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Monomer partitioning and composition drift in emulsioncopolymerizationCitation for published version (APA):Verdurmen-Noël, E. F. J. (1994). Monomer partitioning and composition drift in emulsion copolymerization.Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR426298

DOI:10.6100/IR426298

Document status and date:Published: 01/01/1994

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https://doi.org/10.6100/IR426298

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https://research.tue.nl/en/publications/monomer-partitioning-and-composition-drift-in-emulsion-copolymerization(dbb9fe02-5967-49a3-a43d-2508370fc047).html

MONOMER PARTITIONING AND COMPOSITION DRIFT

IN EMULSION COPOLYMERIZATION

E.F.J. Verdurmen-Noel



PROEFSCHRIFf

ter verkrijging van de graad van doctor aan de

Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof. dr. J .H. van Lint, voor een commissie aangewezen door bet College van Dekanen in het openbaar te verdedigen op

dinsdag 29 november 1994 om 16.00 uur

door

Elisabeth Fran~ois Johanna Verdurmen-Noel

geboren te Weert

druk. wfbro dissortatiodrukkorij. holmond.

Dit proefschrift is goedgekeurd door

de promotoren

en de copromotor

prof.dr.ir. A.L. German

prof.dr. J.M. Asua

dr. I.A. Maxwell

Het in dit proefschrift beschreven onderzoek werd gesteund door de Stichting Scheikundig

Onderzoek in Nederland (SON) met een subsidie van de Nederlandse Organisatie voor

Wetenschappelijk Onderzoek (NWO).

aan mijn ouders,

aan Edwin

Summary

Summary

Emulsion copolymerization is a complex process due to the heterogeneity of the

system which consist of three distinct phases, i.e., the aqueous, polymer particle, and

monomer droplet phase. Nowadays, there is still a lack of knowledge on the basic processes

determining emulsion (co )polymerization kinetics. One of the aims of this investigation is

developing a correct and simple model to describe monomer partitioning of two monomers

with limited water solubility in an emulsion system in such a way as to avoid the use of

interaction parameters that are experimentally hard to determine and theoretically rather

vague. Such a model is forming a key barrier if one wants to predict emulsion

copolymerization using only parameters of physical significance.

It has been shown in previous work that the monomer ratios within the polymer

particle and monomer droplet phases are equal and independent of the copolymer

composition. However, no theoretical explanation was given. In chapter 5 the assumptions

required to modify the theory in order to explain this phenomenon are given. Furthermore,

simple equations are depicted to describe monomer partitioning in emulsion systems using

parameters of physical significance only, i.e., no adjustable or interaction parameters are used.

Model development based on the relationships described in chapter 5 provides a

better understanding of the effects of process parameters as for instance the monomer-to

water ratio and the polymer volume on monomer partitioning (chapter 6). A sensitivity

analysis showed that the reactivity ratios are the most important parameters affecting

composition drift. The effect of water solubility of the monomers on composition drift is only

significant in those cases were the amount of monomer in the aqueous phase is not negligible

as compared with the total monomer amount. The rate of polymerization mainly depends on

the maximum swellability of monomers in the polymer phase.

In principle the heterogeneity of the emulsion system can be used to influence the

chemical composition distribution of the copolymer. A second aim in this investigation is the

verification of the concept that minimum composition drift can be reached for monomer

combinations in which the more water soluble monomer also is the more reactive one. This

was tested for the monomer combinations methyl acrylate-indene (MA-Ind: chapter 7) and

methyl acrylate-vinyl esters (MA-VEst: chapter 8). lt was shown for the monomer

Summary

combination MA-Ind that minimum composition drift indeed could be obtained over a wide

range of initial monomer mole fractions, simply by adjusting the initial monomer-to-water

ratio. The strong effect of the ratio of the water solubilities of the monomers was illustrated

using a series of vinyl ester monomers in combination with MA. These MA-VEst monomer

combinations have similar reactivity ratios (chapter 3) and differ only in the water solubility

of the vinyl ester monomer. It was shown that minimum composition drift indeed could be

reached for MA-VEst combinations if the water solubility of the vinyl ester monomer was

low. The difference in water solubility of MA and V Ac was not large enough to compensate

the large difference in reactivity ratios between MA and V Ac. It becomes clear that, despite

of the similarity in reactivity ratios, the chemical composition distribution depends on the

selected monomer-to-water ratio and the water solubility of the vinyl ester monomer.

Apart from achieving a better understanding of composition drift and polymerization

rates through model development, in chapter 4 also efforts are made to monitor emulsion

copolymerization by on-line densimetry and on-line gas chromatography in order to improve

the quality and quantity of data on partial conversions of both monomers participating in the

emulsion polymerization. Using this combination of on-line techniques accurate information

of partial conversions was obtained as a function of time for the monomer combination MA

VAc.

Samenvatting

Samenvatting

Emulsiecopolymerisaties zijn complexe processen ten gevolge van het heterogene

karakter van het emulsiesysteem, dat bestaat uit een waterfase, een polymeerfase en

monomeerdruppels. Er bestaat er nog steeds een gebrek aan basiskennis ten aanzien van

kinetische processen in emulsie(co )polymerisaties. Een van de doelstellingen van dit onderzoek

is het ontwikkelen van een correct en eenvoudig model om de monomeerverdeling van twee

monomeren met een beperkte wateroplosbaarheid in een emulsiesysteem te beschrijven op een

dusdanige manier dat het gebruik van experimenteel moeilijk te bepalen en theoretisch

onduidelijk gedefmieerde interactieparameters vermeden kan worden. Een dergelijk model is

van groot belang indien men emulsiecopolymerisatieprocessen wil beschrijven met behulp van

parameters met fysische betekenis. In voorafgaand werk is aangetoond dat de molfracties

monomeer in de monomeerdruppels en polymeerdeeltjes identiek zijn en onafhankelijk van

de copolymeersamenstelling. Hiervoor is echter geen theoretische verklaring gegeven. In

hoofdstuk S worden de aannames besproken die gebruikt zijn om dit fenomeen te verklaren.

Verder worden eenvoudige relaties gegeven die de monomeer-verdeling in het emulsiesysteem

beschrijven met behulp van parameters met fysische betekenis, met andere woorden, bet

gebruik van interactie of variabele parameters kan vermeden worden.

Modellering gebaseerd op de relaties beschreven in hoofdstuk S geeft meer inzicht in

het effect van procesparameters zoals de monomeer-waterverbouding en bet polymeervolume

op de monomeerverdeling (hoofdstuk 6). Een gevoeligbeidsanalyse geeft aan dat de

reactiviteitsverboudingen de parameters zijn met de grootste invloed op het

samenstellingsverloop. De invloed van de wateroplosbaarheid van de monomeren is aileen

significant voor het samenstellingsverloop indien de boeveelheid monomeer opgelost in de

waterfase niet kan worden verwaarloosd ten opzicbte van de totale boeveelheid monomeer.

De polymerisatiesnelbeid is vooral afbankelijk van de maximale zwelbaarheid van polymeer

met monomeer.

In principe kan bet heterogene karakter van bet emulsiesysteem gebruikt worden om

de chemiscbe samenstellingsverdeling van bet gevormde copolymeer te beinvloeden. Een

tweede doelstelling van dit onderzoek is het verifieren van het concept dat een minimaal

Samenvatting

samenstellingsverloop bereikt kan worden voor monomeersystemen waarin bet beter oplosbare

monomeer tevens het meer reactieve monomeer is. Dit concept is experimenteel geverifieerd

voor de monomeercombinaties methylacrylaat-indene (MA-Ind: boofdstuk 7) en

methylacrylaat-vinylesters (MA-VEst: boofdstuk 8). Het is aangetoond dat een minimaal

samenstellingsverloop inderdaad bereikt kan worden over een breed traject van initiele

molfracties monomeer door simpelweg de monomeer-waterverhouding te varieren voor het

systeem MA-Ind. De sterke invloed van de verhouding van de wateroplosbaarheden van beide

monomeren wordt geYIJustreerd met bebulp van een serie van vinylesters in combinatie met

MA. Deze MA-VEst monomeercombinaties bezitten vergelijkbare reactiviteits-verhoudingen

(hoofdstuk 3) terwijl de wateroplosbaarheid van de vinyl esters sterk verschilt. Het is gebleken

dat een minimaal samenstellingsverloop behaald kan worden voor MA-VEst

monomeercombinaties waarin de wateroplosbaarheid van de vinyl ester laag is. V oor de

monomeercombinatie MA-V Ac is de afhankelijkheid van het samenstellingsverloop van de

monomeer-waterverhouding slecbts gering. In deze monomeercombinatie is het verschil in

wateroplosbaarheid blijkbaar niet groot genoeg om het grote verschil in reactiviteits

verhoudingen te compenseren. Duidelijk wordt dat, ondanks vergelijkbare reactiviteits

verhoudingen, de chemische samenstellingsverdeling van bet resulterende copolymeer

afhankelijk is van de geselecteerde monomeer-waterverhouding en de wateroplosbaarheid van

het vinylester monomeer.

Naast het verkrijgen van een dieper inzicht in samenstellingsverloop en

polymerisatiesnelheid door modellering en experimentele verificatie is in hoofdstuk 4 een

opstelling beschreven om kwalitatief en kwantitatief betere particle conversies van beide

monomeren in een emulsiecopolymerisatie te bepalen met behulp van on-line

gaschromatografie en on-line dichtheidsmetingen. Aangetoond is dat met behulp van deze

opstelling snel en accuraat partiele conversies als functie van de tijd bepaald kunnen worden.

Contents

Contents

Summary

Samenvatting

Chapter 1 Introduction

1.1 1.2 1.3 1.4

Short historic overview Background of the investigation Aim of the investigation Survey of this thesis References

Chapter 2 Theoretical background

2.1

2.2

Emulsion polymerization 2.1.1 Particle nucleation 2.1.2 Particle growth in emulsion polymerization Emulsion copolymerization References

Chapter 3 Experimental

3.1

3.2 3.3 3.4

Experimental (co )polymerization procedures 3.1.1 Purification of chemicals 3.1.2 Copolymerization reactions 3 .1.3 Determination of (partial) conversion Monomer partitioning Densimetry Determination of reactivity ratios by low conversion bulk polymerization References

Chapter 4 On-line gas chromatography and densimetry

4.1 4.2 4.3 4.4

Introduction Theory Experimental Results and Discussion 4.4.1 Density 4.4.2 Homopolymerization

1 2 3 4 6

1 1 8 9

II

13 13 14 15 16 18 19 26

27 29 31 33 33 34

4.5 4.4.3 Emulsion copolymerization of MA and V Ac Conclusions References

Chapter 5 Swelling of latex particles by two monomers

5.1 5.2

5.3

5.4

Introduction Theory 5.2.1 Saturation swelling of latex particles by two monomers 5.2.2 Partial swelling of latex particles by one monomer 5.2.3 Partial swelling of latex particles by two monomers Results and discussion 5.3.1 Monomer partitioning at saturation swelling of latex particles

by two monomers 5.3.2 Monomer partitioning at partial swelling of latex particles by

one monomer 5.3.3 Monomer partitioning at partial swelling of latex particles by

two monomers Conclusions References

Chapter 6 Model prediction of batch emulsion copolymerization

6.1 6.2

6.3

6.4

Introduction Theory 6.2.1 Saturation swelling of latex particles by two monomers:

determination of fpi 6.2.2 Partial swelling of latex particles by two monomers:

determination of fpi 6.2.3 Model calculations in emulsion copolymerization Results and discussion 6.3.1 General monomer partitioning considerations 6.3.2 Monomer partitioning of MA· V Ac monomer systems 6.3.3 Prediction of emulsion copolymerization composition Conclusions Appendix: sensitivity analysis

A-6.1 Introduction A-6.2 Results and discussion

A-6.2.1 Homo-monomer saturation concentrations A-6.2.2 Reactivity ratios A-6.2.3 Monomer and polymer densities

A-6.3 Conclusions References

Contents

39 43 44

45 47 52 54 54 56

57

59

60 63 64

65 67

68

70 73 75 76 78 82 84 86 86 87 88 93 94 95 96

Contents

Chapter 7

7.1 Introduction 7.2 Theory 7.3 Experimental

Monomer-to-water ratios as a tool in controlling emulsion copolymer composition

The methyl acrylate-indene system

7.4 Results and discussion 7.4.1 Optimization of recipe conditions 7.4.2 Model parameters 7.4.3 Composition drift in emulsion copolymerization of MA-Ind

7.5 Conclusions References

Chapter 8 The effect of water solubility of the monomers on composition drift in methyl acrylate-vinyl ester combinations

8.1 Introduction 8.2 Theory 8.3 Experimental 8.4 Results and discussion 8.5 Conclusions

References

Epilogue

List of sy~~~bols

Acknowledgement

Curriculum Vitae

97 99

101 102 102 103 105 112 114

115 117 118 119 124 126

127

130

133

134

Introduetion 1

Chapter 1 Introduction

1.1 Short historic overview

Emulsion polymerization is a free radical process starting from the dispersion of

a monomer in a continuous aqueous phase, commonly using an emulsifier and a water

soluble initiator. During an important part of the process the reaction system consists of

monomer droplets and monomer swollen polymer particles dispersed in the aqueous

phase. The fmal product, known as a latex, is a colloidal dispersion of polymer particles

in water.

The first attempts to perform emulsion copolymerization reactions were made

during World War I aiming at a synthetic substitute for natural rubber. Nowadays these

first attempts would be considered to be suspension polymerizations rather than

emulsion polymerizations. The first description of true emulsion polymerization

appeared in literature in 1927 in a patent granted to Dinsmore. 1 Luther and Heuck2•3

first described the use of emulsifier and initiator in emulsion polymerization. Good

overviews of early work in the field of emulsion polymerization are given by

Hohenstein and Mark4 and by Blacldey 5•

The commercial use of the emulsion polymerization process started in World

War II as a result of the Synthetic Rubber Program in the United States. Since then a

huge nmnber of papers have appeared on basic as well as applied aspects of emulsion

polymerization, indicating the general importance of the process.

Advantageous properties of the emulsion polymerization process include the good

heat transfer and, as a consequence good temperature control during reaction, the

possibility of reaching high conversions, the absence of toxic and flammable organic

solvents, and the possibility of producing high molecular weight copolymers at high

2 Chapter 1

polymerization rates. The resulting latices often can be used directly in coating, ink, and

adhesive applications. Application as elastomers, commodity and engineering plastics

becomes possible after polymer isolation. A disadvantage of the emulsion

polymerization process is the relatively poor film formation properties of the resulting

latex as compared with solvent based systems. Significant economic advantages can be

obtained by a better understanding of the basic principles of emulsion

(co)polymerization, since the latter will lead to better control of polymerization

reactions, in tum allowing fine-tuning of the process and the product performance in

terms of, amongst others, polymerization rates, molecular weight distributions, chemical

composition distributions, and particle morphology.

The first qualitative description of the kinetics of emulsion polymerization

reactions were reported by Harkins6 for the monomer styrene. Smith and Ewart7

developed a mathematical kinetic treatment that quantified the kinetic aspects of

emulsion polymerization for a number of limiting cases. After Smith and Ewart's early

work a large number of papers have been published dealing with modelling of emulsion

polymerization and copolymerization processes.

1.2 Background of the investigation

Although much research has been performed in order to achieve better

understanding of emulsion copolymerization, it is still relatively poorly understood.

Attempts to model emulsion copolymerization in terms of copolymer composition and

polymerization rates have been made by several investigators. 8•9•10

•11

•12

•13

•14

•15 For

this purpose existing basic theories for emulsion homopolymerization usually were

mathematically extended to emulsion copolymerization. The most widely used kinetic

model describing free radical copolymerization is the terminal model, also known as the

Mayo-Lewis16 or ultimate model. For most monomer combinations the copolymer

composition and the composition drift occurring during reaction can be fitted with this

terminal model. 17 Recently, however, many investigators mention the inability of the

terminal model to predict copolymerization rates. 18•19

•20

•21 .22 A model frequently

used to describe non-terminal behaviour of the kinetics is the penultimate model

developed by Fukuda et a/ .. 20 However, at least ten other models are also capable of

explaining the non-terminal behaviour. 16·'

8•22

•23

•24 Due to a lack of sufficiently accurate

experimental information model discrimination has not yet been possible.24•25

Furthermore, as a result of the complexity of the heterogeneous emulsion polymerization

Introduction 3

process until now most kinetic data are obtained from fitting semi·empirical models

resulting in values of the rate parameters that are nothing more than fitted estimations.

On behalf of correct model predictions of polymerization rates per particle in emulsion

homo·polymerization the values of all rate coefficients have to be known. In order to

predict overall polymerization rates also the number of particles needs to be known

since this overall polymerization rate is proportional to the particle number. In emulsion

copolymerization finding correct values for rate coefficients is even more complex.

As mentioned before, in most cases the copolymer composition can be well

predicted using the terminal model. However, the use of this model involves the

knowledge of the monomer concentrations of both monomers in the polymer particle

phase, where polymerization mainly occurs. These monomer concentrations in the

polymer phase can be calculated using relationships describing the monomer partitioning

over the polymer particle, the monomer droplet and the aqueous phases. In the literature,

an empirical and a thermodynamic approach have been proposed for describing

monomer partitioning.8•9

•10·u·12

•13

•14

•15 Disadvantages of these approaches are the lack of

theoretical background,8•9•10

•11

•12 and the use of interaction parameters 14

•15

.26 which are

experimentally hard to determine and theoretically rather vague.

From the above discussion follows the great importance of the availability of

simple relationships that correctly predict monomer concentrations in the polymer phase

since this forms the basis of all models predicting (instead of fitting) copolymer

composition and rates of copolymerization.

1.3 Aims of the investigation

After the above general introduction into the field of emulsion copolymerization

it will be clear that there is still a lack of knowledge of the basic processes governing

emulsion copolymerization kinetics. The first aim of this investigation is the

development of a reliable and simple model to describe monomer partitioning of two

monomers with limited water solubility in an emulsion system, in such a way as to

avoid the use of interaction parameters that are experimentally difficult to access and

theoretically rather vague. For the investigation of monomer partitioning between the

monomer droplet, polymer particle, and aqueous phases, the monomer combination

methyl acrylate-vinyl acetate was selected. In this system both monomers have a

relatively high water solubility making accurate water phase analysis by gas

chromatography possible for each monomer. Model development based on these new

4 Chapter 1

relationships opens possibilities of a better understanding of the effects of process

parameters, e.g. the monomer-to-water ratio and the polymer volume, on monomer

partitioning. A sensitivity analysis of the model will reveal the effects of varying model

parameters (maximum swellability, water solubility, reactivity ratios, and density values)

on the predictions of composition drift and polymerization rates.

