause problems. The next stage in process development is the choice of reactor type and its mode of operation. In the case of continuous polymerization process the residence time distribution of reactor can have an effect on reactor performance and polymer quality. Very often a cascade of reactors is used. The polymerization reactor is the heart of a polymerization process, but the right choice of appropriate physical treatment steps before and after chemical reaction can also have a large impact on performance of a polymerization process. In Tab. 6.1 the different steps of process development in polymer production are summarized. In general the type and amount of polymer to be produced will be given. Decisions have to be made on the type of polymerization reaction, method of polymerization, conditions of polymerization, type of reactor, and on the type of unit operations.

6.2 Processes for Chain-Growth Polymerization

Solution Polymerization/High Density Polyethylene

For polymerization in solution good solvents have to be used to dissolve the monomer and also the polymer formed. The solvent should be chemically inert and easy to recover after polymerization. The advantage of polymerization in solution is the lower viscosity of reaction mixture than in bulk polymerization in the absence of a solvent. By this means good control of mixing and heat removal is possible. Initiator or catalyst efficiency can also be better than in homogeneous bulk polymerization due to better agitation of the reaction mixture. Disadvantages of solution polymerization are the costs for removal and recovery of solvents and the tendency of formation of polymer deposit on the wall of the reactor. The scale of polymer on the walls of the reactor has to be removed in order to maintain good heat transfer and avoid inclusion of gelled polymer in the final product. Polymers are recovered from solution polymerization by flushing off the solvent. The polymer formed is in general a fluffy powder which must be compacted in separate melting and granulation process. Major polymers produced by polymerization in solution are high

140 density polyethylene, 1,4-cis-polybutadiene and polystyrene. Hexane is used in general in the case of ethylene and butadiene polymerization. But also bulk polymerization of ethylene at high pressure and temperature must be regarded as solution polymerization in a homogeneous medium since the polymer formed is completely dissolved in its own monomer at the reaction conditions given. In Fig. 6.2 the flow diagram of solution polymerization process of ethylene with Ziegler-Catalysts is shown. Ethylene, a comonomer, and hexane are mixed in an absorber at low temperature. Then the solution is cooled down to -40 0C and pumped into the stirred tank reactor together with the catalyst solution. The polymerization is run in the temperature range of 130 to 2500C to keep the polymer formed in solution. The corresponding pressure is in the range of 30 to 200 bar. The mean residence time of the reaction mixture is on the order of 10 minutes. This corresponds to a conversion of monomer of about 95%. The concentration of polymer in solution is about 5 to 10 wt % and affects strongly the viscosity of the reaction mixture. The viscosity is also affected by the molecular weight of polymer. The molecular weight of polymer is controlled by the temperature of polymerization. The viscosity is controlled on-line during the course of polymerization. After passing the reactor the reaction mixture is pumped into a flash tank where solvent and monomer are removed partially from the reaction mixture by evaporation and desorption. The concentrated polymer solution is then pumped into a mixer and mixed with additives like stabilizers, pigments, processing agents, and so on. Then the concentrated polymer solution is pumped into a second flash tank where most of the solvent is removed. Finally, the polymer melt is transfered into an extruder where it is mixed with further additives and degassed. At the exit of the extruder the polymer melt is cut by a rotating knife and simultaneously cooled down by rinsing with water. After drying, the polymer granules are ready for packaging. The production performance of a solution process is due to the high rate of polymerization, with approximately 1 kg of polymer produced per liter of reactor volume and hour at 1300C. The polymer produced is characterized by relatively low molecular weight and narrow molecular weight distribution, and therefore used as material for injection moulding processing.

