Kinetic modeling of the initiator decomposition for...

Faculteit Ingenieurswetenschappen

Vakgroep Chemische Proceskunde en Technische Chemie

Laboratorium voor Petrochemische Techniek

Voorzitter: Prof. dr. ir. G. B. Marin

Kinetic modeling of the initiatordecomposition for suspension

polymerization of vinyl chloride

Auteur: Sophie Van Nevel

Promotor: Prof. dr. ir. G. B. Marin

Prof. dr. lic. M. F. Reyniers

Begeleider: ir. J. Wieme

Afstudeerwerk ingediend tot het behalen van de graad van

burgerlijk scheikundig ingenieur

Academiejaar 2006–2007

Kinetic modeling of the initiator decomposition for suspension


door

Sophie Van Nevel

Scriptie ingediend tot het behalen van de graad van burgerlijk scheikundig ingenieur

Academiejaar 2006-2007

Universiteit Gent

Faculteit Toegepaste Wetenschappen

Promotor: Prof. dr. ir. G. B. Marin

Promotor: Prof. dr. lic. M.-F. Reyniers

Begeleider: ir. J. Wieme

Overview

In this master thesis, the kinetic modeling of the initiator decomposition in the sus-

pension polymerization of vinyl chloride is discussed into detail. In a preliminary chapter

(Chapter 1), some general aspects of the vinyl chloride suspension polymerization are dis-

cussed. Special attention is given to the role of the initiator in the industrial production

of PVC.

After this preliminary chapter, the main work consists of 2 parts: the modeling of the

initiator efficiency and network generation.

A detailed study of the initiator efficiency f can only be made when the reaction me-

chanism of the decomposition of the initiator is completely understood. Hence, Chapter

2 gives a classificiation of the initiators commonly used in industry, and presents their

decomposition mechanism. Chapter 3 deals with a more detailed study of the initiator

efficiency f . Two modeling strategies for the initiator efficiency will be discussed. An

analytical expression is derived for the initiator efficiency f based on a reaction scheme as

presented by Kurdikar and Peppas (1994).

In Chapter 4, the kinetic parameters used in the model of Kurdikar and Peppas (1994)

are reported and the kinetic modeling results are presented for each class of industrial

initiator.

The concept of initiator efficiency is used because of the difficulty of tracing all possible

occuring reactions and accompanying kinetic parameters. Once the kinetics of the initi-

ator decomposition, both standalone and embedded in a complete reaction network, are

described into detail, the initiator efficiency is no longer required. In the second part of

this thesis, the concept of generating a reaction network is presented (Chapter 5). An ap-

propriate representation for reactants and products is obtained. With this representation,

an investigation of how to track a reaction is performed. Finally, a computer simulation

program is developed, which allows for the generation of complete reaction network.

Chapter 6 gives a general conclusion of this thesis and mentions recommendations for

further work. This thesis ends with a Dutch summary (Chapter 7).

Thank you...

All good things come to an end... en dus ook mijn studententijd in Gent. Dit laatste

jaartje werd in het bijzonder ’gekleurd’ door het thesissen. Het tot stand komen van zo’n

werk kan niet zonder de nodige steun, waardering en ontspanning. Daarom wil ik ook een

aantal mensen een woordje van dank toewerpen.

Vooreerst is er mijn begeleider Joris Wieme, die ik wil danken om dit werk door te le-

zen en aanwijzingen te geven. Mijn promotoren Prof. dr. ir. G.B. Marin en Prof. dr. lic.

M.F. Reyniers verdienen een woordje van dank voor de geboden kansen aan dit labo.

Geen thesisdag ging voorbij zonder de klasgenootjes in de sterre of dat klasgenootje buiten

het lpt. Pieter voor vele amusante gesprekken en het gedichtje, Jan ’Jantje Smit’ voor de

muzikale noot, de brugstudenten Wim, Jeroen, Hans en Jerry om me het leven als brugstu-

dent te verduidelijken, Steven voor de kritische opmerkingen, Kim voor het verhogen van

de chauffage, en tot slot Anneleen voor de vele onvergetelijke verhaaltjes, feestjes die we

samen beleefden, en gewoon schitterende studententijd in Gent! Daarnaast wil ik ook mijn

vrienden buiten de scheikunde bedanken, want zonder jullie zouden die fuiven, goliardes,

kotfeestjes en sportactiviteiten heel wat minder leuk geweest zijn. Het gaat jullie allemaal

goed!

Zonder de aanmoedigingen van mijn ouders en broer zouden deze studies er heel anders

uitgezien hebben. Ik wil hen niet alleen voor de studiekansen bedanken, maar nog meer

voor de warmte en steun thuis.

Misschien op het einde van dit woordje, maar het beste voor ’t laatste: dankje schat, geen

dag was zo zonnig, relaxed en liefdevol als met jou erbij!

Sophie

Kinetic modeling of the initiator decomposition forsuspension polymerization of vinyl chloride

Sophie Van Nevel

Supervisor(s): Prof. Dr. Ir. G. B. Marin, Prof. Dr. Lic. M.-F. Reyniers

Abstract—The kinetics of the initiator decomposition can be modeled in se-veral ways. The concept of initiator efficiency f is introduced first. For mostindustrial initiators the kinetic modeling of Kurdikar and Peppas (1994) [1] isable to model the initiator efficiency in an accurate way. In a second model, areaction network is generated to describe the kinetics of initiator decompositionmore into detail. If the kinetics of the initiator decomposition, both standaloneand embedded in a complete reaction network, are described accurately, a morefundamental description of the kinetics of initiator decomposition is obtained.The initiator efficiency then results from this description.

Keywords—vinyl chloride, suspension polymerization, initiator decomposi-tion, initiator efficiency, reaction network

I. Introduction

POLYMERS are one of the most widespread consumer pro-ducts in the world. Because of its versatility and low pro-

duction cost, poly(vinyl chloride) (PVC) has become an impor-tant polymer with an annual world production of 30 Mton. Thesuspension polymerization of vinyl chloride monomer (VCM)contributes for about 80% of the total PVC production. This pro-cess is carried out in a batch reactor with the monomer dispersedin water. The dispersion is maintained by adding suspension sta-bilizers and by stirring. An initiator is dissolved in the monomerphase. Polymerization is started by bringing the reactor to thedesired polymerization temperature. Due to the low solubility ofPVC in VCM, two phases are formed in the reactor: a monomer-rich phase and a polymer-rich phase. The former phase mainlyconsists of monomer, while the latter has a constant composi-tion of approximately 30 wt% monomer and 70wt% polymer.At a conversion of about 65%, the so-called critical conversion,the monomer-rich phase disappears and polymerization occursin the polymer-rich phase only.

II. Kinetic modeling of initiator efficiency

The polymerization of VCM is a free radical polymeriza-tion. During this polymerization, only a fraction of the radicalsformed by dissociation of the initiator is able to initiate a poly-mer chain. This fraction is defined as the initiator efficiency f .Kurdikar and Peppas [1] developed a model that is able to a pri-ori predict the initiator efficiency and continuously calculate theterm f throughout the course of polymerization. This approachdiffers from other modeling approaches in literature [2], becauseempiric relations are excluded, and the calculation is based onan analytical expression with kinetic parameters only. This leadsto a more accurate modeling of the initiator efficiency.

A. Model of Kurdikar and Peppas (1994)

The kinetic scheme of Kurdikar and Peppas is given in Figure1. Inside the solvent cage, depicted by [. . .], the initiator I candecompose into two primary radicals, A• and A1

•. The solventcage defines the region around a radical within which a recom-bination reaction may occur if another radical is found. Becausethe two radicals A• and A1

•, called the ’first radical pair’, are inclose proximity of each other after dissociation, they can recom-bine again. After a single-bond dissociation, this recombinationleads to the formation of the original initiator which will disso-ciate immediately. Hence, this recombination does not lead toa decrease of the initiator efficiency. After a two-bond disso-

ciation, a small molecule is split off and the two initiator radi-cals can recombine to an inert molecule I1. Radicals A1

• maydecompose in the solvent cage to form another primary radi-cal, B•, through a β-scission reaction. Hence a second radicalpair is formed. Again this radical pair is able to recombine toan inert molecule I2. The recombination of A• with A1

• (firstradical pair) and A• with B• (second radical pair) to form in-ert molecules, I1 and I2, are the primary reactions that causethe decrease in initiator efficiency. The radicals A•, B• andA1

• are effective in initiating chains, thus attacking a monomermolecule, M, to form an active monomer molecule. These activemonomers can undergo propagation reactions.

Fig. 1. Reaction scheme of Kurdikar and Peppas

B. Modeling results for industrial initiators

Four classes of initiators are used in industry: peroxydicar-bonates, peroxyesters, dialkyl diazenes and diacyl peroxides.For tert-butyl peroxy-neo-decanoate (TBPD), a peroxyester,the rate coefficients for β-scission are found in literature basedon ab initio calculations. The profile of the diffusion coefficientsis depicted in Figure 2. These diffusion coefficients are calcu-lated with the free volume theory. In this theory, the diffusioncoefficient of the initiator derived radicals is proportional to thevolume of the radicals.

The initator efficiency for industrial initiators varies between0.3 and 0.8. For tert-butyl peroxy-neo-decanoate, the initia-tor efficiency in the monomer-rich phase (f1) is constant, be-cause reactions in the monomer-rich phase are considered tobe reaction-controlled. The polymer-rich phase is consideredto affect the polymerization reactions in becoming diffusion-controlled [2]. The initiator efficiency in polymer-rich phase(f2) drops extremely at the start because of diffusion control,but increases quickly to reach a plateau value which was mod-eled to be 0.69 during the first four hours of the polymerizationprocess (Figure 3). Since the viscosity of the reaction mediumincreases, the diffusive displacement of the radicals away fromeach other becomes difficult and radical recombination reactionsbecome preferred until f2 reaches a limiting value of zero.

For each class of initiator, the kinetic modeling can be per-formed. Together with other initiator characteristics (half-lifetime, reaction heat developed and product quality of the ob-tained PVC), the modeling allows to select the most appropriateinitiator for the used reaction conditions.

10-20

10-18

10-16

10-14

10-12

10-10

10-8

0 2 4 6 8 10

DA

, DB [

m2 s-1

]

polymerization time [h]

DADB

Fig. 2. Diffusion coefficients as a function of polymerization time for tert-butylperoxy-neo-decanoate, for the modeling of Kurdikar and Peppas (1994)

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

f1, f

2 [-

]


f2f1

Fig. 3. Initiator efficiency as a function of polymerization time forTBPD in the monomer-rich phase (f1) and in the polymer-rich phase(f2) (kbd=1.52 10+14exp(-115.47 10+3/RT), kβ =1.00 10+13exp(-50.00 10+3/RT), ktA=ktB1.00 10+4).

III. Generation of a reaction network

A more fundamental way to describe the initiator decomposi-tion into detail is obtained by generating a reaction network, thataccounts for all reaction possibilities for all reactants presentduring initiator decomposition. For this purpose, a computergeneration program is constructed. Each reaction in this net-work assigned a rate coefficient. By taking all reaction possi-bilities into account and describing the kinetics of the initiatordecomposition into detail, the concept of an initiator efficiencyis no longer required but results from the description.

A. Conceptual design of a reaction network

In this work, the network generation principle presented byBroadbelt et. al. [3] is applied. This generation principle al-lows performing the network generation in three steps. The re-actants (molecules or radicals) that are present during the de-composition of the initiator are the input of the network gener-ation program. These reactants need to be represented in sucha way that all relevant structural information is captured. Theselected representation of the reactants must also allow for aneasy description of the reactions, i.e. linking reactant represen-tation and product representation. Six reaction types are takeninto account: dissociation, recombination, addition, β-scission,hydrogen abstraction and Cl-shift. The products (molecules orradicals) are the output of the network generation program. Therepresentation of these products must be analogous to the onefor the reactants. It should be clear that an appropriate represen-tation of the reactants and the products is required. Only oncethis representation is found, operations on these reactants can beexecuted.

B. Representation of the reactants and the products

Basically, the matrix consists of three distinguishable parts:the identification of the atoms, the bonds between the atoms andthe radical position. Each atom receives its own identification

number: 1 for carbon, 2 for oxygen, 3 for nitrogen and 4 forchlorine. This is done because not only C-atoms but also het-eroatoms are involved. These identification numbers are storedin the first row of the matrix.The grey matrix in Figure 4 consists of the bonds between theatoms of the reactant or of the product. There are 4 possibilities:between two atoms there is no bond (’0’), a single bond (’1’), adouble bond (’2’) or a triple bond (’3’).The last row of the matrix shows the radical position. In thisexample the radical is located at atom 1.Consider e.g. a carbonyloxy radical, as depicted in Figure 4 to-gether with its matrix representation. Each atom correspondswith the column in the matrix that has the same number, e.g.atom 1 corresponds with column number 1.

Fig. 4. Matrix representation for an alkoxide radical corresponding with thenumbering of the atoms in the molecule given.

C. Link between reactant and product representation

The selected matrix representation for reactants and productscaptures all structural information: the types of atoms, the bondsbetween the atoms and the radical position. Nevertheless, an ap-propriate representation is only achieved when reactions can bemodeled easily. For each type of reaction, matrix operations onreactants are established, which leads to a stand alone networkgeneration program for each reaction type.

D. Generation of an integrated reaction network

To take into account all reaction types, and thus achieve an in-tegrated network generation program, functionalities need to betraced for each reactant. A decision tree is constructed to com-bine all reaction types. Hence, a network generation programwhich maps all possible reactions for each reaction type sepa-rately, is achieved. To generate this reaction network, a com-puter program has been constructed in Fortran.

IV. Conclusion

Two kinetic modeling strategies to describe the initiator de-composition have been presented in this paper. For most in-dustrial initiators the kinetic modeling of Kurdikar and Peppas(1994) [1] is able to model the initiator efficiency in an accurateway. In a second modeling strategy, a computer program hasbeen devised to generate a reaction network. This allows for amore fundamental view of the kinetics of initiator decomposi-tion.

References[1] Kurdikar D.L. and Peppas N.A., Method of determination of initia-

tor efficiency: application to UV polymerizations using 2,2-dimethoxy-2-phenylacetophenone, Macromolecules, 27:733738, 1994.

[2] De Roo T., Heynderickx G.J. and Marin G.B., Diffusion-controlled re-actions in vinyl chloride suspension polymerization, Macromol. Symp.,206(1):215228, 2004.

[3] Broadbelt L.J., Stark S.M. and Klein M.T., Computer generated reactionmodelling: decomposition and encoding algorithms for determining speciesuniqueness, Comput. Chem. Eng., 20(2):113129, 1996.

i

Contents

1 Vinyl chloride suspension polymerisation 1

1.1 Poly(vinyl chloride) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Suspension polymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Free radical polymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Role of the initiator in the polymerization process of PVC . . . . . . . . . 7

1.4.1 Initiator efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.2 Selection criteria of an initiator for industrial production of PVC . . 9

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Classification of initiators and decomposition mechanism 13

2.1 Reaction types in a decomposition mechanism . . . . . . . . . . . . . . . . 13

2.2 Classification of initiators . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Decomposition mechanism for each initiator class . . . . . . . . . . . . . . 17

2.3.1 Peroxydicarbonates . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.2 Peroxyesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.3 Dialkyl diazenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.4 Diacyl peroxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Modeling of initiator efficiency 27

3.1 Modeling of initiator efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1.1 Semi-empiric modeling of initiator efficiency . . . . . . . . . . . . . 29

3.1.2 Kinetic modelling of initiator efficiency . . . . . . . . . . . . . . . . 30

Contents ii

3.2 Modeling by Kurdikar and Peppas (1994) . . . . . . . . . . . . . . . . . . . 33

3.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2.2 Mass balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.3 Initial and boundary conditions . . . . . . . . . . . . . . . . . . . . 35

3.2.4 Analytical expression of the initiator efficiency f . . . . . . . . . . . 37

3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Implementation of the initiator efficiency 40

4.1 Kinetic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1.1 Effect of kβ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.2 Effect of ktA and ktB . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Diffusion coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.1 Free volume theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.2 Calculation of the free volume . . . . . . . . . . . . . . . . . . . . . 47

4.2.3 Calculation of the diffusion coefficients . . . . . . . . . . . . . . . . 52

4.3 Reaction distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 Modeling results for all initiator classes . . . . . . . . . . . . . . . . . . . . 55

4.4.1 Results for peroxydicarbonates . . . . . . . . . . . . . . . . . . . . 56

4.4.2 Results for peroxyesters . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4.3 Results for dialkyl diazenes . . . . . . . . . . . . . . . . . . . . . . 63

4.4.4 Results for diacyl peroxides . . . . . . . . . . . . . . . . . . . . . . 65

4.5 Selection of the most appropriate initiator for the polymerization of vinyl

chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.5.1 Selection based on characteristics of the polymerization process . . 68

4.5.2 Selection based on characteristics of the polymerization product . . 69

4.5.3 Selection based on kinetic modeling results . . . . . . . . . . . . . . 70

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Generation of a reaction network 72

5.1 Conceptual design of a reaction network . . . . . . . . . . . . . . . . . . . 73

5.2 Matrix representation of the reactants and the products . . . . . . . . . . . 75

Contents iii

5.3 Reactant-product relationships: matrix operations . . . . . . . . . . . . . . 78

5.3.1 Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.3.2 β-scission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3.3 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.3.4 Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3.5 Hydrogen abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.3.6 Cl-shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.4 Construction of a network generation program . . . . . . . . . . . . . . . . 93

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Conclusion 96

6.1 General conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . 99

7 Nederlandstalige samenvatting 100

7.1 Kinetische modellering op basis van initiatorefficientie . . . . . . . . . . . . 101

7.1.1 Initiatorefficientie . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.1.2 Industriele initiatoren . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.1.3 Modellering van de initiatorefficientie . . . . . . . . . . . . . . . . . 102

7.1.4 Simulatieresultaten . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.2 Genereren van een reactienetwerk . . . . . . . . . . . . . . . . . . . . . . . 110

7.2.1 Conceptueel ontwerp van een reactienetwerk . . . . . . . . . . . . . 110

7.2.2 Matrixvoorstelling van de reactanten en de producten . . . . . . . . 111

7.2.3 Link tussen de reactanten en de producten: matrixbewerkingen . . 113

7.2.4 Constructie van een netwerkgenereringsprogramma . . . . . . . . . 114

7.3 Besluit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A Computer code: generating a reaction network 118

A.1 Main program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

A.1.1 Definition of the reactants . . . . . . . . . . . . . . . . . . . . . . . 118

A.1.2 Link with the subroutines . . . . . . . . . . . . . . . . . . . . . . . 120

A.2 Subroutines for each reaction type . . . . . . . . . . . . . . . . . . . . . . . 123

Contents iv

A.2.1 Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

A.2.2 β-scission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

A.2.3 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.2.4 Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.2.5 H-abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.2.6 Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A.3 Complete network generation . . . . . . . . . . . . . . . . . . . . . . . . . 138

B References to labjournal 139

v

List of Figures

1.1 Main applications of PVC . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Three stages during the vinyl chloride suspension polymerization process . 3

1.3 Variation of the initiator efficiency f during polymerization in the monomer-

rich (f1) and polymer-rich phase (f2). . . . . . . . . . . . . . . . . . . . . . 8

1.4 The heat developed during reaction, in case of TBPD. . . . . . . . . . . . . 11

2.1 P,s Cl-shift and s,s Cl-shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Decomposition mechanism of peroxydicarbonates (Verhaert, 2003–2004) . . 19

2.3 Decomposition mechanism of peroxyesters (Verhaert, 2003–2004) . . . . . . 21

2.4 Decomposition mechanism of dialkyl diazenes (Barbe and Ruchardt, 1983;

Krstina et al., 1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Decomposition mechanism of diacyl peroxides (Krstina et al., 1989) . . . . 25

3.1 Schematic representation of the cage effect (De Roo et al., 2004) . . . . . . 28

4.1 Influence of kβ on initiator efficiency f (F0=1, kr1=kr,2=104 m3mol−1s−1

D=10−11 m2 s−1, σA=σB=r0=6 10−10 m)) (Van Pottelberge, 2004–2005) . 43

4.2 Variation of the initiator efficiency f with the rate coefficient ktA (D=10−12

m2 s−1, kβ=105 s−1, ktB=104 m3mol−1s−1, σA=σB=r0=6 10−10 m) (Van

Pottelberge, 2004–2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Variation of the initiator efficiency f with the rate coefficient ktB (kβ=108

s−1, (+) kβ=1010 s−1 (D=10−12 m2 s−1, ktA=104 m3mol−1s−1, σA=σB=r0=6

10−10 m) (Van Pottelberge, 2004–2005) . . . . . . . . . . . . . . . . . . . . 45

List of Figures vi

4.4 Variation of the initiator efficiency f with the initial reaction distance r0

(kβ=108 s−1, (+) kβ=1010 s−1 (D=10−12 m2 s−1, ktA=ktB=104 m3mol−1s−1)

(Van Pottelberge, 2004–2005) . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2)

as a function of polymerization time for di(2-ethylhexyl)peroxydicarbonate

(EHPC), with parameter values as in Table 4.9. . . . . . . . . . . . . . . . 57

4.6 Initiator efficiency in the polymer-rich phase (f2) as a function of polymeriza-

tion time for di(2-ethylhexyl)peroxydicarbonate (EHPC), for the modeling

of De Roo et al. (2004) and Kurdikar and Peppas (1994) . . . . . . . . . . 58

4.7 Diffusion coefficients as a function of polymerization time for di(2-ethyl-

hexyl)peroxydicarbonate (EHPC), for the modeling of De Roo et al. (2004)

(Di) and Kurdikar and Peppas (1994) (DA and DB) . . . . . . . . . . . . . 59

4.8 Monomer conversion as a function of polymerization time for EHPC . . . . 60

4.9 Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2)

as a function of polymerization time for tert-butyl peroxy-neo-decanoate

(TBPD), with parameter values as in Table 4.10. . . . . . . . . . . . . . . 62

4.10 Initiator efficiency in the polymer-rich phase (f2) as a function of polymer-

ization time for tert-butyl peroxy-neo-decanoate (TBPD), for the modeling

of De Roo et al. (2004) and Kurdikar and Peppas (1994) (this work) . . . . 63

4.11 Diffusion coefficients as a function of polymerization time for tert-butyl

peroxy-neo-decanoate (TBPD), for the modeling of De Roo et al. (2004)

(Di) and Kurdikar and Peppas (1994) (DA and DB) . . . . . . . . . . . . . 64

4.12 Monomer conversion as a function of polymerization time for TBPD . . . . 66

4.13 Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2) as

a function of polymerization time for lauroylperoxide, with parameter values

as in Table 4.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.14 Half-life chart for the initiators discussed in this work and produced by Akzo

Nobel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

List of Figures vii

5.1 Simplified methodology for network generation: reactants are able to un-

dergo different reactions, leading to products. These products are regener-

ated as reactants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2 Matrix representation of tert-butyl peroxyactetate (TBPA) corresponding

with the numbering of the atoms in the molecule given. . . . . . . . . . . . 76

5.3 Matrix representation of a tert-butyl radical corresponding with the num-

bering of the atoms in the molecule given. . . . . . . . . . . . . . . . . . . 78

5.4 Methodology for generation of a reaction network with only dissociation

reactions taken into account. . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.5 Matrix operations corresponding with a dissociation reaction of a fictive

molecule ABCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.6 Methodology for generation of a reaction network with only β-scission reac-

tions taken into account. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.7 Matrix operations corresponding with the β-scission reaction of a fictive

radical ABCDE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.8 Methodology for generation of a reaction network with only recombination

reactions taken into account. . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.9 Matrix operations corresponding with the recombination reaction of a fictive

radicals AB• and DC•. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.10 Methodology for generation of a reaction network with only addition reac-


5.11 Matrix operations corresponding with the tail addition reaction of a radical

AB• to VCM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.12 Methodology for generation of a reaction network with only hydrogen ab-

straction reactions taken into account. . . . . . . . . . . . . . . . . . . . . 90

5.13 Matrix operations corresponding with the hydrogen abstraction reaction

(5.10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.14 P,s Cl-shift and s,s Cl-shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.15 Methodology for generation of a reaction network with only Cl-shift reac-


5.16 Matrix operations corresponding with a p,s Cl-shift reaction. . . . . . . . . 93

List of Figures viii

5.17 Decision tree for network generation of initiator decomposition. . . . . . . 94

7.1 Diffusiecoefficienten als functie van de polymerisatietijd voor tert-butyl peroxy-

neo-decanoaat (TBPD), volgens de modellering van Kurdikar en Peppas

(1994) (DA enDB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2 Initiatorefficientie in de monomeerrijke (f1) en polymeerrijke fase (f2) als

functie van de polymerisatietijd voor tert-butyl peroxy-neo-decanoaat (TBPD)107

7.3 Initiatorefficientie in de polymeerrijke fase (f2) als functie van de polymeri-

satietijd voor tert-butyl peroxy-neo-decanoaat (TBPD), voor de modellering

van De Roo et al. (2004) en Kurdikar en Peppas (1994) . . . . . . . . . . . 108

7.4 Monomeerconversie als functie van polymerisatietijd voor tert-butyl peroxy-

neo-decanoaat (TBPD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.5 Eenvoudige voorstelling van de methodologie voor reactienetwerkgenere-

ring: reactanten kunnen verschillende reactietypes ondergaan die leiden to

producten. Deze producten kunnen eventueel opnieuw als reactanten be-

schouwd worden. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.6 Matrixvoorstelling voor tert-butyl peroxyactetaat (TBPA), overeenkomstig

de nummering van de atomen in de zelfde figuur. . . . . . . . . . . . . . . 112

7.7 Matrixbewerkingen overeenstemmend met de netwerkgenering voor dissoci-

atiereacties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.8 Matrixbewerkingen overeenkomstig een dissociatiereactie tussen atomen B

en C van een fictieve molecule ABCD. . . . . . . . . . . . . . . . . . . . . 115

7.9 Beslissingsboom voor netwerkgenerering bij initiatordecompositie. . . . . . 116

ix

List of Tables

1.1 Reactions for vinyl chloride polymerization in the monomer-rich (k = 1) and

the polymer-rich phase (k = 2), with i, j = 1 . . .∞. . . . . . . . . . . . . . 6