In principle the heterogeneity of the emulsion system constitutes a new and

unique parameter to adjust the chemical composition distribution of the copolymer.

Theoretically, minimum composition drift can be obtained for those monomer

combinations in which the more water soluble monomer is also the more reactive one.

The second aim in this investigation is the experimental verification of this concept for

the monomer combination methyl acrylate-indene. Furthermore, the effect of different

monomer water solubilities on composition drift was investigated for the emulsion

copolymerization of methyl acrylate with a series of vinyl esters; viz. vinyl acetate, vinyl

2,2-dimethyl-propanoate, and vinyl 2-ethylhexanoate. These monomer combinations are

ideal for studying the effect of water solubility since the reactivity ratios· are very similar

for the three monomer combinations.

The third aim of this investigation . is increasing the quality and quantity of

experimental data by developing on-line techniques based on on-line densimetry and on

line gas chromatography, for detailed monitoring of emulsion copolymerization.

1.4 Survey of this thesis

In Chapter 2 the basic theoretical aspects of emulsion copolymerization are

briefly discussed.

In Chapter 3 experimental methods used in the study of emulsion

copolymerization are presented. The monomer partitioning experiments needed for

model development are described as well as the determination of the water solubility of

the monomers and of the maximum swellability of the monomers in polymer.

Furthermore, the determination of the relevant monomer reactivity ratios and of the

density of monomer and (co)polymer, needed for model predictions, are outlined.

In Chapter 4 the set-up for on-line densimetry and gas chromatography is given.

Also, the results obtained with these techniques are presented and evaluated.

Monomer partitioning relations for the swelling of two monomers in emulsion

systems at saturation swelling are described in Chapter 5. In addition, relationships for

partitioning of two monomers at partial swelling are derived.

Introduction 5

In Chapter 6 a model is developed to predict the course of emulsion

copolymerization as a function of conversion based on mass balance equations and

monomer partitioning relationships as described in Chapter 5. A sensitivity analysis for

this model is performed using the styrene-methyl methacrylate monomer combination as

an example. The sensitivity of the model to the various parameters is discussed.

The use of monomer-to-water ratios as a tool in controlling emulsion

copolymerizations is depicted in Chapter 7 for the monomer combination methyl

acrylate-indene. In this chapter theoretical predictions of minimum composition drift as a

function of monomer-to-water ratio are compared with experimentally observed data of

emulsion copolymerizations showing minimum composition drift.

In Chapter 8 the effect of different water solubility values of the monomers on

composition drift is presented for the copolymerization of methyl acrylate with a series

of vinyl esters of decreasing water solubilities, viz. vinyl acetate, vinyl 2,2-dimethyl

propanoate, and vinyl 2-ethylhexanoate.

In the Epilogue the results and their impact on future developments will be

evaluated against the background of the above aims.

Parts of this work have been presented at the Gordon Research Conference on

Polymer Colloids (Irsee, Germany, September 1992), the 8th International Conference

on Surface and Colloid Science (Adelaide, Australia, February 1994), and the 3th

International Symposium on Radical Copolymers in Dispersed Media (Lyon, France,

April 1994)

Parts of this thesis have been published or will be published soon: the

determination of the reactivity ratios presented in chapter 3,27•28 the determination of

partial conversion of two monomers in batch emulsion copolymerization by on-line

densimetry in combination with on-line gas chromatography described in chapter 4,29

the monomer partitioning work of chapter 5,30.3

1 the model development 32 and

sensitivity analysis33 described in chapter 6, the work in chapter 7 on achieving

minimum composition drift by adjusting monomer-to-water ratios,23 and the work in

chapter 8 on the effect of water solubility on composition drift in methyl acrylate-vinyl

.ester emulsion copolymerization.34 Furthermore, related work that was considered

beyond the scope of this thesis, viz. the determination of maximum swellabilities using

conductivity measurements/5 and work on the determination of the average number of

growing chains per particle for MMA-Sty emulsion copolymerizations as a function of

particle size, copolymer seed composition and initiator concentration, 36 has been

published or will be published soon.

6 References

I. US 1,732,795 (1929), The goodyear Tire & Rubber Co., lnv.: R. P. Dinsmore 2. US 1,860,681 (1932), !.G. Farbenindustrie A.G., Inv: M. Luther, C. Heuck 3. US 1,846,078 (1932), !.G. Farbenindustrie A.G., lnv: M. Luther, C. Heuck 4. W. P. Hohenstein, H. Mark, J Polym. Sci., 127, 549 (1946) 5. D.C. Blackley, In Emulsion Polymerisation - Theory and Practice, Applied

Publishers Ltd, London 1975, p 26-35 6. W.D. Harkins, J. Am. Chem. Soc., 69, 1428 (1947) 7. W.V. Smith, R.H. Ewart, J. Chem. Phys. 16, 592 (1948) 8. M. Nomura, K. Fujita, Macromol. Chem., Suppl., 10/11, 25 (1985) 9. M. Nomura, I. Rorie, M. Kubo, K. Fujita, J. Appl. Polym. Sci., 37, 1029 (1989) 10. G.H.J. van Doremaele, A.H. van Herk, A.L. German, Polymer International, 27,

95 (1992) 11. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L.

German, Polymer, 33, 1914 (1992) 12. G.H.J. van Doremaele, H.A.S. Schoonbrood, l Kurja, A.L. German, J Appl.

Polym. Sci., 45, 957 (1992) 13. M.J. Ballard, D.H. Napper, R.G. Gilbert, J Polym. Sci., Polym. Chem. Ed, 19,

939 (1981) 14. J. Guillot, Makromol. Chem., Suppl, 10111, 235 (1985) 15. J. Forcada, J. M. Asua, J. Polym. Sci., Polym. Chem. Ed, 28, 987 (1990) 16. F.R. Mayo, F.M. Lewis, JAm. Chem. Soc. 66, 1594 (1944) 17. J. Bandrup, E.H. lmmergut, Polymer Handbook, 3rd ed., Wiley, New York 1989 18. T. Fukuda, Y-D. Ma, H. Inagaki, Polym. J, 14, 705 (1982) 19. D.J.T. Hill, J.H. O'Donnell, P.W. O'Sullivan, Macromolecules, 17, 3913 (1982) 20. T. Fukuda, Y-D. Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 21. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, Macromolecules, 22,

2785 (1989) 22. H.J. Harwood, Makromol. Chem., Makromol. Symp., 10/11, 331 (1987) 23. J. Barton, E. Borsig, Complexes in Free Radical Chemistry, Elsevier, Amsterdam

1988 24. LA Maxwell, A.M. Aerdts, A.L. German, Macromolecules, 26, 1956 (1993) 25. G. Moad, D.H. Solomon, T.H. Spurling, R.A. Stone, Macromolecules, 22, 1145

(1989) 26. M. Morton, S. Kaizermann, M. W. Altier, J Colloid Sci., 9, 300 (1954) 27. L.F.J. Noel, J.L. van Altveer, M.D.F. Timmermans, A.L. German, in press by J

Polym. Sci., Polym. Chem. Ed., xx, xx (1994) 28. L.F.J. Noel, J.M.A.M. van Zon, A.L. German, J Appl. Polym. Sci., 51, 2073

(1994) 29. L.F.J. Noel, E.C.P. Brouwer, A.M. van Herk, A.L. German, to be submitted to J

Appl. Polym. Sci. 30. L.F.J. Noel, LA. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 31. LA. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol. Chem.,

Theory Simul., 2, 269 (1993) 32. L.F.J. Noel, J.M.A.M. van. Zon, LA. Maxwell, A.L. German, J. Polym. Sci.,

Polym. Chem. Ed, 32, 1009 (1994) 33. L.F.J. Noel, I.A. Maxwell, W.J.M. van Well, A.L. German, J Polym. Sci.,

Polym. Chem. Ed. 32, 2161 (1994) 34. L.F.J. Noel, J.L. van Altveer, A.L. German, in preparation 35. L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.M. van Herk, A.L. German, to

be submitted to J. Colloid Sci. 36. L.F.J. Noel, W.J.M. van Well, A.L. German, in preparation

Theoretical baekground 7

Chapter 2 Theoretical background

Abstraet: In this chapter the basic tbeoretieal aspects of emulsion (co)polymerization kineties relevant to this investigation are briefly discussed. It becomes clear that the emulsion process is essentially different from homogeneous processes. Important features are the kineties of emulsion (eo)polymerization, monomer partitioning and the terminal copolymerization modeL

2.1 Emulsion polymerization

The batch emulsion polymerization process can be divided into three distinct intervals

according to the Harkins-Smith-Ewart theory. 1.2 In interval I free radicals are generated

in the aqueous phase nucleating new particles until the end of interval I. In intervals II and

III ideally the particle number remains constant. During interval II the polymerization, which

is assumed to occur in the polymer particle phase, proceeds in the presence of monomer

droplets. In interval II the polymer particles are saturated with monomer leading to a

(sometimes) constant polymerization rate in emulsion homo-polymerizations. In interval III

the monomer concentration in the particle phase will decrease leading to increasingly lower

polymerization rates. Intervals II and III are known as the particle growth stages.

2.1.1 Particle nucleation

Particle nucleation in emulsion polymerization is a phenomenon that is still not well

understood although many investigations have been carried out on the subject. The theories

describing particle nucleation can be divided into two main categories depending on the main

locus of nucleation: (1) micellar nucleation involving the monomer swollen micelles, 1•2 and

(2) homogeneous or coagulative nucleation.3·45

·6

8 Chapter 2

According to the first mechanism radicals that are generated in the aqueous phase

enter monomer swollen micelles and initiate polymerization leading to mature monomer

swollen polymer particles. Due to the large total surface area of the micelles as compared

with the monomer droplets, normally no nucleation occurs in the monomer droplets. When

all micelles have disappeared the particle nucleation is ended approximately.

In case the emulsifier concentration is below the critical micelle concentration or in

the absence of emulsifier a stable latex can still be formed.5•7•8•9

•10

•11

•12 This can be

explained by the so-called homogeneous nucleation model5•6

•13 which states that radicals

generated in the aqueous phase react with solubilized monomer to form growing oligomeric

species. At a critical length at which the oligomers exceed their solubility or become surface

active, the oligomers will precipitate. The precipitated oligomeric chains absorb monomer

and emulsifier to form colloidally unstable precursor particles, which flocculate with each

other or with already existing mature latex particles.

2.1.2 Particle growth in emulsion polymerization

In interval II the polymeric particles have a constant and maximum monomer

concentration as a result of the presence of monomer droplets from which monomer diffuses

through the water as a medium towards the particles at a constant rate. In emulsion homo

polymerization this leads to constant polymerization rates during interval II. In interval III

the polymerization mte will decrease due to decreasing monomer concentration in the

polymer phase. However, increased polymerization rates can be observed due to the

Trommsdorff effect. The rate of polymerization (~ in mohhnw·3·s· 1) in emulsion homo

polymerization during intervals II and III is given by:

RP kP n N [MJP (2.1) N,.

where k., is the propagation rate coefficient (dm3·mol"1·s·1), ii the average number ofmdicals

per particle, [M]P the monomer concentration in the polymer particle phase {mol·dm-3), N

the number of particles per dm3 water and N.v is Avogadro's number (mol-1). The number

of particles, N, is mainly determined by the amount of initiator and emulsifier and dependent

on the kind of monomer. In ab initio reactions low reproducibility of the particle number

is obtained. Therefore, kinetic studies usually are started from a polymer seed, i.e.,

preformed polymer particles, in order to guarantee constant and known particle numbers.

Theoretical background 9

2.2 Emulsion copolymerization

The course of emulsion copolymerization depends mainly on the monomer reactivity

ratios and on the partitioning behaviour of the two monomers between the various phases

of the emulsion system. The knowledge of the concentrations of both monomers in the

polymer particle phase, where the polymerization is assumed to take place, is essential for

the correct use of kinetic models. As a result of monomer partitioning the monomer mole

fraction in the polymer particle phase can be different from the overall monomer mole

fraction. The terminal model14•15 is the model most often used to describe

copolymerization kinetics, the sequence distribution, and the chemical composition of the

copolymers prepared in homogeneous systems such as bulk and solution polymerization.

In this model the monomer addition rate depends on the nature of the terminal group only

and therefore obeys first order Markov Statistics. 16 The copolymerization scheme of the

terminal model is given in Table 2.1.

Table 2.1 Copolymerization scheme according to the terminal model

terminal group added monomer rate final

-M;• [M]; k;;[M•];[M]; -M;M,•

-M;• [M]; k;i[M•];[M]1 -M;Mj•

-Ml [M]; ki;[M•]JM]1 -M_M;•

-Mi• [M]i ~[M•]JM]1 -M_MJ•

The reactivity ratios of monomer i and j are defined as r; = k;/k;i and ri ~

respectively, where k;i is the propagation rate constant of the propagation step between

radical i and monomer j. The instantaneous copolymer composition in mole fraction of

monomer i units (F;) is given as a function of the reactivity ratios and the monomer

composition in the reaction mixture by the instantaneous copolymerization equation: 14•15

F, (2.2)

where ±: and ~ are the actual mole fractions of monomers i and j in the reaction mixture.

The average propagation rate constant (kp) is given by17

10

rJi + 2 JJ; + ri ./] r1 f/k11 + ri J]kjj

Chapter 2

(2.3)

It has been shown for most copolymer systems that the copolymer composition is well

predicted using this terminal model. 13 However, for several monomer systems the mean

propagation rate coefficient of copolymerization was found not to obey the terminal

model. 19•20 This deviation has been explained by invoking the penultimate model for

copolymerization,21 in which the penultimate group of the free radical chain end is

considered to affect its reactivity. In order to accommodate the fact that composition is well

predicted by the terminal model a 'restricted penultimate model' was adopted,22.23 which

reduces to the terminal model when considering copolymer composition only. However,

it should be noted that other models are also capable of explaining the non-terminal

behaviour of the rate of polymerization in copolymerization. 14•24

.25

When using the experimentally determined average propagation r;rte constant, ~.

instead of a homopolymerization rate coeffici~nt, ~in equation 2.1, the same relationship

may be used to describe the rate of polymerization in emulsion copolymerization. However,

it should be noted that theoretical predictions of the average number of growing chains per

particle in copolymerizations is even more complex than in the case ofhomopolymerization

since entry, exit, transfer and termination of radicals may depend on cross-transfer and cross

propagation coefficients which have to be taken into account. In emulsion copolymerizations

the polymerization rate does not have to remain constant in interval II since ~ ii, and [M]P

may change as a function of conversion if composition drift occurs.

Referenees 11

l. W.D. Harkins, J. Am. Chern. Soc., 69, 1428 (1947) 2. W.V. Smith, RH. Ewart, J. Chern. Phys., 16, 592 (1948) 3. W.J. Priest, J. Phys. Chern., 56, 1077 (1974) 4. G. Lichti, R.G. Gilbert, D.H. Napper, J. Polym. Chern., Polym. Chern. Ed, 21, 269

(1983) 5. A.R Goodall, M.C. Wilkinson, J. Hearn, J. Polym. Sci., 15, 2193 (1977) 6. R.M. Fitch, C.H. Tsai, In Polymer Colloids, Plenum Press, New York 1971 7. J.M. Willes, lndust. and Eng. Chern., 41(10), 2272 (1947) 8. J.W. Goodwin, J. Hearn, C.C. Ho, R.H. Ottewill, Br. Polym. J., 5, 347 (1973) 9. J.W. Goodwin, J. Hearn, C.C. Ho, RH. Ottewill, Col. Polym. Sci., 252, 464 (1974) 10. D. Munro, A.R. Goodall, M.C. Wilkinson, K. Randle, J. Hearn, J. Col. Interface. Sci.,

68, I (1979) 11. J.W. Goodwin, R.H. Ottewill, R. Pelton, G. Vianello, D.E. Yates, Br. Polym. J., 10,

173 (1978) 12. Z. Song, G.W. Poehlein, J. Col. Interface Sci., 128, 501 (1989) 13. P.J. Feeney, D.H. Napper, R.G. Gilbert, Macromolecules, 17, 2520 (1984) 14. F.R Mayo, F.M. Lewis, J. Am. Chern. Soc., 66, 1594 (1944) 15. T. Alfrey, G. Goldfinger, J. Chern. Phys., 12, 205 (1944) 16. J.L. Koenig, In Chemical Microstructure of Polymer Chains, John Wiley and Sons,

New York 1980 17. T. Fukuda, Y-D. Ma, H. Inagaki, Makromol. Chern., Suppl., 12, 125 (1985) 18. J. Bandrup, E.H. Immergut, Polymer Handbook, 3rd ed., Wiley, New York 1989 19. T. Fukuda, Y-D. Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 20. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, Macromolecules, 22, 2785

(1989) 21. E. Merz, T. Alfrey, G. Goldfinger, J. Polym. Sci., 1, 75 (1946) 22. T. Fukuda, Y-D. Ma, H. Inagaki, Polym. J., 14, 705 (1982) 23. T. Fukuda, Y-D. Ma, H. Inagaki, Makromol. Chern. Rapid Commun., 8, 495 (1987) 24. D.J.T. Hill, J.H. O'Donnell, P.W. O'Sullivan, Macromolecules, 17, 3913 (1982) 25. H.J. Harwood, Makromol. Chern., Makromol. Symp., 10/11, 331 {1987)

12 Chapter 2

Experimental 13

Chapter 3 Experimental

Abstract: In this chapter the experimental procedures and set-up for 116 initio emulsion (co)polymerizations is described. The reactions were monitored by gravimetry and gas chromatography resulting in partial conversion data ofbotla monomers. The determination of the parameters needed for model predictions are described. These comprise the description of monomer partitioning experiments (water solubility and swellability of monomer in polymer), densimetry (monomer and polymer density) and low conversion balk polymerization (reactivity ratios).