Suspension Polymerization/Poly(vinyl chloride) Suspension polymerization is a water-cooled bulk polymerization. Liquid monomer with dissolved initiator is dispersed in water by vigorous stirring. The droplets formed are transformed during polymerization into sticky, highly viscous particles, which become rigid and have diameters in the range of 100 to 1000 m. To prevent coalescence of the sticky particles during the course of polymerization proper stabilizing agents have to be used. In general water soluble natural or synthetic polymers are used, like cellulose derivatives or poly(vinyl alcohol). Proper agitation of the reaction mixture is important since the monomer is less dense than water while polymer is in general more dense

141 than water. The viscosity of the heterogeneous system remains fairly constant during a polymerization reaction and is determined mainly by the water phase, but also by the volume fraction of polymer. The final reaction mixture typically contains about 30 volume percent of polymer. Suspension polymerization is the only procedure of polymerization which cannot be performed in a continuous way. In industry up to now only batch processes are known. This is mainly due to the tendency of the reaction mixture to form deposits of polymer on the wall of reactor. This fact prevents any continuous processing since polymerization must be stopped too often for cleaning of reactor. Suspension polymerization is applied in industry for production of poly(vinyl chloride), expandable polystyrene, and high impact polystyrene. The major process for poly(vinyl chloride) production is suspension polymerization. In Fig. 6.3 the flow diagram of the poly(vinyl chloride) suspension polymerization process is given. It is a batch process with cycle times of less than 8 hours. Liquid vinyl chloride and water with dissolved surfactant and initiator are fed into the stirred tank reactor which can have a volume up to 200 m3. Then the reactor content is heated up to temperatures in the range of 50 to 700C, resulting in pressures of 8 to 12 bar. Very often steam is used for direct heating of the reaction mixture. The temperature of reaction determines the molecular weight of polymer formed. The higher the temperature the higher the rate of initiator decomposition and the lower the molecular weight of the polymer formed. The effect of temperature of reactor and jacket as well as pressure are given in Fig. 6.4 for a typical batch polymerization of vinyl chloride in suspension. From the differences of temperatures one can see that the rate of heat production, resulting from rate of polymerization, is increasing with increasing conversion and reaches a maximum value at a conversion of about 70%. Then the rate of polymerization falls. Simutaneously the pressure of the reactor is falls. This is the stage of polymerization where vinyl chloride is no longer present as a separate liquid phase. The rest of vinyl chloride is completely absorbed by the polymer produced. Heat of reaction is removed by the cooled jacket of the reactor and also by an external heat exchanger via evaporation and condensation of vinyl chloride. At about 90% conversion, which is measured by calorimetry, the reaction is stopped. The hot suspension is filled into a storage tank and from there pumped into a degasifier to remove the vinyl chloride left in the polymer particles. This is done by heating and applying vacuum. After an intensive demonomerization of the polymer the suspension is conveyed into a continuous centrifuge. The wet product (20 to 30% water) is then dried first in a pneumatic dryer and then in a fluidized-bed dryer by using hot air. To remove small polymer particles from the air passing through the dryers, cyclones and gas filters are used. One major parameter of the polymer produced is the porosity of the particles, which is responsible for the absorbing capacity of the particles with respect to liquid plasticizers. The absorbing capacity of the polymer particles can be influenced by the kind of surfactants used for stabilizing the

142 monomer droplets. The size of the particles formed is affected by the physical properties of the monomer/water emulsion (surface tension, viscosities, densities), by the polymerization conditions (stirring speed, temperature, concentration of chemicals), and by the geometries of the reactor and stirrer used.

Emulsion Polymerization/Styrene-Butadiene-Copolymer The most important process for production of synthetic rubber based on styrene and butadiene copolymers is the emulsion polymerization. Emulsion polymerization is also used for production of poly(vinyl chloride) and acrylo nitrile- butadiene-styrene copolymers. The advantages of emulsion polymerization are:

- Low viscosity of the reaction mixture during the entire course of polymerization. - Polymers with high molecular weight are formed at high rates of polymerization. - Highly concentrated polymer latex is formed which can be used directly for further applications.