2.1 Dissociation mode for the different classes of initiators (P = primary, S =

secondary, T = tertiary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1 Values of the Arrhenius parameters of kbd for relevant initiators in industrial

production of poly(vinyl chloride), provided by the producer Akzo Nobel . 41

4.2 Values of the Arrhenius parameters of kβ for relevant initiators in industrial

production of poly(vinyl chloride), produced by Akzo Nobel . . . . . . . . 41

4.3 Atomic volumes by Van Krevelen (1997) . . . . . . . . . . . . . . . . . . . 47

4.4 Volumes by Van Krevelen (1997), applied on tert-butyl peroxy-neo-decanoate

(TBPD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 Molar volumes by Van Krevelen (1997) for all radicals in the reaction scheme

of Kurdikar and Peppas (1994). The volumes are presented in cm3 mol−1 . 51

4.6 Calculation of the diffusion coefficients (D) based on the free volume (V) the-

ory. The volumes are presented in cm3 mol−1, and the diffusion coefficients

in m2 s−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.7 Estimates of the reparameterized pre-exponential factor and activation en-

ergy of the intrinsic rate coefficients for propagation, kp,chem, for chain trans-

fer to monomer, ktr,chem, and for termination, ktc,chem and ktCl,chem(De Roo

et al., 2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.8 Reaction conditions for the simulation of vinyl chloride suspension polymer-

ization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

List of Tables x

4.9 Parameters used for the calculation of the initiator efficiency f for di(2-

ethylhexyl)peroxydicarbonate (EHPC) (Akzo, 2000; Buback, 2005) . . . . 56

4.10 Parameters used for the calculation of the initiator efficiency f for tert-butyl

peroxy-neo-decanoate (TBPD) (Akzo, 2000; Buback, 2005) . . . . . . . . . 61

4.11 Parameters used for the calculation of the initiator efficiency f for azo-

bis(isobutyronitrille) (AIBN) Akzo (2000); Buback (2005) . . . . . . . . . . 65

4.12 Parameters used for the calculation of the initiator efficiency f for lau-

roylperoxide (Akzo, 2000; Buback, 2005) . . . . . . . . . . . . . . . . . . . 65

4.13 Kinetic data for relevant initiators in industrial production of poly(vinyl

chloride), provided by Akzo Nobel . . . . . . . . . . . . . . . . . . . . . . . 68

5.1 Identification numbers of the atoms used in the first row of the matrix

representation of a reactant or a product . . . . . . . . . . . . . . . . . . . 77

5.2 Bond dissociation energy for the relevant bonds in the production of poly(vinyl

chloride) (Endo, 2002; Van Pottelberge, 2004–2005) . . . . . . . . . . . . . 79

7.1 Verschillende klassen initiatoren met bijhorende soort dissociatie. . . . . . 102

7.2 Berekening van de diffusiecoefficienten voor tert-butyl peroxy-neo-decanoaat

(TBPD), met de volumes in cm3 mol−1 en diffusieoefficienten weergeven in

m2 s−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.3 Identificatienummers van de atomen betrokken bij initiatordecompositie . . 111

B.1 Overview of the references to the labjournal . . . . . . . . . . . . . . . . . 139

xi

List of symbols

A Pre-exponential factor of an intrinsic rate coefficient [s−1]

A•, A•1, B• Radicals

C Concentration [mol m−3]

Cl•k Chloride radical in monomer rich (k=1) or polymer rich

(k=2) phase

D Diffusion coefficient [m2 s−1]

DA Relative diffusion coefficient, sum of diffusion coeffi-

cients of the initiator radicals A• en A•1

[m2 s−1]

DB Relative diffusion coefficient, sum of diffusion coeffi-

cients of the initiator radicals A• en B•

[m2 s−1]

Ea Activation energy [J mol−1]

f Initiator efficiency [-]

f0 Intrinsic initiator efficiency [-]

F0 Propability of propagation [-]

FiA Probability that the first radical pair will recombine be-

fore β-scission

[-]

FiB Probability that the second radical pair will recombine

after β-scission

[-]

I Initiator molecule

I• Initiator radical

[I•] Initiator concentration [mol m−3]

[I•0 ] Initial initiator concentration [mol m−3]

List of Tables xii

Ik Initiator molecule in monomer rich (k=1) or polymer

rich (k=2) phase

kapp Apparent rate coefficient [m3mol−1s−1]

kadd Radical addition to monomer rate coefficient [m3mol−1s−1]

kbd Rate coefficient [s−1],

[m3mol−1s−1]

kbd−1 Rate coefficient for single bond dissociation [s−1],

[m3mol−1s−1]

kbd−2 Bond dissociation rate coefficient for double bond disso-

ciation

[s−1],

[m3mol−1s−1]

kβ β-scission rate coefficient [s−1]

kchem Intrinsic rate coefficient [m3mol−1s−1]

kdiff Diffusional contribution to apparant rate coefficient [m3mol−1s−1]

kp Propagation rate coefficient [s−1],

[m3mol−1s−1]

kr Recombination rate coefficient [s−1],

[m3mol−1s−1]

kt Termination rate coefficient [m3mol−1s−1]

ktA Rate coefficient for the primary recombination of radi-

cals in the solvent cage

[m3mol−1s−1]

ktB Rate coefficient for the primary recombination of radi-

cals in the solvent cage

[m3mol−1s−1]

[M ] Monomer concentration [mol m−3]

[M0] Initial monomer concentration [mol m−3]

NA Avogadro constant (6,02 1023) [mol−1]

pA Probability that a radical pair will recombine before β-

scission

[-]

pB Probability that a radical pair will recombine after β-

scission

[-]

R Universal gas constant [J mol−1K−1]

List of Tables xiii

R•n Macroradical consisting of n monomer units

R0,k Radical in monomer rich (k=1) or polymer rich (k=2)

phase, before polymerization

Ri,k Radical in monomer rich (k=1) or polymer rich (k=2)

phase, during polymerization

r0 Initial separation distance between two initiator radicals [m]

r Relative distance between two radicals [m]

r Reactiesnelheid [s−1],

[mol m−3s−1]

ri Reaction rate of initiation [s−1],

[mol m−3 s−1]

rr Reaction rate of recombination [s−1],

[mol m−3s−1]

ry, rz Radius of the molecules y and z [m]

t Time [s]

t1/2 Half-life time [s−1]

T Temperature [K]

V Volume [m3], [m3mol−1]

V ∗ Critical molar hole free volume required for a jumping

unit of species in the binary liquid to migrate

[m3mol−1]

VFH Available hole free volume for diffusion per mol of all

individual jumping units in the solution

[m3mol−1]

Subscripts

k Monomer rich phase (k=1), polymer rich phase (k=2)

i, j Chain length

List of Tables xiv

Abbreviations

1BD Single bond dissociation

2BD Double bond dissociation

AIBN Azo(isobutyronitrille)

DFT Density Functional Theory

DSC-TAM Differential Scanning Calorimetry - Thermal Activity

Monitoring

EHPC Di(2-ethylhexyl)peroxydicarbonate

PVC Poly(vinyl chloride)

TBPD tert-butyl peroxy-neo-decanoate

VCM Vinyl chloride monomer

Greek

symbols

φ Probability per unit of volume [m−3]

σ Reaction distance [m]

σA Reaction distance of a related radical pair before β-

scission

[m]

σB Reaction distance of a related radical pair after β-

scission

[m]

1

Chapter 1

Vinyl chloride suspension

polymerisation

1.1 Poly(vinyl chloride)

Poly(vinyl chloride) (PVC) is, by volume, the third largest thermoplastic manufactured

in the world. Its demand in 2006 was estimated to be around 30 million tonnes 1. Most

commodity plastics have carbon and hydrogen as their main component elements. PVC

differs by containing chlorine (around 57 wt%) as well as carbon and hydrogen. The

presence of chlorine in the molecule turns PVC into a particularly versatile plastic because

of its compatibility with a wide range of other materials. In the mean time, the chlorine

content in PVC evokes criticism by environmental organisations. Free chlorine radicals are

one of the main causes of the greenhouse effect.

PVC is chemically stable, neutral and non-toxic. PVC formulations have a wide range

of applications. Figure 1.1 gives a shortlist of the main applications of PVC.

PVC is the most widely used polymer in building and construction applications and

over 50% of the annual PVC production in Western Europe is used in this sector. Piping

is a major application of PVC in construction. Demanding applications, such as sewerage

pipes, are able to compete with other solutions in terms of cost, ease of installation and

low maintenance requirements. The other applications of PVC account for a smaller part.

1Association of Plastics Manufacturers in Europe, www.apme.org

Chapter 1. Vinyl chloride suspension polymerisation 2

Figure 1.1: Main applications of PVC

Four types of polymerizations are employed in PVC manufacturing: suspension, bulk,

emulsion and solution. Approximately 80% of the world’s PVC is produced by the suspen-

sion polymerization process.

1.2 Suspension polymerization

The suspension polymerization of vinyl chloride is performed in a batch reactor with the

monomer dispersed in water. The dispersion is maintained by adding suspension stabilizers

and by stirring. An initiator is dissolved in the monomer phase. Polymerization starts by

heating the reactor to the desired temperature. The reactor operates at a pressure of

about 10 bar, corresponding to the water and monomer vapour pressure. Three stages are

distinguished during the vinyl chloride suspension polymerization process (Burgess, 1982;

Kiparissides et al., 1997; Talamini et al., 1998a,b; Xie et al., 1991a,b), as shown in Figure

1.2.

Each stage is characterized by the number of phases present in the polymerization re-

actor (Figure 1.2). During the first stage, the polymerization takes place in the monomer

phase, called the monomer-rich phase. Because the polymer is almost insoluble in its

monomer, it almost immediately forms a separate phase in the monomor phase, called the

polymer-rich phase. This second stage starts at about 0.1% monomer conversion (De Roo

et al., 2004). During the second stage, polymerization occurs both in the monomer-rich

phase and in the polymer-rich phase. The polymer molecules formed in the monomer-rich

phase, are transferred to the polymer-rich phase. The polymer-rich phase has a constant


suspension

batchreactor

gasphase

droplet

monomer-richphase

polymer-richphase

time, c

on

vers

ion

sta

ge 1

sta

ge 2

sta

ge 3

Figure 1.2: Three stages during the vinyl chloride suspension polymerization process

composition of approximately 30 wt% of monomer, the latter being determined by the sol-

ubility of the monomer in the polymer-rich phase. Due to the constant composition of the

polymer-rich phase and the conversion of vinyl chloride, the monomer-rich phase decreases

in volume while the polymer-rich phase volume increases. At a conversion of about 65%,

the so-called critical conversion, the monomer-rich phase disappears and the third stage

starts. During this stage, polymerization takes place in the polymer-rich phase only, the

composition of which now changes due to the consumption of the monomer. As a result the

viscosity of this phase increases notably. During the third stage, the reactor pressure drops.

Reactions can occur in the monomer-rich phase and the polymer-rich phase. The polymer-

ization kinetics in terms of effect of diffusion in both polymerization phases are different as

the physical properties of these phases differ. The reactions in the monomer-rich phase are

considered to be reaction-controlled, while in the polymer-rich phase they are considered to

become diffusion-controlled. Therefore, in the modeling of polymerization kinetics, effects

of diffusional limitations need to be taken into account. Diffusional effects are commonly

known as the cage, the glass and the gel effect. These are the effects of diffusion on respec-

tively the initiator decomposition, on the propagation reactions and on the termination


reactions. Apart from the latter reactions that can become diffusion-controlled, other re-

actions in the polymerization kinetics can also become diffusion-controlled. The origin of

diffusional effects lies in the fact that molecules first need to diffuse towards each other

before they can react. In what follows, the cage, the glass and the gel effect are explained

(De Roo et al., 2004). These effects, especially the cage effect, will be useful to explain

some phenomenons further on in this work.

• Cage effect

The cage effect has an influence on the initiator decomposition. Due to the cage effect the

initiator efficiency decreases strongly as soon as the monomer phase has disappeared. The

cage effect refers to the less than 100% efficiency of the initiator in initiating a new macro-

radical (Moad and Solomon, 1995; Reichardt, 2003). After decomposition, the initiator

derived radicals are still in close proximity of each other and can therefore recombine to

form an inert molecule. A lower than 100% initiator efficiency results.

• Glass effect

The glass effect affects the propagation reactions. Due to the transition of the monomer-

polymer mixture to the glassy state, the propagation reaction becomes diffusion-controlled.

This is called the glass effect. According to experimental data for the monomer-polymer

glass transition temperature as a function of concentration and temperature, the glass

effect should appear only at very high conversions (< 90%), at least at some time in the

third stage (discussed later) of the polymerization De Roo et al. (2004). Also, experimental

data of Starnes Jr. et al. (1995) on butyl branching indicates these conversion levels.

• Gel effect

Finally, the gel effect affects the termination reactions. The gel effect always occurs in

the polymer-rich phase and results in a decrease of the termination rate coefficient at the

start of the third stage in the polymerization process (De Roo et al., 2004). The effects

of diffusion on the termination reactions between (macro)radicals is called the gel effect

or the Trommsdorff-Norrisch effect. The gel effect has an extra complication compared


with other diffusion controlled reactions. Next to the effect of diffusion playing a role

in the polymerization kinetics, the chain lengths of the terminating macroradicals also

affect the apparent termination rate coefficients. Therefore every termination between a

macroradical with a chain length i and a chain length j results in a different apparent

termination rate coefficient. The (macro)radicals have a chain length which covers a range

in vinyl chloride suspension polymerization of 1 to theoretically infinity. In practice the

maximum chain length is about 20, 000 (De Roo et al., 2004).

1.3 Free radical polymerization

Two basic types of polymerization are found: chain-reaction (or addition) and step-reaction

(or condensation) polymerization (Duprez, 2004).

Addition polymerization involves the linking together of molecules incorporating double or

triple chemical bonds. These unsaturated monomers (the identical molecules which make

up the polymers) have extra internal bonds which are able to break, thus to form free

radicals, and link up with other monomers to form the repeating chain. Addition poly-

merization is involved in the manufacture of polymers such as polyethene, polypropylene

and poly(vinyl chloride) (PVC), which are all free radical polymerizations. A special case

of addition polymerization leads to living polymerization.

On the contrary, step growth polymers are defined as polymers formed by the stepwise reac-

tion between functional groups of monomer. Most step growth polymers are also classified

as condensation polymers, but not all step growth polymers (like polyurethanes formed

from isocyanate and alcohol bifunctional monomers) release condensates. Step growth

polymers increase in molecular weight at a very slow rate at lower conversions and only

reach moderately high molecular weights at very high conversion (i.e. more than 95%).

In this work, the addition polymerization of vinyl chloride, which is a free radical polymer-

ization, is discussed into detail.

The main reaction steps during the free radical polymerization are (Table 1.1):

• Decomposition of the initiator : Two radicals are formed by dissociation of the initia-


Table 1.1: Reactions for vinyl chloride polymerization in the monomer-rich (k = 1) and thepolymer-rich phase (k = 2), with i, j = 1 . . .∞.

Type of reaction

Decomposition of the initiator Ik

fkkd,k−−−→ 2R0,k (1)

Chain initiation R0,k + Mk

kinI,k−−−→ R1,k (2)

Termination through combination Ri,k + Rj,k

kijtc,k−−→ Pi+j,k (3)

Termination with Cl-radicals Ri,k + ClkktCl,k−−−→ Pi,k

Chain transfer to monomer Ri,k + Mk

ktr,k−−→ Pi+1,k + Clk (4)

Clk + Mk

kinCl,k−−−−→ R1,k

tor.

• Initiation: Free radical sites for polymerization are formed by reaction between pri-

mary initiator free radical fragments and monomer molecules.

• Propagation: Polymerization proceeds through a series of additions of monomer

molecules to the growing polymer chains, with the free radical site moving to the

end of the growing chain after each addition.

• Termination: Active free radicals disappear by two free radical sites coming together

and reacting to form either one or two dead polymer chains.

• Chain transfer reactions : Active free radical sites at the ends of growing chains

move to another site on the same polymer molecule, another polymer molecule, or a

solvent, monomer, or modifier molecule. In Table 1.1, only chain transfer to monomer

is considered.

The three reactions steps (initiation, propagation and termination) are part of the

mechanism that determines the polymerization rate: initiator type and concentration, as

well as reactor temperature control the initiation rate. The propagation rate increases

with temperature. Propagation is an exothermic reaction as vinyl chloride double bonds

are converted into single bonds.


The rate of chain termination is a.o. controlled by the free radical concentration. The chain

tranfer reactions can determine the molecular weight and molecular weight distribution of

the polymer. Moreover, chain transfer affects size, structure and end groups of polymers.

1.4 Role of the initiator in the polymerization process

of PVC

1.4.1 Initiator efficiency

In this work, the focus will be on the decomposition of the initiator. The first step in the

initiator decomposition mechanism is a dissociation step, in which the initiator molecule

dissociates into two radicals (reaction (1.1)).

Ifkbd→ R′•

0 + R′′•0 (1.1)

The formed radicals can be equal or not. The intrinsic rate coefficient of this reaction

is fkbd, in which f is the initiator efficiency and kbd is the rate coefficient of dissociation.

In a free radical polymerization, only a fraction of the radicals formed by dissociation

of the initiator is able to initiate a polymer chain. This fraction is defined as the initiator

efficiency f . Initiator derived radicals may fail in formation due to side reactions: cage

termination reactions (Reichardt, 2003) and -under certain conditions- by a termination

reaction with polymer radicals. These side reactions occur because the initiator derived

radicals, which are the radicals formed at the dissociation step, are still in close proximity

to each other after dissociation. Hence, their recombination is possible. If the dissociation

reaction is accompanied with the escape of a small molecule from the cage, e.g. because

of a β-scission reaction, recombination of the radicals results in the formation of an inert

molecule. Hence, the rate of dissociation of an initiator does not equal the rate of initiation.

For most systems, the initiator efficiency f assumes a value between 0.3 and 0.8 at

the start of the polymerization reaction (Kurdikar and Peppas, 1994; Westmijze, 1999). A

value lower than 1 is obtained because of side reactions, as mentioned above.

Because of changing polymerization conditions, the initiator efficiency is not constant


during the polymerization process. The initiator efficiency in the monomer-rich and

polymer-rich phase is plotted in Figure 1.3. The initiator efficiency in the monomer-rich

phase (f1) is constant throughout the polymerization, while the initiator efficiency in the

polymer-rich phase (f2) varies with the polymerization time. Due to the cage effect the

initiator efficiency decreases strongly as soon as the monomer phase has disappeared. The

polymerization becomes diffusion-controlled, whereas in the monomer-rich phase it was

reaction controlled. The initiator efficiecy increases again and remains constant until suf-

ficient conversion is reached. The initiator efficiency decreases again when the segmental

mobility of the medium decreases, because this prevents the initiator radicals from escaping

the surrounding solvent cage. Thus, the diffusive displacement of the radicals away from

each other becomes difficult and radical recombination reactions become preferred until f2

reaches a limiting value of zero.

Figure 1.3: Variation of the initiator efficiency f during polymerization in the monomer-rich(f1) and polymer-rich phase (f2).


1.4.2 Selection criteria of an initiator for industrial production

of PVC

For the industrial production of poly(vinyl chloride) a wide range of initiators is available.

To choose the initiator which meets all requirements for an efficient and qualitative pro-

duction of PVC, with respect to polymerization temperature, rate of radical formation and

storage facilities, some characteristics of the initiators need to be taken into account. In

this section the main characteristics of the initiators are discussed. In Chapter 4, the most

appropriate initiator for the production of poly(vinyl chloride) will be selected, based on

the characteristics discussed here and on kinetic modeling results.

Some characteristics influence the polymerization process, while others influence the poly-

merization product.

Characteristics influencing the polymerization process First, the characteristics

of the initiator which have an influence on the polymerization process are discussed.

• Half-life time

The most important characteristic of an initiator is its rate of decomposition. The

decomposition rate is characterized by its half-life time, t1/2, at a given temperature. The

half-life time of an initiator is the time required to reduce the original initiator content

by 50% at a given temperature. Because the efficiency of a free radical initiator depends

primarily on its rate of thermal decomposition, half-life data are essential for selecting the

optimum initiator for specific time-temperature applications. Remark that the half-life

data are different in other solvents, because the polarity of the solvent used will influence

the initiator decomposition kinetics. Hence, to compare the half-life times of different

initiators, it is important to compare half-life data generated in the same solvent.

An expression for the half-life time can be derived. The concentration of the initiator

as a function of time can be calculated by means of the differential equation (1.2) and the

initial condition (1.3).

d [I]

dt= −kbd [I] (1.2)


t = 0 [I] = [I0] (1.3)

in which [I0] is the initial initiator concentration, [I] is the initiator concentration at

time t and t is the time measured form the start of the decomposition.

The residual initiator concentration is given by means of equation (1.4).

[I] = [I0] exp(−kbdt) (1.4)

The half-life time of an initiator is the time required to reduce the original initiator

content at a given temperature by 50%, or

[I] (t1/2) = [I0] /2 (1.5)

Based on equations (1.4) and (1.5), the half-life time can be calculated. This half-life

time is given in equation (1.6).

t1/2 = ln(2/kbd) (1.6)

The rate coefficient for initiator dissociation, kbd, is given by an Arrhenius expression

(equation (1.7)). In this expression, the values for the pre-exponential factor (A) and the

activation energy (Ea) can be found in literature or can be provided by the producer. R

represents the universal gas constant (8.314 J mol−1 K−1) and T is the reaction tempera-

ture. Hence, it is possible to calculate the half-life t1/2 for different initiators.

k = A exp(−Ea/(RT )) (1.7)


• Heat developed

The rate of radical formation is also important to predict the heat developed during

the reaction. In 1.4.2, the peak shows the amount of heat developed during the reaction.

Figure 1.4: The heat developed during reaction, in case of TBPD.

Generally, the heat developed during the reaction, may not be greater than two times

the heat in equilibrium. This is an important characteristic, because the heat developed

has influence on reactor choice, reaction conditions and safety.

Characteristics influencing the polymerization product Secondly, some charac-

teristics of the initiator influence the polymerization product. The most important char-

acteristics are the product quality and the storage temperature.

• Product quality

Another parameter to consider in the selection of initiators is the desired product

quality. First of all, the nature of the initiator decomposition products plays an important

role in this quality. The initiator decomposition products may remain in the polymer

resulting in undesirable properties such as poor organoleptic performance, yellowing and

low weathering performances (Akzo, 2000).


• Storage temperatures

To maintain product quality, the recommended storage temperatures of the initiators (Ts)

have to be observed. The maximum storage temperature Ts,max is the recommended max-

imum storage temperature at which the chemical product is stable and quality loss will be

minimal. A minimum storage tempeature Ts,min is given if phase separation, crystallization

or solidification of the product is known to occur below the temperature indicated. For

safety reasons it is also recommended to store the product above the Ts,min indicated.

In Chapter 4, the most appropriate initiator for the production of poly(vinyl chloride)

will be selected, based on the characteristics discussed in this section and on kinetic mod-

eling results.

1.5 Conclusion

Poly(vinyl chloride) is mainly produced by suspension polymerization of vinyl chloride,

via a free radical mechanism, of which the dissociation of the initiator is the first reaction

step. The performance of the initiator can be described by the initiator efficiency f . In

a free radical polymerization, only a fraction of the radicals formed by dissociation of

the initiator is able to initiate a polymer chain. This fraction is defined as the initiator

efficiency f . The initiator efficiency is not the only selection criterium of an initiator for

industrial production of PVC. The half-life time, the polymerization temperature, desired

product quality and storage temperatures of the initiators will determine the choice of an

appropriate initiator.

13

Chapter 2

Classification of initiators and

decomposition mechanism

A more detailed study of the initiator efficiency f can only be made when the reaction

mechanism of the decomposition of the initiator is completely understood. In this chap-

ter, the different reactions involved in the decomposition of the initiator are described

first. Next, a classification of the initiators is made. For each of the initiator classes the

decomposition mechanism is discussed.

2.1 Reaction types in a decomposition mechanism

In the decomposition mechanism of the initiator, different reactions take place. Six types of

reactions are distinguished: dissociation, β-scission, recombination, addition, H-abstraction

and Cl-shift. In order to understand and describe the initiator decomposition mechanism

into detail, the main characteristics of the reaction types need to be known. Moreover,

this will be useful to find out all possible occuring reactions during initiator decomposition

(Chapter 5).

Dissociation In a dissociation reaction, a bond of an initiator is broken to form two

radicals. Depending on the class of initiator, the initiator undergoes a single- or two-bond

dissociation.

Chapter 2. Classification of initiators and decomposition mechanism 14

• Single-bond dissociation: In a single-bond dissociation reaction only one bond is

broken to form two radicals.

In reaction (2.1), an example of a single-bond dissociation reaction of a peroxide is

given. Only the oxygen-oxygen bond of the considered reactant is broken.

ROCOO

O

COR

Ok1−bd //ROCO•

O

+ •OCOR

O

(2.1)

• Two-bond dissociation: A two-bond dissociation reaction is a concerted reaction,

which means that more than one bond break simultaneously. Because of this reaction,

a small molecule is formed.

A typical example of a reactant which undergoes two-bond dissociation, is a peroxyester.

The two-bond dissociation reaction is shown in reaction (2.2). Two bonds are broken, and

a small CO2-molecule is formed.

RCO

O

OR’k2−bd // R• + CO2 +• OR’ (2.2)

β-scission In a β-scission reaction a C-X bond (X=C,O or H) is broken in β-position to

the radical. An example of a C-C β-scission for an alkoxyradical is presented in reaction

(2.3).

C

R1

R2

R3

O• kβ(CC) // R•1+R2R3CO (2.3)

Recombination In a recombination reaction two radicals recombine to form one molecule.

Hence this reaction is a termination reaction.

A• +• A1kr // I (2.4)


Addition In an addition reaction a radical adds to a double bond. The radical can add to

monomer in two different ways: addition to the non-substituted C or to the substituted C.

These two possibilities are respectively shown in reactions (2.5) and (2.6) for the addition

of an initiator radical to vinyl chloride.

I•+ CH2=CHClkadd,tail // C•

H

I-CH2

Cl

(2.5)

I•+ CH2=CHClkadd,head // C

H

I

Cl

CH2• (2.6)

H-abstraction In a H-abstraction reaction a H-atom is abstracted from a H-donor

present in the reaction medium. The reaction can be presented as shown in reaction

(2.7).

I•+ HDkH // IH + D• (2.7)

Cl-shift During a Cl-shift reaction, a Cl-atom is shifted from a β-position to the radical

position. The two types of Cl-shift are shown in Figure 5.14: a primary-secondary (p,s)

and a secondary-secondary (s,s) Cl-shift. A primary-secondary Cl-shift (p,s Cl-shift) is

an intramolecular process during which a primary C-radical is converted into a secondary

C-radical. During a secondary-secondary Cl-shift (s,s Cl-shift) a secondary C-radical is

converted into another secondary radical.

A p,s Cl-shift is accompanied by the transformation of a primary radical to a more

stable secondary radical, whereas for a s,s Cl-shift an equally stable radical is formed.