3.1 Experimental (co)polymerization procedures.

3.1.1 Purification of chemicals

The following materials were used for emulsion (co )polymerization, monomer

partitioning experiments and for determination of the density: reagent-grade methyl aaylate

(MA, Janssen Chimica, Tilburg, The Netherlands), styrene (S, Merck, Darmstadt, Germany),

vinyl acetate (V Ac, Janssen Chimica, Tilburg, The Netherlands), vinyl 2,2-dimethyl

propanoate (VPV, product names VEOV A-5, Shell Research and Vynate NE0-5, Union

Carbide Corporation), vinyl 2-ethylhexanoate (V2EH, product name Vynate 2EH, Union

Carbide Corporation), and indene, tech., 90+% (lnd, Janssen Chimica, Tilburg, The

Netherlands), doubly distilled water, sodium persulphate (NaPS, p.a., Fluka AG, Buchs,

Switzerland) and 2,2'-azobis(2-methylpropionitrile) (AIBN, Janssen Chimica, Tilburg, The

Netherlands) as initiators, sodium dodecyl sulphate (SDS, Fluka AG, Buchs, Switzerland)

and Antarox C0-990 (Ant C0-990, C9HwC4H60(CH2CHP)100H, GAF, Delft, The

Netherlands) as surfactants, and sodium carbonate (Na2C03, p.a., Merck, Darmstadt,

Germany) as buffer. Before use, the MA, VAc, VPV, and V2EH were distilled under

reduced pressure to remove the inhibitor. The middle fraction was cut and stored at 4°C.

14 Chapter 3

The indene which was only 90% pure and contained some polymerizable components was

purified by shaking 0.5 dm3 indene with 0.4 dm3, 6M HCL for 24 h in order to remove basic

nitrogenous material, then refluxed with 40% NaOH for 2 h to remove benzonitrile.

Extraction by n-hexane was followed by washing with water (three times), drying with

MgS04 and evaporation of the n-hexane. Fractional distillation under reduced pressure is

repeated until gas chromatography showed that indene fractions of purities higher than 98%

were obtained. Gas chromatography in combination with mass spectroscopy (GC-MS)

showed that the amount of polymerizable impurities were negligible ( undecene concentration

< 0.03%). It was concluded that at this point the indene was sufficiently purified to be used.

The indene is stored under argon at 4°C. To prevent polymerization during the monomer

partitioning experiments, in these cases MA and V Ac were applied as received and some

inhibitor (hydroquinone) was added to the indene after its purification. The calibration of

the density cell was performed using doubly deionized water and toluene (p.a., Merck,

Darmstadt, Germany).

3.1.2 Copolymerization reactions

Emulsion polymerizations were performed under nitrogen atmosphere in a 1.3-dm3

stainless steel reactor equipped with four baffles at 90° intervals and with a six-bladed

turbine impeller. The impeller speed was between 200 and 300 rpm. In Figure 3.1 a cross

section of the reactor is shown. All batch emulsion (co )polymerizations for seed preparation

or for the study of copolymerization behaviour in terms of composition drift or

polymerization rate were performed in this or similar reactors.

Reactor dimensions in mm:

turbine position (from top) 120

turbine diameter 60

blade diameter 18

blade height 15

reactor diameter 96

baffle diameter 13.4

reactor height 205

Figure 3.1: Cross-section (}{the reactor used for emulsion (co)polymerizations

Experimental 15

All MA-VAc, MA-VPV, and MA-V2EH emulsion polymerizations were performed

at 50°C for 8 h using SDS as surfactant. On behalf of the application of the resulting seed

for monomer partitioning purposes, the temperature was raised to 80°C for 15 h to reach

high conversion and to dissociate any residual initiator. The MA-Ind copolymerizations were

performed at 70°C for 12 h using non-ionic Ant C0-990 as surfactant.

All reactions performed to study copolymerization behaviour in terms of composition

drift or polymerization rate were monitored by gravimetry to obtain conversion-time curves

and by gas chromatography to determine the overall monomer ratios as a function of time.

For off-line purposes a Hewlett Packard (HP) 5890A gas chromotograph was used in

combination with a HP 3393A integrator, a HP 7673A automatic sampler and a capillary

HP-5 column (crosslinked 5% Ph. Me. Silicone; 30m x 0.53 mm x 2.65 J.lm). Combining

results of gravimetry and gas chromatography yields the partial conversion of both

monomers in the copolymerization reaction. Monitoring emulsion reactions off-line at the

end of each reaction is a very laborious method. Although the results given in chapters 5-8

have been obtained off-line, effort has been put into developing an accurate and fast on-line

method to determine the partial conversions of the separate monomers in the emulsion

copolymerization. For this purpose the standard reactor shown in Figure 3.1 is equipped with

an on-line densimeter, capable of monitoring overall weight conversion, and an on-line gas

chromatograph, capable of monitoring the overall ratios of the residual monomers. The use

of this new combination of on-line teclmiques makes fast monitoring of the monomer

concentrations possible, thus allowing process control (e.g. reaction heat) as well as product

control (e.g. composition drift). The configuration developed for on-line monitoring and the

results obtained using this set-up are described in more detail in chapter 4.

3.1.3 Determination of (partial) conversion

The total overall conversion x101(t) can be determined by gravimetry using the

following equation:

x,.,(t) (3.1)

where DS(t) is the dry solids content at time t determined by weighing the latex mass of

a sample before and after drying (% ), M1 is the total mass of the emulsion mixture, Mmon

is the mass of the initially added monomers, and M., is the mass of the non-polymerizable

and non-evaporative components as the initiator, the buffer and the surfactant. Contrary to

homo-polymerizations where measuring the conversion is sufficient to describe the total

16 Chapter 3

course of the reaction, in copolymerizations two independent measuring techniques must

be used. For this purpose gas chromatography of a (diluted) sample taken during reaction

was used to determine the overall ratio of the residual monomers as a function of reaction

time. Combining the conversion and overall monomer ratio allows calculation of the partial

conversion of both monomers in emulsion copolymerization as a function of time or

conversion according to eqs 3.2 and 3.3.

x., = 1 - (Mio + Mio) . (1 - xto,,t ) J, Mjo(l + 1/qj/i,t)

(3.2)

x. = 1 - (Mio + Mi) . (1 - xtot,t ) 1,1

(3.3)

where xi.'' xi,t• and x..,.(t) represent the partial conversion of monomers j and i and the total,

overall conversion at timet, respectively, ~o and Mio represent the initial mass of monomers

i and j at the beginning of the reaction and qyi,t represents the overall ratio of monomer j

over i at timet. Combining conversion (X.01(t)) and gas chromatography (<Iy~J results in the

partial conversions of the separate monomers as a function of time. The residual monomer

concentrations in the reaction mixture can be determined directly from gas chromatography

by adding an internal standard to the reaction samples. This alternative approach to calculate

the partial conversion of both monomers was used to estimate the accuracy of the above

described method of determining partial conversions. Excellent agreement is obtained for

MA-Ind emulsion copolymerizations (chapter 7: Figure 7.3) when comparing conversion

results determined by gravimetry with those from gas chromatography.

3.2 Monomer partitioning

Seed preparation: The seed latices used in the monomer partitioning experiments were

prepared under conditions similar to the batch emulsion copolymerizations described in

section 3.1.2. The recipes for the MA-V Ac and MA-Ind seeds used in monomer partitioning

experiments with their respective monomers are given in Table 3.1. Before using the seed

latices for monomer partitioning experiments, the latices were dialysed in a membrane tube

to remove excess surfactant, initiator, buffer, and monomer. The dialysis water was changed

every 2 h until the conductivity of the water surrounding the membrane tube remained

constant in time at a value close to the value of distilled water. After this, the solids content

was determined by gravimetry, the mole fraction of monomer unit MA (FMA) in the polymer

Experimental 17

was determined by 1H-NMR, and the weight average particle diameter was determined using

dynamic light scattering (Malvern Autosizer lie 90° fixed angle at 25°C. The sample

preparation consisted of latex dilution followed by filtering). The particle size and solids

content of the latices used for monomer partitioning experiments are collected in Table 3.1.

Table 3.1: Emulsion copolymerization recipes (in grams), particle size (nm) and solids content (%) of latices used in monomer partitioning experiments.

Ingredient MA-VAc MA-Ind

MA 80 26.68 VAc 80 Ind 34.53

water 800 599.1

SDS 1.317

Ant C0-990 20.806

N~C03 0.141 0.660

NaPS 0.256 3.534

d,. 90 30

solids content 16.50 10.40

Monomer partitioning experiments: Monomer partitioning experiments were performed

using the ultracentrifuge method. 1•2 A latex with known solids content was mixed with

known amounts of monomer at the desired temperature in the absence of initiator.

Equilibrium was reached within 24 h of shaking. The polymer particle, monomer droplet

(at saturation swelling) and aqueous phases, were separated using an ultracentrifuge (45000

rpm Centrikon T-2060, 1-2 h, maximum centrifugal force is 2·107 mmin.2) at the desired

temperature (the maximum centrifugation temperature is 45°C). The concentrations of MA,

VAc, and Ind in the aqueous phase were determined by gas chromatography (GC) using

2-propanol as internal standard for MA and V Ac, and acetone as internal standard for Ind.

Assuming that (I) the volumes of monomer and polymer are additive, and (2) the copolymer

density is a linear function of the mole fraction of the monomer units, the monomer content

in the polymer particles was determined from mass balance calculations for partial swelling.

At saturation swelling a separate droplet phase prevents determination of the monomer

content in the polymer particles by mass balance considerations. Monomer concentrations

in the particles were then determined by GC after dissolving the monomer-swollen polymer

phase in toluene with 2-propanol as internal standard for MA-V Ac and MA-Ind.

18 Chapter 3

Determination of the dry solids content of the sample gave the polymer content, which was

needed to make corrections for the amount of aqueous phase within the polymer phase. The

monomer droplet phase was analyzed by GC in terms of monomer ratios for the MA-V Ac

monomer partitioning experiments.

Due to temperature limitations of the ultracentrifuge, the ultracentrifugation method

could not be used above 45°C. The maximum water solubilities at temperatures higher than

45°C where determined using a densimeter forMA and V Ac (see chapter 4), and using gas

chromatography for Ind. The Ind concentration at 70"C in the aqueous phase was determined

by taking a sample from the saturated aqueous phase of a thermostated water-indene mixture

at equilibrium with complete phase separation, using an acetone solution as internal standard.

The maximum swellabilities in the polymer phase ([M]p,sat(h) in mol'<inf3) and the water

solubility ([M].,sa~(h) in mol-dm'3) at various temperatures for several monomers in their

respective copolymers are shown in Table 3.2.

3.3 Densimetry

The measuring principle of the densimetry instrument is based on the change of the

frequency of a vibrating U-shaped sample tube, which is statically filled with sample liquid

or through which the sample flows continuously. The relationship between the period of

oscillation of the sample tube, T, and the density, p, is given by:

p _!_ (T2 - B) A

(3.4)

where A and B are the temperature dependent instrument constants which are determined

by calibration with fluids (toluene and water) of known density.

Densimetry was performed using a thermostated Anton Paar DMA 10 density cell.

The density of monomers or solutions can be calculated directly from the oscillation period

of the sample tube and the calibration constants using eq. 3.4. In order to obtain accurate

density values of (co)polymers all latices are diluted (to prevent coagulation) and degassed

at the same temperature as the statically density determination was performed. The

(co )polymer density can be calculated from the latex density and the solids content of the

diluted latex using the following equation: 3

(3.5)

where xP and x,. are the mass fractions of the polymer and serum (aqueous phase including

Experimental 19

dissolved initiator, surfactant, and buffer) which can be calculated from the solids content,

and p1, pP, and Ps represent the density of the total diluted latex, the (co)polymer, and the

serum, respectively.

Table 3.2: Homo-monomer saturation concentrations forMA, VAc, VPV, V2EH, and lnd detennined at several temperatures (C).

Monomer/(T'C)

MA (20°C) MA (50°C)

MA (70°C)

VAc (20°C)

VAc (50°C)

VPV (20°C)

V2EH (20°C)

Ind {20°C)

Ind (70°C)

7.05" 0.60" 0.55b

0.53b

6.11" 0.30" 0.28b

4d 7.3 •10"3 c

2.5d 0.23 •10"3 c

2.9" 2.8·10"3 •

2.8·10"3•

a determined by the ultracentrifugation method b determined by densimetry c = gas chromatography determination of the saturated aqueous phase of

a water-monomer mixture d solids content determination of the polymer phase

3.4 Determination of reactivity ratios by low conversion bulk polymerization

Accurate reactivity ratios are needed to predict the course of copolymer composition

in emulsion copolymerization as a function of conversion. For monomer combinations like

MA-Ind which have not been extensively studied, low conversion bulk copolymerizations

have to be performed to determine reliable reactivity ratios. The bulk copolymerizations were

carried out in 20 cm3 bottles thermostated at 70°C (MA-lnd). The reaction mixtures were

magnetically stirred. The reaction mixture consisted of 20 g of monomer with different

monomer mole fractions going from 10% to 90% MA, and 0.1 g AIBN as initiator. The

reactions were stopped at low conversion(< 3%) to prevent composition drift. The resulting

copolymer compositions were determined by 'H-NMR. Figure 3.2 depicts a typical example

of a 400-MHz 1H-NMR spectrum of low-conversion bulk MA-Ind copolymers dissolved

in CDC13 at 25°C. The average copolymer composition (mole fraction MA: FMA) can be

calculated with the following formula: FMA

2B- 2A 2B +A

(3.6)

20 Chapter 3

where A and B represent the total peak area of the aromatic (4 H oflnd) and aliphatic (4

H of lnd and 6 H of MA) protons, respectively.

A B

......... ---.----, -·-··~- .... ..,_......, "•·~--..--.. ·~~--·,-··~~.,

8 7 6 3 2

ppm

Figure 3.2: A 400 MHz 1 H-NMR spectrum typical of a MA-Ind copolymer dissolved in CDC/3 at 25°C. A and B stand for the total peak areas in the aromatic and aliphatic regions, respectively.

1.00

0.1S

J o.so

0.2S

0.00 0.00 0.2S o.so 0.1S 1.00

fMA

Figure 3.3: Comparison of the initial monomer composition-polymer composition data predicted with the instantaneous copolymer equation using the reactivity values of rw = 0.92 and r1nd 0.086 (- - -) and experimentally determined data from low conversion bulk polymerizations (o).

Experimental 21

Table 3.3: Low conversion bulk copolymerization data of MA-Ind copolymerizations at 7(J'C. F MA.cvk is calculated with the instantaneous copolymer equation using the reactivity ratios rMA = 0.92 and r1m~ 0.086

initial monomer fraction copolymer composition copolymer composition fMA F MA.experimenral FMA,calc

0.105 0.393 0.379 0.210 0.483 0.478

0.308 0.534 0.537

0.405 0.585 0.587

0.510 0.642 0.641

0.606 0.700 0.694

0.655 0.726 0.723

0.711 0.766 0.758

0.804 0.825 0.823

0.903 0.904 0.904

The reactivity ratios were determined by non-linear optimisation 4•5 of the initial monomer

mole fraction-copolymer composition data summarized in Table 3.3. When calculating

reactivity ratios with this non-linear optimisation method, errors in both the initial monomer

composition (estimated to be I%) and the copolymer composition (estimated to be 5%) are

taken into account. This results in the following reactivity data: rMA = 0.92 ± 0.16 and rind

0.086 ± 0.025. When using these reactivity ratios the initial monomer mole fraction

copolymer composition relation can be described theoretically using the instantaneous

copolymer equation (eq 2.2). Comparison of the experimental results with the theoretical

prediction of the instantaneous copolymer equation gives good agreement as can be seen

in Figure 3.3 and Table 3.3. This indicates that reliable values for the reactivity ratios for

MA-Ind have been obtained.

For more common monomer combinations like MA-V Ac and methyl methacrylate

styrene (MMA-S), the reactivity ratios may be found in the literature. 6.7 Although only

small differences in reactivity ratios have been observed in vinyl acetate-vinyl esters (V Ac

VEst) copolymerization reactions (rvAc "' rvEs1), composition drift occurring in

copolymerization reactions of an acrylic monomer such as MA with V Ac may be affected

by replacing V Ac by another vinyl ester. Since acrylic polymers are often used in various

applications, it is important to know whether or not the reactivity ratios of MA with vinyl

esters can be approximated by the reactivity ratios of MA and V Ac. For this reason the

reactivity ratios ofMA-VEst have been determined for V Ac, vinyl 2,2-dimethyl-propanaoate

(VPV), and vinyl 2-ethylhexanoate (V2EH) at 50°C in a similar way as described above for

22 Chapter 3

the system MA-Ind.

The general structure of the MA-VEst copolymers is given by:

-+rH-CH2-t-)x-+-( yH~CH2T

O=r ? 0 O=C I •• Rl

CH3

In this structural formula the left hand side group (x) represents the MA units and the right

hand side group (y) represents the vinyl ester units in the copolymer. The R-group in the

structural formula stands for the CH3, C4f4, and C7H15 group, respectively.

The reactivity ratios of MA-VAc copolymerizations have been determined before

by several investigators using different copolymer analysis methods, for example polymer

hydrolysis followed by acetic acid determinations, 8 infrared spectroscopy,9

interferometry,10 and 1H-NMR. 6 However, the initial monomer mole fraction-copolymer

composition data thus obtained may lack accuracy. 8 Furthermore, the reactivity ratios have

been calculated by traditional linearization procedures 11•12

•13 of the instantaneous

copolymer equation11•14 (eq 2.2) In this thesis, more accurate nonlinear optimisation

techniques have been used to determine reactivity ratios.4.s The MA-VEst reactivity ratios

are determined by the nonlinear optimisation technique described by Dube et al. 5 taking into

account the estimated experimental error in both initial monomer mole fraction and

copolymer composition.

A typical 400 MHz 1H-NMR spectrum of a low conversion bulk MA-V2EH

copolymer is given in Figure 3.4. The total peak area represented by A in Figure 3.4 is

generated as a result of the resonance of the V2EH proton marked by '*' in the above

structural formula of the copolymer. The peak area B is generated by the three methyl group

protons of MA in the copolymer. This methyl group is indicated by '**' in the structural

formula The peak area generated by all other protons is represented by C in Figure 3.4.