These benefits make emulsion polymerization a frequently used process of polymer production in free radical polymerization. The polymer particles of the latex produced are normally in the range of 100 nm in diameter and the latex contains in general 50% polymer. In Fig. 6.5 the flow diagram of an emulsion polymerization process for production of styrene-butadiene copolymer is shown. Since polymerization is run at 50C the rubber produced is called “cold“ rubber and is characterized by a relatively high content of trans-1,4- butadiene units, which has a positive effect on some technological properties of the rubber. The process starts with the emulsification of monomers and molecular weight modifiers in water with dissolved emulsifiers, which are in general natural soaps. The emulsion is than cooled down to 50C and the redox initiator is added. First the reducing agent (sodium formaldehyde sulfoxylate), then the hydroperoxide is added. The polymerization is performed in a series of six to ten well agitated reactors. Since the reaction temperature greatly influences polymer properties, the heat removing system must be well designed. In general heat is removed by evaporation cooling of ammonia, which is pumped through coils placed within the reactors. After an average reaction time of 8 to 10 hours the polymerization reaction is stopped at a conversion of 60 to 70%. At higher conversions polymer properties would be affected in a negative way due to formation of long chain branching and crosslinking. The latex is then flashed into two drums. The first one being at atmospheric pressure and the second one working under vacuum. In these drums butadiene is removed. The latex is then

143 pumped to the top of a stripping column operating in vacuum. The latex passes downward over perforated plates counter-current to steam. The monomer-free polymer dispersion is then mixed with additives like carbon black, oil, antioxidant and then pumped into a coagulation tank where acid (H2SO4) and brine (Al2(SO4)3) is added. Coagulation usually takes place in two well-agitated vessels. During this operation the rubber is precipitated in the form of porous crumbs, which are washed free of salt and acid and then dried and baled.

Slurry Polymerization Process/High Density Polyethylene The polymerization of olefins in a suspension or slurry is a suitable process for production of polyolefins like polyethylene and polypropylene. The polymerization is catalysed by different types of heterogeneous catalysts dispersed in an inert liquid, like hydrocarbons with low boiling points. The polymer formed is insoluble in the liquid phase at the polymerization temperature. It forms particles with morphologies which are more or less a replication of the catalyst particles. The major advantage of a slurry polymerization process is the relative low viscosity of the reaction mixture, which favours good mixing and heat removal in the reactors used. Stirred tank and loop reactors are used in general, with reactor volumes up to 100 m3. The reactors are run at pressures of 10 to 20 bar and temperatures of 80 to 1000C. The average residence time in stirred tank reactor is 2 to 3 hours and in loop reactors 0.5 to 2 hours. The performance of reactors is in general controlled by the process of heat removal. The slurry leaving the reactor has a solid content of about 50 wt %. Unit operations for isolation of the polymer are centrifugation, steam stripping, and drying of the powder. The powder is then mixed with additives and granules are formed by using extruders. The molecular weight of the polymer is controlled by hydrogen or by temperature. The distribution of the molecular weight can be controlled by the nature of the catalyst used or by means of process technology, like using a train of reactors run at different reaction conditions. Small amount of comonomers are used to modify the density of the polymer and to increase the toughness or resistance to stress cracking. In Fig. 6.6 the flow diagram of a slurry polymerization process for polyethylene production is given. It is based on developments of former Hoechst company. The ethylene used for polymerization is in general supplied by modern plants in such a quality that it may be polymerized with little or no further purification. In Tab. 6.2 the specification for such a polymerization grade ethylene is given. Commercial catalysts for polymerization of olefins are in generel heterogeneous catalysts. The catalytic active complexes are fixed on the surface of appropriate supports, which are porous particles with diameters in the range of 50 to 100 m. These catalyst particles are first dispersed in a diluent and then pumped into the reactor with such a rate that the performance of the reactor is kept at a

144 constant level. Pressure and temperature are also kept constant during polymerization. In Fig. 6.6 only one reactor is shown but also two or more reactors in series are used. The slurry is passed into a pressure release vessel where most of the ethylene is removed and then pumped into a centrifuge to remove most of the diluent from the polymer. The diluent is recycled directly to the reactor. The polymer is transferred from the centrifuge into a stripper, where the rest of the diluent is stripped off the polymer by using steam, which is blown into the stirred product. After a second centrifugation step the wet product is dried in a fluidized-bed drier using hot air. Additives are then added to the polymer powder in a mixer, and this mixture is then pelletized in an extruder and finally dried in a moving bed dryer.