Hence, the activation energy for the p,s Cl-shift reaction will be lower than for s,s Cl-shift

and the p,s Cl-shift will have a higher occurance (Starnes Jr. et al., 1992; Van Pottelberge,

2004–2005).


Figure 2.1: P,s Cl-shift and s,s Cl-shift

2.2 Classification of initiators

The production of poly(vinyl chloride) is performed with different types of initiators, de-

pending on the producer, the half-life time, the polymerization temperature, the product

quality and the storage facilities of the initiator, as discussed in previous chapter. Based

on a survey of industrial patents, four classes of initiators can be distinguished, based on

their chemical structure. The different classes of initiators are: peroxydicarbonates, per-

oxyesters, dialkyl diazenes (azo-initiators) and diacyl peroxides.

Because of the strong correlation of initiator decomposition kinetics and initiator efficiency,

it is of primary importance to obtain a detailed insight into the decomposition mechanism.

For the four classes of industrial initiators studied in this work, the dissociation (the first

step in the decomposition mechanism) mode is given in Table 2.1. A distinction is made

between single-bond (1bd) and two-bond (2bd) dissociation.

Table 2.1: Dissociation mode for the different classes of initiators (P = primary, S = secondary,T = tertiary)

Class Type 1BD 2BDPeroxydicarbonates P,S and T xPeroxyesters P x

S and T xDialkyl diazenes P,S and T xDiacyl peroxides P,S and T x


Analysis of the temperature and pressure dependence of the initiator dissociation rate

provides evidence on the dissociation mode. The dissociation step, single-bond or two-bond

scission, bears important consequences for the initiator efficiency in radical polymerization.

In case of a two-bond scission and thus of simultaneous formation of a small molecule,

subsequent cage combination reaction of the produced radicals leads to relative stable

products. Such components will not decompose under typical polymerization conditions

and the loss of primary radical concentration upon their formation can be associated with a

significant reduction in overall initiator efficiency. On the other hand, in case of single-bond

dissociation, recombination restores the peroxyester molecule, which may undergo another

decomposition step and therefore may finally result in addition of primary radicals to

monomer molecules an thus in formation of growing radicals.

2.3 Decomposition mechanism for each initiator class

In this section, the decomposition mechanism for each initiator class is discussed into

detail based on decomposition mechanisms presented in Verhaert (2003–2004). Moreover,

an important example of each class is presented.

2.3.1 Peroxydicarbonates

Peroxydicarbonates are one of the most widely used initiators in poly(vinyl chloride) pro-

duction. The typical peroxide structure (oxygen-oxygen bond) of initiators is found in

these peroxydicarbonates, as shown in formula (2.8).

ROCOO

O

COR

O

(2.8)

The decomposition mechanism of peroxydicarbonates is studied into detail in Verhaert

(2003–2004), as is shown in Figure 2.2. In this decomposition mechanism, the R-groups

are considered to be equal, which is mostly the case. All peroxydicarbonates undergo

single-bond scission, in which two equal (alkoxycarbonyl)oxyradicals are formed. The rate

coefficient of this reaction is k1−bd. The formed (alkoxycarbonyl)radicals can undergo a


β(CO)-scission reaction, resulting in the formation of a CO2 molecule and an alkoxyradical.

This reaction can be followed by a β(CC)-scission, generating another CO2 molecule and

alkylradical.

When the alkoxyradicals formed by the first β-scission, recombine again to form a

peroxide, the formed peroxide can dissociate again. In contrast, when the alkoxyradicals

formed in the second β-scission, recombine again to form a peroxide, that can no longer

dissociate. The same holds true for the recombination of an alkylradical with an alkoxyl-

radical.

The peroxydicarbonate studied in this work is di(2-ethylhexyl)peroxydicarbonate (EHPC):

CH3 CH

C2H5

(CH2)3 CH2 O COO

O

C

O

O CH2 CH

C2H5

(CH2)3 CH3 (2.9)

Because modeling of the initiator efficiency as a function of polymerization time requires

knowledge of the rate coefficients of the relevant individual reaction steps, the values for

the rate coefficients are given. In this work, the rate coefficients for dissociation and β-

scission are given and are represented by their Arrhenius parameters (equation (1.7)). The

Arrhenius parameters of the dissociation rate coefficient k1−bd are provided by the producer

Akzo (2000). The pre-exponential factor A is 1.52 10+14 s−1 and the activation energy Ea

is 115.47 kJ mol−1. The rate coefficient for the β-scission reaction is also given by an

Arrhenius equation and is based on ab initio calculations. The pre-exponential factor A is

1.83 10+15 s−1 and the activation energy Ea is 122.45 kJ mol−1 (Buback, 2005).


O

O

||

||

R O C O O C O R

O

O

||

||

R O C O

•

+

•

O C O R

O

||

R O O C OR + CO2

O

||

R O C O

•

+ RO

•

+ CO2

O

||

R O C O

•

+ R2O + R1

•

+ CO2

ROOR

+ CO2

2RO

•

+ 2CO2

2R2O + 2R1

•

+ 2CO2

RO

•

+ R2O + R1

•

+ 2CO2

ROR1 + R2O + 2CO2

k1-bd

k1-bd

kβ,1

kβ,2

kβ

kβ

kβ

kβ

kr

kβ

kr

kr

kr

Fig

ure

2.2:

Dec

ompo

siti

onm

echa

nism

ofpe

roxy

dica

rbon

ates

(Ver

haer

t,20

03–2

004)


2.3.2 Peroxyesters

Analogous to peroxydicarbonates, peroxyesters have the typical peroxide structure (oxygen-

oxygen single bond), as shown in formula (2.10). However, peroxyesters are characterized

by a carbonylgroup, resulting in a destabilisation of the oxygen-oxygen bond.

RCO

O

OR’ (2.10)

The decomposition mechanism of peroxyesters is studied into detail in Verhaert (2003–

2004) and is shown in Figure 2.3. Not all peroxydicarbonates undergo the same sort of bond

dissociation. Primary peroxyesters, where R is a primary group, undergo a single-bond

dissociation with a rate coefficient k1−bd, followed by a β-scission of the carbonyloxy radical

with a rate coefficient kβ (Buback et al., 2002). Secondary and tertiary peroxyesters, where

R is a secondary respectively tertiary group, undergo a two-bond dissociation with a rate

coefficient k2−bd. The two bonds that are broken in primary peroxyesters in two different

reactions, are now broken simultaneously (Kochi, 1973). The decomposition mechanism

for these two peroxyesters is shown in Figure 2.3.

In this work the investigated peroxyester is tert-butyl peroxy-neo-decanoate (TBPD).

The chemical structure is shown in formula (2.11), in which R1+R2 is equal to C7H16

C

CH3

R1

R2

COO

O

C

CH3

CH3

CH3 (2.11)

The Arrhenius parameters of the dissociation rate coefficient k1−bd are provided by the

producer (Akzo, 2000). The pre-exponential factor A is 1.52 10+14 s−1 and the activation

energy Ea is 115.47 kJ mol−1. The rate coefficient for the β-scission reaction is also given

by an Arrhenius equation and is based on ab initio calculations. The pre-exponential factor

A is 1 10+13 s−1 and the activation energy Ea is 50 kJ mol−1 (Buback, 2005).


O

||

R C O O R’

O

||

R C O

•

+

•

O R’

ROR’

+ C O

2

R•

+ R’O

•

+ CO2

O

||

R1

•

+ R2O + R C O

•

RR1 + R2O + CO2

R

•

+ R1

•

+ R2O + CO2

O

||

R C O R1 + R2O

kr

kr

kr kr

kβ

kβ

k2-bd

k1-bd

kβ

kβ

Fig

ure

2.3:

Dec

ompo

siti

onm

echa

nism

ofpe

roxy

este

rs(V

erha

ert,

2003

–200

4)


2.3.3 Dialkyl diazenes

The chemical structure of dialkyl diazenes or azo compounds is shown in formula (2.12).

The extended delocalization of electrons in the benzene and azo groups forms a conjugated

system.

R-N=N-R (2.12)

The decomposition mechanism of azo-compounds is described in literature (Barbe and

Ruchardt, 1983; Krstina et al., 1989). Dialkyl diazenes undergo a two-bond dissociation

with a rate coefficient k2−bd, as shown in Figure 2.4. Aliphatic azo compounds are unstable

and the loss of nitrogen gas occurs by the simultaneous cleavage of carbon-nitrogen bonds,

resulting in carbon-centered radicals (Krstina et al., 1989).

In this work, the investigated dialkyl diazene is azobis(isobutyronitrille) or AIBN:

C

CH3

CH3

CN

N=NC

CH3

CN

CH3 (2.13)

The Arrhenius parameters of the dissociation rate coefficient k2−bd are provided by the

producer (Akzo, 2000). The pre-exponential factor A is 2.89 10+15 s−1 and the activation

energy Ea is 130.23 kJ mol−1. The rate coefficient for the β-scission reaction is obtained

by ab initio calculations. The pre-exponential factor A is 1.3 10+14 s−1 and the activation

energy Ea is 62.6 kJ mol−1 (Barbe and Ruchardt, 1983).


R1

||

NC C

•

+ R2

•

R2

||

NC C

•

+ R1

•

R1

R1

|

|

NC C N = C = C

|

|

R2

R2

R1

R1

R1

|

||

|

NC C H + NC C + NC C

|

|

||

R2

R2

R2

R1

R1

|

|

NC C N = N C CN

|

|

R2

R2

R1

N

|

|| + 2 NC

C•

N

|

R2

R1 R1

| |

NC C C CN

| |

R2 R2

k2-bd kr

kr

kr

kβ

kβ

Fig

ure

2.4:

Dec

ompo

siti

onm

echa

nism

ofdi

alky

ldi

azen

es(B

arbe

and

Ruc

hard

t,19

83;K

rsti

naet

al.,

1989

)


2.3.4 Diacyl peroxides

The last class of initiators used in the industrial production of poly(vinyl chloride), is the

class of the diacyl peroxides. These initiators have a similar structure to peroxydicarbon-

ates, as shown in formula (2.14).

RCOO

O

CR

O

(2.14)

In contrast to peroxydicarbonates, the preferred pathway for the decomposition of the

diacyl peroxides is a two-bond dissociation (Krstina et al., 1989). Through ab initio cal-

culations (Gu et al., 2006) the transition state for a single-bond dissociation pathway can

not be found, whereas the transition state for a two-bond dissociation pathway can. The

decomposition mechanism of diacyl peroxides is shown in Figure 2.5.

In this work, the investigated diacyl peroxide is lauroylperoxide. In this diacyl peroxide,

the radical R in formula (2.14) is given by C11H23

The Arrhenius parameters of the dissociation rate coefficient kd are provided by Akzo

(2000). The pre-exponential factor A is 3.92 10+14 s−1 and the activation energy Ea is

123.37 kJ mol−1. The rate coefficient for β-scission reaction is based on ab initio calcula-

tions. The pre-exponential factor A is 1 10+14 s−1 and the activation energy Ea is 45.7 kJ

mol−1 (Buback, 2005).


O

O

||

||

R C O O C R

O

O

||

||

R C O

•

+

•

O C R

O

||

R C O R + CO2

O

||

R C O

•

+ R

•

+ CO2

RR

+ CO2

2R

•

+ 2CO2

k1-bd

k1-bd

kβ

kβ

kr kr kr

k2-bd

Fig

ure

2.5:

Dec

ompo

siti

onm

echa

nism

ofdi

acyl

pero

xide

s(K

rsti

naet

al.,

1989

)


2.4 Conclusion

The industrial production of PVC can be performed with four classes of initiators: peroxy-

dicarbonates, peroxyesters, dialkyl diazenes (azo-initiators) and diacyl peroxides. Modeling

of the initiator efficiency as a function of the polymerization time, the monomer conversion

and the polymerization conditions for these initiators requires knowledge of the dissoci-

ation mode, which may be single-bond dissociation or two-bond dissociation. Based on

a literature study, one can conclude that peroxydicarbonates and primary peroxyesters

undergo single-bond dissociation, whereas the other initiator classes are characterized by

two-bond dissociation.

Moreover, an initiator decomposition mechanism was developed for each class of initiators,

based on literature (Barbe and Ruchardt, 1983; Krstina et al., 1989; Verhaert, 2003–2004).

27

Chapter 3

Modeling of initiator efficiency

The decomposition mechanism of different initiators is discussed in the Chapter 2. In

this Chapter, a more detailed study of the modeling strategies to calculate the initiator

efficiency f is made. The strategies to model the initiator efficiency will be discussed.

Semi-empiric modeling of the initiator efficiency f implies that f is calculated based on

empiric relations, whereas in kinetic modeling, the empiric relations are excluded and are

replaced by an expression with kinetic, adjustable parameters. An analytic expression to

calculate f will be presented for both modeling strategies.

The dissociation of an initiator molecule, which is the first step in the initiator decom-

position, is shown in reaction (3.1).

Ifkbd→ R′•

0 + R′′•0 (3.1)

In this reaction, an initiator molecule dissociates to form two primary radicals which

are not necessarily equal. The intrinsic rate coefficient of this reaction is kbd. Due to the

cage effect, this rate coefficient needs to be corrected with f , the initiator efficiency. Hence,

the first order reaction (equation (3.1)) has an apparent rate coefficient of fkbd.

The cage effect refers to the less than 100% efficiency of the initiator in initiating a new

macroradical (Moad and Solomon, 1995; Reichardt, 2003). After dissociation, the initiator

derived radicals are still in close proximity of each other and can therefore recombine to

Chapter 3. Modeling of initiator efficiency 28

Figure 3.1: Schematic representation of the cage effect (De Roo et al., 2004)

form an inert molecule. A lower than 100% initiator efficiency results.

The cage effect is presented in Figure 3.1. Not all the initiator derived radicals in the

polymer-rich phase, R0,2, are able to initiate the polymerization. Recombination of the

R0,2 radicals at the reaction distance σm (solid circle in Figure 3.1) in the cage (R0,2...R0,2)

cage (dotted circle in Figure 3.1), results in the formation of an inert molecule I0 and,

hence, in a lower than 100% initiator efficiency f . In some cases, the decomposition of the

initiator is accompanied by the escape of a small molecule, such as CO2 or N2. The time

axis in Figure 3.1 indicates the considered initiator decomposition reactions.

The initiator efficiency f depends on the decomposition reactions of the considered

initiator, on the composition of the polymerization mixture and on the polymerization

temperature. It is now widely accepted that assigning a constant value to the initiator

efficiency can lead to significant errors in both conversion and molecular mass distribution

calculations (Biesenberger and Sebastian, 1983), especially at high monomer conversions

(more than 80%).

Precisely knowing the initiator dissociation rate coefficients, kbd, is required for the

simulation of polymerization processes. As it is the amount of free radicals which goes

into modeling, in addition with the initiator efficiency, f , these data need to be known

for modeling the polymerization of a particular monomer under given reaction conditions.


The initiator efficiency f is defined as the fraction of initiator derived free radicals that

starts monomer addition. The efficiency f is thus related to a maximum concentration of

primary radicals. It should be noted that each value of f must be accompanied by the

reference kbd value. With the product fkbd, being the relevant quantity for characterizing

the availability of primary growing radicals, it is easily understood that the determination

of kbd values should be carried out under conditions that are as close as possible to the

situation met during the actual polymerization process(Buback et al., 2002).

3.1 Modeling of initiator efficiency

In this section, two modeling strategies to calculate the initiator efficiency are presented:

a semi-empiric and kinetic modeling strategy. Semi-empiric modeling of the initiator effi-

ciency f implies that f is calculated based on empiric relations, whereas in kinetic mod-

eling, the empiric relations are excluded and are replaced by an expression with kinetic

parameters.

3.1.1 Semi-empiric modeling of initiator efficiency

In De Roo et al. (2004) the vinyl chloride suspension polymerization is modeled with a

general approach for the independent calculation of diffusion effects on polymerization

reactions. For the initiator decomposition, propagation and termination, an apparent rate

coefficient is determined, built up from two contributions: the intrinsic rate coefficient kchem

and a diffusional contribution kdiff . This fundamental expression is given in equation (3.2).

1

kapp

=1

kchem

+1

kdiff

(3.2)

The diffusional contribution is calculated with the Smoluchowski model (Smoluchowski,

1917), the diffusion coefficients being determined from the free volume theory. The free

volume theory is entirely based on the physical properties of the diffusing components

and the other components of the polymerizing mixture. This approach provides a way for

calculating the influence of diffusion on the polymerization reactions. The intrinsic rate

coefficients are taken from literature.


In order to account for the effect of diffusion on the initiator efficiency, f is calculated

in a similar way as in equation (3.2), leading to a semi-empiric expression:

1

f=

1

f0

+1

kdiff

(3.3)

In equation (3.3) f0 is the intrinsic initiator efficiency, which is defined as the initiator

efficiency when no diffusional limitations are present. The intrinsic initiator efficiency f0 is

constant and is fixed for all calculations to 0.7 based on empiric relations. The diffusional

contribution kdiff is calculated with the Smoluchowski model (Smoluchowski, 1917). For

two species y and z, the apparent rate coefficient kdiff is given by equation (3.4) (Russell

et al., 1992, 1993).

kdiff = 4(ry + rz)(Dy + Dz)NA (3.4)

In this equation, ry + rz is the distance between the two species upon reaction. The

latter is taken as the Lennard-Jones diameter of a monomer molecule (Clay and Gilbert,

1995), which equals 4.69 10−10 m. NA is the Avogadro constant. Dy + Dz is the mutual

diffusion coefficient consisting of two individual diffusion coefficients of the reacting species

y and z (Russell et al., 1993).

3.1.2 Kinetic modelling of initiator efficiency

Kurdikar and Peppas (1994) developed a model that is able to predict a priori the initiator

efficiency and continuously calculate the term f throughout the course of the polymeriza-

tion. This differs from other modeling approaches in literature (De Roo et al., 2004;

Kiparissides et al., 1997; Xie et al., 1991b). A more detailed description of the initiator

decomposition mechanism is obtained, which leads to a more accurate modeling of the

initiator efficiency.

The model developed by Kurdikar and Peppas (1994) is based on the following kinetic

scheme.


I1

Ikbd // [A• + A•

1]

kβ

��

ktA

OO

DA // A• + A•1 first radical pair

[A• + B•]

ktB

��

DB // A• + B• second radical pair

I2

(3.5)

Inside the solvent cage, depicted by [. . .], the initiator I can decompose into two equal or

unequal primary radicals, A• and A1•. The solvent cage defines the region around a radical

within which a recombination reaction may occur if another radical is found. Because the

two radicals A• and A1•, called the ’first radical pair’, are in close proximity of each other

after dissociation, they can recombine again.

After a single-bond dissociation this leads to the formation of the original initiator which

will dissociate immediately. Hence, this recombination does not lead to a decrease of the

initiator efficiency. After a two-bond dissociation, a small molecule is split off and the

two initiator radicals can recombine to an inert molecule I1. Radicals A1• may decompose

in the solvent cage to form another primary radical, B•, through a β-scission reaction.

Hence a second radical pair is formed. Again this radical pair is able to recombine to

an inert molecule I2. The recombination of A• with A1• (first radical pair) and A• with

B• (second radical pair) to form inactive molecules, I1 and I2, are the primary reactions

that cause the decrease in initiator efficiency. The radicals A•, B• and A1• are effective

in initiating chains, thus attacking a monomer molecule, M, to form an active monomer

molecule which can undergo propagation reactions. On the other hand, A• and B• can

undergo termination with growing chains to form dead polymer chains. In the reaction

scheme (3.5)

• kbd is the rate coefficient for dissociation of I to form A• and A1•

• kβ is the rate coefficient for β-scission of A1• to form B•

• ktA and ktB are the rate coefficients for the primary recombination of radicals in the


solvent cage

These are not the only effects through which the calculation of the initiator efficiency

is affected. When radical pairs do not recombine, they can diffuse out of the solvent cage

(reactions (3.6)-(3.7)).

[A• + A•1]

kdiff,1→ A• + A•1 (3.6)

[A• + B•]kdiff,2→ A• + B• (3.7)

After diffusion out of the solvent cage, the escaped radicals can recombine with other

radicals present in the reaction environment. This effect encloses recombination with grow-

ing polymer chains, as shown in reactions (3.8), (3.9) and (3.10) or recombination with

radicals coming from another initiator molecules (reactions (3.11) and (3.12)).

A•1 + R•

m

kt,1→ Pm (3.8)

A• + R•p

kt,2→ Pp (3.9)

B• + R•q

kt,3→ Pq (3.10)

A• + A•1

ktA→ I1 (3.11)

A• + B• ktB→ I2 (3.12)

When the radicals do not recombine, they will initiate a chain by reacting with the

monomer molecule (reactions (3.13) and (3.14)). The radicals A•, B• and A1• will initiate

the chains or terminate with other macroradicals outside the solvent cage.

A• + Mkadd,1→ M•

1 (3.13)

B• + Mkadd,2→ M•

2 (3.14)

A•1 + M

kadd,3→ M•3 (3.15)


3.2 Modeling by Kurdikar and Peppas (1994)

In this section an analytic expression for the initiator efficiency is derived, based on the

kinetic scheme of Kurdikar and Peppas (1994) (scheme (3.5)). This model is able to

predict a priori the initiator efficiency and continouously calculate the term f throughout

the course of the polymerization. The advantage of this modeling strategy is that empiric

relations are no longer required (as in De Roo et al. (2004); Kiparissides et al. (1997);

Xie et al. (1991b)) to calculate the initiator efficiency, but an expression in which the

kinetic parameters are adjustable, can be used. Hence, a more detailed description of the

initiator decomposition mechanism is obtained, which leads to a more accurate modeling

of the initiator effiency. The analytic expression with kinetic parameters is derived in this

section.

3.2.1 Preliminaries

Kurdikar and Peppas (1994) describe the decomposition of one single initiator molecule

and generalize this to all initiator molecules in the reaction mixture. This methodology is

justified, because the local behaviour of one single initiator molecule is independent of the

behaviour of all other initiator molecules in the reaction mixture.

Kurdikar and Peppas (1994) derived an analytical expression for the initiator efficiency

from the kinetic scheme (3.5). For the radicals to be able to initiate chains, the radicals

must escape recombination within the solvent cage. Once they have escaped recombination,

the radicals must initiate chains as opposed to terminate growing chains. Thus, the initiator

efficiency, f , can be written as

f = FoFi (3.16)

where Fo is the probability that the primary radicals initiate chains rather than ter-

minate growing chains once they escape the solvent cage, and Fi is the probability that

radicals escape recombination within the solvent cage. The definition of Fo can mathemat-

ically be expressed as:


Fo =kadd[M ]

kadd[M ] + kt[R•](3.17)

in which [M ] is the monomer concentration and [R•] the total concentration of radicals

in the reacting system. kadd and kt are respectively the rate coefficient for addition to the

polymer chain and recombination reactions with other radicals. In the main part of the

polymerization process, the concentration of monomer is orders of magnitude larger than

the concentration of free radicals and initiator radicals. The probability that the radicals

initiate chains, becomes high and Fo is approximately 1.

The term Fi can be further written as

Fi = FiAFiB (3.18)

where FiA is the probability that A• and A1• will escape primary recombination, and FiB

is the probability that A• and B• will escape primary recombination. Thus the product of

FiA and FiB gives the total probability that the radicals will escape primary recombination.

Assume that pA is the total probability for the recombination of A• and A1• and pB is

the total probability for the recombination of A• and B•. Calculating the probability of

recombination pA en pB enables the evaluation of FiA and FiB.

FiA = 1− pA (3.19)

FiB = 1− pB (3.20)

In fact, pA and pB are the probabilities that radicals A1• respectively B• are at a

certain distance to A•. In the following section, the calculation of these possiblities will be

elaborated.


3.2.2 Mass balances

Let φA be the probability per unit of volume of finding an A1• radical at a distance r from

an A• radical at a time t. Fixing the frame of reference on the A• radical allows to write

a mass balance for A1• in the region outside the solvent cage as

∂φA

∂t= DA[

∂2φA

∂r2+

2

r

∂φA

∂r]− kβφA (3.21)

where DA is the relative diffusional coefficient given by the sum of diffusional coefficients

of radicals A• and A•1 and kβ the rate coefficient for the β-scission of A•

1. The left hand

side of equation (3.21) is the accumulation term. The right hand side exists of two parts.

The first part represents the probability per unit of volume that the A•1 radical enters the

’jacket’ with a thickness dr. The second part gives the probability per unit volume that

the A•1 radical reacts away because of β-scission.

A similar expression is obtained for φB, the probability per unit volume of locating a

B• radical at a distance r from an A• radical at time t. Again, writing a balance for the

probability of locating a B• radical in the region outside the solvent cage of radius b, the

following equation is obtained

∂φB

∂t= DB[

∂2φB

∂r2+

2

r

∂φB

∂r] + kβφA (3.22)

In this equation, DB is the relative diffusional coefficient of A• en B•. Normally, the

right hand side of these mass balances are subtracted by K. An expression for K which

accounts for the chain initiation and chain termination reactions, is shown in equation

(3.23). The effect of K in the modeling is negligible, hence in further work, this K is not

taken into account anymore.

K = 2kp,1[M ] + 2kt,1[M•] (3.23)

3.2.3 Initial and boundary conditions

In order to write the initial and boundary conditions, it is necessary to define characteristic

distances between initiator radicals: initial reaction distance r0 and reaction distance σ.


Initially, two radicals from the same initiator molecule are located at the initial reaction

distance r0 from each other. When the two reactants diffuse to each other, the distance

between both radicals becomes so small that reaction is successful. This distance is called

the reaction distance σ.

To solve the mass balances (equations (3.21) and (3.22)) two situations can occur:

• single-bond dissociation: only one bond is broken during the dissociation of the

initiator. In this case, the reaction distance σ is assumed to be equal to the initial

separation distance r0

• two-bond dissociation: more than one bond is broken simultaneously during the

dissociation of the initiator. In this case, the reaction distance σ is not equal to the

initial separation distance r0

As initial condition for the A•1 radical, it is assumed that A• and A•

1 are initially found

at a distance r=r0 of each other (equations (3.24) and (3.25))

t = 0 φA(r, 0) = 0 (3.24)

φA(r0, 0) = 1 (3.25)

As initial condition for the B• radical, it is assumed that at time t=0 no B• radicals

are present in the reaction mixture (equation(3.26)).

t = 0 φB(r, 0) = 0 (3.26)

Collins and Kimball (1949) concluded that when in a chemically activated process an

approached pair reacts with the formation of products, this occurs with a rate proportional

to the probability of the existence of the approached pair. The probability that A•1 is found

within a distance σA of A• is given by φA(σA) and the probalility that B• is found within

a distance σB of A• is given by φB(σB). The recombination rate of the approached pair is

given by respectively ktA φA(σA) and ktB φB(σB).