Note that the number of protons in the side group (and, therefore, the total peak area of C

as compared with A and B) will vary with the selected vinyl ester. Calculation of the

average copolymer composition of all MA-VEst copolymers (mole fraction MA: FMA) can

be determined from the peak areas A and Bin the 1H-NMR spectra by using the following

relationship:

Experimental 23

B (3.7) 3A + B

When calculating the reactivity ratios using a nonlinear optimisation method, from the initial

monomer mole fraction-copolymer composition data listed in Table 3.4, errors in both the

initial monomer composition (estimated to be 0.1%) and the copolymer composition

(estimated to be 3%) were taken into account.

B

5 4 3 2 0

ppm Figure 3.4: A typical 1 H-NMR spectrum of a MA-VEst copolymer. The total peak areas represented by A, B, and C result from 1 VEst proton, 3 MA protons, and all other protons, respectively.

The reactivity ratios resulting from nonlinear optimisation of the initial monomer

mole fraction-copolymer composition data (Table 3.4) are:

MA-VAc: rMA 6.9 ± 1.4 and rvAc = 0.013 ± 0.03;

MA-VPV: rMA 5.5 ± 1.2 and rvpv = 0.017 ± 0.035;

MA-V2EH: rMA 6.9 ± 2.7 and rvzEH 0.093 ± 0.23

On the basis of the 95% reliability interval depicted in Figure 3.5 it was concluded that the

reactivity of the three MA-VEst monomer systems can be described by one pair of reactivity

ratios. It should be mentioned that the large reliability interval on the reactivity ratio of

V2EH in the MA· V2EH monomer combination is a result of the lack of initial monomer

24 Chapter 3

mole fraction-copolymer composition data at low MA mole fractions. Bulk polymerizations

of MA-V2EH, performed at low MA mole fractions, were extremely sensitive to inhibition.

For this reason no reactions at low MA mole fractions could be performed.

Table 3.4 Initial monomer mole fractions (fu)-copolymer composition (Fu) dataofMAVAc, MA-VPV. and MA-V2EH, obtained by 1H-NMR of low conversion bulk copolymers.

fMA MA.VAc

0.100 0.181

0.200

0.300

0.600

0.700

0.800

i > 0 ·::: I'!! .t·s: .... I

FMA MA-VAc

0.616 0.704

0.71

0.803

0.935

0.924

0.979

0.40

0.20

fMA FMA fMA FMA MA-VPV MA-VPV MA-V2EH MA-V2EH

0.144 0.637 0.329 0.784 0.275 0.742 0.400 0.832

0.393 0.826 0.462 0.873

0.597 0.889 0.600 0.916

0.691 0.926 0.658 0.935

0.779 0.966 0.670 0.934

0.700 0.930

0.800 0.959

0.900 0.984

-0.20 L-----or-----.-----.----.---~ 0 2 4 6 8 10

reactivity ratio MA

Figure 3.5: The 95% reliability intervals are given for the reactivity ratios of MA-VAc, MA-VPV, MA-V2EH, and all MA-VEst combined

Due to the increased number of data points when combining all initial monomer mole

fraction-copolymer composition data, the reliability interval of the reactivity ratios has

decreased resulting in the following values:

rMA = 6.1 ± 0.6 and rvEst = 8.7·10"3 ± 23·10·3•

This result is in acceptable agreement with the reactivity ratios determined by Kulkarni et

Experimental 25

al. 6 for MA-VAc (rMA = 6.3 ± 0.4 and rvAc = 31·10·3 ± 6·10"3).

Comparison of the experimental results with the theoretical prediction given by the

instantaneous copolymer equation (eq 2.2) using the reactivity ratios rMA 6.1 and rVEst =

8.7·10·3, gives good agreement, as can be seen in Figure 3.6. From these results it can be

concluded that all three monomer combinations indeed can be described by one set of

reactivity mtios.

- 0.80 c:l 0 -.... u 0.60 Clll .::: 0 g 0.40

J 0.20

0.00 .!r-----.--......---....1 0.00 0.20 0.40 0.60 0.80 1.00

fMA (mol fraction)

Figure 3. 6: Comparison of the experimentally determined initial monomer mole fraction-copolymer composition data of MA with VAc (.t:.), VPV (o), and V2EH (D) with the theoretical instantaneous copolymer equation (- -

-) using the reactivity ratios r MA = 6.1 and r v&1 8. 7 ·10·3•

An advantage of the approximately equal reactivity mtios for V Ac, VPV, and V2EH

in MA-VEst monomer systems is that these systems are very suitable to study the important

effect of the monomer solubility in water on the course of emulsion copolymerization as

a function of the monomer-to-water ratio. This will be discussed in more detail in chapter

8. The reactivity ratios of the monomer combinations used in this thesis are summarized

in Table 3.5.

Table 3.5: Reactivity ratios of the monomer combinations MA-VEst, MA-lnd and MMA-S.

monomer 1-monomer 2 rl r2 references

MA-VEst (so•q 6.1 ± 0.6 8.7•10'3 ± 23·10'3 this work

MA-Ind (70°C) 0.92 ± 0.16 8.6•10'2 ± 2.5 •10'2 this work

MMA-S (4o•q 0.46 0.523 Fukuda et al. 7

26

I.

2.

3. 4.

5.

6.

7. 8. 9. 10. II. 12. 13. 14.

References

LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chem., 193, 2065 (1992) LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison, Makromol. Chem., 193, 2049 (1992) F.J. Schork, W.H. Ray, AC'S Symp., 165, 505 (1981) F.L.M. Hautus, H.N. Linssen, A.L. German, J. Polym. Sci., Polym. Chem Ed., 22, 3487, 3661 (1984) M. Dube, A. Sanayei, A. Penlidis, K. F. O'Driscoll, P. M. Reilly, J. Polym. Sci., Polym. Chem. Ed., 29, 703 (1991) N.G. Kulkarni, N. Krishnamurti, P.C. Chatteljee, M.A. Sivasamban, Makromol. Chem, 139, 165 (1970) T. Fukuda, Y-D. Ma, H. lnagaki, Macromolecules, 18, 17 (1985) F.R. Mayo, C. Walling, F.M. Lewis, W.F. Hulse, J. Am. Chem. Soc., 70, 1523 (1958) T.A. Garrett, G.S. Park, J. Polym. &i., 4, A-1, 2714 (1966) I.S. Avetisyan, V.I. Eliseeva, O.G. Laronovo, Vysokomol. Soedin, 3, A 9, 570 (1967) F.R. Mayo, F.M. Lewis, J. Am. Chem. Soc., 66, 1594 (1944) M. Fineman, S.D. Ross, J. Polym. Sci., 5, 259 (1950) T. Kelen, F. Tiidos, J. Macromol. &i., Chem., A9, 1 (1975) T. Alfrey, G. Goldfinger, J. Chem. Phys., 12, 205 (1944)

On-line monitoring 1.7

Cbapter 4 On-line gas ebromatograpby and densimetry

Abstract: Monitoring and controlling composition drift is an important issue in emulsion copolymerization. Due to the heterogeneity of the polymerization system often combined with non-ideal kinetics, predicting copolymer composition and changes in monomer composition as a function of time is not straightforward. Therefore, accurate and fast on-line determination of partial conversions of the separate monomers is a key to understanding and controUing the copolymer system studied. For this reason on-line densimetry, resulting in overall weigllt conversion, is combined with on-line gas chromatography, resulting in the overall ratios of the residual monomer. Combining these two on-line data gives the partial conversion of each monomer as a function of time without the need of an internal standard. The determination of partial conversion of monomers in batch emulsion copolymerization from on-line gas chromatography and on-line densimetry is illustrated for the monomer system methyl acrylate-vinyl acetate.

4.1 Introduction

Composition drift is a typical aspect of (emulsion) copolymerization resulting in

chemically heterogeneous copolymers. Monitoring and controlling the occurrence of

composition drift is extremely important since copolymer properties strongly depend on,

among others, the chemical heterogeneity of the product. Prediction of copolymer composition

and changes in the composition of the reaction mixture as a function of time is often hampered

by non-ideal circumstances or the lack of parameters needed for model predictions. Therefore,

accurate and fast on-line determination of partial conversions of the separate monomers is

of great importance.

The use of on-line densimetry in obtaining conversion data for homopolymerizations

is already well established. Successful applications have been reported for the polymerization

of methyl methacrylate (MMA), 1•2

•3 vinyl acetate (VAc),4•

5•6 styrene (S),7 and even for

the gaseous monomer butadiene.3 Apart from the butadiene work that fitted the densimetry

data with gravimetry results at the end of each reaction, all other experiments have been based

28 Chapter 4

on the assumption that the volumes of monomer, polymer, and water are additive.

Furthermore, it is assumed that the specific volume of the (co )polymer is a linear function

of the homo-polymer specific volumes. As a consequence the specific volume of

heterogeneous and homogeneous copolymer of the same overall copolymer composition is

assumed to be equal. Using these assumptions in combination with pre-run data of the total

density difference going from I to 100% conversion, the on-line density signal can be

transformed into an on-line conversion signal. Note that, in cases where conversion

determination is based on calibration techniques or pre-run data, densimetry is a relative

method rather then an absolute one.

For copolymerization reactions the use of on-line densimetry becomes more complex

because composition drift will lead to changing specific volumes of the monomer and polymer

phase. Nevertheless, some attempts have been made to monitor batch emulsion

copolymerizations using a densimeter. One of the first attempts was made by Abbey1 for

the monomer combination butyl acrylate (BA)-MMA. Abbey made a rough estimation of

the resulting conversion-time curve for the BA-MMA emulsion copolymerization by simply

neglecting the occurrence of composition drift although he knew that this would lead to a

skewed conversion-time plot Canegallo et aC recently monitored emulsion copolymerizations

by densimetry for the monomer systems S-MMA, acrylonitrile-MMA and V Ac-MMA. They

accounted for composition drift by modelling this phenomenon and taking into account the

effect on density of changing monomer and polymer compositions as a function of conversion.

In order to obtain conversion from densimetry data Canegallo et al. 7 calculated the calibration

constants from a pre-run based on the theoretically calculated begin and end densities.

Although they were able to transform density into conversion data not only for

homopolymerization but also for copolymerization, care should be taken that the density

cell is calibrated at the same temperature and flow conditions as during reaction to ensure

that correct and absolute density values are obtained. The calibration constants used by

Canegallo et af were determined using density values of polymer and monomer at the reaction

temperature although the temperature in the density cell was approximately 6 oc lower. This

indicates that, although they were able to convert density into conversion successfully, the

density values obtained were not absolute ones.

Monitoring the partial conversion of both monomers as a function of time in emulsion

copolymerization instead of modelling the copolymerization, as Canegallo et al. 7 did, can

only be performed if additional information is available to convert density data into partial

conversion data. This extra information must be related to either the monomer ratio or the

copolymer composition.

On-line monitoring 29

Accurate ratios of residual monomers can be obtained by gas chromatography (GC).

Gas chromatography of the liquid phase is a well established method to obtain overall

monomer ratios in an emulsion system. Successful liquid phase on-line GC applications have

been reported by Rios eta/. 9 and van Doremaele. 10 Alternatively, on-line head space analysis

of the gas phase above the reactor content can be an option 11 although this method is not

straightforward since it involves the knowledge of monomer partitioning behaviour between

the reaction mixture and the gas above it, under the relevant reaction conditions. The complete

characterization in terms of absolute concentrations of both monomers as a function of time

during emulsion copolymerization is possible using only GC analysis, given the use of an

internal standard or a constant injection volume. However, the addition of an internal standard

to the reaction medium can influence polymerization kinetics and monomer partitioning12

leading to different conversion-time curves. Furthermore, the internal standard will remain

in the product. Accurate and reproducible injection volumes can only be obtained by taking

relatively large samples from the reaction mixture. Since injecting these large samples directly

into the GC-column leads to overload of the column and the use of a splitter does not give

reproducible absolute amounts of monomer, an approach has to be used in which an internal

standard must be added to the sample, followed by sample dilution and injection in the GC.

It is obvious that this method can only be applied on-line if expensive robotics are included

in the system. In the approach presented herein the on-line gas chromatography is nsed only

to obtain the overall ratio of the monomers present in the batch emulsion copolymerization,

thus avoiding the complications of using an internal standard or a constant injection volume.

Combining on-line gas chromatography and on-line densimetry is then required to

obtain absolute monomer concentrations of both monomers as a function of time. The use

of this new combination of on-line techniques, in principle, makes fast monitoring of the

monomer concentrations possible, thus allowing product control (e.g. composition drift) as

well as process control (e.g. reaction heat).

4.2 Theory

Calculation of conversion based on density data obtained by on-line densimetry is

mostly based on the volume additivity assumption. 1·2.3.45

·13 When this assumption is valid,

the monomer conversion is a linear function of the specific volume of the emulsion. In these

cases the conversion can be calculated with:2

30 Chapter 4

0 t p~

t v. - v. Pe (4.1) X

o I v. - v.

0 I Pe Pe

where x, v (cm3/g), and p (glcm3} stand for the conversion, specific volume, and density

respectively, and where the subscript e stands for the total emulsion and the superscripts

o, t, and I stand for the conversion at the beginning of the reaction, time t, and complete

conversion, respectively. Note that the specific volume equals the reciprocal density value

for each component. The initial and final specific volumes of the reaction can be determined

experimentally from a pre-run or they can be approximated as weighted averages of the

component specific volumes:

(4.2a)

(4.2b)

where x stands for mass fraction and the subscripts m, p, and s stand for monomer, polymer,

and serum (the aqueous phase), respectively. Note that the initial mass fraction of monomer

in the reaction equals the mass fraction of polymer at complete conversion. The density values

(i.e., reciprocal specific volumes) of the monomers and polymers used in this chapter are

listed in Table 4.1. 14•15

Table 4.1 Densityvaluesofpurewater, monomers, and polymers used in the emulsion (co)polymerizations at the reaction temperature of 50"C.

density (glcm3)

Ingredient monomer polymer

styrene 0.8781 1.0438

vinyl acetate 0.8935 1.1696

methyl acrylate 0.9186 I.l987

water15 0.9881

toluene14 0.8375


4.3 Experimental

Emulsion (co)polymerization: For on-line monitoring of batch emulsion

(co )polymerizations the standard reactor depicted in Figure 3.1 was equipped with an on-line

densimeter and an on-line gas chromatograph. In Figure 4.1 the configuration of the batch

reactor system with on-line densimeter and on-line gas chromatograph is given. The reaction

volume in the sampling loops is approximately 21 em\ which normally is about 2% of the

total reaction volume. Since this volume is divided over two loops and since the flow through

each membrane piston pump is about 11.7 cm3/min, it takes approximately 1 minute for a

small sample volume to pass the loop for on-line measurements. Considering this relatively

small sample volume and the short residence time in the sampling loop the density and

monomer ratio values obtained from on-line measurements are assumed to be similar to the

conditions in the reactor itself. Furthermore, all effects of possible different reaction rates

(due to lower temperatures in the sampling loop) of the emulsion mixture in the sampling

loop as compared with the reaction mixture remaining in the reactor, are assumed to be of

negligible influence on the total reaction mixture in the reactor. The recipes of the emulsion

homo- and copolymerization reactions are depicted in Table 4.2.

N2

lie

lh

Air

I c

t [@l--<><1----<><J---+-------,

I B

[)I '

~----rr~,- M - ¥

~L(.)~r R

GC

.. .

Figure 4.1: Schematic representation of the configuration for on-line monitoring batch emulsion copolymerizations using densimetry and gas chromatography. The on-line densimeter (Dl). the on-line gas chromatograph (GC), the thermostatic baths (B), the reactor suited with baffles and a healing jacket (R), the on-line computer (C) and the double membrane piston pump (P). are indicated.

32 Chapter 4

Table 4.2 Batch emulsion polymerization recipes for the homopolymerization of Sand VAc and the copolymerization of MA-VAc.

Ingredients (g) homo-S homo-VAc co-MA-VAc

s 99.743

MA 50.454

VAc 50.193 50.411

SDS 2.299 0.296 0.299

NaPS 1.904 0.201 0.212

NaaC03 0.894 0.088 0.085

water 1031.96 979.37 992.34

The S and V Ac homopolymerizations and the MA-V Ac copolymerization were performed

under nitrogen at 50°C. Previous to the addition of the initiator solution. the rest of the

reaction mixture was stirred with ca. 800 rpm to ensure a relatively homogeneous reaction

mixture. At the moment of addition of the initiator solution the on-line monitoring is started.

All reactions were monitored by gravimetry and on-line densimetry yielding conversion-time

curves. The copolymerization reaction was also monitored by gas chromatography (both on

line and off-line) providing the overall monomer fractions as a function of time. Combining

both data gives the conversion of both monomers at the moment of sampling.

Densimetry: The on-line measurements described in this chapter were performed using an

Anton Paar DMA 512 density cell thermostated with a M3 LAUDA thermostatic bath and

an Anton Paar DMA 60 Densimeter. The DMA 512 remote cell can be used for high pressure

and high temperature applications. The U-shaped density cell (U-tube) is made of stainless

steel with an internal diameter of 2.4 mm and with an internal volume of approximately I

cm3• A membrane piston pump was used for continuous transport of the reaction mixture

through the on-line density cell. A pre-heater (length 15 em, internal diameter= 2 em)

was placed around the sampling tube just in front of the densimeter. The temperature of the

bath was set at such a temperature (53.0°C ± 0.1) that the reactor and the density cell where

at the same temperature (50.0°C). Contrary to the results of Canegallo et af.? the density-time

curves obtained from on-line densimetry were not sensitive to large scatter of density values

resulting from the formation of gas bubbles or coalescence of monomer droplets in the U-tube. 1

Therefore, in our set-up no phase separator was installed.

Gas chromatography: For on-line gas chromatography a Carlo Erba 8030 gas

chromatograph was used, equipped with an extra heated zone in which the on-line injection


system was installed. Continuous flow of helium for GC analysis and continuous flow of

the reaction mixture through a sampling disc valve 16 (diameter sampling hole= 1.56 mm;

thickness disc = 2.95 mm) was maintained during reaction. After the completion of each

GC analysis a new reaction mixture sample with a volume of approximately 5.6 l!l was

injected into the GC apparatus by simply rotating the sample disc. The GC sampling valve

could be operated either fully automatically by using a computer, or manually. The column

used for on-line GC analyses was a J & C Scientific Capillary DB5 column with a length

of 30m, an internal diameter of 0.53 mm and a film thickness of 1.5 lim. For the MA-V Ac

reactions consecutive samples could be taken every three minutes resulting in a sufficient

number of values of overall monomer ratios as a function of time. The on-line gas

chromatography values where compared to those obtained off-line to check the validity of

the system used. The apparatus for off-line purposes have been described in chapter 3.