Gas Phase Polymerization Process/High Density Polyethylene Gas phase polymerization is applied only for production of polyolefins like polyethylene and polypropylene or copolymers of ethylene and propylene by using heterogeneous catalysts with particle diameters of about 50 m. Gas phase polymerization processes are relatively simple processes, particularly if the customers are able to use the directly produced polymer particles without any pelletization process. A further advantage of the process is that no diluents are used. Since the process operates close to the melting point of the polymer, accurate temperature control is necessary, and is done by regulating the rate of catalyst addition into the reactor. If a thermal run away polymerization is detected, carbon dioxide can be injected into the reactor to poison the catalyst. Problems may also arise if polymer films are formed on the surface of reactor due to electrostatic charge of the fluidized particles. In Fig. 6.7 the flow diagram of the gas phase polymerization process for high density polyethylene production is shown. Ethylene, comonomer, hydrogen, and catalyst are injected into a fluidized-bed reactor. The reaction zone is the lower part of the reactor. In the upper expanded section of reactor the gas velocity is lowered, allowing the particles to fall back into the reaction zone. The lower part of the reactor has a diameter of about 4 m and a height of 10 m. The overall height of the reactor is ca. 30 m. The gas phase enters the reactor through a distributor plate, which manages an even distribution of the gas phase across the cross-sectional area of reactor. The reactor operates at 80 to 1000C and a pressure of 20 bar. The average residence time of the particles is 3 to 5 hours. The residence time distribution corresponds more or less to a continuous stirred tank reactor with back mixing of material and heat throughout the total reaction zone. The conversion of monomer per pass of reactor is ca. 2%. Heat removal takes place more or less by the circulating gas phase. The gas flow necessary for heat removal is given by following equation:

145 m   H  V  R  c p  T with m being the production rate of polymer, HR is the reaction enthalpy of polymerization,  and cp are the density and specific heat capacity of the gas phase, and T is the temperature difference of gas phase before entering the reactor and the reaction temperature. The recycled gas flow is cooled down by passing through a gas cooler before entering the reactor. Polymer particles are taken out of reactor by a sluice working in short intervals via sequenced valves. The polymer powder passes a cyclone, from which residual monomers are recovered. Then it is recompressed and transferred back into the main pipeline of monomer. The polymer powder flows from the cyclone into a purge tank where final amounts of monomers are removed from the product.

6.3 Processes for Step-Growth Polymerization In typical step-growth polymerization reactions like polyester or polyamide synthesis the growth of macromolecules is a relatively slow process compared to chain-growth polymerization reactions. The activation energies of these step growth reactions are in the order of 85 kJ/mol. To accelerate the rate of reaction catalysts and elevated temperatures are used. The enthalpy of polyester or polyamide synthesis is relatively low at –10 to –20 kJ/mol. In this case heat removal is not a problem. When these kinds of condensation reactions are accelerated by application of heat and catalysts, depolymerization reactions become important. This will affect the conditions under which the reactions are carried out. Since step-growth polymerization reactions have unfavorable equilibrium constants it is therefore customary to operate the process at high temperatures and reduced pressure to remove condensation products like water or alcohol from the reacting system. Very high conversions have to be achieved in order to get polymers with high molecular weights suitable for technical applications. The rate of condensation polymerization is often limited by the rate of transfer of condensation products like water or alcohol from the liquid, or the solid phase into the vapor phase. A kinetic model must then include both the kinetics of the chemical reaction and mass transfer. Mass transfer will strongly depend on reactor design and operation conditions like stirring. But step-growth polymerization reactions can also be very fast and very exothermic reactions. The synthesis of polyurethanes or phenol-formaldehyde resins are examples of such reactions. In this case lower reaction temperatures are applied. The following examples of step-growth polymerization processes will refer to the synthesis of linear and crosslinked products. Linear polymers are

146 thermoplastic materials, crosslinked polymers are non-meltable materials at their final stage of production.