The first boundary condition (equations (3.27) and (3.29)) expresses that not all colli-

sions lead to recombination. When r equals σa, the rate of diffusion of the initiator radical

to a related radical has to be equal to the rate of reaction. Hence, no accumulation occurs

and the radical pair reaches a steady state. The first boundary condition for the A•1 radical

is thus:

t > 0 4πσ2ANADA(

∂φA

∂r)r=σA

= ktAφA(σA, t) (3.27)

and for the B• radical

t > 0 4πσ2BNADB(

∂φB

∂r)r=σB

= ktBφB(σB, t) (3.28)

The second boundary condition (equations (3.29) and (3.30)) expresses the probability

per unit of volume of two radicals being at infinite distance of each other, to be zero. For

both radicals this results in:

t > 0 φA(∞, t) = 0 (3.29)

t > 0 φB(∞, t) = 0 (3.30)

3.2.4 Analytical expression of the initiator efficiency f

The differential equations (3.21) and (3.22) cannot be solved explicitly to φA respectively

φB. Instead of calculating φA and φB, it is better to calculate the recombination probabil-

ities, pA respectively pB, of the two radical pairs. These can be calculated via equations

(3.31) and (3.32), in which an integration over time is done for pA and pB. The integration

is first done over the whole time range. This ensures that the total probability per unit

of volume is calculated in a way that the radicals can be found once on reaction distance.

To calculate the total probability of recombination it is necessary to take into account the

recombination rate coefficient. The integral must be multiplied with ktA respectively ktB.


pA = ktA

∫ ∞

0

φA(σA, t)dt (3.31)

pB = ktB

∫ ∞

0

φB(σB, t)dt (3.32)

The total probability of A• and A•1 respectively A• and B• not recombining is given by

FiA = 1− pA (3.33)

FiB = 1− pB (3.34)

An analytic expression can be found for pA and pB through transformation of the whole

problem to the Laplace field. The problem can be solved in this field and transformed back

to the time domain, leading to an analytic expression for the initiator efficiency:

f = FOFiAFiB (3.35)

Fia en Fib are given by equations (3.36) and (3.37) and FO by equation(3.17).

FiA = 1− ktAe

(√kβ(σA−r0)√

DA

)

4πNAr0

(σA

√DA

√kβ + ktA

4πσANA+ DA

) (3.36)

FiB = 1−

ktB

−kβ

(DA + ktA

4πσANA

)e

(√kβ(σA−r0)√

DA

)+ kβ

ktA

4πσANA+ kβDA + k

32β σA

√DA

4πNAr0

(σA

√DA

√kβ + ktA

4πσANA+ DB

) (ktA

4πσANA+ DA

)kβ

(3.37)

Based on this general expression, the initiator efficiency can be calculated for each

initiator.


3.3 Conclusion

The kinetic modeling of the initiator efficiency f is performed based on the kinetic scheme

of Kurdikar and Peppas (1994). An analytical expression has been derived for the initiator

efficiency. In this expression, only kinetic parameters occur, whereas in former studies a

semi-empirical expression was used. Hence, the kinetic modeling leads to a more accurate

calculation of the initiator efficiency.

40

Chapter 4

Implementation of the initiator

efficiency

Kurdikar and Peppas (1994) developed a model that is able to a priori predict the initiator

efficiency and continuously calculate the initiator efficiency f throughout the polymeriza-

tion process. The model is based on the kinetic scheme (3.5). The initiator efficiency is

calculated with equation (3.18), using equations (3.36) and (3.37).

This approach of modeling the initiator effiency differs from other modeling approaches

in literature (De Roo et al., 2004; Kiparissides et al., 1997; Xie et al., 1991b) since the

initiator efficiency is calculated based on an expression without any non-adjustable pa-

rameters, being kinetic parameters. Empiric relations are excluded and a more detailed

description of the initiator decomposition mechanism is taken into account, which leads to

a more accurate modeling of the initiator efficiency.

To calculate the initiator efficiency f , the different parameters in the model of Kurdikar

and Peppas (1994), rate coefficients and diffusion coefficients, need to be known. In the

next sections, these parameters are discussed and evaluated.

Chapter 4. Implementation of the initiator efficiency 41

Table 4.1: Values of the Arrhenius parameters of kbd for relevant initiators in industrial produc-tion of poly(vinyl chloride), provided by the producer Akzo Nobel

Initiator A [s−1] E [kJ mol−1]Trigonox EHPC 1.83 10+15 122.45Trigonox TBPD 1.52 10+14 115.47Perkadox AIBN 2.89 10+15 130.23Laurox 3.92 10+14 123.37

Table 4.2: Values of the Arrhenius parameters of kβ for relevant initiators in industrial produc-tion of poly(vinyl chloride), produced by Akzo Nobel

Initiator A [s−1] E [kJ mol−1]Trigonox EHPC 1.00 10+14 45.70Trigonox TBPD 1.00 10+13 50.00Perkadox AIBN 1.30 10+14 62.60Laurox 1.00 10+14 45.70

4.1 Kinetic parameters

The kinetic parameters present in the model of Kurdikar and Peppas (1994) are

• kbd: the rate coefficient for dissociation of I to form A• and A1•

• kβ: the rate coefficient for β-scission of A1• to form B•

• ktA and ktB: the rate coefficients for the primary recombination of radicals in the

solvent cage

The values of the kinetic parameters kbd and kβ are already discussed in Chapter 2. Ta-

ble 4.1 respectively 4.2 gives an overview of the Arrhenius parameters of the rate coeffients

kbd respectively kβ. The rate coefficients ktA and ktB are taken equal, with values varying

in the range 103 - 105 m3 mol−1 s−1 (Fischer and Radom, 2002).

As presented in Chapter 2, the Arrhenius parameters are found in Buback (2005) or

delivered by the producer.


The influence of these rate coefficients on the kinetic modeling of Kurdikar and Peppas

(1994) needs to be known, because this influence gives an indication of how sensitive the

model is to variations of its kinetic parameters.

4.1.1 Effect of kβ

The effect of the rate coefficient for β-scission, kβ, on the initiator efficiency can be ex-

plained by studying the influence of kβ on FiA and FiB. These effects were studied into

detail in Van Pottelberge (2004–2005). FiA, respectively FiB, represents the possibility

that the first, respectively the second radical pair does not recombine with another radical.

Figure 4.1 shows that FiA increases while FiB decreases for increasing values of kβ. In

this figure, both diffusion coefficients are taken 10−12 m2 s−1, which are realistic values.

Both recombination rate coefficients ktA and ktB are assumed equal and evaluated at 10+5

m3mol−1s−1. The reaction distance σ and the initial distance r0 are taken equal to 8 10−10

m.

The decrease of the initiator efficiency with decreasing values of kβ is explained by a hin-

dered possibility of the first radical pair escaping to recombination. This because the first

radical pair is less easily converted to a second radical pair. This leads to a lower value

for FiA. Because the second radical pair is hardly formed, it can not recombine and the

value of FiB approaches 1. With increasing values of kβ, the probability of the first radical

pair not recombining increases. At the same time, FiB decreases, because the probability

of B•-radicals recombining with A•-radicals will increase. This because the number of

B•-radicals in the polymer solution will increase. When kβ reaches extremely high values,

the initiator efficiency will decrease again, because of very low values of FiB. This is ex-

plained by the presence of only A• and B• radicals in the polymer solution in case of high

kβ-values. Hence, the probability of recombination between these radicals is high.

4.1.2 Effect of ktA and ktB

In this work, the rate coefficients ktA and ktB for the recombination of radicals in the

solvent cage are considered to be equal. In reality, this is not the case. The influence of

the variation of ktA is shown in Figure 4.2.


Figure 4.1: Influence of kβ on initiator efficiency f (F0=1, kr1=kr,2=104 m3mol−1s−1 D=10−11

m2 s−1, σA=σB=r0=6 10−10 m)) (Van Pottelberge, 2004–2005)

The initiator efficiency decreases with an increasing value for the rate coefficient ktA,

while the diffusion coefficients and the rate coefficient kβ are considered to be constant.

When ktA increases, the fraction of the radicals that recombines will increase. More radical

recombination implies a decrease of the initiator efficiency.

The same holds true for the influence of the variation of ktB on the initiator efficiency,

as shown in Figure 4.3. It should be noted that the rate coefficient kβ has a value of about

10+6 s−1 for TBPD, which implies that there is an appreciable chance that β-scission will

take place.

The variation of ktA, respectively ktB, shows that the initiator efficiency varies, but not

in an excessive way.


Figure 4.2: Variation of the initiator efficiency f with the rate coefficient ktA (D=10−12 m2

s−1, kβ=105 s−1, ktB=104 m3mol−1s−1, σA=σB=r0=6 10−10 m) (Van Pottelberge,2004–2005)

4.2 Diffusion coefficients

In this section, the effect of the diffusion coefficients on the calculation of the initiator

efficiency is discussed. In the modeling of Kurdikar and Peppas (1994) two diffusion coef-

ficients, DA and DB, are calculated using the free volume theory. This theory is presented

and applied to calculate the diffusion coefficients used in the analytic expression for the

initiator efficiency, as shown in equations (3.36) and (3.37).

4.2.1 Free volume theory

The free volume theory is the most generally used theory for predicting diffusion coefficients

in polymer-solvent systems (Neogi, 1996; De Roo et al., 2004). The expression of the free

volume self-diffusion coefficients resulting from this theory has three contributions: a pre-

exponential factor, an activation energy and a free volume part. In this subsection, the

free volume theory is discussed briefly.


Figure 4.3: Variation of the initiator efficiency f with the rate coefficient ktB (kβ=108 s−1,(+) kβ=1010 s−1 (D=10−12 m2 s−1, ktA=104 m3mol−1s−1, σA=σB=r0=6 10−10 m)(Van Pottelberge, 2004–2005)

Free volume part The free volume theory divides the volume of (polymer) liquids into

three parts (De Roo et al., 2004; Neogi, 1996): the occupied volume of a component, the

interstitial free volume and the hole free volume.

A molecule in a substance undergoes one step in the diffusion process if the molecule

is adjacent to a hole or void existing (or created by thermal motion of the molecules) in

the substance and jumps to that hole. The probability that the molecule finds a hole of

a size large enough to jump to, was derived by Cohen and Turnbull (1959). The diffusion

coefficient is proportional to the probability of finding a hole with a volume equal to or

larger than the minimum volume required for the diffusion step, as shown in equation (4.1).

D ∝ exp (− V∗

VFH/γ) (4.1)

D is the self-diffusion coefficient of the molecules, V∗ is the minimum molar hole free

volume that a molecule needs to jump (in other words the size of the molecule) and γ

is an overlap factor (between 0.5 and 1) because the free volume elements are shared

with neighbouring molecules (De Roo et al., 2004). Hence, in this exponential function


the ratio of the size of a diffusing molecule and the free volume available per molecule is

taken. Originally, this theory was formulated for van der Waals and metallic liquids (liquids

who can be represented as spheres), but it is also successful in describing mass transfer in

solutions with long polymer chains mixed with small solvent molecules. A distinction must

be made between self-diffusion and mutual diffusion coefficients (Masaro and Zhu, 1999;

Neogi, 1996). The driving force for self-diffusion is entropic in origin, while mutual diffusion

is driven by concentration gradients. In previous studies (De Roo et al., 2004; Verhaert,

2003–2004; Van Pottelberge, 2004–2005) the system was considered to be in equilibrium:

there were no concentration gradients and the self-diffusion coefficients were applied. In

what follows, a different approach is followed, where diffusion coefficients refer to mutual

diffusion.

Pre-exponential factor and activation energy The equation for the Cohen-Turnbull

diffusion coefficient, shown in equation (4.1), is extended for the calculation of the diffusion

coefficient in a binary mixture containing solvent and polymer chains. For this extension

the concept of a jumping unit of a diffusing molecule is introduced (Neogi, 1996). A jumping

unit of a diffusing molecule is the volume part of a molecule that makes the jump to a void

in the substance or mixture. For small molecules (solvent, monomer, etc.) the jumping

unit is the volume of the molecule itself. For polymer molecules it is clear that diffusion

occurs through the consecutive movement of parts of the macromolecule because a free

volume hole of the size of a complete polymer molecule does not exist. The fraction of the

macromolecule that makes the jump to a void is the jumping unit of the macromolecule.

As a result of this model, a liquid must be considered as consisting of jumping units. The

diffusion coefficient of a single species x in a binary mixture of components m (monomer)

and p (polymer) is then written as (De Roo et al., 2004):

Dx = Dx,0exp(− V∗

VFH/γ) (4.2)

V ∗ is the critical molar hole free volume required for a jumping unit of species x in the

binary liquid to migrate. VFH is the available hole free volume for diffusion per mol of all

individual jumping units in the solution. Dx,0 is the pre-exponential factor.


The free volume theory presented above is now applied for the calculation of the diffu-

sion coefficients DA and DB in the simple kinetic scheme of Kurdikar and Peppas (1994),

shown in scheme (3.5).

4.2.2 Calculation of the free volume

The free volume contribution of the diffusion coefficients depends on the volumetric proper-

ties of the monomer, the polymer and the initiator. Because the free volume contribution,

hence the diffusion coefficient, is very sensitive to the values of the volumetric properties,

a thorough study of these values is required. In this section, the volumetric properties of

the different classes of initiators are considered.

In Van Krevelen (1997) the atomic volumes of the most common atoms in organic

chemistry are given, as shown in Table 4.3. Van Krevelen (1997) uses the group contribution

theory to calculate the volume of a molecule or radical, which means that the sum of the

volumes of the consisting atoms is equal to the volume of the sum of the atoms. The

volume taken by the bonds is also given by the same author.

Table 4.3: Atomic volumes by Van Krevelen (1997)

Atom or bond Volume [cm3 mol−1]H 6.7C 1.1N 3.6O 5.0Cl 19.3

Double bond 8.0Triple bond 15.5

In case of e.g. tert-butyl peroxy-neo-decanoate (TBPD), shown in formula (2.11), the

volume of the molecule is calculated as shown in Table 4.4.

In the modeling of De Roo et al. (2004), the diffusion coefficients are calculated based

on half of the volume of the whole molecule. In a new approach, the diffusion coefficients


Table 4.4: Volumes by Van Krevelen (1997), applied on tert-butyl peroxy-neo-decanoate(TBPD)

Atom or bond Number Volume per atom or bond Volume of all atoms or bonds[cm3 mol−1] [cm3 mol−1]

H 28 6.7 187.6C 14 1.1 15.4N 0 3.6 0O 3 5.0 15.0Cl 0 19.3 0

Double bond 1 8.0 8.0Triple bond 0 15.5 0

Total 226.0

are calculated based on the reaction scheme represented by Kurdikar and Peppas (1994).

Hence, the diffusion coefficients DA and DB are given by equations (4.3) and (4.4).

DA = DA• + DA•1(4.3)

DB = DA• + DB• (4.4)

Based on these equations, the diffusion coefficients DA and DB are calculated for each

initiator investigated in this work.

Peroxydicarbonates Reaction scheme (3.5) is now applied to di(2-ethylhexyl)peroxydi-

carbonate (EHPC). The chemical structure of this initiator is shown in formula (2.9). The

initiator molecule I dissociates to form the first radical pair, as shown in reaction (4.5).

This reaction is the same as the first reaction in Figure 2.2, which shows the decomposition

mechanism of a peroxyester in general.

ROCOO

O

COR

Ok1−bd //ROCO•

O

+ •OCOR

O

(4.5)


The first radical on the right hand side of this reaction represents A• in reaction scheme

(3.5), while the second radical represents A1•.

The radical A1• can recombine again with the radical A• or can diffuse out of the solvent

cage. This radical A1• can also undergo a β-scission reaction, resulting in the formation of

radical B•, as shown for EHPC in reaction (4.6). This reaction corresponds with the first

β-scission in Figure 2.2.

ROCO•

Okβ(CO) // RO•+CO2 (4.6)

The resulting radical represents radical B• in reaction scheme (3.5). For these radicals

the volumes are calculated based on the volumes of Van Krevelen (1997). The results are

presented in Table 4.5.

Peroxyesters Secondly, reaction scheme (3.5) is applied to tert-butyl peroxy-neo-deca-

noate (TBPD). The initiator molecule I dissociates to form the first radical pair and

a CO2-molecule, which corresponds with a two-bond dissociation (reaction (4.7)). This

reaction is the same as the first reaction in Figure 2.3, which shows the decomposition

mechanism of a peroxyester in general.

C

CH3

R1

R2

COO

O

C

CH3

CH3

CH3

k2−bd // C•

CH3

R1

R2

+ CO2 + •OC

CH3

CH3

CH3 (4.7)

The first radical on the right hand side of this reaction represents A• in the reaction

scheme of Kurdikar and Peppas (1994), while the second radical represents A1•.



radical B•, as shown for TBPD in reaction (4.8).

CO•

CH3

CH3

CH3

kβ // CH•3 + CH3CCH3

O

(4.8)


The resulting radical represents radical B• in reaction scheme (3.5). For these radicals

the volumes are calculated based on the volumes of Van Krevelen (1997). The results for

TBPD are presented in Table 4.5.

Dialkyldiazenes For azobis(isobutyronitrille) (AIBN), of which the chemical structure

is shown in formula (2.13), the dissociation of the initiator is presented in the first reaction

of Figure 2.4, which shows the decomposition mechanism of a dialkyldiazene in general.





radical B•. In case of AIBN, a methylradical can be formed, as shown in reaction (4.9).

C•

CH3

CN

CH3

kβ // CH•3 + •CCN

CH2

(4.9)

The resulting radical represents radical B•. For all of these radicals the volumes are

calculated based on the volumes of Van Krevelen (1997). The results are presented in

Table 4.5.

Diacyl peroxides Finally, the diffusion coefficients for the last initiator class are calcu-

lated. The reaction scheme of Kurdikar and Peppas (1994) is applied to lauroylperoxide.

The chemical structure of this initiator is shown in formula (2.14) with R equal to C11H23.

The initiator molecule I dissociates to form the first radical pair, as shown in reaction

(4.10). This reaction is the same as the first reaction in Figure 2.5, which shows the de-

composition mechanism of a diacyl peroxide in general. Remark that the dissociation is a

single-bond dissociation.

RCOO

O

CR

Ok1−bd // RCO•

O

+ •OCR

O

(4.10)





cage. This radical A1• can also undergo a β-scission reaction, resulting in the formation

of radical B•, as shown for lauroylperoxide in reaction (4.11). This reaction corresponds

with the first β-scission in Figure 2.5.

RCO•

Okβ(CO) // R•+CO2 (4.11)

The resulting radical represents radical B•. For these radicals in the decomposition

mechanism of lauroylperoxide, the volumes are calculated based on the volumes of Van

Krevelen (1997). The results are presented in Table 4.5.

Finally, Table 4.5 gives an overview of the radical volumes for the different initiators

investigated in this work.

Table 4.5: Molar volumes by Van Krevelen (1997) for all radicals in the reaction scheme ofKurdikar and Peppas (1994). The volumes are presented in cm3 mol−1

Initiator I/2 A• A1• B•

EHPC 149.5 146.8 146.8 127.7TBPD 158.1 137.2 68.6 21.2AIBN 73.1 63.7 63.7 21.2Lauroylperoxide 185.3 185.3 185.3 166.2


Table 4.6: Calculation of the diffusion coefficients (D) based on the free volume (V) theory. Thevolumes are presented in cm3 mol−1, and the diffusion coefficients in m2 s−1

Initiator I/2 A• A1• B•

TBPD V 158.1 137.2 68.6 21.2D 1.36 10−15 6.89 10−15 1.41 10−12 2.86 10−10

EHPC V 149.5 146.8 146.8 127.7D 2.66 10−15 3.28 10−15 3.28 10−15 1.44 10−14

AIBN V 73.1 63.7 63.7 21.2D 9.91 10−13 2.05 10−12 2.05 10−12 2.86 10−10

Lauroylperoxide V 185.3 185.3 162.2 162.2D 1.66 10−16 1.66 10−16 7.28 10−16 7.28 10−16

4.2.3 Calculation of the diffusion coefficients

Based on the volumes represented in Table 4.5 and equation (4.1), the diffusion coefficient

for each radical can be calculated. The calculation of the mutual diffusion coefficients

DA and DB is done with equations (4.3) and (4.4). The diffusion coefficients presented

here, are those accompagnying a fixed conversion. A diffusion coefficient decreases with

increasing conversion, until a plateau value is reached. At high conversions, the diffusion

coefficient decreases again. In this section, the diffusion coefficients are those for which a

plateau is reached (conversion of 40%). For each type of initiator, the diffusion coefficients

are shown in Table 4.6. It should be noted that the polymerization temperature was taken

328K and the initial concentration of vinyl chloride monomer 0.02354 wt%.


4.3 Reaction distance

In the analytic expression of the initiator efficiency f , shown in equation (3.35) using

equations (3.36) and (3.37), two characteristic distances between initiator radicals occur:

initial distance r0 and reaction distance σ.

Initially, two initiator radicals coming from the same initiator molecule are on a relative

distance of each other, defined as the initial distance r0. In order to react, two species need

to approach to each other and the distance between them becomes so small that reaction

is successful. This distance is called the reaction distance σ.

Two situations can occur:

• single-bond dissociation: only one bond is broken during the dissociation of the

initiator. In this case, the reaction distance is assumed to be equal to the initial

separation distance

• two-bond dissociation: more than one bond is broken simultaneously during the

dissociation of the initiator. In this case, the reaction distance is not equal to the

initial separation distance

The calculation of the volumes (Table 4.5) enables the calculation of the initial reaction

distance r0 and reaction distance σ, based on the equations (4.12) and (4.13).

V0 =3

4πr3

0 (4.12)

V =3

4πσ3 (4.13)

Linking with the model of Kurdikar and Peppas (1994) (scheme (3.5)), the initial re-

action distance r0 and the reaction distance σ are given by equations (4.14) and (4.15).

In these equations, rI is the radius of the initiator and rA• and rB• are the radius of A•

respectievely B•.

r0 = rI/2 (4.14)

σ = rA• + rB• (4.15)


The influence of the reaction distance on the kinetic modeling of Kurdikar and Peppas

(1994) needs to be known, because this influence gives an indication of how sensitive the

model of Kurdikar and Peppas (1994) is to variations of its parameters.

Figure 4.4 shows the influence of the initial reaction distance between two initiator

radicals.

Figure 4.4: Variation of the initiator efficiency f with the initial reaction distance r0 (kβ=108

s−1, (+) kβ=1010 s−1 (D=10−12 m2 s−1, ktA=ktB=104 m3mol−1s−1) (Van Pottel-berge, 2004–2005)

The initiator efficiency increases as the initial reaction distance increases. This implies

that initiator radicals with a higher initial reaction distance will have a higher initiator

efficiency than initiator radicals that are initially close to each other. The closer the

radicals are initially, the more probable the recombination is. Hence, the probability of

an initiator radical leaving the solvent cage and adding to monomer, decreases. When

the initiator efficiency is modeled with the same values for the kinetic parameters and the

same calculation method for the diffusion coefficients, one can conclude that the initiator

efficiency for initiators undergoing two-bond dissociation will be higher than for initiators

undergoing single-bond dissociation.


Table 4.7: Estimates of the reparameterized pre-exponential factor and activation energy of theintrinsic rate coefficients for propagation, kp,chem, for chain transfer to monomer,ktr,chem, and for termination, ktc,chem and ktCl,chem(De Roo et al., 2004)

Rate coefficient A Ekp,chem 9.2 10−1 26.7 2.1ktr,chem 9.3 10+4 57.0 3.3ktc,chem 9.4 10+4 0ktCl,chem 6.9 10+5 0

Table 4.8: Reaction conditions for the simulation of vinyl chloride suspension polymerization

Condition Value UnitsTemperature 328 [K]

Initial initiator concentration 0.02354 [wt%]

4.4 Modeling results for all initiator classes

In this section, the results of the calculation of the initiator efficiency according to the

modeling presented in previous sections are discussed.

The calculation model of the initiator efficiency also takes into account other parame-

ters corresponding with the whole polymerization process and not only with the initiator

decomposition. The values of these parameters are presented in Table 4.7 (De Roo et al.,

2004). It should also be noted that the simulations are executed under the reaction condi-

tions shown in Table 4.8.


4.4.1 Results for peroxydicarbonates

The peroxydicarbonate investigated in this work is di(2-ethylhexyl)peroxydicarbonate or

EHPC. The initiator efficiency f is calculated based on equation (3.35), using equations

(3.36) and (3.37). In these equations, the kinetic parameters, diffusion coefficients and

reaction distances are evaluated as discussed above (Tables 4.1 and 4.2). The parameters

used in this work for di(2-ethylhexyl)peroxydicarbonate (EHPC) are shown in Table 4.9.

The modeling is performed with the reaction conditions given in Table 4.8.

Table 4.9: Parameters used for the calculation of the initiator efficiency f for di(2-ethylhexyl)peroxydicarbonate (EHPC) (Akzo, 2000; Buback, 2005)

Parameter Value Unitskbd 1.83 10+15 exp(-122.45 10+3/RT) [s−1]kβ 1.00 10+14 exp(-45.70 10+3/RT) [s−1]ktA 1.00 10+4 [m3mol−1s−1]ktB 1.00 10+4 [m3mol−1s−1]σA 7.75 10−10 [m]σB 7.75 10−10 [m]r0 7.75 10−10 [m]

The diffusion coefficients for EHPC are given in Table 4.6, taking into account that

these values are plateau values. It should be noted that the values of the diffusion co-

efficients are rather low compared to those for e.g. TBPD. Due to this lower value, the

radicals diffuse away more slowly, hence the probability of recombination increases.

The initiator efficiency in the monomer-rich phase (f1) is constant throughout the poly-

merization process. With the parameters of Table 4.9 and under the conditions of Table

4.8, the initiator efficiency in the polymer-rich phase (f2) was modeled to be 0.66 during

the first 4 hours of the polymerization process, calculated with the analytic expression

of Kurdikar and Peppas (1994) (Figure 4.5). Since the viscosity of the reaction medium

increases, the diffusive displacement of the radicals away from each other becomes more

difficult and radical recombination reactions become preferred until f2 reaches a limiting

value of zero.


Figure 4.5: Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2) as a func-tion of polymerization time for di(2-ethylhexyl)peroxydicarbonate (EHPC), withparameter values as in Table 4.9.