4.4 Results and discussion

4.4.1 Density

Theoretically the conversion can be calculated from density measurements without

performing a pre-run if the specific volumes (i.e, reciprocal densities) of the components

in the three phases and mass fractions of the aqueous phase, the monomer phase, and the

polymer phase are known. However, small errors in density will lead to large deviations in

conversion determination for low solids reactions where the total density difference is small.

Therefore, on-line conversion determination from densimetry without the use of pre-run data

can only be performed accurately if the measured density value is an accurate and absolute

one. It should be noted that measuring absolute density in an on-line system as presented

herein is hampered by several complications. For instance, the density signal depends on

flow rate through the density cell, temperature, "homogeneity" of the heterogeneous system

(i.e., mixing to avoid phase separation in intervals I and II in emulsion polymerizations),

and pressure. The influence of each individual parameter on the density signal depends on

the sensitivity of the selected density cell towards these parameters. Extra complications will

occur as the viscosity will change as a function of conversion since this may lead to changing

flow rates and temperatures in the density cell. It should be noted that temperature control

in the density cell is difficult due to slow heat transfer between heating system and the U

shaped tube which is surrounded by vacuum. Good temperature control can only be obtained

by using a good pre-heater or using low flow rates. Conversion determination from absolute

34 Chapter 4

density values may be obtained if a flow controller is installed or by calibration of the density

cell under a series of(flow) conditions. Using the experimental set-up presented in this thesis,

the specific volume determined from on-line densimetry can deviate approximately 0.003

cm3/g from the absolute specific volume as a result of flow effects, the accuracy of the

measuring device, and scatter on the calibration constants. This implies that the method will

result in accurate conversion determinations for high solids content emulsion polymerizations

(40% solids; v. v."' 0.1; 3% error on conversion determinations), whereas, for very low

solids content reactions large errors in conversion determination may occur (5% solids; v.

v. "' 0.01; 300/o error on conversion determination). However, for two identical reactions

where flow and temperature fluctuations are approximately equal, the error on the specific

volume will be so small(< 0.0005 cm3/g) that the pre-run data of the frrst reaction can be

used for on-line determination of conversion in the second reaction. This can either be done

by measuring the total density difference and assuming volume additivity (eq 4.1), or

calculation of the calibration constants using the theoretical initial and final densities, 7 or

by using the aqueous phase density as a fitting pararneter,6 or by calibration of the density

data on conversion data. 8

From the above discussion it can be concluded that, as long as densimetry does not

result in accurate absolute density values, the quantitative use of densimetry during a reaction

is limited to high solids content reactions and to reactions for which a pre-run has been

performed. This makes densimetry a very useful method of on-line monitoring of standard

reactions, i.e., the method is extremely useful for industrial application in which pump

plugging can be avoided. In the literature it has been reported that solids contents at least

up to 30% are possible. 4 On-line densimetry always gives valuable qualitative information

during reaction, even if no direct information about absolute conversion is gained. Moreover,

it is a very quick and accurate method to gather much data from an experiment since as soon

as the reaction is finished a complete and detailed conversion-time curve can be determined.

4.4.2 Homopolymerization

For batch emulsion homopolymerization reactions on-line densimetry is sufficient

to monitor conversio.? as a function of time during reaction. In the case of homo

polymerizations transforming density values into conversion values is straightforward (eq

4.1).

Styrene: For S homopolymerizations the conversion-specific volume curve depicted


in Figure 4.2 shows that the specific volume indeed is a linear function of the conversion

of the reaction mixture. This justifies the use of eq. 4.1 to calculate conversion from the

density data. Comparison of conversion-time data resulting from gravimetry and densimetry

(using eq. 4.1) shows acceptable agreement as can be seen in Figure 4.3.

1.03

1.02

1.01

1.00

0.99 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 4.2: Comparison of experimental and theoretically linear (fitted) conversion-specific volume results for the batch homopolymerization of styrene.

1.00 0

0.80

c:l 0 0.60 ... G!l

~ ~ c:l 0.40 0 u

0.20

0.00 0 so 100 150 200

Time (min)

Figure 4.3: Comparison of conversion results determined using on-line densimetry and gravimetry for the batch homopolymerization of styrene.

The bend in the density curve at 80% conversion is probably caused by fouling of the density

cell. Although membrane piston pumps are known as low shear pumps, the use of this type

of pump for on-line measurements of ab initio batch homo-polymerizations of S may cause

some pump plugging. Since this will influence the flow through the density cell and as a

direct consequence the value of the calibration constants, pump plugging will directly affect

36 Chapter 4

the density-time curve resulting from on-line densimetry. Less plugging can be expected

when using a peristaltic pump. However, finding proper tubing resistant to both monomers

needed in emulsion copolymerization is difficult. Furthermore, possible swelling of the tubes

and deposit of polymer on the tubing will also affect the flow and therefore the calibration

constants. Since monitoring emulsion copolymerization reactions is the main purpose of this

set-up, a membrane piston pump in combination with stainless steel tubing was selected.

Vinyl acetate: The specific volume-conversion results for a V Ac homopolymerization

depicted in Figure 4.4 show clearly that not one single linear relationship exists between

specific volume and conversion over the whole conversion range. This can only mean that

the assumption of additive volumes is not valid for the emulsion polymerization of V Ac,

i.e., eq. 4.1 cannot be used. The deviating behaviour is caused by volume contraction

occurring when V Ac is added to water. This volume contraction will lead to a density increase

(instead of the expected decrease in case the volumes where additive) when VAc is added

to water as can be seen in Figure 4.5 where the density of V Ac-water solutions is depicted

as a function of increasing amounts of V Ac (increasing monomer-to-water ratios MIW). The

volume contraction was determined off-line with a Anton Paar DMA I 0 density cell. All

density values depicted in Figure 4.5 are below the maximum water solubility of V Ac in

water. Higher MlW ratios lead to a separate aqueous phase, saturated with monomer, and

a separate monomer droplet phase. This immediately leads to phase separation and therefore

to huge scatter on the density values.

1.02 ..... 1:10 ~ saturated s u '-' C) g

1.01 -0 >

partially saturated u ;;:

l IZI

1.00 L.---...---=---.---....... -----.----"""'1 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 4.4: Experimental (o) conversion-specific volume results for the batch homopolymerization ofVAc are fitted in two linear regions (saturated and below saturation; solid lines).


0.990

0.988 '------.-----,...-1--....----....--1---,

0.00 0.01 0.02 0.03 0.04 0.05

Monomer/water (gig)

Figure 4.5: Experimentally determined density values for VAc-water (!!.)and MA-water (o) solutions as a function of the MIW ratio. The data are fitted with two linear relations.

Due to the linearity between density and monomer-to-water ratio, the solubility of V Ac in

water at 50"C can be determined from measuring the density of the saturated aqueous phase.

This resulted in a water solubility for VAc of 0.28 moVdm3• That the volume additivity

assumption is not valid for other reasonably water soluble monomers either, is also illustrated

in Figure 4.5 for MA. The water solubility of MA at 50"C resulting from density

measurements is 0.55 moVdm3• The kink in linearity shown in Figure 4.4 is primarily caused

by the dissolved monomer in the aqueous phase. Due to the relatively high water solubility

of V Ac (0.28 moVdm3) in combination with the relatively low monomer-to-water ratio (M/W

= 0.051), a percentage of 48% of the VAc was dissolved in the aqueous phase at the

beginning of the reaction. The difference between the one linear line and two linear regions

situations will be smaller if a smaller percentage of the monomers is located in the aqueous

phase, i.e., for higher MIW ratios and/or for monomers with lower water solubilities. This

is illustrated by Penlidis et al. 4 who found reasonable agreement between gravimetry and

densimetry conversion results calculated using eq 4.1 for the batch emulsion

homopolymerization of VAc at a M/W ratio of 0.33 g/g (ca 8% of the V Ac is dissolved

in the aqueous phase at the start of the reaction).

During the homopolymerization of V Ac (Table 4.2) a substantial amount of the

monomer will be located in the aqueous phase (48%). Using eq. 4.1 to calculate the

conversion-time curve for this reaction will lead to a large difference between the conversion

data based on eq. 4.1 and gravimetry as can be seen in Figure 4.6 (top line and triangles).

38 Chapter 4

1.00

0.80

c:l 0.60 .9 U}

~ 0.40 > c:l 0

I;) 0.20

0.00

-0.20 0 so 100 150 200 250

Time (min)

Figure 4.6: For the batch homopolymerization ofVAc the calculated (3 methods) and gravimetry based conversion-time curves are compared; calculation based on one (top line) and two linear regions (middle line) between conversion and specific volume; gravimetry data (ll.); and calibration using gravimetry results (bottom line).

These problems can be solved in the following three ways:

1) Dividing the reaction into a saturated (Interval II) and partially saturated (Interval

III) region. By doing so we can assume that we have two linear regions in which we can

nse eq. 4.1 again. For the presented V Ac reaction the end of the saturation interval can be

calculated based on the water solubility value (0.28 molldm3) and the swellability of monomer

in the polymer phase (6.11 molldm3 swollen polymer phase) showing that Interval II is ended

at 26% conversion. The assumption of a linear region in the saturation region is quite

acceptable since the total amount of V Ac in the aqueous phase remains constant. Note,

however, that by assuming a linear region in interval II volume additivity between the polymer

and the monomer in the swollen particle phase is assumed. For the partially saturated region

the concentrations in both the aqueous phase and polymer particle phase will decrease.

Deviations of the linear behaviour will occur in this partially saturated region due to the fact

that the aqueous phase is always closer to saturation than the polymer particle phase. 12

However, the results of this approach are quite acceptable as can be seen by the reasonable

agreement between the conversion-time curve resulting from this approach and gravimetry

data (Figure 4.6; middle line and triangles).

2) Calibration of the density-time curve with a density-conversion relationship (fitted

with a polynomial of the 6th power) obtained by comparing on-line density values with

gravimetry results. 8 Using this approach accurate conversion-time curves can be obtained


after calibration of the results or, on-line by using the density-conversion relationship from

a pre-run. Using this approach excellent agreement between conversion-time curves resulting

from densimetry and gravimetry is obtained (Figure 4.6; bottom line and triangles).

3) Determining the specific volume of the monomer in the three phases and adjusting

eqs 4.1 and 4.2a.,b. However, this approach again only works when accurate absolute densities

are obtainable.

Conclusions about on-line densimetry in emulsion homopolymerization: In cases where more

than approximately 5% of the monomer is dissolved in the aqueous phase at the beginning

of the reaction, the volume additivity assumption cannot be used and the maximum water

solubility of the monomer has to be taken into account.

Note that in cases where conversion information is needed at the end of the reaction,

the calibration method is the most simple and accurate way to obtain conversion information

since temperature and flow deviations, and water solubility effects are all accounted for as

long as these phenomena are reproducible from one run to the other. Furthermore, this method

can be used in a similar way to obtain conversion data for emulsion polymerizations involving

two or more monomers.

4.4.3 Emulsion copolymerization of MA and V Ae

In emulsion copolymerization reactions the monomer and copolymer compositions

will also change as a function of conversion, probably leading to nonlinear conversion-specific

volume curves (unless both monomers and polymers have similar densities). For the emulsion

copolymerization of reasonably water soluble monomers as MA and V Ac even more

deviations from linearity of the conversion-specific volume curves can be expected. To avoid

these problems the gravimetry calibration method described in the previous section is used

to obtain accurate conversion-time curves.

A typical density-time curve resulting from on-line measurements of the batch emulsion

copolymerization ofMA and V Ac is shown in Figure 4. 7. Note that there is remarkably little

scatter on the density data, even at the beginning of the reaction (interval II) where phase

separation might occur. This can only be a result of the continuous pumping at turbulent

conditions that prohibits phase separation in the density cell. It also must be mentioned that

in case of V Ac homo- and MA-V Ac copolymerization hardly any pump plugging occurred

during reaction, i.e., a stable latex mixture is obtained. Transforming the density values into

specific volumes and thereafter combining the specific volume-time values with conversion-

40 Chapter 4

time values obtained gravimetrically, results in a nonlinear conversion·specific volume

relationship depicted in Figure 4.8.

1.01

1.00

0.99 .. ' . •

J 0.98 C....,.-~~ ....... --....-,..........--....-,..........--..,.....,

0 so 100 lSO 200

Time (min)

Figure 4. 7: Density-time curve typical of the batch emulsion copolymerization of VAc with MA.

1.02

1.01

1.00

0.99 L----..----...----......---....,.......--.., 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 4.8: Experimentally determined relation (--)between specific volume and conversion for the batch copolymerization of MA-VAc; (o) conversion determined by gravimetry.

Using the relationship found by fitting the conversion·specific volume data, the

specific volume values where transformed into conversion values (Figure 4.9).

Similar, on-line results can be obtained if the conversion is calculated based on

the total difference in specific volume as a function of conversion from a pre-run.


As can be seen in Figure 4.9 good agreetnent is obtained between the densimetry

based and gravimetry-based conversion-time curve for this copolymerization of

MA and V Ac. From this it can be concluded that densimetry can be used as a

qualitative method to obtain on-line conversion in emulsion copolymerizations

if reactions are performed repeatedly. Note that at ca. 700/o conversion all MA

has reacted as a consequence of composition drift. The increased polymerization

rate at 700/o conversion can be explained by a different kinetic behaviour of V Ac

(different average number of radicals).

1.00

0.80

0.60

0.40

0.20 f • 0.00 YA--.-~-,.........--.....-,..----.--..--.--.--,

0 100 200 300 400

Time (min)

Figure 4. 9: Conversion as a function of time determined gravimetrically ( t:.) and calibrated using densimetry (line consisting of data point (small o)) for the batch copolymerization of MA-VAc.

The use of on-line gas chromatography to determine overall monomer ratios proved

to be a valuable method to monitor composition drift. Comparison of on-line gas -

chromatography with off-line monomer ratio results (qvAc/MA = overall concentration of

VAc/concentration ofMA) shows good agreement as can be seen in Figure 4.10. For the

monomer system MA-V Ac a complete on-line gas chromatographic analysis of the reaction

mixture could be performed every three minutes. Although total conversion was completed

only after approximately 9 hours, a considerable composition drift led to complete conversion

of MA within lh. Therefore, the number of samples was limited and no duplicate

measurements could be taken. Fitting the monomer ratio-time data enables one to calculate

the overall monomer ratio at any time during the copolymerization reaction.

Combining conversion-time values with overall monomer ratio-time values enables

one to calculate the partial conversion of the separate monomers as a function of time (or

42 Chapter 4

conversion) using eq 3.2 and 3.3.

30

20

10

ot=~==~~~~--~--~~ 0 SOO 1000 lSOO 2000 2SOO 3000 3SOO

Time (s)

Figure 4.10: On-line (o) and off-line ( .0.) monomer ratios determined .from gas chromatography for the emulsion copolymerization of MA-VAc are depicted as a jUnction of time together with a fit through both sets of data (line).

That this indeed results in very detailed information about the partial conversion of the

separate monomers MA and V Ac in a batch emulsion copolymerization (recipe Table 4.2)

can be seen in Figure 4.11. Comparison of theoretical predictions17 with experimental results

for the copolymerization ofMA and V Ac shows excellent agreement as can be seen in Figure

4.12 where the absolute numbers of moles of MA and VAc are depicted as a function of

conversion.

1.00

0.80

d .2 0.60 ... t I» g 0.40 u

0.20

0.00 0 5 10 15 20 25

(Thousands) Time (s)

Figure 4.11: Partial and total conversion calculated from on-line densimetry and on-line gas chromatography are shown for MA (top line) and VAc (bottom line) as a jUnction of time. The overall conversion is calculated from on-line measurements (middle line) and the gravimetry data (o).

On-line monitoring

0.60

~ 0.50 :>

1 0.40

< 0.30 ::s 'S 0.20 "' 0

1 0.10

0.00 0.0 0.2 0.4 0.6 0.8 1.0

conversion

Figure 4.12: Experimentally determined absolute monomer amounts ofMA and VAc (MA, bottom symbols; VAc, top symbols) resulting from on-line densimetry and on-line gas chromatography are compared with theoretical predictions (MA, bottom line; VAc, top line).

4.5 Conclusions

43

For relatively water soluble monomers such as VAc and MA it has been shown that

the specific volume of the monomers in the aqueous phase is different from the specific

volume of the pure (monomer droplets) monomers leading to two linear regions in the specific

volume-conversion curve of an emulsion homopolymerization. It was illustrated that for low

solids reactions of V Ac the volume additivity assumption no longer is valid. In these

complicated situations conversion can be calculated from densimetry data either by assuming

two linear regions for saturation and partial swelling and using the volume additivity

assumption in the separate regions, or by calibrating the specific volume values with

gravimetry values.

For the emulsion copolymerization of MA and V Ac the combination of on-line

densimetry with on-line gas chromatography proved to be a powerful method of determining

the partial conversion of both monomers as a function of time. Comparison of the on-line

data with off-line results and theoretical predictions gave satisfactory agreement. On-line

densimetry always can be used as a qualitative method to obtain on-line conversion data

for emulsion (co)polymerizations if reactions are performed repeatedly. It should be noted

that the approach presented in this thesis, viz. the on-line determination of partial conversions

of both monomers participating in the batch emulsion copolymerization reaction, can be used

for any desired monomer pair.

44 References

I. K.J. Abbey, ACS Symp. Ser., 165, 345 (1981) 2. F. J. Schork. W. H. Ray, ACS Symp., 165, 505 (1981) 3. C. H. M. Caris, R. P.M. Kuijpers, A.M. van Herk, A. L. German, Makromol. Chem.,

Macromol. Symp., 35136, 535 (1990) 4. A. Penlidis, J. F. MacGregor, A. E. Hamielec, Polym. Proc. Eng., 3(3), 185 (1985) 5. D. C. H. Chien, A. Penlidis, JMS-REV. Macromol. Chem. Phys., C30(l), I (1990) 6. P.D. Gossen, J.F. MacGregor, J. Colloid Inter. Sci., 160, 24 (1993) 1. S. Canegallo, G. Storti, M. Morbidelli, S. Carra, J. Appl. Polym. Sci., 47,961 (1993) 8. E.M. Verdurmen, E.H. Dohmen, J.M. Verstegen, I.A. Maxwell, A.L. German, R.G.