Condensation Polymerization in Solution/Phenolic resins An important type of polymers produced by step-growth polymerization are nonlinear polymers formed by condensation polymerization of monomers with more than two functional groups per molecule. One major type of network polymers are the phenolic resins. Phenolic resins are polycondensation products of phenol and formaldehyde. The ring hydrogens in para- and ortho-position of the phenol molecule can react with formaldehyde to form hydroxymethyl- substituted phenols which can then start condensation reactions with the formation of methylene bridges or dimethylene ether bridges and elimination of water. The production of phenolic resins is stopped at a stage where oligomers are formed, which are thermoplastic materials and can be cured afterwards during processing in molds. Phenolic resins are classified as novolacs and resols. They have different curing properties and are used in different applications. The production of phenolic resins takes place in general in batchwise processes because a very great variety of types are produced in relatively small quantities. The phenolic resin plant shown in Fig. 6.8 can be used for all steps in batchwise production. Phenol in the molten state is fed into the reactor first and catalyst and formaldehyde dissolved in water (30 w-%) are then added. The rate of formaldehyde addition is controlled depending on the heat evolved. Substitution and condensation reactions between phenol and formaldehyde are strongly exothermic with about -99 kJ/mol and can proceed very vigorously. Therefore appropriate cooling is important. Cooling is done by evaporation of volatile liquids. The temperature of reaction is either 60 or 1000C, depending on synthesis of resols or novolacs. At the end of the reaction the volatile parts of the reaction mixture are distilled off under reduced pressure. The molten resin as residue is then removed from the reactor. Rapid emptying of the reactor and cooling of the resin is important to avoid further condensation of the product. Cooling is done in a cooling conveyer filled with water. The product is then milled, sieved, and mixed with different additives and fillers.

Condensation Polymerization in Melt and Solid State/Poly(ethylene terephthalate) In Fig. 6.9 the flow diagram of continuous polymerization process for production of poly(ethylene terephthalate) is shown. Dimethyl terephthalate, ethylene glycol and catalysts are fed into a series of Robert-evaporators in which the ester interchange reaction takes place at temperatures of 150 to 2100C and atmospheric pressure. Bis (hydroxyethyl) terephthalate and methanol are formed primarily. Methanol and ethylene glycol emerging from the reactors are passed through a rectifying column and ethylene glycol is fed back into the reactors. At

147 a conversion of about 90 to 95%, which is achieved at a hold up time of 4 to 6 hours, the reaction mixture is transferred into the first stage of a condensation polymerization unit. The reaction mixture consists of oligomers, mainly dimers and trimers. In this series of stirred tank reactors the temperature is increased to 265-2850C and the pressure is lowered to about 50 mbar to keep the condensation fast and the reaction mixture molten. After a hold-up time of 2 to 3 hours, which corresponds to a conversion of functional groups of about 0.95 to 0.97, the melt with a degree of polymerization of 20 to 30 is passed into a rotating disc reactor. In this reactor the pressure is lowered even further to 1 mbar in order to remove ethylene glycol almost completely from the polymer melt. The reaction temperature is kept at 265 to 2850C. The reaction rate is controlled by mass transfer limitation. After a residence time of 2 to 3 hours the polymer melt leaves the rotating disc reactor with a number average degree of polymerization of about 120, which corresponds to a conversion of functional groups of 0.99. To attain even higher molecular weights the products may be subjected to solid-state post condensation within moving bed reactors at 2500C for 20 hours. The reactor is then purged with nitrogen gas or put under vacuum. The direct esterification of terephthalic acid with ethylene glycol is gaining more importance because of some advantages like better polymer properties, no usage of catalyst, and no handling of methanol.

Addition Polymerization in Liquid Medium Polyurethanes Polyurethanes are produced either by the so called prepolymer process or by the one-shot process. In case of the prepolymer process a diol is reacted with an excess of a diisocyanate. The prepolymer formed contains an excess of isocyanate groups which are reacted in a second step with low molecular weight diols, diamines, or water to form the final end product. The polyurethanes formed are two phase systems containing hard and soft domains. In general they are used as elastomers. The one-shot process is a much more simple process. In this case all reaction components are well mixed simultaneously and react with each other in a rather short time to a nearly complete conversion. If the reacting partners have the same reactivity the polyurethanes formed have a statistical composition of the two monomer units. The one-shot process is used in general for production of polyurethane foams. The fundamental reaction in this case is the reaction of the isocyanate group with water. The resulting carbon dioxide is used as the foam formation agent. In Fig. 6.10 the flow sheet of a foam forming plant is shown. The process consists of two storage vessels, which can be heated. In one vessel polyol, catalyst, surfactant, foaming agent and other additives are placed. The other vessel contains the multifunctional isocyanate. Both reaction mixtures are in the liquid state at reaction temperatures above 500C. Before injecting the liquids into the mixing head the feed streams are first recycled by using accurate dosing