When comparing the semi-empiric modeling of De Roo et al. (2004) with the kinetic

modeling of Kurdikar and Peppas (1994), nearly the same plateau value for the initiator

efficiency in the polymer-rich phase (f2) is obtained (Figure 4.6).

Two aspects play a role in the comparison between the two modeling strategies. First,

the calculation approach differs. The semi-empiric modeling of De Roo et al. (2004) starts

from an intrinsic initiator efficiency f0 of 0.7, which is an empirical value. When accounting

for the effect of diffusion (kdiff ), the initiator efficiency f is calculated as shown in equation

(3.3).

Whereas equation (3.3) is based on semi-empiric values, the modeling of Kurdikar and

Peppas (1994) is based on kinetic parameters (equation (3.35)). This approach offers a

more detailed and more accurate description of the initiator efficiency.


Figure 4.6: Initiator efficiency in the polymer-rich phase (f2) as a function of polymerizationtime for di(2-ethylhexyl)peroxydicarbonate (EHPC), for the modeling of De Rooet al. (2004) and Kurdikar and Peppas (1994)

In the model of Kurdikar and Peppas (1994), the effect of diffusion is also taken into

account, as can be seen in equations (3.36) and (3.37). The second aspect in the comparison

of the two modeling strategies is the different calculation of the diffusion coefficients. In the

modeling of De Roo et al. (2004), the diffusion coefficients are taken equal (Di), while the

modeling of Kurdikar and Peppas (1994) calculates with different diffusion coefficients (DA

and DB). These diffusion coefficients are calculated for each class of initiator as shown in

Table 4.6. The difference between the values of the diffusion coefficients for both modeling

methods is shown for EHPC in Figure 4.7.

The diffusion coefficients in the modeling of De Roo et al. (2004) (Di) are equal and

have a value shown in Table 4.6. The diffusion coefficients DA and DB have a higher value

than Di, but DB still has a higher value than DA. This lower value of the diffusion coef-

ficient DA makes sure that the diffusion of A• and A•1 out of the solvent cage occurs less

quickly than the diffusion of A• and B•. The more quickly the escape out of the solvent

cage occurs, the more easily the polymerization reaction is started, and the higher the

initiator efficiency, as can be seen in Figure 4.6. In the modeling of De Roo et al. (2004),

the initiator efficiency stays longer at the plateau value (Figure 4.7) and reaches more


Figure 4.7: Diffusion coefficients as a function of polymerization time for di(2-ethylhexyl)-peroxydicarbonate (EHPC), for the modeling of De Roo et al. (2004) (Di) andKurdikar and Peppas (1994) (DA and DB)

slowly value of zero. Moreover, the plateau value for initiator efficiency in the modeling of

De Roo et al. (2004) has a lower value. This effect is explained by the lower value of the

diffusion coefficient (Di) compared to the mutual diffusion coefficients (DA and DB). The

escape out of the solvent cage goes less quickly, and initiation of the polymer chain does

not become preferred and reaches a lower plateau value.

To see whether the kinetic modeling of Kurdikar and Peppas (1994) is not only able to

predict the initiator efficiency in an accurate way, the monomer conversion as a function of

polymerization time is also plotted (Figure 4.8). This monomer conversion profile is given

under the reaction conditions of Table 4.8. In vinyl chloride polymerization, the polymer-

rich phase is formed at the start (0.1% conversion) of the polymerization process with a

concentration of 70 wt% of polymer and 30 wt% of monomer in this phase (De Roo et al.,

2004). This latter concentration region is considered to affect the polymerization reactions

in becoming diffusion-controlled (the cage effect). In contrast, the monomer-rich phase

is considered to be reaction-controlled. Therefore, from the start of the polymerization

until final conversion (in this case about 95%) all reactions have to be diffusion-controlled.


Figure 4.8: Monomer conversion as a function of polymerization time for EHPC

Figure 4.5 in combination with Figure 4.8, proves that the cage effect is taken into account

in the kinetic modeling.

4.4.2 Results for peroxyesters

The peroxyester investigated in this work is tert-butyl peroxy-neo-decanoate or TBPD.

The calculation results for this peroxyester are presented in this section. The initiator

efficiency is calculated analogously as for peroxydicarbonates. The parameters used in this

work for tert-butyl peroxy-neo-decanoate (TBPD) are shown in Table 4.10. Again, the

modeling is performed with the reaction conditions given in Table 4.8.

The diffusion coefficients for TBPD are given in Table 4.6, taking into account that this

values are plateau values. It should be noted that the values of the diffusion coefficients

have rather high values compared to those for e.g. EHPC. Due to this higher value, the

radicals diffuse away more quickly, hence the probability of recombination decreases. The

initiator efficiency in the monomer-rich phase (f1) is constant throughout the polymeriza-

tion process. With the parameters of Table 4.10 and under the conditions of Table 4.8,

the initiator efficiency in the polymer-rich phase (f2) was modeled to be 0.69 during the


Table 4.10: Parameters used for the calculation of the initiator efficiency f for tert-butyl peroxy-neo-decanoate (TBPD) (Akzo, 2000; Buback, 2005)


first 4 hours of the polymerization process. Since the viscosity of the reaction medium

increases, the diffusive displacement of the radicals away from each other becomes difficult

and radical recombination reactions become preferred until f2 reaches a limiting value of

zero.

When comparing the semi-empiric modeling of De Roo et al. (2004) with the kinetic

modeling of Kurdikar and Peppas (1994), nearly the same plateau value for the initiator

efficiency is obtained (Figure 4.10).

Again, the calculation method (semi-empirical expression versus kinetic analytical ex-

pression) differs. In addition, the diffusion coefficients have again different values in both

modeling methods. In the modeling of De Roo et al. (2004), the diffusion coefficients

are taken equal (Di), while the modeling of Kurdikar and Peppas (1994) calculates with

non-equal diffusion coefficients (DA and DB). These diffusion coefficients are calculated

for each class of initiator as shown in Table 4.6. The difference between the values of the

diffusion coefficients for both modeling methods are shown for TBPD in Figure 4.11.

The diffusion coefficients in the modeling of De Roo et al. (2004) are equal. The values

of DA and Di do not differ much, nevertheless the value of Di is lower. The diffusion

coefficient DB is the highest of the three (Figure 4.11).


Figure 4.9: Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2) as a func-tion of polymerization time for tert-butyl peroxy-neo-decanoate (TBPD), with pa-rameter values as in Table 4.10.

This lower value of the diffusion coefficient DA compared to DB makes sure that the

diffusion of A• and A•1 out of the solvent cage occurs less quickly than the diffusion of A•

and B•. The more quickly the escape out of the solvent cage occurs, the more easily the

polymerization reaction is started, and the higher the initiator efficiency, as can be seen

from Figure 4.10.

In the modeling of De Roo et al. (2004), the initiator efficiency drops at the nearly

the same time for the modeling of Kurdikar and Peppas (1994), but the initiator efficiency

reaches a lower plateau value. This effect is explained by the lower value of the diffusion

coefficient (Di) compared to the mutual diffusion coefficients (DA and DB). The escape out

of the solvent cage goes less quickly, and initiation of the polymer chain does not become

preferred and reaches a lower plateau value.

Finally, the monomer conversion profile is plotted to see whether the kinetic modeling

of Kurdikar and Peppas (1994) is able to not only predict the initiator efficiency in an

accurate way (Figure 4.12). This monomer conversion profile is given under the reaction

conditions of Table 4.8. Figures 4.12 and Figure 4.9 prove that the model of Kurdikar and

Peppas (1994) is able to model the initiator properties in an accurate way.


Figure 4.10: Initiator efficiency in the polymer-rich phase (f2) as a function of polymerizationtime for tert-butyl peroxy-neo-decanoate (TBPD), for the modeling of De Rooet al. (2004) and Kurdikar and Peppas (1994) (this work)

4.4.3 Results for dialkyl diazenes

The calculation results for the dialkyl diazene investigated in this work, which is azo-

bis(isobutyronitrille) or AIBN, are presented in this section. The parameters in the model

of Kurdikar and Peppas (1994) for AIBN are given in Table 4.11. The modeling is per-

formed with the reaction conditions given in Table 4.8.

The diffusion coefficients for AIBN are given in Table 4.6, taking into account that these

values are plateau values. It should be noted that the values of the diffusion coefficients

have much higher values compared to those for e.g. EHPC or TBPD (Table 4.6). Due to

this higher value, the radicals diffuse away more quickly, hence the probability of recombi-

nation decreases. Again, the initiator efficiency in the monomer-rich phase (f1) is constant

throughout the polymerization process. With the parameters of Table 4.11 and under the

conditions of Table 4.8, the initiator efficiency in the polymer-rich phase (f2) was modeled

to be 0.97 during the whole polymerization process, calculated with the analytic expression

of Kurdikar and Peppas (1994). This modeling result does not agree with reality. First of

all, the practical range in which the values for initiator efficiency are situated, is 0.3-0.8


Figure 4.11: Diffusion coefficients as a function of polymerization time for tert-butyl peroxy-neo-decanoate (TBPD), for the modeling of De Roo et al. (2004) (Di) and Kurdikarand Peppas (1994) (DA and DB)

(Kurdikar and Peppas, 1994; Westmijze, 1999). Secondly, the initiator efficiency should

decrease after a certain polymerization time, since the viscosity of the reaction medium

increases in reality. This effect is explained by the difficult diffusive displacement of the

radicals away from each other, leading to preferred radical recombination reactions until

f2 reaches a limiting value of zero. With the modeling of Kurdikar and Peppas (1994),

the monomer conversion is too low (less than 1%), hence the reaction does not become

diffusion controlled and the initiator efficiency can not decrease because of the diffusive

displacement of radicals away from each other. Hence, the model of Kurdikar and Peppas

(1994) is not able to describe this effect.

It can be concluded that the modeling code based on the kinetic scheme of Kurdikar

and Peppas (1994) is not able to predict the initiator efficiency in an accurate way for

AIBN. Indeed, the reactions taking place during the decomposition of AIBN (Figure 2.4)

can not be summerized into the kinetic scheme of Kurdikar and Peppas (1994) (equation

(3.5)). For AIBN, a more detailed kinetic modeling scheme is required, but searching for

such a scheme remains for future work.


Table 4.11: Parameters used for the calculation of the initiator efficiency f for azo-bis(isobutyronitrille) (AIBN) Akzo (2000); Buback (2005)


4.4.4 Results for diacyl peroxides

Finally, the modeling results for the diacyl peroxide investigated in this work, lauroylper-

oxide, are discussed. This modeling was performed with the parameters of Table 4.12 and

under the reaction conditions of Table 4.8.

Table 4.12: Parameters used for the calculation of the initiator efficiency f for lauroylperoxide(Akzo, 2000; Buback, 2005)


The diffusion coefficients are calculated in the same way as for TBPD, EHPC and AIBN.

Note that the diffusion coefficients have a much lower value than in case of e.g. TBPD,

which can be explained by the high volume of the radicals A•, A•1 and B• (Table 4.6).

Due to this lower value, the radicals can diffuse away less quickly, hence the probability of

recombination increases. A decrease of initiator efficiency is expected.

The initiator efficiency in the monomer-rich phase (f1) is constant throughout the


Figure 4.12: Monomer conversion as a function of polymerization time for TBPD

polymerization process. With the parameters of Table 4.12 and under the conditions of

Table 4.8, the initiator efficiency in the polymer-rich phase (f2) was modeled to be 0.29

during the first four hours, calculated with the analytic expression of Kurdikar and Peppas

(1994) (Figure 4.13).

Since the viscosity of the reaction medium increases, the diffusive displacement of the

radicals away from each other becomes difficult and radical recombination reactions become

preferred until f2 reaches a limiting value of zero.

The practical range in which the values for initiator efficiency are situated, is 0.3-0.8

(Kurdikar and Peppas, 1994; Westmijze, 1999). The modeling of Kurdikar and Peppas

(1994) for lauroylperoxide results in rather low values for the initiator efficiency. This can

be explained by the very high volume of radicals A•,A•1 and B•, of which are given in

equation (2.14). Due to this very low value of the diffusion coefficients, the radicals can

diffuse away less quickly (because they are too big to diffuse), hence the probability of

recombination increases. Thus, the initiator efficiency is rather low.

It can be concluded that the model of Kurdikar and Peppas (1994) is able to describe

the decomposition scheme given in Figure 2.5, but, because of the high volume of the


Figure 4.13: Initiator efficiency in the monomer-rich (f1) and polymer-rich phase (f2) as afunction of polymerization time for lauroylperoxide, with parameter values as inTable 4.12.

radicals (A•,A•1 and B•) rather low values of the initiator efficiency are obtained.


4.5 Selection of the most appropriate initiator for the


Initiators play an important role in the manufacturing of polymers. The initiator controls

the production of radicals, which determines the vinyl chloride monomer polymerization

rate. This is a determining factor for the output of a PVC plant. For this reason it is

essential to select the appropriate initiator for all production conditions of the polymeriza-

tion of VCM. A description of selection criteria has been presented previously in Chapter

1. In this section, an initiator is selected based upon these selection criteria and the results

of the kinetic modeling presented in previous section.

4.5.1 Selection based on characteristics of the polymerization

process

The polymerization process is a.o. characterized by the half-life time of the initiator. Table

4.13 shows the half-life times and temperatures for the initiators discussed in this work.

Table 4.13: Kinetic data for relevant initiators in industrial production of poly(vinyl chloride),provided by Akzo Nobel

Initiator T (K) for t1/2 A [s−1] E [kJ mol−1]0.1 h 1.0 h 10h

EHPC 356 337 320 1.83E+15 122.45TBPD 357 337 319 1.52E+14 115.47AIBN 374 355 337 2.89E+15 130.23Lauroyl peroxide 372 352 334 3.92E+14 123.37

Initiator type and concentration, as well as reactor temperature control the initiation

rate. The thermal stability of the initiators are expressed in terms of 0.1 h, 1 h, and 10 h

half-life temperatures, the temperatures at which 50% of the initiator has decomposed in

0.1 h, 1 h, and 10 h respectively. Figure 4.14 shows the half-life chart for the initiators of

concern.

It should be noted that the half-life data of EHPC and TBPD does not differ much.


Figure 4.14: Half-life chart for the initiators discussed in this work and produced by Akzo Nobel

The half-life temperatures of AIBN and lauroylperoxide are higher. Depending on the

type of initiator, the polymerization temperature for the polymerization of vinyl chloride

to poly(vinylchloride) varies between 303 and 348 K. For peroxyesters, e.g. tert-butyl

peroxy-neo-decanoate (TBPD), the dissociation starts at 308 K, while for peroxydicarbon-

ates, e.g. di(2-ethylhexyl)peroxydicarbonate (EHPC), the dissociation starts at 323 K ((De

Roo et al., 2004)). For azo-initiators, e.g. azobis(isobutyronitrille) (AIBN), and diacyl per-

oxides, e.g. lauroylperoxide (Laurox), the dissociation only starts at higher temperatures.

EHPC and TBPD are consumed in the temperature range of 300-350K, whereas AIBN

and lauroylperoxide require higher temperatures.

In conclusion, when only the half-life time and polymerization temperature is taken

into account, EHPC and TBPD are most appropriate for the common reaction conditions

for the polymerization of vinyl chloride.

4.5.2 Selection based on characteristics of the polymerization

product

The initiator has also an important influence on the polymerization product quality. The

nature of the decomposition products plays an important role in this quality, because


they remain in the products. The peroxydicarbonates have alcohols and CO2 as their

main decomposition products, whereas for peroxyesters these are CO2, carboxylic acids,

acetone, alkanes and t-butyl alcohol. The main decomposition products for diacyl peroxides

are CO2, carboxylic acids and alkanes.

To maintain the product quality, the storage temperatures of the initiators play an im-

portant role. For the initiators used in this work, the Ts,max varies between 253 K (EHPC)

and 303 K (AIBN), while Ts,min varies between 243 K (EHPC) and 298 K (lauroylperoxide).

Thus, this criterium makes no selection possible.

4.5.3 Selection based on kinetic modeling results

The initiator efficiency and the monomer conversion as a function of time were modeled

based on the simple kinetic scheme of Kurdikar and Peppas (1994). The modeling was

done for four classes of initiators: peroxydicarbonates, peroxyesters, dialkyl diazenes and

diacyl peroxides. The results of this kinetic modeling were presented in section 4.4.

Efficient use of an initiator is realised if, after a polymerization cycle, most of the

initiator is consumed and converted into polymer. The polymerization of vinyl chloride

is performed in a temperature range between 300 and 350 K. The half-life chart (Figure

4.14) for the discussed initiators already shows the fact that AIBN and lauroylperoxide

are more suitable in higher temperature ranges. Because the efficiency of the initiator

is temperature dependent, this effect should also be found in the kinetic modeling. The

performed kinetic modeling proves this temperature effect.

Based on the modeling performed in this work, the peroxydicarbonate EHPC and the

peroxyester TBPD turn out to be most appropriate initiators within the temperature

range of 300 - 350 K. Hence, one can conclude that EHPC or TBPD are one of the most

appropriate initiators for the polymerization of vinyl chloride.


4.6 Conclusion

In this chapter, the initiator efficiency f was calculated based on a kinetic scheme that

accounts for the most important reactions that initiator derived radicals can undergo.

In this scheme, different rate coefficients and diffusion coefficients are present. In order to

evalutate f during the course of polymerization, it is necessary to evaluate these parame-

ters. The rate coefficients were obtained from literature, whereas the diffusion coefficients

were calculated based on the free volume theory. The free volume was calculated differ-

ently as in former studies (De Roo et al., 2004). Analogous, the free volume of a molecule

or a radical was calculated by the group contribution method (Van Krevelen, 1997), but

different species were considered. The reaction distance was evaluated based on the type

of dissociation of the initiator (single-bond or two-bond dissociation).

For the four classes of initiators, the initiator efficiency f was kinetically modeled based

on the kinetic scheme of Kurdikar and Peppas (1994). All parameters in this model were

evaluated and implemented in the modeling. The initiator efficiency as a function of the

polymerization time was plotted for all classes of initiators. The modeling results are in

accordance with the results found in literature. The plot of the monomer conversion as a

function of polymerization time proves that the cage effect was taken into account in the

modeling.

72

Chapter 5

Generation of a reaction network

The first step in the decomposition mechanism of the initiator is a dissociation step. This

dissociation step is described by a first order reaction, as shown in reaction (3.1), in the

modeling of e.g. Kurdikar and Peppas (1994) and De Roo et al. (2004). The intrinsic rate

coefficient of this reaction is kbd. This rate coefficient is corrected with f , the initiator

efficiency, as not all initiator derived radicals initiate the polymerization. Hence, the first

order reaction has an apparent rate coefficient fkbd.

In this Chapter, a fundamental model to describe the initiator decomposition is de-

veloped. This is done by generating a reaction network that accounts for all reaction

possibilities for all occuring reactants. This enables not to take explicitely into account

the initiator efficiency. As the number of reaction possibilities and reactants is large, the

network needs to be generated by a computer program. This reaction network program

needs to take into account all reaction possibilities for all occurring reactants. Each reac-

tion possibility can be assigned a rate coefficient. In the model of Kurdikar and Peppas

(1994), only the most decisive reaction steps were assigned a rate coefficient. The intrinsic

rate coefficient for dissociation was corrected by the initiator efficiency. By taking all re-

action possibilities into account and describing the kinetics of the initiator decomposition

into detail, the concept of an initiator efficiency is no longer required but results from the

description.

First, the most appropriate methodology to construct a reaction network that is able to

Chapter 5. Generation of a reaction network 73

describe the initiator decomposition into detail is investigated. Depending on the chosen

methodology, the ingredients in the generation principle must be traced. These ingredients

are a.o. the representation of the reactants, the representation of reactions and the tracing

of all reaction possibilities. Once these items are described into detail, a network generation

computer program can be constructed. In the next section, the methodology for the

generation of a reaction network is discussed.

5.1 Conceptual design of a reaction network

In order to generate a reaction network that describes the initiator decomposition mech-

anism into detail, a methodology for developing a detailed network is required. Because

it is essential to select a generation principle that accounts for all reaction possibilities

for all reactants, a literature review was performed to find out which network generation

methodologies are available.

Antoniewicz et al. (2007) proposes the development of a reaction network based on three

entities. First, a molecule pattern entity is drawn up, in which the bonds and the atoms

of the molecule are identified. The second entity, the reaction entity, consists of the el-

ementary reactions. Finally, the reaction mechanism entity contains the transformations

or operations between the molecules. The entity approach shows similarity with the ap-

proach of Broadbelt et al. (1996) and Li et al. (2004). Broadbelt et al. (1996) suggests

the development of an integrated system for computer generation of a kinetic model. The

required input consists of the structure of the reactants, the rules by which the reactant

and product species react and the parameters of a structure/property kinetics correlation

(Li et al., 2004). The algorithm transforms this information into reactant-product rela-

tionships, i.e. a reaction network, species properties, rate coefficients and a Fortran code

corresponding to the governing species’ balance equations. Moreover, the likelihood of the

generated pathways of the reaction network can be evaluated.

In this work, a combination of the modeling strategies of Broadbelt et al. (1996), Li

et al. (2004) and Antoniewicz et al. (2007) is applied. The network generation principle

is based on three entities, being the reactants, the reaction types, and the reactions (to


form the products). It should be noticed that the determination of the likelihood of the

generated pathways of the reaction network is out of the scope of this master thesis.

The considered generation principle allows for a network generation in three steps, as

shown in Figure 5.1:

Figure 5.1: Simplified methodology for network generation: reactants are able to undergo dif-ferent reactions, leading to products. These products are regenerated as reactants.

1. The reactants (molecules or radicals) that are present during the decomposition of

the initiator are the input of the network generation program. These reactants need

to be represented in such a way that all structural information is captured.

2. The selected representation of the reactants must also allow for an easy description

of the reactions, i.e. linking reactant representation and product representation.

Six reaction types are taken into account: dissociation, recombination, addition, β-

scission, hydrogen abstraction and Cl-shift. These reaction types are already briefly

discussed in Chapter 2 (section 2.1)

3. The products (molecules or radicals) are the output of the network generation pro-

gram. The representation of these products must be analogous to the one of the

reactants, because some of the products are still able to undergo reaction.

It should be clear that an appropriate representation of the reactants and the products

is critical. Once such a representation is found, the reactions on these reactants can be

performed. The selected representation used in this master thesis is discussed in the next

section.


5.2 Matrix representation of the reactants and the

products

An appropriate representation of the reactants and the products present during initiator

decomposition is discussed in this section. Appropriate means that all structural informa-

tion is captured and reactions can be described easily. In this work, a matrix representation

is used based on principles described by Marin and Wauters (2001) and Li et al. (2004).

Consider e.g. a primary peroxyester, tert-butyl peroxyactetate (TBPA), as depicted in

formula (5.1). The matrix representation of this molecule is given in Figure 5.2, with the

numbering of the atoms of the molecule as shown on the same picture. Each atom corre-

sponds with the column in the matrix that has the same number, e.g. atom 1 corresponds

with column number 1.

CH3CO

O

OC(CH3)3 (5.1)

The matrix representation consists of three distinguishable parts: the identification of

the atoms, the bonds between the atoms and the radical position.

1. Identification of the atoms Each atom receives its own identification number,

as shown in Table 5.1. This is done because not only C-atoms but also heteroatoms are

involved. This identification number will be useful to detect which atom types are involved

during a reaction and to assign rate coefficients to this reaction.

These identification numbers are stored in the first row of the matrix that represents

the reactant or the product.

2. Representation of the bonds The grey matrix in Figure 5.2 shows which atoms of

the reactant (or of the product) are connected to each other. There are four possiblities:

between two atoms there is

• no bond, indicated as ’0’ in the matrix

• a single bond, indicated as ’1’ in the matrix


Figure 5.2: Matrix representation of tert-butyl peroxyactetate (TBPA) corresponding with thenumbering of the atoms in the molecule given.

• a double bond, indicated as ’2’ in the matrix

• a triple bond, indicated as ’3’ in the matrix

When a molecule reacts, some bonds are formed and/or broken. The main matrix (the

grey part in Figure 5.2) shows which atoms are connected, thus is a measurement for which

bonds are formed or broken when the matrices of the reactants and products are compared.

3. Representation of the radical position The last row of the matrix represents

where the radical is positioned. In this example, there is no radical present, so all elements

of the last row are equal to zero. In case a radical species is considered, the radical position

corresponds to an element of the last row that equals 1. E.g. the matrix of a tert-butyl

radical (formula (5.2)) is visualised in Figure 5.3.


Table 5.1: Identification numbers of the atoms used in the first row of the matrix representationof a reactant or a product

Atom Indentification numberCarbon C 1Oxygen O 2Nitrogen N 3Chloride Cl 4

C•

CH3

CH3

CH3

(5.2)

The last row has a ’1’ element on the position of atom 1, corresponding with the radical

position.

The selected matrix representation for reactants and products captures all structural infor-

mation: the type of atoms, the bonds between the atoms and the eventual radical position.

Nevertheless, an appropriate visualization is only achieved when the representation of the

reactants and products allows the tracking of reactions easily. This will be investigated in

the next section.


Figure 5.3: Matrix representation of a tert-butyl radical corresponding with the numbering ofthe atoms in the molecule given.

5.3 Reactant-product relationships: matrix operations

In this section, the representation of the reactants and the products are linked by a reaction.

Because these representations are matrices, it must be clear that a reaction is described by

matrix operations. In this master thesis, six types of reactions are distinguished: dissoci-

ation, β-scission, recombination, addition, hydrogen abstraction and Cl-shift. For each of

these reactions, a procedure that describes the matrix operations is developed.

5.3.1 Dissociation

A bond dissociation reaction is a homolytic splitting of a bond because of a temperature rise

during polymerization. In a complete network generation program all reaction possibilities

are taken into account. This means that each bond between two atoms can break, regardless

of the bond dissociation energy. The extent to which dissociation reactions occur, depends

on the bond dissociation energy. In Table 5.2, the bond dissociation energies for the relevant

bonds in the production of poly(vinyl chloride) are shown. For a dissociation reaction to

take place, the bond dissociation energy of the considered bond must be sufficiently low.

Table 5.2 shows that the oxygen-oxygen bond has the highest probability for dissociation,

because the bond dissociation energy is the lowest. The probability of dissociation of


a carbon-carbon single bond, a nitrogen-carbon bond or a carbon-oxygen single bond is

similar. The bond dissociation energy of the carbon-oxygen double bond is the highest,

hence this bond is least likely to dissociate.

Table 5.2: Bond dissociation energy for the relevant bonds in the production of poly(vinyl chlo-ride) (Endo, 2002; Van Pottelberge, 2004–2005)

Bond Bond dissociationenergy [kJ mol−1]

C-C 348.20O-O 146.60N-C 305.00N=N 408.90C-O 358.20C=O 750.00

-(CH2)- C-H 397.75-CHCl- C-H 360.06

C-Cl 322.38

In this section, a procedure for the representation of the dissociation reaction is devel-

oped and illustrated.