Gilbert, Macromolecules, 26, 268 (1993) 9. L. Rios, C Pichot, J. Guillot, Makromol. Chem., 181, 677 (1980) 10. G. H. J. van Doremaele, Ph.D. Thesis, Eindhoven University of Technology (1990) 11. M. Alonso, M. Alivers, L. Puigjaner, F. Recasens, Ind Eng. Chem. Res., 26,65 (1987) 12. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 13. 0. Levenspiel, "Chemical Reaction Engineering", 2nd. ed. Wiley, New York 1972 14. E.W. Washburn, C.J. West, N.E. Dorsey, F.R. Bichowsky, A. Klemenc, International

Critical Tables of Numerical Data, Physics, Chemistry and Technology, Mcgraw-Hill Book Company, Inc, New York and London 1985

15. R.C. Weast, CRC Handbook of Chemistry and Physics, 66th Ed, NY, 1985 16. A.L. German, D. Heikens, J. Polym. Sci., Al, 9, 2255 (1971) 17. L.F.J. Noel, J.M.A.M. van Zon, I.A. Maxwell, A.L. German, J. Polym. Sci., Polym.

Chem. Ed., 32, 1009 (1994)

Monomer partitioning 45

Chapter 5 Swelling of latex particles by two monomers

Abstract: The swelling of polymeric latex particles with solvent and monomer is important for the emulsion polymerization process since it influences composition drift and rate of polymerization. For the monomer combination, methyl acrylatevinyl acetate, both saturation and partial swelling were determined experimentally. Theories for saturation swelling and partial swelling of the separate monomers are in good agreement with experimental results. Based on previous work an extended thermodynamic model for monomer partitioning at partial swelling of latex particles by two monomers with limited water solubility is developed. Results predicted by this model are in good agreement with observed monomer partitioning behaviour. ·

5.1 Introduction

Partitioning of two monomers between latex particles, monomer droplets, and the

aqueous phase in an emulsion polymerization is, amongst other things, important for modelling

both the composition drift occurring during reaction and the rate of polymerization. In order

to accurately describe emulsion copolymerization in terms of composition drift, monomer

partitioning between the different phases should be taken into account.

Morton et a/. 1 dealt with saturation swelling of latex particles primarily by monomers

indicating that the mixing of monomer and polymer (expressed in terms of the Flory-Huggings

theorf) together with the interfacial Gibbs free energy term (Gibbs-Thomson equation1•3

)

determines the monomer concentration in the polymer particles. For two monomer partitioning

it has been found experimentally for several monomer combinations45 that the monomer

mole fractions in the polymer particle and monomer droplet phases are equal. This phenomenon

is clearly illustrated in Figure 5.1 where experimental data on the partitioning of MA and

V Ac between the particle and the monomer droplet phases are displayed together with

experimental data from the literature for the monomer combinations MA-S, 6 BA-S, 6 MA-BA, 6

46 Chapter 5

MA-MMA, 11 and MMA-8,14 on a series of (co)polymer seeds varying in composition.

1.00

111-4~ 0.50

0.00 ~~~"--------.--------... 0.00 0.50 1.00

fd Figure 5. 1: Experimentally determined monomer fractions in latex particles (f) as a jUnction of the monomer fraction · in the droplet phase (f) for the monomer combination MA-VAc (O) on apoly-(MA-VAc) latex and for the monomer combinations MA-S (t:.);6 BA-S (0};6 MA-BA (•); 6 MA-MMA r-J; 11 MMA-S (e)14 on several (co)polymer seeds. The solid line represents the prediction given by eq 5.12a,b.

The results presented in Figure 5.1 imply that the entropy of mixing of the monomers must

be the main factor determining the monomer mole fractions. Note that even in these cases

the absolute monomer concentrations will depend on contributions of the mixing of monomer

and polymer and the interfacial Gibbs free energy. Based on these considerations Maxwell

et al.6•7 formulated three assumptions, that simplify existing thermodynamical relationships,

resulting in basic equations that confirm the experimental results represented in Figure 5.1.

Using this approach, simple relationships were developed dealing with saturation swelling

of a polymer latex by two monomers. The basic thermodynamic relationships will be presented

together with the three assumptions and the resulting simplified relationships in the theory

section (5.2).

At partial swelling of latex particles, however, occurring in the so-called interval III

of emulsion polymerization, there are no monomer droplets present in the system and the

monomer is solubilized in both the particle and the aqueous phases. Based on work done

by Vanzo et al.8 and Gardon,9 a simple model was developed by Maxwell et a/. 10 for the

estimation of monomer partitioning, for one monomer of limited water solubility. Both

models, describing saturation swelling and partial swelling, are tested for the monomer

combination MA-V Ac.

Based on the three assumptions previously formulated in the work of Maxwell et

al.,6•7•10 now in this thesis an extended model is developed to predict the partial swelling


of latex particles with two monomers of limited water solubilities. The results predicted by

this extended model are compared with observed monomer partitioning results for the

monomer combination MA-V Ac. Note that the theoretical developments described here are

specific for the swelling of latex particles with monomers. However, the conclusions drawn

are quite general, and are valid for all partially water soluble solvents. Furthermore, the theory

can be trivially extended to take into account three or more solvents or monomers. 11

5.2 Theory

Morton et a/. 1 considered the saturation swelling of latex particles by a monomer

having limited solubility in the water phase. When the homogeneously swollen latex particle

phase is in equilibrium with the free-monomer phase the partial molar Gibbs free energy

of the monomer is given in terms of the Flory-Huggins theory2 and the Gibbs-Thomson

equation1•3

[ l l 2 2V ?{V

113

l1p. /(RT) = ln(1 - v \ + v 1 - - + xvP + ml P P P' P ]J R RT

n •

(5.1)

where AJlp is the partial molar Gibbs free energy (or chemical potential) of monomer in

polymer phase relative to the partial molar Gibbs free energy of pure monomer, vP is the

volume fraction of polymer in the latex particles, P';. the number-average degree of

polymerization, x the Flory-Huggins interaction parameter, R the gas constant, T the

temperature, y the particle-water interfacial tension, V mi is the molar volume of monomer

i, and R0 is the unswollen radius of the latex particle. The first two terms at the right hand

side in eq 5.1 represent the combinatorial entropy of mixing (denoted as the 'configurational

entropy' by Flory), the third expression represents the so-called 'residual' free energy

containing both enthalpic and entropic terms, and the fourth expression represents the

contribution from the latex particle-water surface interfacial Gibbs free energy. Note that.

since P';. is normally large, eq 5.1 may usually be written in a simpler form

.1. J.lp I(RT) = ln(l (5.2)

For simplicity, in the following theoretical development we use the form of eq 5.2 and not

eq 5.1 (i.e., we assume 1/P,. is small for the polymers of interest).

For two-monomer partitioning in an emulsion system the partial molar Gibbs free

energy of monomer i in the monomer droplet (e. J.id,) and polymer particle (A !lp;) phases can

48 Chapter 5

be calculated from the Flory-Huggins theory: 2•3

•12

Ll!J.d./(RD = lnv~, ,(r) + (l - m.)vd. 1(r) + xv~;sa~(r)

1 w,sa u !f,Sa '1 tt•

(5.3)

LlJ.!p; /(RD lnvP, + (1 (5.4)

where vdi, Vq;, vP, and vl!i are the respective volume fractions of monomers i andj in the

monomer droplets and latex particles, x,i is the interaction parameter between monomers i

and j, and X;p and ;ware the interaction parameters between each of the respective monomers

i andj and the polymer. The term mu is the ratio of the molar volumes of pure monomers

i andj (i.e., my= Vm/Vm;, where Vm, and Vm; are the molar volumes of monomers i andj,

respectively). The derivation of eq 5.3 involves the reasonable assumption3 that m;p and mlP,

the ratios of the respective molar volumes of monomers i and j and the molar volume of

polymer, are negligible as compared with all other terms. The use of the Flory-Huggins theory

in this case will be discussed later in this chapter. In this thesis the postscript (r) always

represents the saturation value of the quantity at a certain monomer mole ratio in the particle

or droplet phases, and the subscripts a, p, and d represent the aqueous phase, the polymer

particle phase, and the monomer droplet phase, respectively. Note that we are always dealing

with saturation swelling if there are monomer droplets present. The use of eq 5.3 assumes

that the lattice model is valid for mixtures of small molecules; this is valid for two organic

monomers of equal or similar molar volumes. Note also that due to the normally large size

of monomer droplets we have not considered contributions from the monomer droplet-water

interfacial free energy in eq 5.3 (this assumption may not be valid for a system containing

very small monomer droplets). An example of typical saturation values for all parameters

in eq 5.4 together with the resulting values for all terms in eq 5.4 is given in Table 5.1. Note

that the total sum of the expressions in eq 5.4 in the example given in Table 5.1, as in several

other situations, is dominated by the entropy of mixing monomer and polymer (the absolute

value of In vi>l + vP is much larger then the sum of all other terms).

The partial molar Gibbs energy of the monomer in the aqueous phase (c.J..L.;) is given

6!!., IRT =In a1 (5.5)

where the activity of monomer i, a,, is given by a1 = (y [M,].)/(y o [M,].0); where y is the

activity coefficient of the monomer; yo the activity coefficient of the monomer at some


Table 5.1 The values of the terms in the Flory-Huggins expression for the polymer phase (eq. 5.4) are given for the following typical parameters values: vP = 0.3; vp; = 0.2; vPi = 0.4; m!i = 0.9; X!i = 0.5; X;p = 0.2; Xjp = 0.3; 'Y = 20·10-1 N·dm-1

; V.,; = 0.1 d1fl·mot1;

R0 = Ur dm; R = 83.1 N ·dm ·mot1 • K 1

; T = 300 K. The affect of deviations in the separate parameters on the total sum is illustrated by assuming X;p = 0.3; x!i = 0.4; and m9 = 1.

X.;p = 0.2

x.!i = 0.5

mr = 0.9

lnvp; -1.61 -1.61 -1.61 -1.61

(I - m!i)vw 0.04 0.04 0.04 0

vP 0.3 0.3 0.3 0.3

x.!ivw2 0.08 0.08 0.06 0.08

X.;pV/ 0.02 O.o3 0.02 0.02

vpjvp(x.9 + X.;p - x.~!i) 0.05 0.06 0.04 0.05

2V .rurvp•nfRoRT 0.01 0.01 0.01 0.01

total sum -1.11 -1.09 -1.14 -1.15

standard state, [M;]. the concentration of monomer in water, and [M;].o the concentration

of monomer in water at standard state. We chose the standard state to be just homo-saturation

of the monomer in water, i.e., [M;].o = [M;]._,.,(h). In this thesis the postscript (h) always

represents the saturation concentration in the absence of other monomers (homo-saturation).

The activity coefficients describe the solute-solute and the solute-solvent interactions; up

to a concentrations of a few molar solute the solute-solute interactions are insignificant; hence,

y = y 0• Therefore, eq 5.5 becomes

L\J.L IRT =In [ [MJ. ] ., [M J •.••• c h)

(5.6)

Equation 5.6 has been shown to be true for a variety of monomer-latex systems. 6•10

At equilibrium the partial molar Gibbs free energy of each monomer will be equal

in each of the three phases, i.e., the polymer particle, the monomer droplet, and the aqueous

phases.

(5.7)

Applying this condition to eqs 5.3-5.6, for saturation swelling the following equations

for monomer i are found: 6'7'2'3'12

lnvpi.sat(r) + (1 - mY)vpJ,salr) + vp,sat(r) + x.uv!1,,..(r) + X.;pv!,.a~(r) +

2V miyv~~.,(r) vpJ,s.lr)vp,sa.Cr)(X.# + X.;p 'X.;pmij) + RaRT (5.8a)

In v • ..,i'l • (I - m,)v•~(') • x,v~..(') " In [ i~~::;~;]

Similarly, for monomer j we find:

(5.8b)

where 1p is related to x.ij by 'X.ii = 'X.ii m1;. All other terms are as previously described, and the

subscript 'sat' combined with the term (r), indicates saturation values at a particular monomer

ratio, r.

At partial swelling (i.e., no droplet phase) the equations will be more simple because

the expression for the droplet phase can be neglected. For monomer i the equation will be

(5.8c)

Similarly, for monomer j

(5.8d)

Equation 5.8a-d can be used to predict monomer partitioning for latex systems containing

two monomers in both, saturation (eq 5.8a,b) and partial (eq 5.8c,d) swelling. There are,

however, difficulties in determining the values for the interaction parameters and the interfacial

tension because, amongst other things, both may be dependent upon the volume fraction of

polymer in the latex particles as well as on the monomer ratio. 2

The experimentally found result of equal monomer mole fraction in the polymer particle

and monomer droplet phase can also be obtained theoretically when using the following

assumptions which were formulated by Maxwell et al. 6 for saturation swelling:


Assumption (1): The difference between the molar volumes of many pairs of monomers

is slight; therefore, the ratio of the molar volumes of monomer i and j is well approximated

by unity; i.e., mu = mji = L Note that in this case the interaction parameters Xu and Xji will

be equal. Note also that this assumption validates the use of eq 5.3 in what follows since

mole fraction is then equivalent to volume fraction. The mixing of two small molecules should,

in principle, be considered in terms of mole fraction. We adopt the form of eq 5.3 for simplicity

and note here that, because of assumption (I), further theoretical development utilizing this

simplification is validated.

Assumption (2): The contribution to the partial molar free energy of the terms containing

X;p are small as compared with all other terms. As a result slight changes in X;p are relatively

unimportant for monomer partitioning, as can be seen in Table 5.1.

At saturation swelling these assumptions lead to the following result for monomer i:6

(5.9a)

An analogous equation can be derived in a similar manner for monomer j.

(5.9b)

An analogous equation can be derived for monomer j at partial swelling.

Using eq 5.9a for monomer i together with a similar equation for monomer j, we find

for saturation swelling6

vdi.sat(r) l + ::dvd ..• (r) - v.,..,(r)) = v di_...(r) '' '·- ...

[M)._...(r) ]]

[M)._...(h) (5.10a)

and for partial swelling

In [ ::] • x,<vw - v,) • In

[M.J.

[MJ .... ,(h)

[ [M). l (5.10b)

[M) •. ,.,(h)

52 Chapter 5

Assumption (3): The contribution to the partial molar free energy arising from the residual

partial molar free energy of mixing of the two monomers is small relative to all other terms

in eq 5.4, i.e., all terms in eqs 5.9a,b and 5.10a,b containing xij, can be neglected.

5.2.1 Saturation swelling of latex particles by two monomers

For saturation swelling Maxwell et al.6 derived the following relationships when using

assumptions (1)-(3) in combination with the right hand equality of eqs 5.8a.,b:6

(M Ja,mt(r)

(M Ja,sat( h)

[M) •.• ir)

[M) • .sat(h)

(S.lla)

(S.llb)

where [M,].,.,,(r) and [MJla.sat(r) are the saturation solubility values for monomers i andj in

the aqueous phase at a certain monomer ratio, r. Equations 5.11 a.,b show that the concentrations

of monomer i and j in the aqueous phase are linear functions of the mole fraction of the

respective monomers in the monomer droplet phase.

Using eq 5.1 Oa with assumption (3) gives the following relationships between the

droplet phase and the particle phase: 6

(5.12a)

fpj,sat = f <ji,sat (5.12b)

where fp;.sat• fdi,sat• fw,sat• and f.y,sat represent successively the mole fraction of monomers i and

j in the monomer droplet and polymer particle phases at saturation swelling. Note that in

the particle phase the monomer mole fraction does not include the mole fraction of polymer

(fp; = vp/(vpi + vw)). We may state that eq 5.12a,b, which results from the use of the three

assumptions formulated in this thesis, gives a good approximation of the monomer partitioning

behaviour for the polymers and monomers studied, as can be seen in Figure 5.1. Furthermore,

it has been shown that eq 5.12a,b is approximately valid over a wide range of conditions

typical of emulsion polymer systems even when the three assumptions ((1)-(3)) utilized in

their derivation do not hold exactly. Numerical analysis of the full equation that results when

eq 5.8b is subtracted from eq 5.8a has shown that the mole fractions predicted by eq 5.12a,b

are almost always correct.7 Equation 5.12a,b appears to be insensitive to the validity of

assumptions (1)-(3), i.e., the three assumptions are of algebraic necessity only. This is an


important result, since it points to the general applicability of eq 5.12a,b even if one or more

of the assumptions described above would not hold exactly. This implies that the entropy

of mixing of the monomers is the main factor determining the monomer mole fractions.

Polymer phase. Using eq 5.12a,b Maxwell et a/.6 also developed an empirical description

for the concentration of two monomers at saturation swelling within polymer latices. These

relations can be derived using eq 5.12a,b, the relation fpi,sat = [M;]p,sa1(r)/([M;]p,sa.(r) + [Mj]p.sa~.(r))

and the assumptions that (1) the total monomer concentration in the latex particles is just

equal to the sum of the concentrations of the individual monomers and (2) the total monomer

concentration in the latex particles is a linear function of the fraction of the monomers in

the droplet phase. For a particular seed latex the concentration of monomer i within the

particles, at a certain monomer ratio r ([M,]p.sat(r)), as a function of the fraction of monomer

i in the droplets is given by6

Similarly, for the monomer j

where [M;]p,sat(h) and [M1]p,sat(h) are the maximum saturation concentrations of monomers

i and j in the latex particles at homo-monomer saturation swelling. Note that the monomer

mole fraction in the droplets just equals the monomer mole fraction in the polymer particles;

hence, in eq 5.13a,b the monomer mole fractions can be replaced by fpi,sat and fl?i.sat if required.