148 pumps. When the right feed ratio is adjusted the fluids are pumped into the mixing chamber via nozzles, and are well mixed by the turbulence created in a very short time. The further processing of the reaction mixture depends on the product to be produced. In case of foam slabs or blocks the reaction mixture is sprayed on a circulating band. If the reacting components are very reactive the so called technique of reaction injection molding (RIM-technique) can be used for production of moldings of different shape. In this case the exit of the mixing chamber is pressed against the entry of the mold and the reaction mixture is injected into the mold. The entire polyurethane formation is completed within a few minutes. The mold is then split open to discharge the final product. So called integral foams are obtained if the foaming process is controlled so that moldings are produced that have a closed surface and a cellular core. The mixing head of the reaction injection molding plant is a very sophisticated part of the plant. The sketch of a pressure controlled mixing chamber is shown in Fig. 6.11. The upper sketch shows the mixing chamber at mixing conditions. The lower sketch refers to the state of cleaning of the mixing head.

6.4 References - „Ullmann´s Encyclopedia of Industrial Chemistry“, Vol A 21 and 23,VCH, 1992 - „Encyclopedia of Polymer Science and Engineering“, 19 Volumes, H.F. Mark, N.M. Bikales, C.G. Overberger, G. Menges (Eds.), John Wiley and Sons, 1990 - F. Rodriguez: „Principles of Polymer Systems“, Hemisphere Publishing Corporation, 1989

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6.5 Tables and Figures

Polymerization Chain or stepwise polymerization Reaction reaction

Polymerization Solution, bulk, suspension, Method emulsion, slurry, gas phase

Polymerization Temperature, pressure, conversion, Conditions continuous, batch, semi-batch

Polymerization Stirred tank or loop, bubble Reactor column, fluidized bed, tubular reactor

Unit Operations Purification, Mixing, Conveying, Separation, Molding

Tab. 6.1: Steps of decision in development of a polymerization process

C2H4 > 99.9 vol %

CH4, C2H6, N2 < 1000 vol ppm Olefins + diolefins < 10 vol ppm Acetylene < 2 vol ppm

H2 < 5 vol ppm CO < 1 vol ppm

CO2 < 1 vol ppm

O2 < 5 vol ppm Alcohols (as MeOH) < 1 vol ppm

H2O < 2.5 vol ppm Sulfur < 1 vol ppm Carbonyl sulfide < 1 vol ppm

150 Tab. 6.2: Specifications for polymerization-grade ethylene (Data from Repsol)

Fig. 6.1: Structure of a typical polymerization process

Fig. 6.2: Flow diagram of solution polymerization process for high density polyethylene production

151

Fig. 6.3: Flow diagram of suspension polymerization process for poly(vinyl chloride) production

Fig. 6.4: Course of temperature and pressure during suspension polymerization of vinyl chloride

152

Fig. 6.5: Flow diagram of emulsion polymerization process for production of styrene-butadiene copolymer

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Fig. 6.6: Flow sheet of liquid slurry polymerization process for high density polyethylene production (Hoechst)

154

Fig. 6.7: Flow diagram of gas phase polymerization process for production of high density polyethylene (Union Carbide)

Fig. 6.8: Flow sheet of condensation polymerization process of phenol and formaldehyde in solution

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Fig. 6.9: Flow diagram of polycondensation process for production of poly(ethylene terephthalate) (Vickers-Zimmer)

Fig. 6.10: Flow sheet of a polyurethane foam production process

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Fig. 6.11: Sketch of the mixing chamber for polyurethane production

157