In Figure 5.1, the methodology of network generation used in this work is shown. If only

dissociation reactions are taken into account, the reaction network based on this methodol-

ogy will be as presented in this paragraph. Figure 5.4 shows the procedure for representing

a dissociation reaction.

As reactant, a general molecule ABCD is considered. The bonds between the atoms are

all single bonds. In the considered molecule, three bonds can be broken due to dissociation,

namely the bonds between A and B, B and C and C and D. Consider e.g. that the bond

between atoms B and C is broken. This dissociation reaction leads to the formation of 2

products, namely the radicals AB• and DC•. It should be noted that the products are still

able to undergo another dissociation reaction, which is mentioned by the feedback loop.

The matrix representation of the reactant is shown in Figure 5.5: all bonds are single

bonds and the reactant is a molecule. In this example, as identification number, the atoms


Figure 5.4: Methodology for generation of a reaction network with only dissociation reactionstaken into account.

A and D have ’1’ (carbon), while atoms B and C have ’2’ (oxygen). Hence, the considered

molecule corresponds with a dimethyl peroxide molecule (formula (5.3)).

H3C-O-O-CH3 (5.3)

The matrix representation of the products can be derived based on the procedure

shown in Figure 5.4, and is depicted in Figure 5.5. The bond between atoms B and C

is selected and broken. The bonding partners of B, respectively C, are detected. After

dissociation, atom B is only connected to A, whereas C is only connected to D. The

products of this dissociation reaction are given by deleting the rows and columns in the

matrix representation of ABCD, corresponding with C and D respectively with A en B.

Since radicals are formed, the radical row is filled with a ’1’ for atom B respectively C. The

products are still able to undergo another dissociation reaction, mentioned by the feedback


loop in Figure 5.4.

Figure 5.5: Matrix operations corresponding with a dissociation reaction of a fictive moleculeABCD.


5.3.2 β-scission

In a β-scission reaction a bond in β-position of a radical is broken. Thus, only radicals

can undergo β-scission. Moreover, a double bond is formed between the atom in radical

position and the atom in α-position to the radical position. In this work, every bond in

β-position of a radical can break. A procedure for the representation of the β-scission

reaction is developed and illustrated in this section.

The methodology of network generation used in this work is shown in Figure 5.1. Fig-

ure 5.6 shows the procedure for representing a β-scission reaction.

Figure 5.6: Methodology for generation of a reaction network with only β-scission reactionstaken into account.

Note that the procedure that can be followed is exactly identical to dissociation, with

the condition that only bonds in β-position of a radical can break.

The reactant considered is a general radical consisting of 5 atoms, as shown in formula

(5.4). In this example, the bonds between the atoms are all single bonds.


BA•

C

D

E

(5.4)

The β-position in this radical is taken by atom B. In the considered radical, three bonds

can be broken due to β-scission, namely the bonds between B and C, B and D and B and

E. Consider e.g. that the bond between atom B and C is broken. This β-scission reaction

leads to the formation of 2 products, which are shown in reaction (5.5).

BA•

C

D

E

kβ // C• + DBE

A

(5.5)

The products are not able to undergo another β-scission reaction and are not recycled as

reactants (Figure 5.6).

The matrix representation of the reactant is shown in Figure 5.7: all bonds are single

bonds and the reactant is a radical, with radical position in A. Note that in this illustrative

reactant, the identification number of the atoms B, C, D and E is ’1’ (carbon), whereas

the one of atom A is ’2’ (oxygen). This corresponds with a tert-butyloxy radical. The

β-scission reaction of this radical is shown in reaction (5.6).

CO•

CH3

CH3

CH3


O

(5.6)

The matrix representation of the products can be derived based on the procedure

shown in Figure 5.6, and is depicted in Figure 5.7. The atom in β-position of the radical

is considered, which is atom B. The bond between e.g. atoms B and C is selected and

broken. The bonding partners of B, respectively C, are detected. After β-scission, atom B

is connected to A, D and E, whereas C has no bonding partners anymore. The products

of this dissociation reaction are obtained by deleting the rows and columns in the matrix

representation of the reactant, corresponding with C respectively with A, B, D and E.

Because a new radical is formed (reaction 5.5), the radical row is filled with a ’1’ for atom


C. The radical in position of A is deleted and a double bond between A and B is formed.

Figure 5.7: Matrix operations corresponding with the β-scission reaction of a fictive radicalABCDE.


5.3.3 Recombination

The next reaction that is considered, is the recombination reaction. A recombination re-

action is the reverse of a dissociation reaction: two radicals combine to form one molecule.

To generate a complete reaction network, it is required that all reaction possibilities are

taken into account. This means that all radicals can recombine with each other.

A procedure for the representation of the recombination reaction is developed and illus-

trated in this section.

Again, the methodology for network generation used, is the one of Figure 5.1. In this

section, only recombination reactions are considered. Figure 5.8 shows the procedure for

representing a recombination reaction.

Figure 5.8: Methodology for generation of a reaction network with only recombination reactionstaken into account.

The reactant considered for recombination are AB• and DC•. Both reactants are

radicals, and the bonds between the atoms are single bonds. These radicals (reactants)


can recombine to form one molecule ABCD: a bond between atoms B and C is formed.

The matrix representation of the reactants is shown in Figure 5.9: all bonds are single

bonds and the reactants are radicals. In this example, both radicals are methyloxy radicals.

The matrix representation of the products can be derived based on the procedure shown

in Figure 5.8, and is depicted in Figure 5.9. A bond between atom B and C can be formed,

since these are the radical centers. The bonding partners of B, respectively C, are detected.

Before recombination, atom B is only connected to A, whereas C is only connected to D.

The product of this recombination reaction is given by adding, by means of enlarging the

matrix, rows corresponding with atom C and D to the matrix of atom A and B. The

radical positions disappear, hence disabling further recombination reaction. In Figure 5.8

no feedback loop is shown.

Figure 5.9: Matrix operations corresponding with the recombination reaction of a fictive radi-cals AB• and DC•.


5.3.4 Addition

During an addition reaction, a radical adds to a double bond. In this work, only the

addition of radicals to a carbon-carbon double bond is considered, more precisely only

addition to the vinyl chloride monomer. The radical can add to a monomer in two different

ways: to the non-substituted C or to the substituted C. These two possibilities are shown

in reactions (5.7) and (5.8).

I•+ CH2=CHClkadd,tail // C•

H

I-CH2

Cl

(5.7)

I•+ CH2=CHClkadd,head // C

H

I

Cl

CH2• (5.8)

Reaction (5.7) shows the tail addition reaction, while reaction (5.8) reports the head

addition. In this section only a procedure for the representation of tail addition reactions

is developed and illustrated. The procedure for head addition reactions is analogous.

The methodology for an addition reaction network is again based on the methodology

of Figure 5.1. Figure 5.10 shows the procedure for representing an addition reaction.

The reactants taken into account in this section are a general reactant AB• and a vinyl

chloride monomer molecule, as shown in Figure 5.10. The considered radical can add to

the double bond in two ways: tail addition (reaction (5.7)) and head addition (reaction

(5.8)).

The addition of AB• to the tail leads to the formation of the product, which is shown

in the reaction (5.9). A new radical is formed.

AB•+ CH2=CHClkadd,tail // C•

H

AB-CH2

Cl

(5.9)


Figure 5.10: Methodology for generation of a reaction network with only addition reactionstaken into account.

It should be noted that the product is still able to undergo another addition reaction and

can be reconsidered as a reactant, which results in a feedback loop in Figure 5.10.

The matrix representation of the reactants is shown in Figure 5.11: the first reactant

is a radical that can add to the double bond of the vinyl chloride monomer molecule (the

second reactant). The matrix representation of the product can be derived based on the

procedure shown in Figure 5.10, and is depicted in Figure 5.11. The double bond between

atoms 1 and 2 of the second reactant is broken, and a single bond between atom B (of

the first reactant) and atom 1 (of the second reactant) is formed. As a consequence, a

new radical is formed. The product of this addition reaction is given by a matrix, which

contains all atoms of the product and in which the atoms 1 and B are connected. The

double bond is broken, and the radical position is now located at the atom to which no

radical has added.


Figure 5.11: Matrix operations corresponding with the tail addition reaction of a radical AB•

to VCM.

5.3.5 Hydrogen abstraction

In a H-abstraction reaction a H-atom is abstracted from a H-donor present in the reaction

medium:

I•+ HDkH // IH + D• (5.10)

In this work, all hydrogen abstraction reactions are taken into account. Consider e.g.

the hydrogen abstraction reaction (5.10). The methodology for a reaction network with

hydrogen abstraction reactions is based on the methodology of Figure 5.1. Figure 5.12

shows the procedure for representing a hydrogen abstraction reaction.

The reactants considered here are an initiator molecule I• and a H-donor present in

the reaction medium (HD). A hydrogen atom can be abstracted from the H-donor by the

radical. This leads to the formation of a molecule (IH) and a radical (D•), as shown in

reaction (5.10). Again, it should be noted that the products are still able to undergo an-

other hydrogen abstraction reaction and can be retaken as reactants, which is represented

by the feedback loop in Figure 5.12.


Figure 5.12: Methodology for generation of a reaction network with only hydrogen abstractionreactions taken into account.

The matrix representation of the reactants are shown in Figure 5.13: all bonds are single

bonds, the first reactant is a radical and the second a molecule. The matrix representa-

tion of the products can be derived based on the procedure shown in Figure 5.12, and is

depicted in Figure 5.13. The radical (I•) abstracts a H-atom to form a molecule. A new

radical is formed out of the second reactant, and the radical row is filled with a ’1’ in the

position of D. Finally, the products are still able to undergo reaction: D• can act again as

abstracting radical and HI can act as molecule from which a H-atom can be abstracted.


Figure 5.13: Matrix operations corresponding with the hydrogen abstraction reaction (5.10).

5.3.6 Cl-shift

Finally, the Cl-shift is discussed in this section. During a Cl-shift reaction, a Cl-atom

is shifted from a β-position to the radical position. The two types of Cl-shift are shown

in Figure 5.14: a primary-secondary (p,s) and a secondary-secondary (s,s) Cl-shift. A

primary-secondary Cl-shift (p,s Cl-shift) is an intramolecular process during which a pri-

mary C-radical is converted into a secondary C-radical. During a secondary-secondary

Cl-shift (s,s Cl-shift) a secondary C-radical is converted into another secondary radical.

Figure 5.14: P,s Cl-shift and s,s Cl-shift

A p,s Cl-shift is accompanied by the transformation of a primary radical to a more sta-

ble secondary radical, whereas for a s,s Cl-shift an equally stable radical is formed. Hence,

the activation energy for the p,s Cl-shift reaction will be lower than for s,s Cl-shift. Thus,

the p,s Cl-shift will have a higher occurance (Starnes Jr. et al., 1992; Van Pottelberge,

2004–2005). In this section, only the p,s Cl-shift will be considered.


In Figure 5.1, the methodology of network generation used in this work is shown. Based

on this methodology, a reaction network for Cl-shift reactions is constructed. Figure 5.15

shows the procedure for representing a Cl-shift reaction.

Figure 5.15: Methodology for generation of a reaction network with only Cl-shift reactionstaken into account.

As reactant, a primary radical or growing polymer chain is chosen. The matrix rep-

resentation of the considered reactant is shown in Figure 5.16: all bonds are single bonds

and the reactant is a primary radical. A primary-secondary Cl-shift is executed on the

considered primary radical based on the methodology of Figure 5.15, leading to the matrix

representation of the products (Figure 5.16).

The radical position is taken by atom 1. The atoms in α-position (atom 2), respectively

in β-position (atom 3), of atom 1 are detected. The bond between these atoms (atom 2

and 3) is broken first. A new bond is formed between atom 1 and 3. The radical position

shifts to atom 2. Hence, the product of this p,s Cl-shift is a secondary radical, as shown

in Figure 5.16. Since the products are still able to undergo another Cl-shift reaction (s,s

Cl-shift), a recycle loop is considered in Figure 5.15.


Figure 5.16: Matrix operations corresponding with a p,s Cl-shift reaction.

5.4 Construction of a network generation program

The goal of the previous sections was to establish an appropriate visualization for reactants,

reactions and products. The selected matrix representation for reactants and products

captures all structural information: the type of atoms, the bonds between the atoms and

the eventual radical position. Moreover, the representation of the reactants and products

allows for the tracking of reactions easily. This was investigated into detail in previous

section. Hence, the representation proves to be appropriate.

For each type of reaction, matrix operations on reactants were established, which leads

to a stand alone representation of each reaction type. To take into account all reaction

types, and hence achieve an integrated network generation program, functionalities need to

be traced for each reactant. Based on a decision tree (Figure 5.17), the reactant can only

undergo certain reactions. When all reactions for all reactants are mapped, a complete

reaction network is achieved.

Finally, a computer program is constructed in Fortran to generate the reaction network.

This exact simulation code is explained in Appendix 1. For each reaction type a complete

computer code is constructed but a link between those reaction types remains for future


Figure 5.17: Decision tree for network generation of initiator decomposition.

work.


5.5 Conclusion

In this chapter, a fundamental model to describe the initiator decomposition was devel-

oped. For this purpose, a reaction network which describes the initiator decomposition

into detail, was generated. This reaction network should take into account all reaction

possibilities for all occurring reactants.

To frame a reaction network that is able to describe the initiator decomposition into de-

tail, the most suited methodology for this purpose had to be found. In this work the

methodology of Broadbelt et al. (1996), Li et al. (2004) and Antoniewicz et al. (2007) was

used. The reactants form the input of the network generation program. These reactants

are represented in such a way that all structural information is captured. The products,

which form the output of the program, have an analogous representation. A matrix repre-

sentation was chosen including the identification of the composing atoms of the reactant,

the representation of the bond and the radical position. The selected representation also

allows reactions to be described easily (Li et al., 2004; Marin and Wauters, 2001). For

each type of reaction, a general procedure is established in order to describe the matrix

operations between reactant and product. Hence, a stand-alone reaction network for each

reaction type separatly was generated. Finally, a decision tree was constructed to combine

all reaction types. Hence, a complete network generation program which maps all possible

reactions was achieved. To generate a complete reaction network, a computer simulation

program was constructed in Fortran.

96

Chapter 6

Conclusion

In this chapter, the most important items that were discussed in previous chapters, are

resumed. First the kinetic modeling of the initiator efficiency f based on the model of

Kurdikar and Peppas (1994) was discussed into detail in this work. By generating this

reaction network, it is possible not to take explicitely into account the initiator efficiency. A

reaction network generation computer program takes into account all reaction possibilities

for all reactants. By taking all reaction possibilities into account, hence describing the

kinetics of the initiator decomposition into detail, the concept of an initiator efficiency is

no longer required but results from the description.

While significant progress has been made, additional work remains to be done in order

to develop a complete understanding of the initiator decompsition of the vinyl chloride

suspension polymerization. Hence, recommendations for future work are made.

6.1 General conclusion

Poly(vinyl chloride) is produced by suspension polymerization of vinyl chloride. The first

step in this free radical polymerization, is the decomposition of the initiator. The per-

formance of the initiator can be described by the initiator efficiency f . In a free radical

polymerization, only a fraction of the radicals formed by dissociation of the initiator is

able to initiate a polymer chain. This fraction is defined as the initiator efficiency f . The

initiator efficiency is not the only selection criterium of an initiator for industrial produc-

Chapter 6. Conclusion 97

tion of PVC: also the half-life time, the polymerization temperature and desired product

quality will determine the choice of an appropriate initiator.

The industrial production of PVC can be performed with four classes of initiators: peroxy-

dicarbonates, peroxyesters, dialkyl diazenes (azo-initiators) and diacyl peroxides. Modeling

the initiator efficiency as a function of the polymerization time, the monomer conversion

and the polymerization conditions for these initiators requires knowledge of the dissocia-

tion mechanism, which may be single-bond dissociation or two-bond dissociation. Based

on a literature study, one can conclude that peroxydicarbonates and primary peroxyesters

undergo single-bond dissociation, whereas the other initiator classes are characterized by

two-bond dissociation.

Moreover, an initiator decomposition mechanism was developed for each class of initiators,

based on literature (Verhaert, 2003–2004). The kinetic modeling of the initiator efficiency

f was performed based on the kinetic scheme of Kurdikar and Peppas (1994). An analytic

expression was derived for the initiator efficiency. In this expression, only kinetic param-

eters occur, whereas in former studies a semi-empirical expression was used. Hence, the

kinetic modeling leads to a more accurate calculation of the initiator efficiency.

In this work, the initiator efficiency f was calculated based on a kinetic scheme that

accounts for the most important reactions that initiator derived radicals can undergo (Kur-

dikar and Peppas, 1994). In this scheme, different rate coefficients and diffusion coefficients

are present. In order to evalutate f throughout the polymerization process, these parame-

ters are required. The rate coefficients were obtained from literature, whereas the diffusion

coefficients were calculated based on the free volume theory. The free volume was calcu-

lated differently as in former studies (De Roo et al., 2004). Analogous, the free volume of

a molecule or a radical was calculated by the group contribution method (Van Krevelen,

1997), but different species were considered. The reaction distance was evaluated based on

the type of dissociation of the initiator (single-bond or two-bond dissociation).

For the four classes of initiators, the initiator efficiency f was kinetically modeled based

on the kinetic scheme of Kurdikar and Peppas (1994). All parameters in this model were

evaluated, and implemented in the modeling. The initiator efficiency as a function of the

polymerization time was plotted for all classes of initiators. The modeling results were in


accordance with the results found in literature, except for azobis(isobutyronitrille). The

plot of the monomer conversion as a function of polymerization time proved that the cage

effect was taken into account into the modeling. Hence, the kinetic modeling of Kurdikar

and Peppas (1994) proves to be able to model the initiator decomposition in a correct way.

Finally, a fundamental model to describe the initiator decomposition is developed. By

generating this reaction network, it became possible not to take explicitely into account

the initiator efficiency. For this purpose, a reaction network that describes the initiator

decomposition into detail, had to be generated by a computer program (in Fortran). This

reaction network program needs to take into account all reaction possibilities for all occur-

ring reactants. Each reaction is assigned a rate coefficient. In the model of Kurdikar and

Peppas (1994), only a few reactions were considered. The intrinsic rate coefficient for dis-

sociation was corrected by the initiator efficiency. By taking all reaction possibilities into

account and describing the kinetics of the initiator decomposition into detail, the concept

of an initiator efficiency was no longer required but results from the description.

To frame a reaction network which is able to describe the initiator decomposition into

detail, the most suited methodology for this purpose was required. In this work the

methodology of Antoniewicz et al. (2007), Broadbelt et al. (1996), Li et al. (2004) and

Marin and Wauters (2001) was used, consisting of 3 steps. The reactants form the input

of the network generation program. These reactants need to be represented in such a way

that all structural information is captured. The products, which are the output of the pro-

gram, need to have an analogous representation. For this purpose, a matrix representation

was chosen including the identification of the composing atoms of the reactant, the rep-

resentation of the bond and the radical position. This selected representation also allows

for an easy description of reactions. For each type of reaction, a general procedure has

been established in order to describe the matrix operations between reactant and product.

Hence, a stand-alone reaction network has been generated for each reaction type separatly.

Finally, a decision tree was constructed to combine all reaction types. Hence, a program

which maps all possible reactions separately, was achieved.


6.2 Recommendations for future work

While significant progress has been made, additional work remains to be done in order

to develop a complete understanding of the initiator decompsition of the vinyl chloride

suspension polymerization.

First, a kinetic model is required to describe the initiator efficiency f more accurately for

all classes of initiators. The model of Kurdikar and Peppas (1994) is not able to describe

the initiator efficiency appropriately for azo-initiators. A more fundamental model, which

takes into account more reactions steps, is required.

Secondly, in order to generate all reaction possibilities during the initiator decomposi-

tion, and thus to describe the kinetics of initiator decomposition, a reaction network was

constructed. First, a conceptual design of a reaction network, was made. A representation

for the reactants which contains all structural information was found. Moreover, this rep-

resentation is able to represent reactions easily. The way reactants are transformed into

products, is already discussed based on matrix operations. A computer program has been

developed in order to generate all reactions during initiator decomposition.

In future work, kinetic parameters could be assigned to each reaction occuring in the

reaction network. Hence, the possibility of the occurence of the given reaction can be

computed. In such a way, the kinetics of the initiator decomposition can be described

into detail. The future worker should also pay attention to the link between ’intitiator

network’ and ’polymerization network’. A polymerization network could be linked with

the existing simulation code for the initiator network. Hence, the kinetics of the complete

free radical polymerization of vinyl chloride could be described. Moreover, the complete

computer code could be made reusable for other polymerization reactions, and this with

minimal adjustments.

100

Hoofdstuk 7

Nederlandstalige samenvatting

In dit afstudeerwerk wordt de initiatordecompositie bij de suspensiepolymerisatie van vi-

nylchloride behandeld. Er wordt een onderscheid gemaakt tussen een kinetische model-

lering van de initiatordecompositie aan de hand van het begrip initiatorefficientie en aan

de hand van het genereren van een reactienetwerk. De reden voor het hanteren van het

begrip initiatorefficientie, ligt hoofdzakelijk bij de moeilijkheid van het in kaart brengen

van alle optredende reacties tijdens initiatordecompositie en het bepalen van bijhorende

snelheidscoefficienten. Als de kinetiek van de initiatordecompositie op zich en de initiat-

ordecompositie ingebed in het volledige reactienetwerk, in detail wordt beschreven, dient

de efficientiefactor f niet meer gebruikt te worden. Dit geeft een meer fundamenteel beeld

van de kinetiek van de initiatordecompositie, waaruit de initiatorefficientie volgt.

Hoofdstuk 7. Nederlandstalige samenvatting 101

7.1 Kinetische modellering op basis van initiatoreffi-

cientie

7.1.1 Initiatorefficientie

De eigenschappen van het polymeerproduct worden in belangrijke mate bepaald door de

reactiecondities (polymerisatietemperatuur, initiatorkeuze en initiatorconcentratie). Ver-

mits de eigenschappen van het polymeerproduct bepalend zijn voor de verdere verwerking

en toepassingen ervan, is het belangrijk deze reactiecondities te kunnen linken aan poly-

meereigenschappen. Deze link kan gelegd worden door een fundamenteel kinetisch model

te ontwikkelen. Bij de polymerisatie van vinylchloride tot polyvinylchloride treden tijdens

de initiatiestap een groot aantal reacties op. Deze problematiek wordt in de literatuur

behandeld door de eerste stap in de decompositie van de initiator te modelleren als een 1e

orde reactie met een schijnbare snelheidscoefficient fkbd (reactie (7.1)).

Ifkbd→ R′•

0 + R′′•0 (7.1)

Hierin is kbd de intrinsieke snelheidscoefficient voor de dissociatiereactie en f de initi-

atorefficientie. De initiatorefficientie staat voor de fractie van het totaal aantal gevormde

radicalen die een keten initieren. In praktijk varieert de initiatorefficientie tussen 0.3 en

0.8 (Kurdikar en Peppas, 1994; Westmijze, 1999). De waarde 1 zal nooit bereikt worden

vermits er steeds zijreacties, zoals recombinatie, optreden.

7.1.2 Industriele initiatoren

Het is mogelijk de industrieel gangbare initiatoren onder te verdelen in vier klassen: per-

oxydicarbonaten, peroxyesters, dialkyldiazenen en diacylperoxides. De dissociatie van de

initiator, de eerste stap in het decompositiemechanisme, heeft belangrijke gevolgen voor de

berekening van de initiatorefficientie. Er kan een onderscheid gemaakt worden tussen een-

bindingsdissociatie (1BD) en tweebindingsdissociatie (2BD). Tabel 7.1 geeft een overzicht

van het dissociatiemechanisme van de verschillende klassen initiatoren. Voor peroxyesters

moet een onderscheid gemaakt worden tussen primaire, secundaire en tertiaire peroxyes-


ters.

Tabel 7.1: Verschillende klassen initiatoren met bijhorende soort dissociatie.

Klasse Type 1BD 2BDPeroxydicarbonaten x

Peroxyesters Primair xSecundair en tertair x

Dialkyldiazenen xDiacylperoxides x

Voor elk van deze klassen kan het decompositiemechanisme worden opgesteld. De

geınteresseerde lezer wordt verwezen naar Hoofdstuk 2 (Figuren 2.2, 2.3, 2.4 en 2.5).

7.1.3 Modellering van de initiatorefficientie

In dit afstudeerwerk wordt de modellering van Kurdikar en Peppas (1994) gevolgd. Kurdi-

kar en Peppas (1994) ontwikkelden een model dat in staat is de initiatorefficientie a priori

te voorspellen en gedurende de polymerisatie te berekenen. Deze aanpak verschilt van

deze vermeld in literatuur (De Roo et al., 2004) vermits de initiatorefficientie berekend

wordt op basis van een uitdrukking waarin enkel kinetische parameters voorkomen. Bij-

gevolg worden empirische relaties, die wel voorkomen in de modellering van De Roo et al.

(2004), uitgesloten en kan een meer gedetailleerde beschrijving van het initiatordecompo-

sitiemechanisme verkregen worden. Dit alles leidt tot een meer accurate modellering van

de initiatorefficientie. Het model van Kurdikar en Peppas (1994) wordt gegeven door het

schema (7.2).


I1

Ikbd // [A• + A•

1]

kβ

��

ktA

OO

DA // A• + A•1 eerste radicaalpaar

[A• + B•]

ktB

��

DB // A• + B• tweede radicaalpaar

I2

(7.2)

Binnenin de solventkooi, voorgesteld door [. . .], ontbindt een initiatormolecule op tijd-

stip t = 0 s met vorming van twee verschillende of twee identieke radicalen A• en A1•. Met

de solventkooi wordt de omgeving rond het initiatorradicaal bedoeld waarin een recombi-

natiereactie kan plaatsvinden indien het andere radicaal aanwezig is. Aangezien de twee

radicalen, ook het ’eerste radicaalpaar’ genaamd, zich na dissociatie dicht bij elkaar bevin-

den, kunnen zij terug recombineren. Na een eenbindingsdissociatie leidt dit tot de vorming

van de oorspronkelijke initiator, die onmiddellijk terug zal dissocieren. Deze recombinatie

leidt bijgevolg niet tot een afname van de initiatorefficientie. Na een tweebindingsdissoci-

atie kunnen de twee initiatorradicalen recombineren tot een inerte molecule I1. Het eerste

radicaalpaar kan ook een β-scissie ondergaan waardoor een tweede radicaalpaar [A•+B•]

wordt gegenereerd. Het tweede radicaalpaar [A•+B•] kan op zijn beurt recombineren met

vorming van een inerte molecule I2. De recombinatie van het eerste en het tweede radicaal-

paar met vorming van een inerte molecule leidt tot de afname van de initiatorefficientie.