Aqueous phase. Utilising the three assumptions described above, Maxwell et al.6 found from

eq 5.9a and its analogue for monomer j the following relationships:

(5.14a)

(5.14b)

Based on eq 5.14a,b, the following simple relationship between the mole fraction of monomer

i in the polymer phase (fp~,sat) and in the aqueous phase (fa;_,J can be developed:

f [I [M )._,.,(h) I + P•.sat ~ (M Ja,sat(h)

[M ).,""(h) (5.15)

[M J •. sat(h)

54 Chapter 5

An analogous equation for monomer j can also be developed, where the subscripts i and

j in eq 5.15 are replaced by j and i, respectively. Note that when [M;].,,11(h) "" [M1] ..... (h),

the mole fraction of monomer i in the aqueous phase is equal to that in the polymer phase,

i.e., fai,sat "" fpl,sat fdi,sat). Note also that when monomer j has a low water solubility, i.e.,

[MJ1a.sat<h) "" 0, the mole fraction of monomer i in the aqueous phase will be close to unity

( fai,.., "" I).

5.2.2 Partial swelling of latex particles by one monomer

Based on the Vanzo equation, Maxwell et a/. 10 derived a semi-empirical equation to

describe partial swelling of latex particles by one monomer. Maxwell et al. showed that

the dominant factor determining monomer partitioning of one monomer at partial swelling

is the Gibbs energy due to the entropy of mixing of monomer and polymer. All other terms

as the residual free energy and the polymer particle-water interfacial free-energy terms (see

eq 5.2) are relatively small and approximately constant (const.) as a function of the volume

fraction of polymer. 10•2 The partial swelling of latex particles by one monomer is then

described by

[ [M] l ln(l - v) + vP + const. = In •

p [MJ ..... (h) (5.16)

where [M]. and [M] .. ,..(h) are the respective concentrations of monomer in the aqueous phase

below saturation and at homo-saturation swelling. A similar relationship can be formulated

for saturation swelling when replacing the volume fraction of polymer and the monomer

concentration in the aqueous phase below saturation by those quantities at saturation swelling,

i.e., replacing vP by vp,sat and [M]. by [M].,.ih). Subtracting this eq from eq 5.16 results in

a semi-empirical relationship that describes partial swelling of latex particles by one monomer.

In (1 v) + v - v = In [ [MJ. I (1 - V ) p p,sat [MJ (h)

p,sat a.sat

(5.17)

5.2.3 Partial swelling of latex particles by two monomers

At partial swelling there is no droplet phase present so eq 5.10b must be used. If

the polymer fraction within the particles, vr. is relatively large, then vPJ- vP1 is small. In this

case the following inequality holds: abs(xy(vp~- vr1)) << abs(ln (vp/vp1)) in which abs means


that the absolute values of these quantities should be used. Alternatively, if 'Xii < I, then this

inequality also holds. The assumptions used to derive this inequality will be discussed in

more detail in the Results and Discussion section in the light of the experimental results. 13

Using this inequality, the simplified eq 5.10b becomes:

[MJ.

[M).

[M) •. ,ih)

[M J •. sar(h) (5.18)

Note that for a certain ratio of monomers, r, at saturation [M;}. [M;]a,sa~(r) where [M,]a,sa~(r)

is the saturation value at that ratio of monomers. Hence, the saturation values in eq 5.18 must

be the saturation values for homo-monomer saturation swelling ([M;]a,sa~(h) and [Mj]a,sa~(h)).

This is an important result since the homo-monomer saturation values are readily accessible

parameters.

From saturation swelling we know that the volume fractions of monomer i over

monomer j in the droplet phase are equal to the volume fractions of monomer i over monomer

j in the polymer particles. Knowing this and combining eqs 5.1la,b and 5.18 gives the

following equation: [MJ.

[MJ.,, •• (r)

From eqs 5.1la,b, 5.18, and 5.19 we also find

[M).

[M) •. , •• (r)

[M)P

[M)p,sa~(r)

(5.19)

(5.20)

The use of eqs 5.19 and 5.20 is very convenient when realizing that with known mole

fractions of monomer i within the particle phase, fp1, the saturation concentrations at any

monomer ratio r can be calculated directly from the saturation swelling equations ( eqs 5 .16a,b

and 5.17a,b). Hence, eqs 5.19 and 5.20 give readily accessible relationships between the

concentrations of monomer i and monomer j in the aqueous phase ( eq 5 .19) and the polymer

phase (eq 5.20) at partial swelling of the latex particles.

The monomer concentrations in the particle phase and the aqueous phase at partial

swelling can be related in a manner similar to that used by Maxwell et a/. 10 when developing

the semi-empirical equation for the one-monomer situation (eq 5.17). The sum of all terms

containing interaction parameters and monomer molar volumes is assumed to be approximately

constant at all volume fractions of polymer. This assumption arises from the fact that the

dominant term for partial swelling of latex particles is the combinatorial entropy of mixing

monomer and polymer. All other terms have been shown to be small and approximately

56 Chapter 5

constant at partial swelling. 10 For two-monomer swelling, from eq 5.8c for monomer i we

find an equation similar to eq 5.17:

ln~+v V pi.sat(r) P

[M] v (r) = In I a

p,sat [M.] () I ll,Sllt r

(5.21)

Note that the saturation volume fractions can be calculated from eq 5.13a,b and molar volumes

and require only a knowledge of the homo-saturation concentrations of the monomers in

the particles (i.e., each monomer in the absence of the other). For monomer j analogous

relations can be derived where the subscripts i in eq 5.21 are replaced by the subscript j.

Rewriting eq 5.18 gives a similar relationship between the polymer and aqueons phases

at partial swelling to that developed for saturation swelling oflatex particles (i.e., eq 5.15).

fpi

f . [ 1 - [M) ..... (h) l + pi [M.] (h)

r a,sat

[M).,sa~(h)

[M ;)., ... (h)

(5.22)

From this we can conclude that eq 5.15 holds for both saturation and partial swelling oflatex

particles by two monomers with limited water solubility.

The important equations for partial swelling are eqs 5.18 and 5.22, because they relate

the concentration of one monomer in the aqueous phase with the concentration of the same

monomer in the polymer phase; eqs 5.19 and 5.20, because they give relationships for the

concentrations of monomer i and j in the aqueous phase ( eq 5 .19) and the polymer phase

(eq 5.20), respectively; and eq 5.21 since the partially saturated polymer phase is related

to the saturated polymer phase for each monomer in this equation.


Jt has been shown6 that one-monomer partitioning between the polymer particle phase

and aqueous phase can be described with eq. 5.17 for a series of particle diameters (unswollen:

30-100 nm), temperatures (20-45"C), number average degrees of polymerization (P'. = 87-

15000), and copolymer compositions (S-MA: going from poly-MA to poly-(MA-S) and poly

S). Therefore, the use of one seed (Table 3.3: MA-V Ac seed) for the partitioning experiments

was sufficient to develop relationships predicting monomer partitioning at partial swelling

even though the particle size distribution may be broad and composition drift during seed

preparation may have led to different copolymer compositions.

For saturation swelling Maxwell et a/.6 made three assumptions to develop expressions


for two-monomer partitioning. It seems reasonable to suggest that these assumptions should

also be valid for partial swelling. Based on these three assumptions described in section 5.2,

relationships were derived for two-monomer partitioning at partial swelling. Considering

these assumptions in regards to our experimental system, we note the following:

Assumption (1): The differences between molar volumes of monomers is generally

small. In the case of MA and V Ac the differences will be extremely small because the

molecular mass of MA is equal to the molecular mass of V Ac and also because the densities

of the monomers are nearly equal (VMA = 90.1 and VvAc = 92.2 cm3 mot·• at 20"C).

Assumption (2): It is hard to assess whether the contribution to the partial molar free

energy of the terms containing the interaction parameter between monomer and polymer are

indeed small as compared with all other terms since only few reliable values for these

parameters exist for any monomer-polymer system. This is because it is hard to measure

these parameters independently. Furthermore, the theoretical nature of these parameters is

rather vague since they are supposed to include both temperature-dependent enthalpic and

temperature-independent entropic terms. That the situation is even more complex has been

shown by Flory,2 who pointed out that the interaction parameters should also be polymer

concentration-dependent at high volume fractions of polymer. However, the justification of

the use of assumption (2) is supported by Table 5.1 where it is shown that the contribution

of the expressions containing lip to the partial molar free energy of monomer in polymer

is relatively small as compared with the sum of all other expressions.

Assumption (3): The contribution to the partial molar free energy arising from the

residual partial free energy of the mixing of two monomers is small relative to all other terms

in eq 5.l0b ifx.9 is small and/or if the polymer fraction within the particles, vp, is relatively

large (i.e., vPi- Vp; is small). In this case the following inequality holds: abs(x.!t(vPi- vp;)) <<

abs(ln (vp/vP.i)). The use of assumption (3) is supported by Table 5.1 where it is shown that

the contribution to the partial molar free energy of monomer in polymer of the terms

containing '4• is relatively small as compared with the sum of all other expressions.

5.3.1 Monomer partitioning at saturation swelling oflatex particles by two monomers.

As predicted by eq 5 .12a,b the fractions of monomer in the droplet and particle phases

are equal for several monomer combinations in a series of latex systems varying in copolymer

composition (see Figure 5.1). This suggests that the three assumptions used by Maxwell et

a/.6 in the derivation of this equation are (sufficiently) valid for all these combinations,

including the monomer combination MA-VAc in a poly-(MA-VAc) seed latex.

58 Chapter 5

That the concentrations of monomer i and j in the polymer phase and aqueous phase

can be described with eqs 5.13a,b and 5.14a,b is shown by the good agreement between

experiments and theory (Figure 5.2a,b) for the monomer combination MA-VAc. Equations

5.13a,b and 5.14a,b are very useful because they only require the individual homo-saturation

values in the polymer and aqueous phases to be known in order to calculate the relevant

monomer concentrations.

Based on the relationships developed for saturation swelling and based on experiments

performed, it can be concluded that the entropy of mixing of two monomers is the dominant

contribution to monomer partitioning, and as a result of this the presence of polymer has

no significant effect upon the ratio of the two monomers in the polymer phase. Although

the monomer ratio in the polymer phase is independent of the polymer composition, the

absolute monomer concentrations at saturation do depend upon the polymer and monomer

type (in terms of mixing of monomer and polymer and latex particle-water surface interfacial

energy). Knowing that the polymer composition has no effect on the monomer ratios,6•14

we can conclude that composition drift occurring during emulsion copolymerization as a

direct result of the monomer ratio within the polymer particles is independent of polymer

compositions. Different polymer compositions leading to other absolute concentrations in

the polymer particles will only influence the polymerization rates in the latex particles. Mass

balance shows that, for monomer systems where either one or both the monomers have a

high but still limited water solubility, changing the monomer-to-water ratio has an effect

on the monomer ratios within the particles. In this way composition drift and polymerization

rate will depend on the monomer-to-water ratio.

8 A 8 0.7

i ""' a:::' 0.6 6 6 -o a

:::=- T :::=-"' o.s 0 o:::r !. a o

1 '-'! 0.4

~ 4 T 4 ....... 18 0.3

.L ~ ! 2 2 ~~

0.2

~- 0.1 0 0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0

fp,MA

B

T T l .L

0.2 0.4 0.6 0.8

0.7 0.6 o.s 0.4 0.3 0.2 0.1

0.0 1.0

(!;'

.9 ;:::,. 0

! 8 I :i ~

Figure 5.2: Comparison of the predictions of eqs 5.13a,b and 5.14a,b (---:) with experimentally determined monomer concentrations ofMA (O) and VAc (D) inapoly-(MAVAc) particle phase (Fig. 5.2a; eq 5.13a,b) and in the aqueous phase (Fig. 5.2b; 5.14a,b) as a function of the monomer .fractions in the polymer phase.


5.3.2 Monomer partitioning at partial swelling of latex particles by one monomer

For monomer partitioning at partial swelling by one monomer with limited water

solubility, Maxwell et al. 10 derived a semi-empirical relation where the value of the sum of

the residual free energy and the particle-water interfacial free energy terms are estimated

from the saturation swelling volume fraction of polymer (eq 5.17). To use this model, only

the saturation concentrations in the polymer and aqueous phases are needed. Experiments

were performed to determine whether there is good agreement between this semi-empirical

expression and experiments. As can be seen in Figure 5.3, good agreement for both MA

and V Ac is reached when taking experimental errors into account.

o.so ........ 0.00 r===trff=====4~..l..Q B -O.SO ! ~ -1.00

i -l.SO

:i -2.00

-2.50

-3.00 L....--..----.---.----..---,.---T-----1'-o 0.30 0.40 0.50 0.60 0. 70 0.80 0.90 1.00

v,

Figure 5.3: Comparison of the predictions of eq 5.17 and experimental measurements of MA ( o ) and VAc ( o ). The volume fraction of polymer at saturation swelling was 0.365 forMA (--) and 0.437 for VAc (- - -).

At partial swelling the relationship between the monomer concentration in the aqueous

phase and the polymer phase is nonlinear leading to a monomer concentration in the aqueous

phase that is closer to saturation than the monomer concentration in the polymer phase.

Therefore, it can be concluded that in interval III of an emulsion polymerization with a

monomer with relatively high (but still limited) water solubility, a significant amount of the

monomer will be located in the aqueous phase. In this way the monomer concentration in

the polymer phase will be reduced and the polymerization rate may be lowered as the

monomer-to-water ratio is reduced. Note that also other factors may affect the rate of

polymerization (e.g., the Trommsdorff-Norrish gel effect, initiator efficiency, diffusion

controlled propagation, etc.), but these considerations are outside the scope of this thesis

and are discussed elsewhere. 15

60 Chapter 5

5.3.3 Monomer partitioning at partial swelling of latex particles by two monomers

In Figure 5.4 the relationship derived between the concentration of MA and V Ac in

the aqueous phase and polymer particles (eq 5.18) is compared with experimental results.

From the good agreement between theory and experiments it can be concluded that assumptions

(1)-(3) seem to be justified during the development of eq 5.18. It is important to note that

a sensitivity analysis has shown, 7 for typical values of all interaction parameters and molar

volumes of monomers, that the three assumptions are of algebraic necessity only: numerical

solutions of the full equations for two-monomer swelling described by eq 5 .Sa-d almost always

verify the use of the three assumptions, and also the simplified equations that result from

the use of these assumptions (e.g., eq 5.18).

2.0

~ 1.5

>p,. 1.0 J 0.5

0.0 0.0 0.5 1.0 1.5 2.0

([MA]J[V Ac].)cx

Figure 5.4: Comparison of predicted (eq 5.18; --.)and experimentally determined volume fractions of MA and VAc in the polymer phase as a function of monomer ratios in the aqueous phase multiplied by a constant a (a= 0.3010.60 for MA-VAc).

1.00

........ 0.80 ~ !

'Q' 0.60

~ '"""' 0.40

~ r;... 0.20

0.00 ""---..----.----.----....-------. 0.00 0.20 0.40 0.60 0.80 1.00

[MA]J[MA]....,(r)

Figure 5.5: Comparison of the predictions ofeq 5.19 (---)with experimentally measured concentrations forMA and VAc in the aqueous phase ([MAla.-(h) = 0.60 mol/dm3 and [VAcJ •.. ,alh) = 0.30 mol/dm3

}.

Monomer partitioning

1.00

';::;- 0.80

:;0.60 > 5o.4o ~ :::. 0.20

0.00 ~---......----.----.---........ --..... 0.00 0.20 0.40 0.60 0.80 1.00

[MA],I[MA]...,...(r)

Figure 5. 6: Comparison oft he predictions of eq 5. 20 with experimentally measured concentrations forMA and VAc in the polymer particle phase ([MA ]p.sa~(h) = 7.05 mol/dm3 and [VAc]p,safh) = 6.11 molldm3

).

61

Based on eq 5.18 relationships between monomers i andj in the aqueous phase (eq

5.19) and in the polymer phase ( eq 5.20) were developed. Here also good agreement between

experiments and theory was found as shown in Figures 5.5 and 5.6. From these results it

can be concluded that at equilibrium at a certain monomer ratio, r, the concentrations of both

monomers in the aqueous phase are equally far away from saturation values at that ratio.

The concentrations of one monomer in both the polymer and aqueous phases can be

related by eq 5 .21. As can be seen in Figure 5. 7 experiments and theory show good agreement.

Equation 5.21 was developed in analogy with a similar equation developed for homo-saturation

swelling, utilizing the concept that the free energy of mixing is dominated by combinatorial

entropy at partial swelling.

0.0

-2.5

-3.0 1...--....--....--....----....----....----......-u..., 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

v, Figure 5. 7: Comparison between predictions of eq 5.21 forMA (top line; "pMA..Jr

0.618) = 0.409) and VAc (bottom line; "pvAc,wlr 0.382) = 0.409) with experimental measurements for MA ( o ) and VAc ( o ).

62 Chapter 5

That this assumption is valid is shown by the agreement between experiments and theory

in Figure 5.7. From eq 5.21 it can be concluded that the monomer concentration in the aqueous

phase is closer to saturation than the monomer concentration in the polymer phase. For

monomers with relatively high (but still limited) water solubility a significant amount of the

monomer will be located in the aqueous phase.

For partial swelling, as for saturation swelling, it may be concluded that the entropy

of mixing of two monomers is dominant in the equilibrium reached during monomer

partitioning. The monomer ratios within the polymer phase are independent of the polymer

composition. However, in a manner similar to saturation swelling, absolute monomer

concentrations in both the polymer and the aqueous phase do depend on the polymer

composition.

The relation between the mole fraction of monomer i in the aqueous phase and the

mole fraction of monomer i in the polymer phase for saturation swelling is given by eq 5.18.

The exact same expression was also found for partial swelling (eq 5.22). Using this simple

relation(s) for both saturation and partial swelling requires only the knowledge of the individual

homo-saturation concentrations of the monomers in the aqueous phase. To prove that this

relation indeed is valid for both partial and saturation swelling theory and experiments are

compared in Figure 5.8.

1.00

0.80

0.60

·~J 0.40

0.20

0.00 "----.-----....----........ --....-----. 0.00 0.20 0.40 0.60 0.80 1.00

fp.MA

Figure 5. 8: Comparison of the predictions of eqs 5. 15 and 5. 22 (----:) with experimentally determined mole fractions of MA in the aqueous phase as a jUnction of the mole .fraction ofMA in the polymer particle phase for MA-VAc in apoly(MAVAc) latex at saturation ( o ) and partial swelling ( o ).


5.4 Conclusions

It has been shown for several monomer combinations (including MA-V Ac) that monomer

partitioning at saturation swelling can be predicted with the simplified relationships developed

by Maxwell et a/. 6 It became clear that the mixing of two monomers is independent of the

polymer type and that the ratios of monomers in the droplet and particle phases are equal.