Een uitdrukking voor de initiatorefficientie kan worden afgeleid op basis van:

f = FoFi (7.3)

Hierin stelt Fo de propagatiekans voor, met andere woorden de kans dat een initiatorra-

dicaal na het verlaten van de solventkooi een keten initieert in plaats van een groeiende

keten te termineren en Fi de kans dat twee radicaalparen onderling niet recombineren in

de solventkooi.

Aangezien FO de waarschijnlijkheid voorstelt dat de radicalen een keten initieren in plaats

van te recombineren met andere radicalen, waarvoor verondersteld wordt dat ze homogeen


verdeeld zijn over de reactor, kan deze term gelijk gesteld worden aan 1.

De term Fi kan op zijn beurt geschreven worden als:

Fi = FiAFiB (7.4)

waarin FiA de kans voorstelt dat het radicaalpaar [A•+A1•] niet recombineert en FiB

de kans dat [A•+B•] niet recombineert.

Door de recombinatiekansen pA en pB van respectievelijk het A1•- en het B•-radicaal met

A• te berekenen, kunnen FiA en FiB begroot worden via:

FiA = 1− pA (7.5)

FiB = 1− pB (7.6)

De recombinatiekansen pA en pB zijn de kansen dat het radicaal A1•, respectievelijk B•,

zich op de reactieafstand van A• bevinden voor het volledige tijdsbereik.

7.1.4 Simulatieresultaten

In het kinetisch schema van Kurdikar en Peppas (1994) (schema (7.2)) zitten volgende

parameters vervat:

• Kinetische parameters

– kbd is de snelheidscoefficient voor de dissociatie van I tot A• en A1•

– kβ is de snelheidscoefficient voor de β-scissie van A1• tot B•

– ktA en ktB zijn de snelheidscoefficienten voor de primaire recombinatie van ra-

dicalen in de solventkooi

• Diffusiecoefficienten

– DA is de diffusiecoefficient, gegeven door de som van de diffusiecoefficienten voor

de radicalen A• en A•1

– DB is de diffusiecoefficient, gegeven door de som van de diffusiecoefficienten voor

de radicalen A• and B•


Voor de dissociatiereactie zijn voor alle bestudeerde initiatoren snelheidscoefficienten

beschikbaar via de producent Akzo Nobel. De waarden voor de snelheidscoefficienten van

de β-scissiereacties werden verkregen uit de literatuur (Buback, 2005). De waarden voor de

snelheidscoefficienten voor terminatie werden in overeenstemming gekozen met de geschatte

terminatiesnelheidscoefficienten van De Roo et al. (2004).

De in het model optredende diffusiecoefficienten worden berekend met behulp van de vrije

volume theorie. In deze theorie is de diffusiecoefficient afhankelijk van het volume van

het beschouwde radicaal. Vermits in het decompositiemechanisme van alle initiatoren

verschillende types radicalen met verschillende groottes gevormd worden, dient voor elk

van deze radicalen afzonderlijk de diffusiecoefficient berekend te worden.

Voor tert-butyl peroxy-neo-decanoaat (TBPD) wordt de berekening van de diffusie-

coefficienten hieronder voorgesteld. De optredende reacties bij de decompositie van deze

initiator zijn dissociatie (reactie (7.7)) en β-scissie (reactie (7.9)).

C

CH3

R1

R2

COO

O

C

CH3

CH3

CH3

k2−bd // C•

CH3

R1

R2

+ CO2 + •OC

CH3

CH3

CH3 (7.7)

Het eerste, respectievelijk tweede, radicaal in het rechterlid van deze reactie geeft A•,

respectievelijk A1•, weer uit het schema van Kurdikar en Peppas (1994).

De diffusiecoefficient DA wordt gegeven door vergelijking (7.8).

DA = DA• + DA•1(7.8)

De β-scissie reactie wordt voorgesteld in (7.9).

CO•

CH3

CH3

CH3


O

(7.9)

De diffusiecoefficient DB wordt gegeven door vergelijking (7.10).

DB = DA• + DB• (7.10)


Het volume van een molecule of radicaal kan berekend worden door een som te maken

van de volumes van de samenstellende atomen (Van Krevelen, 1997).

Nu zijn alle gegevens voorhanden om de diffusiecoefficienten te berekenen en worden

deze voor voor TBPD weergegeven in Tabel 7.2.

Tabel 7.2: Berekening van de diffusiecoefficienten voor tert-butyl peroxy-neo-decanoaat(TBPD), met de volumes in cm3 mol−1 en diffusieoefficienten weergeven in m2 s−1

I/2 A• A1• B•

Volume 158.1 137.2 68.6 21.2Diffusion coefficient 1.36 10−15 6.89 10−15 1.41 10−12 2.86 10−10

Merk op dat de waarden voor de diffusiecoefficienten plateauwaarden zijn. Het ver-

loop van de diffusiecoefficienten wordt voorgesteld in Figuur 7.1. Hieruit blijkt dat de

diffusiecoefficienten toenemen tot ze een bepaalde plateauwaarde bereiken. Na een zekere

polymerizatietijd dalen deze opnieuw, vermtis de diffuse verplaatsing van moleculen in het

reactiemedium vermindert.

Figuur 7.1: Diffusiecoefficienten als functie van de polymerisatietijd voor tert-butyl peroxy-neo-decanoaat (TBPD), volgens de modellering van Kurdikar en Peppas (1994)(DA enDB)


Voor TBPD wordt de initiatorefficientie tijdens de monomeerrijke fase (f1) als een

constante gemodelleerd, terwijl de waarde van de initiatorefficientie in de polymeerrijke

fase (f2) 0.69 bedraagt gedurende de eerste vier reactieuren (Figure 7.2). Vermits de

viscositeit of het reactiemedium toeneemt, wordt de diffusieve verplaatsing van radicalen

weg van elkaar bemoeilijkt waardoor recombinatiereacties bevoordeeld worden zodat f2

een limietwaarde nul bereikt.

Figuur 7.2: Initiatorefficientie in de monomeerrijke (f1) en polymeerrijke fase (f2) als functievan de polymerisatietijd voor tert-butyl peroxy-neo-decanoaat (TBPD)

Wanneer de semi-empirische modellering van De Roo et al. (2004) vergeleken wordt

met de kinetische modellering van Kurdikar en Peppas (1994) wordt ongeveer dezelfde

plateauwaarde voor de initiatorefficientie bereikt (Figuur 7.3).

Vooreerst verschillen de beide berekeningswijzen fundamenteel. Het model van De Roo

et al. (2004) werkt met een semi-empirische vergelijking, terwijl het model van Kurdikar

en Peppas (1994) werken met een analytische uitdrukking die enkel kinetische parameters

bevat.

Daarnaast hebben de diffusiecoefficienten verschillende waarden in beide modellerings-

methodes. In de modellering van De Roo et al. (2004) worden de diffusiecoefficienten gelijk

ondersteld, terwijl deze in de modellering van Kurdikar en Peppas (1994) verschillend zijn


Figuur 7.3: Initiatorefficientie in de polymeerrijke fase (f2) als functie van de polymerisatietijdvoor tert-butyl peroxy-neo-decanoaat (TBPD), voor de modellering van De Rooet al. (2004) en Kurdikar en Peppas (1994)

(DA en DB). Het verschil tussen de twee benaderingen wordt gegeven voor TBPD in

Figuur 7.3.

De diffusiecoefficienten in de modellering van De Roo et al. (2004) zijn kleiner dan DA

en DB. Waar de waarden van DA en Di maar weinig verschillen, verschillen de waarden

van Di (en DA) en DB veel sterker (Figuur 7.1). Deze lagere waarde voor DA zorgt ervoor

dat de diffusie van A• en A•1 uit de solventkooi trager verloopt dan de diffusie van A• en

B•. Hoe sneller radicalen uit de solventkooi kunnen ontsnappen, des te sneller de polyme-

risatiereactie kan worden gestart en des te hoger de initiatorefficientie is. Dit effect wordt

waargenomen in Figuur 7.3.

De monomeerconversie als functie van de polymerisatietijd wordt ook bekeken om te

zien of de kinetische modellering van Kurdikar en Peppas (1994) in staat is niet enkel

de initiator efficientie correct te modelleren. Figuren 7.4 en 7.2 bewijzen dat het model

van Kurdikar en Peppas (1994) in staat het kooieffect in de modellering op te nemen.

Tijdens de polymerisatie van vinylchloride wordt de polymeerrijke fase gevormd vanaf

0.1% conversie. De samenstelling van deze fase bedraagt 70 wt% polymeer en 30 wt%


monomeer (De Roo et al., 2004). In deze laatste concentratieregio zijn polymerisatiereacties

diffusiegecontroleerd (kooieffect). In de monomeerrijke fase daarentegen zijn de reacties

reactiegecontroleerd. Hierdoor zullen vanaf de start van de polymerisatie tot de finale

conversie alle reacties diffusiegecontroleerd zijn. Dit is het geval in Figuur 7.4.

Figuur 7.4: Monomeerconversie als functie van polymerisatietijd voor tert-butyl peroxy-neo-decanoaat (TBPD)

Ook voor de andere klassen initiatoren worden simulaties uitgevoerd. De resultaten

hiervan zijn te vinden in het volledige werk.

Naast deze simulatieresultaten voor de initiatorefficientie bepalen nog andere karakteristie-

ken de geschiktheid van de initiator: halfwaardetijd, product kwaliteit en ontwikkelde reac-

tievermogen. Op basis van al deze karakteristieken blijkt tert-butyl peroxy-neo-decanoaat

(TBPD) een van de meest geschikte initiatoren te zijn voor de polymerisatie van vinylchlo-

ride, in een temperatuursgebied tussen 300 en 350 K.


7.2 Genereren van een reactienetwerk

De reden voor het hanteren van het begrip initiatorefficientie, ligt hoofdzakelijk bij de

moeilijkheid van het in kaart brengen van alle optredende reacties en het bepalen van bij-

horende kinetische parameters. Als de kinetiek van de initiatordecompositie op zich en

de initiatordecompositie ingebed in het volledige reactienetwerk, in detail wordt beschre-

ven, dient de efficientiefactor f niet meer geıntroduceerd te worden. Dit geeft een meer

fundamenteel beeld van de kinetiek van de initiatordecompositie, waaruit de initiatoreffi-

cientie volgt. In dit werk wordt een reactienetwerkgenereringsprogramma ontwikkeld dat

in staat is alle mogelijke reacties die optreden gedurende de initiatordecompositie, in kaart

te brengen.

7.2.1 Conceptueel ontwerp van een reactienetwerk

Om een reactienetwerk te kunnen genereren dat in staat is het initiatordecompositie me-

chanisme in detail te beschrijven, dient vooreerst een geschikte methodologie gezocht te

worden. Verschillende mogelijkheden zijn beschikbaar, waarbij in dit werk wordt gebruikt

gemaakt van de methodologie van Broadbelt et al. (1996) en Li et al. (2004). De netwerk-

generering kan uitgevoerd worden in drie stappen, zoals weergegeven in Figuur 7.5.

Figuur 7.5: Eenvoudige voorstelling van de methodologie voor reactienetwerkgenerering: reac-tanten kunnen verschillende reactietypes ondergaan die leiden to producten. Dezeproducten kunnen eventueel opnieuw als reactanten beschouwd worden.

1. De reactanten (moleculen of radicalen) die optreden gedurende initiatordecompositie

vormen de input van het netwerkgenereringsprogramma. Deze dienen voorgesteld

worden zodat alle structurele informatie erin vervat zit.


2. Bovendien moet de gekozen voorstelling toelaten op een eenvoudige manier reacties

voor te stellen. Zes reactietypes kunnen onderscheiden worden: dissociatie, β-scissie,

recombinatie, additie, H-abstractie en Cl-shift.

3. De producten (moleculen of radicalen) vormen de output van het netwerkgenere-

ringsprogramma. De voorstellingswijze van de producten is analoog aan deze voor

de reactanten. Eventueel kunnen de producten nog reacties ondergaan, en kunnen

deze dus opnieuw beschouwd worden als reactanten.

In hetgeen volgt, wordt vooreerst een geschikte voorstellingswijze voor de reactanten

en producten gezocht.

7.2.2 Matrixvoorstelling van de reactanten en de producten

De reactanten moeten op zodanige wijze worden voorgesteld dat ze alle structurele informa-

tie bevatten. In dit werk werd gekozen voor een matrixvoorstelling. Beschouw bijvoorbeeld

een primair peroxyester, tert-butyl peroxyacetaat (TBPA), waarvan de matrixvoorstelling

is weergegeven in Figuur 7.6.

Essentieel bestaat deze matrix uit 3 te onderscheiden delen: de identificatie van de

atomen, de voorstelling van de bindingen en de voorstelling van de radicaalpositie.

1. Indentificatie van de atomen Vermits bij initiatordecompositie niet alleen koolstof-

atomen betrokken zijn, maar ook andere atomen, wordt elk atoom een identificatienummer

toegekend, zoals wordt voorgesteld in Tabel 7.3. Dit identificatienummer zal zijn nut be-

wijzen wanneer snelheidscoefficienten moeten worden toegekend aan een bepaalde reactie.

Tabel 7.3: Identificatienummers van de atomen betrokken bij initiatordecompositie

Atom Indentification numberKoolstof C 1Zuurstof O 2Stikstof N 3Chloor Cl 4


Figuur 7.6: Matrixvoorstelling voor tert-butyl peroxyactetaat (TBPA), overeenkomstig de num-mering van de atomen in de zelfde figuur.

De identificatienummers worden gestockeerd in de eerste rij van de matrix.

2. Voorstelling van de bindingen De grijze matrix in Figuur 7.6 stelt de hoofdmatrix

voor, waarin de bindingen tussen de atomen zijn weergegeven. Wanneer er een enkele

respectievelijk dubbele binding bestaat tussen twee atomen, wordt dit voorgesteld door ’1’

respectievelijk ’2’. Wanneer er geen binding is, wordt ’0’ geplaatst.

3. Voorstelling van de radicaalpositie De laatste rij van de matrix stelt voor of

een bepaald atoom een radicaalcentrum bezit of niet. Het atoom waar zich het radicaal

bevindt, krijgt een ’1’ in deze rij.

In de gekozen matrixvoorstelling zit nu alle structurele informatie vervat. Desondanks

is slechts een geschikte voorstelling verkregen wanneer reacties op een eenvoudige manier

kunnen worden voorgesteld.


7.2.3 Link tussen de reactanten en de producten: matrixbewer-

kingen

Vermits een reactie de link vormt tussen reactant en product, en deze weergeven zijn door

matrices, kan een reactie worden voorgesteld door een matrixbewerking. Voor elk van de 6

beschouwde reactietypes kan een algemene procedure die de matrixbewerkingen beschrijft,

worden opgesteld. In deze korte samenvatting worden deze procedures niet opgenomen

voor alle reacties: enkel de algemene procedure voor dissociatie wordt uitgelegd.

In Figuur 7.5 werd de methodologie voor netwerkgenerering in dit werk weergegeven.

Gebaseerd op deze methodologie wordt nu een reactienetwerk gegenereerd zoals getoond

in Figuur 7.7.

Figuur 7.7: Matrixbewerkingen overeenstemmend met de netwerkgenering voor dissociatiereac-ties.

Als reactant wordt een algemene molecule ABCD gekozen. In de beschouwde molecule

kunnen 3 bindingen gebroken worden door dissociatie, namelijk de binding tussen A en B,


tussen B en C en tussen C en D. Veronderstel dat de binding tussen atoom B en C wordt

gebroken. Deze dissociatiereactie leidt tot de vorming van twee producten, namelijk AB•

en DC•.

De matrixvoorstelling van het reactant is weergegeven in Figuur 7.8: alle bindingen zijn

enkelvoudig en het reactant is een molecule. De matrixvoorstelling van de producten kan

worden afgeleid uit de procedure uit Figuur 7.7, zoals voorgesteld in Figuur 7.8. De binding

tussen B en C wordt geselecteerd en gebroken. De bindingspartners van B respectievelijk

C worden opgespoord. Na dissociatie is atoom B enkel verbonden met atoom A, terwijl C

enkel verbonden is met D. De producten van deze dissociatiereactie worden gegeven door de

rijen en kolommen te schrappen in de matrixvoorstelling van ABCD, overeenkomstig met

C en D, respectievelijk met A en B. Vermits radicalen gevormd worden wordt de radicaalrij

gevuld met ’1’ op positie B en C. Merk op dat de producten nog in staat zijn om andere

reacties te ondergaan, en deze dus terug kunnen worden opgenomen als reactant (Figuur

7.7), wat resulteert in een feedback lus.

Vermits nu een geschikte matrixvoorstelling werd gevonden die alle structurele info

bevat en toelaat reacties eenvoudig voor te stellen, kan de eigenlijke netwerkgenerering

starten.

7.2.4 Constructie van een netwerkgenereringsprogramma

Voor elk reactietype kunnen matrixoperaties op de reactanten worden uitgevoerd, wat

leidt tot een stand-alone netwerkgenerering voor elk reactietype. Om tot een geıntegreerd

netwerkgenereringsprogramma te komen, dienen voor elk reactant de functionaliteiten voor

een bepaalde reactie te worden getraceeerd. Op basis van een beslissingsboom (Figuur 7.9)

kan worden beslist welke reacties kunnen optreden.


Figuur 7.8: Matrixbewerkingen overeenkomstig een dissociatiereactie tussen atomen B en C vaneen fictieve molecule ABCD.

Wanneer alle reacties in kaart worden gebracht, wordt een volledig netwerk verkregen.

Om dit tot stand te brengen, wordt een computer programma in Fortran ontwikkeld. De

exacte simulatiecode is te vinden in Appendix 1.


Figuur 7.9: Beslissingsboom voor netwerkgenerering bij initiatordecompositie.

7.3 Besluit

In dit werk worden vier klassen initiatoren besproken: peroxydicarbonaten, peroxyesters,

azo-initiatoren en diacylperoxides. De performantie van elk van deze initiatoren wordt on-

der andere bepaald door de initiatorefficientie f . De modellering van de initiatorefficientie

kan gebeuren op verschillende manieren, waarvan de voornaamste een semi-empirische en

een kinetische modellering zijn. In dit werk werd de kinetische modellering volgens het

model van Kurdikar en Peppas (1994) uitgewerkt. Deze modellering heeft als voordeel dat

de initiatorefficientie a priori kan berekend worden op basis van een analytische uitdruk-

king zonder empirische waarden, maar enkel met kinetische parameters. In het kinetisch

model van Kurdikar en Peppas (1994) treden verschillende snelheidscoefficienten en dif-

fusiecoefficienten op. Om de initiatorefficientie te simuleren gedurende de polymerisatie,

dienen de waarden van deze parameters gekend te zijn. De waarden voor de eerstgenoem-

den werden in literatuur gevonden, terwijl de diffusiecoefficienten berekend werden op basis

van de vrije volume theorie. Het vrij volume van een molecule of een radicaal werd be-

rekend op basis van de atoomvolumes van de samenstellende atomen van een molecule of


een radicaal.

Met de kennis van de kinetische parameters en diffusiecoefficienten, werd de initiatoreffi-

cientie als functie van reactietijd en conversie berekend. Uit de resultaten is gebleken dat

het model van Kurdikar en Peppas (1994) in staat was de initiator decompositie kinetisch

correct te beschrijven.

In een tweede luik van deze thesis, werd een reactienetwerk gegenereerd dat in staat is

alle mogelijke reacties tijdens initiatordecompositie in kaart te brengen. Dit reactienetwerk

laat toe het begrip initiatorefficientie niet meer expliciet te gebruiken. Het begrip initi-

atorefficientie houdt immers geen rekening met alle mogelijke optredende reacties tijdens

initiatordecompositie, maar brengt enkel de meest belangrijke reactiestappen in rekening.

Door de kinetiek van initiatordecompositie in detail te beschrijven, volgt de initiatoref-

ficientie uit de aangewende beschrijving. In dit werk werd bijgevolg eerst conceptueel

bepaald hoe een reactienetwerk kan worden gegeneerd. Daarna werd gezocht naar een ge-

schikte representatie van reactanten. Er werd gekozen voor een matrixvoorstelling, waarin

alle structurele informatie (atoomtypes, bindingen en radicaalpositie) vervat zit. Tenslotte

werd beschreven hoe vanuit de gegeven reactanten de gewenste producten kunnen gege-

nereerd worden. Al deze gegevens hebben geleid tot de ontwikkeling van een computer

programma (Fortran), die in staat is alle reactietypes te behandelen.

118

Appendix A

Computer code: generating a

reaction network

The developed reaction generation simulation code (in Fortran) consists of two parts: on

the one hand, a main program reads the matrices of the reactants and writes the matrices

of the products. On the other hand, different subroutines contain the matrix operations

for each reaction type discussed in Chapter 5. In this appendix, the main program and

the subroutines for each reaction type are presented and discussed.

A.1 Main program

The main program will compute all products for the six different reactions (dissociation,

β-scission, recombination, addition, H-abstraction and Cl-shift) considered in Chapter 5.

A.1.1 Definition of the reactants

First of all, the reactants are defined for each type of reaction.

• Dissociation

integer dimd

integer, allocatable :: Atoomd(:)

integer, allocatable :: Md(:,:)

integer, allocatable :: Rd(:)

Appendix A. Computer code: generating a reaction network 119

• β-scission

integer dimb

integer, allocatable :: Atoomb(:)

integer, allocatable :: Mb(:,:)

integer, allocatable :: Rb(:)

• Recombination

integer dimr1, dimr2, dimr

integer, allocatable :: Atoomr1(:)

integer, allocatable :: Mr1(:,:)

integer, allocatable :: Rr1(:)

integer, allocatable :: Atoomr2(:)

integer, allocatable :: Mr2(:,:)

integer, allocatable :: Rr2(:)

integer, allocatable :: Mr(:,:)

integer, allocatable :: Rr(:)

• Addition

integer dima1, dima2, dima12

integer, allocatable :: Atooma1(:)

integer, allocatable :: Ma1(:,:)

integer, allocatable :: Ra1(:)

integer, allocatable :: Atooma2(:)

integer, allocatable :: Ma2(:,:)

integer, allocatable :: Ra2(:)

• H-abstraction

integer dimha

integer, allocatable :: Atoomha(:)

integer, allocatable :: Mha(:,:)

integer, allocatable :: Rha(:)

• Shift

integer dims

integer, allocatable :: Atooms(:)

integer, allocatable :: Ms(:,:)

integer, allocatable :: Rs(:)


A.1.2 Link with the subroutines

Secondly, the dimension, the types of consisting atoms, the principal matrix and the radical

position of the reactants are read. Afterwards, the main code invokes the subroutines which

present an algorithm for any reaction.

• Dissociation

Open(16,File=’MatrixDissociatie.txt’)

Read(16,*) dimd

Read(16,*) (Atoomd(k),k=1,dimd)

DO i=1,dimd

Read(16,*) (Md(i,j),j=1,dimd)

END DO

Read(16,*) (Rd(j),j=1,dimd)

Close(16)

call Dissociation(dimd,Atoomd,Md,Rd)

• β-scission

Open(17,File=’MatrixBetascissie.txt’)

Read(17,*) dimb

Read(17,*) (Atoomb(k),k=1,dimb)

DO i=1,dimb

Read(17,*) (Mb(i,j),j=1,dimb)

END DO

Read(17,*) (Rb(j),j=1,dimb)

Close(17)

call Betascission(dimb,Atoomb,Mb,Rb)

• Recombination

Open(10,File=’MatrixRecombinatie1.txt’)

Read(10,*) dimr1

Read(10,*) (Atoomr1(k),k=1,dimr1)

DO i=1,dimr1

Read(10,*) (Mr1(i,j),j=1,dimr1)

END DO

Read(10,*) (Rr1(j),j=1,dimr1)

Close(10)


Open(11,File=’MatrixRecombinatie2.txt’)

Read(11,*) dimr2

Read(11,*) (Atoomr2(k),k=1,dimr2)

DO i=1,dimr2

Read(11,*) (Mr2(i,j),j=1,dimr2)

END DO

Read(11,*) (Rr2(j),j=1,dimr2)

Close(11)

call Recombination(dimr1,Atoomr1,Mr1,Rr1,dimr2,Atoomr2,Mr2,Rr2)

• Addition

Open(12,File=’MatrixAdditie1.txt’)

Read(12,*) dima1

Read(12,*) (Atooma1(k),k=1,dima1)

DO i=1,dima1

Read(12,*) (Ma1(i,j),j=1,dima1)

END DO

Read(12,*) (Ra1(j),j=1,dima1)

Close(12)

Open(13,File=’MatrixAdditie2.txt’)

Read(13,*) dima2

Read(13,*) (Atooma2(k),k=1,dima2)

DO i=1,dima2

Read(13,*) (Ma2(i,j),j=1,dima2)

END DO

Read(13,*) (Ra2(j),j=1,dima2)

Close(13)

call Addition(dima1,Atooma1,Ma1,Ra1,dima2,Atooma2,Ma2,Ra2)

• H-abstraction

Open(14,File=’MatrixHabstractie.txt’)

Read(14,*) dimha

Read(14,*) (Atoomha(k),k=1,dimha)

DO i=1,dimha

Read(14,*) (Mha(i,j),j=1,dimha)

END DO

Read(14,*) (Rha(j),j=1,dimha)


Close(14)

call Habstraction(dimha,Atoomha,Mha,Rha)

• Shift

Open(15,File=’MatrixShift.txt’)

Read(15,*) dims

Read(15,*) (Atooms(k),k=1,dims)

DO i=1,dims

Read(15,*) (Ms(i,j),j=1,dims)

END DO

Read(15,*) (Rs(j),j=1,dims)

Close(15)

call Shift(dims,Atooms,Ms,Rs)


A.2 Subroutines for each reaction type

Six different reactions are considered: dissociation, β-scission, recombination, addition,

H-abstraction and Cl-shift. The algorithm for each reaction type is different, and is placed

in different subroutines. These subroutines are now presented and discussed.

A.2.1 Dissociation

In this algorithm for dissociation, one considers that each bond between two atoms can

break. Moreover, all possible breakable bonds are traced and the accompagnying products

are generated.

First, the subroutine is invoked, with 4 arguments: the dimension of the main matrix,

the identification numbers of the atoms, the main matrix and the radical position of the

reactant.

subroutine Dissociation(dimdiss,Atoomdiss,Mdiss,Rdiss)

It is considered that a bond between atom i and j breaks. In the subroutine, all

breakable bonds will be traced, resulting in an do-loop. A breakable bond is found if an

element of the main dissociation matrix does not equal zero.

i_start=1

i_end=dimdiss

j_start=1

j_end=dimdiss

k_start=1

k_end=dimdiss

mineen=-1

OPEN(26,FILE=’ProductenDissociatie.res’)

DO i=i_start,i_end

DO j=j_start,j_end

IF(Mdiss(i,j) .NE. 0) Then


Two rows are considerd, row A and row B, with a dimension equal to the one of the

main matrix. Both matrices are initialized. The first element of each row is the atom

number of the atoms between which the bond is broken (i and j). The other elements are

set minus one.

A(1)=i

B(1)=j

DO k=2,dimdiss

A(k) = mineen

B(k) = mineen

END DO

In row A, all atoms bonded with i need to be stored. Once all those atoms are traced,

the atoms bonded with these atoms need to be traced and stored in A. This loop ends

when no bonded atoms are found anymore. Row A represents the constituent atoms of the

first reactant.

indexa = 1

DO WHILE (A(indexa) .NE. mineen)

rijvul_start=1

rijvul_end=dimdiss

dum2=A(indexa)

DO rijvul=rijvul_start,rijvul_end

RIJ(rijvul) = Mdiss(dum2,rijvul)

END DO

l=1

DO k=1,dimdiss

found = 0

IF (k .NE. i .AND. k .NE. j .AND. RIJ(k) .NE. 0) THEN

If an atom is already an element of A, this element does not have to be considered

anymore. If not, the atom is added to row A.

DO WHILE (A(l) .NE. mineen)

l=l+1


IF(A(l) .EQ. k) THEN

found = 1

ENDIF

END DO

IF(found .EQ. 0) THEN

A(l) = k

ENDIF

ENDIF

END DO

indexa=indexa+1

END DO

The matrix representation for the first product is determined.

dima=1

DO dimaa=1,dima

IF(A(dimaa) .NE. mineen) THEN

dima=dima+1

ENDIF

END DO

allocate (Mmatra(dima,dima))

DO inii=1,dima

DO inij=1,dima

Mmatra(inii,inij)=0

END DO

END DO

DO matra1=1,dima

DO matra2=1,dima

IF(A(matra1) .NE. mineen

& .AND. A(matra2) .NE. mineen) THEN

Mmatra(matra1,matra2)=Mbeta(A(matra1),A(matra2))

ENDIF

END DO

END DO


allocate (Radrija(1,dima))

DO inii=1,dima

Radrija(1,inii)=0

END DO

The first row is then written to a seperate file. The elements equal to minus one are

not shown. Besides, the dimension, the matrix itself and the radical row of the matrix

representation are written to a seperate file.

Write(26,*)’** Binding gebroken tussen:’,i,j

Write(26,*)’ ’

Write(26,*) ’ ’

Write(26,*) ’Component 1 ’

Write(26,*)’--------------’

Do awrite=1,ahigher

IF(A(awrite) .NE. mineen) THEN

WRITE(26,*) A(awrite)

ENDIF

end do

Write(26,*) ’ ’

The second row B consists of all the elements that are not part of row A. These atoms

are traced and stored in row B, representing the second reactant.

indexb = 1

k_start=1

k_end=dimdiss

DO k=k_start,k_end

found = 0

l = 1

DO WHILE (A(l) .NE. mineen)

IF(A(l) .EQ. k) THEN

found = 1

ENDIF

l=l+1

END DO


IF (found .EQ. 0) Then

B(indexb) = k

indexb = indexb + 1

ENDIF

END DO

The matrix representation of the second product is determined.

dimb=dimbeta-dima

allocate (Mmatrb(dimb,dimb))

DO iniib=1,dimb

DO inijb=1,dimb

Mmatrb(iniib,inijb)=0

END DO

END DO

DO matrb1=1,dimb

DO matrb2=1,dimb

IF(B(matrb1) .NE. mineen .AND. B(matrb2) .NE. mineen) THEN

Mmatrb(matrb1,matrb2)=Mbeta(B(matrb1),B(matrb2))

ENDIF

END DO

END DO

allocate (Radrijb(1,dimb))

DO iniib=1,dimb

Radrijb(1,iniib)=0

END DO

The second row B is then written to a seperate file. The elements equal to minus one

are not shown. The matrix representation of the second product is written too.

Write(27,*)’Component 2’

Write(27,*)’--------------’

Do bwrite=1,bhigher

IF(B(bwrite) .NE. mineen) THEN

WRITE(27,*) B(bwrite)


ENDIF

end do

Write(27,*)’Bijhorende matrix’

Write(27,*)’------------------’

Write(27,*)’Dimensie’

Write(27,*) dimb

Write(27,*)’Hoofdmatrix’

DO matrbiwrite=1,dimb

WRITE(27,*) (Mmatrb(matrbiwrite,matrbjwrite),

& matrbjwrite=1,dimb)

END DO

Write(27,*)’Radicaalrij’

Write(27,*) (Radrijb(1,radbwrite), radbwrite=1,dimb)

Write(27,*) ’ ’

ENDIF

END DO

END DO

Close(26)

END

A.2.2 β-scission

In the algorithm for β-scission, one considers that each bond in β-position of a radical can

be broken. This is accompanied by the formation of a double bond between the atoms in

the α-position to the radical position and the one in the radical position. With the follow-

ing algorithm, all possible breakable bonds are traced and the accompanying products are

generated.


the identification of the atom, the main matrix and the radical position.

subroutine Betascission(dimbeta,Atoombeta,Mbeta,Rbeta)

The algorithm for β-scission is completely the same as for dissociation, except an extra

condition which need to be fulfilled. For a beta-scission, one needs to have a radical and


only the atom in β-position of this radical can be broken and a double bond is formed

between the atoms in α-position and in the radical position.

IF(Mbeta(i,j) .NE. 0 .AND. Rbeta(j) .EQ. 0) Then

A.2.3 Recombination

In the algorithm for recombination, one considers that only two radicals can undergo re-

combination. The products of this recombination will be generated.


the identification of the atoms, the main matrix and the radical row of the matrix repre-

sentation of the two reactants.

subroutine Recombination(dimrec1,Atoomrec1,Mrec1,Rrec1,

dimrec2,Atoomrec2,Mrec2,Rrec2)

Because recombination reactants can only occur between radicals, the radical position

is traced for both reactants.

k1_start=1

k1_end=dim1

radpos1 = 1

DO k1=k1_start,k1_end

IF(R1(k1) .NE. 0) THEN

radpos1 = k1

ENDIF

END DO

k2_start=1

k2_end=dim2

radpos2 = 1



radpos2 = k2

ENDIF

END DO


When the two radicals undergo recombination, a bond is formed between the atoms

on which the radical position was located. The matrix representation of the product is a

matrix with dimension equal to the sum of the dimensions of the composite matrices.

i1_start=1

i1_end=dim1

j1_start=1

j1_end=dim1

DO i1=i1_start,i1_end

DO j1=j1_start,j1_end

M(i1,j1)=M1(i1,j1)

END DO

END DO

i2_start=dim1+1

i2_end=dim1+dim2

j2_start=dim1+1

j2_end=dim1+dim2



M(i2,j2)=M2(i2-4,j2-4)

END DO

END DO

M(radpos1,radpos2+dim1)=1

M(radpos2+dim1,radpos1)=1

The product of a recombination reaction is a molecule, so the radical row of the product

matrix is filled with ’0’ elements.

k3_start=1

k3_end=dim1+dim2


R(k3)=0

END DO

The product dimension, the matrix elements and the radical row are written to a

separate file.


OPEN(22,FILE=’ProductenRecombinatie.res’)

Write(22,*)’RECOMBINATION’

Write(22,*) ’Product’

DO miwrite=1,6

WRITE(12,*) (M(miwrite,mjwrite), mjwrite=1,6)

END DO

Write(12,*) ’Radicaalrij’

WRITE(12,*) (R(rwrite), rwrite=1,6)

Close(12)

A.2.4 Addition

In this algorithm for addition, only addition on a C=C bond of a vinyl chloride monomer

is taken into account. The products of this addition will be generated.


the atom types, the main matrix and the radical row of the matrix representation of the

two reactants.

subroutine Addition(dimadd1,Atoomadd1,Madd1,Radd1,

dimadd2,Atoomadd2,Madd2,Radd2)

The first reactant in an addition reaction is a vinyl cloride monomer. The second

reactant is a radical. The radical position of this radical needs to be traced.

k2_start=1

k2_end=dim2

radpos = 1



radpos = k2

ENDIF

END DO

Two possible reactions can take place: a head and a tail addition. For both, a matrix

needs to be created based on the reactants. Consider first the head addition.

i1_start=1

i1_end=dim1


j1_start=1

j1_end=dim1



Mkop(i1,j1)=M1(i1,j1)

END DO

END DO

i2_start=dim1+1

i2_end=dim1+dim2

j2_start=dim1+1

j2_end=dim1+dim2



Mkop(i2,j2)=M2(i2-dim1,j2-dim1)

END DO

END DO

Because the radical can only attack on the double bond, the location of this double

bond needs to be traced:

db1_start=1

db1_end=dim1

db2_start=1

db2_end=dim1

DO db1=db1_start,db1_end

DO db2=db2_start,db2_end

IF(M1(db1,db2) .EQ. 2) THEN

kop=db1

staart=db2

END IF

END DO

END DO

The double bond is broken and two single bonds are formed.

Mkop(radpos+dim1,kop)=1

Mkop(kop,radpos+dim1)=1

Mkop(kop,staart)=1

Mkop(staart,kop)=1


Because of an addition reaction, a neutral molecule is formed. The radical row of the

product is thus filled with zeros.

k3_start=1

k3_end=dim1+dim2


R(k3)=0

END DO

The results for the head addition are written to a separate file.

OPEN(22,FILE=’ProductenKopadditie.res’)

Write(22,*)’ADDITIE: kop’

Write(22,*) ’****************************************’


DO mikwrite=1,5

WRITE(22,*) (Mkop(mikwrite,mjkwrite), mjkwrite=1,5)

END DO


Write(22,*) (R(rwrite), rwrite=1,5)

Close(22)

The same is now done for the tail addition, but the position of addition is different.

ms1_start=1

ms1_end=dim1+dim2

ms2_start=1

ms2_end=dim1+dim2

DO ms1=ms1_start,ms1_end


Mstaart(ms1,ms2)=Mkop(ms1,ms2)

END DO

END DO

Mstaart(radpos+dim1,staart)=1

Mstaart(staart,radpos+dim1)=1

Mstaart(radpos+dim1,kop)=0

Mstaart(kop,radpos+dim1)=0

Finally, the results are written to a seperate file.


OPEN(23,FILE=’ProductenStaartadditie.res’)

Write(23,*)’ADDITIE: staart’

Write(23,*) ’****************************************’


DO miswrite=1,5

WRITE(23,*) (Mstaart(miswrite,mjswrite), mjswrite=1,5)

END DO


WRITE(23,*) (R(rwrite), rwrite=1,5)

Close(23)

A.2.5 H-abstraction

In this algorithm for H-abstraction, one considers that each H-atom on a carbon atom can

be abstracted.

Again, first, the subroutine is invoked, with 4 arguments: the dimension of the main

matrix, the identification of the atoms, the main matrix and the radical position of the

reactant.

subroutine Habstraction(dimh,Atoomh,Mh,Rh)

Because only H-abstraction from carbon atoms is considered, the identification numbers

of the atoms are of importance in this case.

Only the abstraction from C-atoms is considered. Hence, the positions which can not

be taken into account are sought first.

i_start=1

i_end=dim

j_start=1

j_end=dim

DO i=i_start,i_end

DO j=j_start,j_end

IF(Atoom(j) .EQ. 2 .AND. nietmee .NE. j) THEN

nietmee=j

ENDIF

END DO

END DO


When a H atom is abstracted, a double bond can be formed. To seek all possible atoms

of which a H-atom can be abstracted, the radical position needs to be traced. The products

are directly written to a separate file.

OPEN(11,FILE=’ProductenHabstractie.res’)

k_start=1

k_end=dim

l_start=1

l_end=dim

ms1_start=1

ms1_end=dim

ms2_start=1

ms2_end=dim



Mna(ms1,ms2)=Mvoor(ms1,ms2)

END DO

END DO

rr_start=1

rr_end=dim

DO rr=rr_start,rr_end

Rna(rr)=0

END DO

DO k=k_start,k_end

DO l=l_start,l_end

IF(Mvoor(k,l) .EQ. 1 .AND. Mvoor(l,k) .EQ. 1) Then

Mna(k,l)=2

Mna(l,k)=2

Write(11,*)’Product waarbij H weg van binding’, k, l

Write(11,*)’ ’

DO miwrite=1,dim

WRITE(11,*) (Mna(miwrite,mjwrite), mjwrite=1,dim)


END DO


Write(11,*) (Rna(rwrite), rwrite=1,5)

Write(11,*) ’ ’

Mna(k,l)=1

Mna(l,k)=1

ENDIF

END DO

END DO

Close(11)

END

A.2.6 Shift

The last algorithm in the program code is the Cl-shift. In the algorithm for Cl-shift, one

considers that a Cl-atom bounded with the carbon radical can be shifted to a carbon atom

in α-position.

First, the subroutine is invoked, with 4 arguments: the dimension, the atom types, the

main matrix and the radical row of the matrix representation of the reactant.

subroutine Shift(dimsh,Atoomsh,Msh,Rsh)

Because the Cl can only shift in β-position of the radical position, the radical position

needs to be located.

krad_start=1

krad_end=dim

radpos = 1

DO krad=krad_start,krad_end

IF(Rvoor(krad) .NE. 0) THEN

radpos = krad

ENDIF

END DO


The main matrix is initialized.

ms1_start=1

ms1_end=dim

ms2_start=1

ms2_end=dim



Mna(ms1,ms2)=Mvoor(ms1,ms2)

END DO

END DO

The carbon atom and the Cl in β-position are tracked.

kbeta_start=1

kbeta_end=dim

betarij=1

betakolom=1

DO kbeta1=kbeta_start,kbeta_end

IF(Mvoor(radpos,kbeta1) .EQ. 1 .AND. Atoom(kbeta1) .EQ. 1) THEN

betakolom=kbeta1

ENDIF

END DO

kCl_start=1

kCl_end=dim

Clpos=1

DO kCl=kCl_start,kCl_end

IF(Atoom(kCl) .EQ. 4) THEN

Clpos=kCl

ENDIF

END DO

The bond between this Cl and C in α-position needs to be broken,

Mna(Clpos, betakolom)=0

Mna(betakolom,Clpos)=0


while the bond between Cl and C in radical position needs to be formed.

Mna(Clpos,radpos)=1

Mna(radpos,Clpos)=1

The radicalposition becomes located on the C in α-position.

Rna(betakolom)=1

Rna(radpos)=0

The results are then written to a separate file.

OPEN(11,FILE=’ProductenShift.res’)

Write(11,*)’SHIFT’

Write(11,*) ’*******************************’


DO miwrite=1,dim

WRITE(11,*) (Mna(miwrite,mjwrite), mjwrite=1,dim)

END DO


WRITE(11,*) (Rna(rwrite), rwrite=1,dim)

Write(11,*) ’ ’

Close(11)

END

A.3 Complete network generation

A complete network generation simulation program is achieved when recycling loops are

taken into account based on the decision tree of Figure 5.17. The recycle loops are not yet

taken into the modeling program and remains for future work.

Moreover, kinetic parameters could be assigned to each reaction occuring in the reaction

network. Hence, the possibility of the occurence of the given reaction can be stipulated. In

such a way, the kinetics of the initiator decomposition can be described into detail. A future

worker could also pay attention to the link between ’intitiator network’ and ’polymerization

network’. A polymerization network could be constructed, and linked with the existing

simulation code for the initiator network. Hence, the kinetics of the complete free radical

polymerization of vinyl chloride can be described. Moreover, the complete simulation code

will be reusable for other polymerization reactions, and this with minimal adjustments.

139

Appendix B

References to labjournal

In Table B.1, an overview of the references to the labjournal is given. The items refer to

executed simulations and developed program code. In the labjournal, the a reference to

the used computer files is given.

Table B.1: Overview of the references to the labjournal

Item PagesPart 1: Initiator efficiency

•Influence of the different parameters pp. 10-14used in the model of Kurdikar and Peppas (1994)• Literature review: classification of industrial initiators pp. 15-16• Literature review: Decomposition mechanism and kinetic parameters pp. 28-30• Influence of diffusion coefficients on initiator efficiency pp. 41-51

pp. 58-68• Influence of rate coefficients on initiator efficiency pp. 68-71

Part 2: Reaction network

• Literature review: generation of a reaction network pp. 80-88• Matrix representation of the reactants pp. 89-93• Design of computer algoritms pp. 98-103

140

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Kinetic modeling of the initiator decomposition forsuspension polymerization of vinyl chloride

Sophie Van Nevel

Supervisor(s): Prof. Dr. Ir. G. B. Marin, Prof. Dr. Lic. M.-F. Reyniers

Abstract—The kinetics of the initiator decomposition can be modeled in se-veral ways. The concept of initiator efficiency f is introduced first. For mostindustrial initiators the kinetic modeling of Kurdikar and Peppas (1994) [1] isable to model the initiator efficiency in an accurate way. In a second model, areaction network is generated to describe the kinetics of initiator decompositionmore into detail. If the kinetics of the initiator decomposition, both standaloneand embedded in a complete reaction network, are described accurately, a morefundamental description of the kinetics of initiator decomposition is obtained.The initiator efficiency then results from this description.

Keywords—vinyl chloride, suspension polymerization, initiator decomposi-tion, initiator efficiency, reaction network

I. Introduction

POLYMERS are one of the most widespread consumer pro-ducts in the world. Because of its versatility and low pro-

duction cost, poly(vinyl chloride) (PVC) has become an impor-tant polymer with an annual world production of 30 Mton. Thesuspension polymerization of vinyl chloride monomer (VCM)contributes for about 80% of the total PVC production. This pro-cess is carried out in a batch reactor with the monomer dispersedin water. The dispersion is maintained by adding suspension sta-bilizers and by stirring. An initiator is dissolved in the monomerphase. Polymerization is started by bringing the reactor to thedesired polymerization temperature. Due to the low solubility ofPVC in VCM, two phases are formed in the reactor: a monomer-rich phase and a polymer-rich phase. The former phase mainlyconsists of monomer, while the latter has a constant composi-tion of approximately 30 wt% monomer and 70wt% polymer.At a conversion of about 65%, the so-called critical conversion,the monomer-rich phase disappears and polymerization occursin the polymer-rich phase only.

II. Kinetic modeling of initiator efficiency

The polymerization of VCM is a free radical polymeriza-tion. During this polymerization, only a fraction of the radicalsformed by dissociation of the initiator is able to initiate a poly-mer chain. This fraction is defined as the initiator efficiency f .Kurdikar and Peppas [1] developed a model that is able to a pri-ori predict the initiator efficiency and continuously calculate theterm f throughout the course of polymerization. This approachdiffers from other modeling approaches in literature [2], becauseempiric relations are excluded, and the calculation is based onan analytical expression with kinetic parameters only. This leadsto a more accurate modeling of the initiator efficiency.

A. Model of Kurdikar and Peppas (1994)

The kinetic scheme of Kurdikar and Peppas is given in Figure1. Inside the solvent cage, depicted by [. . .], the initiator I candecompose into two primary radicals, A• and A1

•. The solventcage defines the region around a radical within which a recom-bination reaction may occur if another radical is found. Becausethe two radicals A• and A1

•, called the ’first radical pair’, are inclose proximity of each other after dissociation, they can recom-bine again. After a single-bond dissociation, this recombinationleads to the formation of the original initiator which will disso-ciate immediately. Hence, this recombination does not lead toa decrease of the initiator efficiency. After a two-bond disso-

ciation, a small molecule is split off and the two initiator radi-cals can recombine to an inert molecule I1. Radicals A1

• maydecompose in the solvent cage to form another primary radi-cal, B•, through a β-scission reaction. Hence a second radicalpair is formed. Again this radical pair is able to recombine toan inert molecule I2. The recombination of A• with A1

• (firstradical pair) and A• with B• (second radical pair) to form in-ert molecules, I1 and I2, are the primary reactions that causethe decrease in initiator efficiency. The radicals A•, B• andA1

• are effective in initiating chains, thus attacking a monomermolecule, M, to form an active monomer molecule. These activemonomers can undergo propagation reactions.

Fig. 1. Reaction scheme of Kurdikar and Peppas

B. Modeling results for industrial initiators

Four classes of initiators are used in industry: peroxydicar-bonates, peroxyesters, dialkyl diazenes and diacyl peroxides.For tert-butyl peroxy-neo-decanoate (TBPD), a peroxyester,the rate coefficients for β-scission are found in literature basedon ab initio calculations. The profile of the diffusion coefficientsis depicted in Figure 2. These diffusion coefficients are calcu-lated with the free volume theory. In this theory, the diffusioncoefficient of the initiator derived radicals is proportional to thevolume of the radicals.

The initator efficiency for industrial initiators varies between0.3 and 0.8. For tert-butyl peroxy-neo-decanoate, the initia-tor efficiency in the monomer-rich phase (f1) is constant, be-cause reactions in the monomer-rich phase are considered tobe reaction-controlled. The polymer-rich phase is consideredto affect the polymerization reactions in becoming diffusion-controlled [2]. The initiator efficiency in polymer-rich phase(f2) drops extremely at the start because of diffusion control,but increases quickly to reach a plateau value which was mod-eled to be 0.69 during the first four hours of the polymerizationprocess (Figure 3). Since the viscosity of the reaction mediumincreases, the diffusive displacement of the radicals away fromeach other becomes difficult and radical recombination reactionsbecome preferred until f2 reaches a limiting value of zero.

For each class of initiator, the kinetic modeling can be per-formed. Together with other initiator characteristics (half-lifetime, reaction heat developed and product quality of the ob-tained PVC), the modeling allows to select the most appropriateinitiator for the used reaction conditions.

10-20

10-18

10-16

10-14

10-12

10-10

10-8

0 2 4 6 8 10

DA

, DB [

m2 s-1

]


DADB

Fig. 2. Diffusion coefficients as a function of polymerization time for tert-butylperoxy-neo-decanoate, for the modeling of Kurdikar and Peppas (1994)

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

f1, f

2 [-

]


f2f1

Fig. 3. Initiator efficiency as a function of polymerization time forTBPD in the monomer-rich phase (f1) and in the polymer-rich phase(f2) (kbd=1.52 10+14exp(-115.47 10+3/RT), kβ =1.00 10+13exp(-50.00 10+3/RT), ktA=ktB1.00 10+4).

III. Generation of a reaction network

A more fundamental way to describe the initiator decomposi-tion into detail is obtained by generating a reaction network, thataccounts for all reaction possibilities for all reactants presentduring initiator decomposition. For this purpose, a computergeneration program is constructed. Each reaction in this net-work assigned a rate coefficient. By taking all reaction possi-bilities into account and describing the kinetics of the initiatordecomposition into detail, the concept of an initiator efficiencyis no longer required but results from the description.

A. Conceptual design of a reaction network

In this work, the network generation principle presented byBroadbelt et. al. [3] is applied. This generation principle al-lows performing the network generation in three steps. The re-actants (molecules or radicals) that are present during the de-composition of the initiator are the input of the network gener-ation program. These reactants need to be represented in sucha way that all relevant structural information is captured. Theselected representation of the reactants must also allow for aneasy description of the reactions, i.e. linking reactant represen-tation and product representation. Six reaction types are takeninto account: dissociation, recombination, addition, β-scission,hydrogen abstraction and Cl-shift. The products (molecules orradicals) are the output of the network generation program. Therepresentation of these products must be analogous to the onefor the reactants. It should be clear that an appropriate represen-tation of the reactants and the products is required. Only oncethis representation is found, operations on these reactants can beexecuted.

B. Representation of the reactants and the products

Basically, the matrix consists of three distinguishable parts:the identification of the atoms, the bonds between the atoms andthe radical position. Each atom receives its own identification

number: 1 for carbon, 2 for oxygen, 3 for nitrogen and 4 forchlorine. This is done because not only C-atoms but also het-eroatoms are involved. These identification numbers are storedin the first row of the matrix.The grey matrix in Figure 4 consists of the bonds between theatoms of the reactant or of the product. There are 4 possibilities:between two atoms there is no bond (’0’), a single bond (’1’), adouble bond (’2’) or a triple bond (’3’).The last row of the matrix shows the radical position. In thisexample the radical is located at atom 1.Consider e.g. a carbonyloxy radical, as depicted in Figure 4 to-gether with its matrix representation. Each atom correspondswith the column in the matrix that has the same number, e.g.atom 1 corresponds with column number 1.

Fig. 4. Matrix representation for an alkoxide radical corresponding with thenumbering of the atoms in the molecule given.

C. Link between reactant and product representation

The selected matrix representation for reactants and productscaptures all structural information: the types of atoms, the bondsbetween the atoms and the radical position. Nevertheless, an ap-propriate representation is only achieved when reactions can bemodeled easily. For each type of reaction, matrix operations onreactants are established, which leads to a stand alone networkgeneration program for each reaction type.

D. Generation of an integrated reaction network

To take into account all reaction types, and thus achieve an in-tegrated network generation program, functionalities need to betraced for each reactant. A decision tree is constructed to com-bine all reaction types. Hence, a network generation programwhich maps all possible reactions for each reaction type sepa-rately, is achieved. To generate this reaction network, a com-puter program has been constructed in Fortran.

IV. Conclusion

Two kinetic modeling strategies to describe the initiator de-composition have been presented in this paper. For most in-dustrial initiators the kinetic modeling of Kurdikar and Peppas(1994) [1] is able to model the initiator efficiency in an accurateway. In a second modeling strategy, a computer program hasbeen devised to generate a reaction network. This allows for amore fundamental view of the kinetics of initiator decomposi-tion.

References[1] Kurdikar D.L. and Peppas N.A., Method of determination of initia-

tor efficiency: application to UV polymerizations using 2,2-dimethoxy-2-phenylacetophenone, Macromolecules, 27:733738, 1994.

[2] De Roo T., Heynderickx G.J. and Marin G.B., Diffusion-controlled re-actions in vinyl chloride suspension polymerization, Macromol. Symp.,206(1):215228, 2004.

[3] Broadbelt L.J., Stark S.M. and Klein M.T., Computer generated reactionmodelling: decomposition and encoding algorithms for determining speciesuniqueness, Comput. Chem. Eng., 20(2):113129, 1996.

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