Only the absolute value of the degree of swelling depends on the monomer and polymer

type. These results indicate that the entropy of mixing of two monomers is the dominant

contribution to the thermodynamic equilibrium reached.

Partial swelling of latex particles with one monomer can be described with the semi

empirical relation developed by Maxwell et a/. 10 This semi-empirical relation is based on

the findings that both the interfacial tension and the residual free energy terms are approximately

constant with the volume fraction of polymer and therefore can be estimated from the volume

fraction of polymer at saturation swelling. Monomer partitioning in these cases is dominated

by the contribution of the entropy of mixing of monomer and polymer.

For partial swelling with two monomers with limited water solubilities simple

relationships have been developed to predict the monomer concentrations and fractions within

the different phases. Comparison of experimental results with the developed relationships

showed excellent agreement. Similar to the saturation swelling theory, the entropy of mixing

of two monomers at partial swelling is the dominant contribution to the equilibrium.

The good agreement between experimental data and theory for monomer partitioning

at both saturation and partial swelling suggests that the theoretical development correctly

describes the thermodynamics oflatex particle swelling. Note that the use of these relationships

merely requires the individual homo-saturation values of the monomers in the polymer particles

and the aqueous phase, which are readily accessible parameters. With the relationships develo

ped for saturation and partial swelling the mole fraction of monomer i and the absolute

concentrations of monomers i and j within the particle phase can be determined. Knowledge

of the mole fraction of monomer i within the particle phase enables the prediction of

composition drift occurring in emulsion copolymerizations; the absolute concentrations of

monomers i and j in the particle phase play an essential role in better understanding and

predicting rates of polymerization. The latter is of paramount importance in determining optimal

addition rate profiles, which are indispensable in preparing compositionally homogeneous

copolymers in semi-batch processes.

64 References

I. M. Morton, S. Kaizerman, M.W. Altier, J Colloid Sci., 9, 300 (1954) 2. P.J. Flory, In Principles of Polymer Science, Cornell University Press, Ithaca, NY,

1953 3. J. Ugelstad, P.C. Mork, H.R. Mfutakamba, E. Soleimany, I. Nordhuus, R. Schmid,

A. Berge, T. Ellingsen, 0. Aune, K. Nustad, In Science and Technology of Polymer Colloids, G.W. Poehlein, R.H. Ottewill, J.W. Goodwin, Eds., NATO ASI Vol. 1, Ser. E, Plenum, NY, 1983

4. M. Nomura, K. Fujita, Makromol. Chern., Suppl., 10/11, 25 (1985) 5. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,

Polymer, 33, 1914 (1992) 6. LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chern., 193,

2065 (1992) 7. LA. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol.

Chern., Theory and Simulation, 2, 269 (1993) 8. E. Vanzo, R.H. Marchessault, V. Stannett, J Colloid Sci, 20, 62 (1965) 9. J.L. Gardon, J Polym. Sci., Polym. Chern. Ed, 6, 2859 (1968) 10. LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison,

Makromol. Chern., 193, 2049 (1992) II. H.A.S. Schoonbrood, M.A.T. van den Boom, A.L. German, J Pol. Sci., Polym. Chern.

Ed. XX, XX (1994) 12. J. Guillot, Acta Polym., 32, 593 (1981) 13. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 14. A.M. Aerdts, M.M.W.A. Boei, A.L. German, Polymer, 34, 574 (1993) 15. I.A. Maxwell, E.M.F.J. Verdurmen, A.L. German, Mak:romol. Chern., 193,2677 (1992)

Model development

Chapter 6 Model prediction of batch

emulsion copolymerization

65

Abstract: Monomer partitioning in emulsion copolymerization plays a key role in determining composition drift and polymerization rates. The combination of thermodynamically based monomer partitioning relationships described in chapter 5 with mass balance equations, makes predictions of monomer partitioning in emulsion copolymerizations possible in terms of monomer mole fractions and monomer concentrations in the particle and aqueous phases. Using this approach, the effects of monomer-to-water ratios and polymer volumes on the monomer mole fraction within the polymer particle phase in a nonpolymerizing system at thermodynamic equilibrium can be determined. Comparison of these monomer partitioning predictions with experiments for the monomer system methyl acrylate-vinyl acetate (MA-VAc) shows good agreement. Furthermore, composition drift occurring in a polymerizing system as a function of conversion can be predicted if the reactivity ratios are known and if the assumption is made that equilibrium is maintained during reaction. Comparison of predictions with experimental results for emulsion copolymerizations of the monomer systems MA-VAc and MA-indene shows good agreement.

6.1 Introduction

Attempts to model emulsion copolymerization have been made by several

investigators. 1•2

•3

•4

•5

•6

•7

•8 For this purpose, basic theories for emulsion

homopolymerization were mathematically extended to emulsion copolymerization. Due to

the complexity of the emulsion polymerization process, most data on kinetics have been

fitted with empirical models. Based on this, the values of many rate parameters have been

fitted. For correct model predictions of emulsion homopolymerization the values for the rate

parameters for entry, exit, termination, transfer and propagation of oligomeric radicals have

66 Chapter 6

to be known, in addition to the number of particles. For emulsion copolymerization, finding

correct values for rate parameters is much more complex than in the case of

homopolymerizations. The use of emulsion copolymerization models also incorporates the

knowledge of monomer ratios in the particle phase, where the reaction takes place. For

describing monomer partitioning behaviour that determines the concentration of both

monomers in the polymer phase, both empirical and a thermodynamic approaches have been

reported in the literature. 1•2•3

•45

•6

•7

•8 In the first approach empirical relationships describing

monomer partitioning were developed often based on questionable assumptions, e.g.,

assuming constant concentrations of monomers in the polymer phase during interval II of

emulsion copolymerization6 or neglecting the monomer in the aqueous phase. 1•2 Another

approach is the experimental determination of monomer partitioning coefficients3•4

•5 fitted

with empirical relationships. The thermodynamic approach developed by Morton9 for

emulsion homopolymerizations and later extended to emulsion copolymerizations 7•8

•12 is a

fundamental and promising approach. However, it involves many parameters of which the

values are often not known. Furthermore, the physical significance of the interaction

parameters used is rather vague since they often include enthalpic and entropic effects -

parameters that often depend on the polymer concentration. It is of great importance to have

(simple) relationships that correctly predict monomer concentrations in the polymer phase

since this is the basis of all models for predicting (instead of fitting) copolymer composition

and rates of polymerization.

Recently, generally accepted thermodynamic relationships9•10

'11

'12

'13 have been

simplified by Maxwell et a/. 14 for saturation swelling and by Noel et al. 15 for partial

swelling of particles by two monomers, see chapter 5. The use of these novel and simple

relationships that will be summarized in the theory part of this chapter is very convenient

since they only require the homo-monomer saturation values of the water solubility and . maximum swell ability in the polymer phase of the individual monomers to be known. It is

very important to realize that the use of these relationships does not involve the use of

ambiguous interaction parameters.

Based on these novel relationships for monomer partitioning, combined with mass

balance equations, monomer mole fractions and absolute concentrations of monomers in the

particle and aqueous phases can be calculated. Using this approach the effects of monomer

to-water ratios (M/W) and polymer volume (V po) on monomer partitioning in a certain

mixture of water, monomer, and polymer can be determined in terms of the mole fraction

of monomer i in the polymer particle phase, fr,. In this chapter results of these experiments

are compared with model predictions for the monomer system MA-VAc. From these static

Model development 67

partitioning experiments, a better understanding of monomer partitioning occurring m

emulsion polymerizations can be gained, leading to better control of copolymer formed

during reactions. The effects of water solubility of the monomers, maximum swellability

of the monomers in the polymer, and different overall monomer mole fractions on monomer

partitioning are described herein.

Apart from predicting monomer partitioning under nonpolymerizing conditions,

predictions under polymerizing conditions are also possible if the assumption is made that

thermodynamic equilibrium is maintained during emulsion copolymerization. This will be

valid if the resistance against mass transport is much lower than the resistance against

reaction. Although model predictions are compared with experimental results of emulsion

copolymerization reactions for only a couple of monomer systems, i.e., MA-vinyl esters

(VEst, this chapter and chapter 8), MA-Ind (chapter 7), and MMA-S, 16 the model in

principle covers any given monomer pair where the polymer swells with the monomer and

of which the monomers have a limited water solubility. For monomer combinations in which

the more water soluble monomer is also the more reactive one, the heterogeneity of the

emulsion system in theory can be used to minimize composition drift occurring during batch

emulsion copolymerization. The monomer system MA-Ind is chosen because it meets these

requirements. Results of these copolymerizations will be discussed in detail in chapter 7.

6.2 Theory

In emulsion systems (co )polymerization is assumed to occur mainly within the

polymer particle phase. Therefore, predictions of composition drift and/or rates of

polymerization can only be performed in a correct manner if the mole fraction of monomer

i in the polymer particle phase is known as a function of conversion. In chapter 5 the

following basic equation for two monomer partitioning in emulsions has been derived14•1s· 17

[MJ.(r)

= In ( [MJ._sa~(h) ) [Mi].(r)

[M) •. ,.lh)

(6.1)

The use of the left hand side of this equation directly results in equal mole fractions in the

polymer and monomer droplet phase (eq 5.12a,b).

With eq 6.1, relationships for saturation and partial swelling were derived describing

monomer partitioning in latex systems with two monomers. However, to predict monomer

68 Chapter 6

concentrations in all phases for a given monomer-water-polymer mixture, the monomer mole

fraction in the polymer phase must be known. These monomer mole fractions in the polymer

phase can be calculated when combining monomer partitioning relationships with mass

balance equations for each component. When using this combination, predictions of

monomer mole fractions in the polymer phase can be made in nonpolymerizing monomer

partitioning experiments using parameters with physical significance (water solubilities,

maximum swellabilities of monomer in polymer) only. Moreover, this procedure can be

extended to model predictions of emulsion copolymer composition and polymerization rate

if thermodynamic equilibrium in monomer partitioning is assumed during reaction. Since

different relationships are valid for saturation and partial swelling, separate model

developments are described in the next two sections.

6.2.1 Saturation swelling of latex particles by two monomers: determination of t;u.

In chapter 5 the following eqs are given to describe the monomer concentration in

the polymer phase, 14

(6.2a)

(6.2b)

and in the aqueous phase,

(6.3a)

(6.3b)

and the relation between the mole fraction of monomer i in the polymer and aqueous

phases Is

(M J.,,.,(r) (6.4a) fpi.sat (I - a) + a

where a is the ratio of the water solubilities of monomer j over monomer i (a =

[M;la.sat(h)/[M.J •. , • .(h)). The self evident relationship between the monomer mole fractions

and the monomer mole ratios (q, [M;]/[M;D is given by:


(6.4b)

where qpl,sat is the mole ratio of monomer i over monomer j in the polymer phase at

saturation swelling. Using eq 6.4b to rewrite eq 6.4a gives:

(6.4c)

where lk,sat is the mole ratio of monomer i over monomer j in the aqueous phase at

saturation swelling. The result shown in eq 6.4c is consistent with the right hand side of eq

6.1. Eqs 6.4a-c have been shown to be valid for both partial and saturation swelling~ in

chapter 5. In case of partial swelling the subscript sat and the extension (r) should be

removed from relationships 6.4a-c.

Using eqs 6.3-6.4 enables one to predict monomer partitioning for known mole

fractions of monomer i in the polymer phase. However, for model development this mole

fraction of monomer i in the polymer phase needs to be predicted for known monomer

water-polymer mixtures. This can be done by taking mass balance equations for monomers

i and j at saturation swelling into account. For this reason the following mass balance

equations were formulated and used for the first time in this context:

M1,, [M Ja,sat(r) V a + [M Jp,sa,(r) V P + [M Jd,sat(r) V d (6.Sa)

(6.5b)

where M1,, and Mj,t are the total moles of monomers i and j in the system; V •' V P' and V d

are the volumes of the saturated aqueous phase (the volume of water+ monomer dissolved

in it), the monomer swollen polymer phase (the volume of the polymer + monomer in the

saturated polymer), and the monomer droplet phase. Using eq 5.l2a and rewriting fdi,sat in

terms of monomer ratios we find for [Mj]d:

(6.6)

Combining eqs 6.5a-b and 6.6 leads to a more simple equation in which the monomer

droplet phase does not appear any more. Using this simplified expression together with eqs

6.2a-b and 6.3a-b yields:

M,,, M,,, = V. ([MJ •. ,.,(h) - [M) •. ,ih))

( 1 - fpi.sat) (6.7)

70 Chapter 6

in which fpi,sat and V. are the two unknowns.

A second expression of V • as a function of fpi,sat can be determined from the mass

balance equation of the aqueous phase when volume additivity of water and monomer

dissolved in the aqueous phase is assumed. This will result in a relationship between v. (volume of the aqueous phase including monomer) and V w (volume of the aqueous phase

without monomer):

v. (6.8)

in which MW1 and MWj are the molecular masses of monomers i and j and P; and pj are

the densities of monomers i and j. Using eqs 6.3a-b to replace the unknowns [M;] .. 581 and

[MJ .... , by a relationship in fp;,sat in eq 6.8, and thereafter combining eqs 6.7 and 6.8, will

lead to a second-order equation in fpi.sat' This can be solved to yield fpi,sat·

Solving the resulting relation for saturation swelling gives the mole fraction of

monomer i in the polymer phase for a certain monomer-water-polymer mixture at saturation

swelling. This prediction can be used to describe monomer partitioning in interval I and II

situations in emulsion copolymerization reactions.

6.2.2 Partial swelling of latex particles by two monomers: determination of t;,..

At partial swelling there is no droplet phase present so the middle expression in eq

6.1 is redundant, resulting in the following equality:

[MJ. [M) •. 581(h)

[M). [M J .. ,.,(h) (6.9)

Note that below saturation the subscript ,..(r) is removed. Rewriting eq 6.9 in terms of

monomer mole ratios will give similar relationships to eqs 6.4a and 6.4c. As stated before

it can be concluded from this that eqs 6.4a-c hold for both saturation and partial swelling

of latex particles by two monomers with limited water solubility. Furthermore, it has been

shown15 that at equilibrium and at a certain monomer ratio, r, the concentrations of both

monomers in the aqueous phase and also in the polymer phase are equally far away from

saturation values at that ratio. For the aqueous phase this leads to:

[MJ. F,., • (6.10)

and for the polymer phase:

Model development

[MJP

[M Jp.sat(r)

[M)P

[M .1 sat(r) jJp,

71

= F, .. P (6.11)

where the degree of saturation of the aqueous and polymer phases is expressed by Fsat. and

F sat P' respectively.

In chapter 5 the relationship between the volume fraction of monomer i in the

polymer and the concentration in the aqueous phase is given by: 15

v. ln __ P_'_ + v

v pi,sat(r) P ( ) 1

[M J. v r = n-:::-::-::---,-.,-

p,sat [M .] (r) 1 a,sat

(6.12)

Using eqs 6.9-6.12 allows one to predict monomer partitioning for known mole

fractions of monomer i in the polymer phase. However, for model development this mole

fraction of monomer i in the polymer phase needs to be predicted for known monomer

water-polymer mixtures. This again can be done by taking mass balance equations for

monomers i andj at partial swelling into account. For this reason the mass balance eqs 6.5a

b were reduced to 6.13a-b:

(6.13a)

(6.13b)

Note that in the following model development for partial swelling the monomer mole ratio

(~) replaces the mole fraction (fp~) of monomer i in the polymer phase. With eq 6.4b a

direct relationship between the monomer ratio and fraction is given. From eqs 6.13a-b and

6.4b we find for [M;]. and [M1],:

(6.14a)

(6.14b)

(6.1Sa)

(6.15b)

Assuming volume additivity of water and monomers dissolved in the aqueous phase the

72 Chapter 6

volume of the aqueous phase v. (water+ monomers), can be calculated with a mass balance

equation similar to eq 6.8:

v. (6.16)

The volume of the swollen polymer phase can be calculated by a mass balance

equation of the polymer phase assuming volume additivity of polymer and monomer located

in the polymer phase:

vpo (6.17)

where Vpo is the volume of the polymer in the polymer phase (i.e., without monomer).

Combining eqs 6.l4a-b and 6.16 results in a relation for v. (aqueous phase +monomer)

with qp; as the only unknown parameter. A similar relation in <~p1 can be found for V P when

combining eqs 6.1 5a-b with eq 6.17. With known monomer mole ratio in the polymer phase,

the volume of the aqueous phase including dissolved monomer (V.) and the swollen volume

of the polymer phase (V p) can be calculated. Using eqs 6.2a-b and 6.3a-b gives the aqueous

and polymer phase monomer concentrations at saturation at that monomer mole ratio, r (i.e.

[M,].,sa~(r}, [M1]a,sat(r), [M;]p,,alr), and [Mj]p,sat(r)). Using the values for V. and VP, [M,]. and

[M1]p the degree of saturation in the aqueous (F,.t.) and polymer (F,at p) phases can be

calculated using eqs 6.14a, 6.15a, and 6.1 0-6.11.

Combining eqs 6.10, 6.11, 6.12, and knowing that vp/vp,,sat(r) equals [M1]/[M1]p,sat(r)

we find: F

In (~) = v ""(r) - v F p, P sat a

(6.18)

6.15b and 6.18 yields:

(6.19)

where qpi,catc stands for the calculated mole ratio of monomer i in the polymer phase at partial

swelling. With known qP, (or fp,) the right-hand term of eq 6.19 can be calculated resulting

in qp;,catc· Continued iteration until abs.(qp,- qpi.catc) reaches a small tolerance value gives the

correct mole ratio of monomer i in the polymer phase.

Based on the model for partial swelling presented in this section, the mole fraction

of monomer i in the polymer phase can be calculated for a certain monomer-water-polymer


mixture. The results of these calculations can be used to describe monomer partitioning at

partial swelling, i.e., in interval III situations in emulsion copolymerization reactions.

6.2.3 Model calculations in emulsion copolymerization.

Since polymerization in emulsions is assumed to occur in the polymer particle phase,

the monomer mole fraction in the polymer phase, fp;, has to be used instead of the overall

monomer mole fraction (f0; MA/(M11 + M~) to calculate the instantaneous copolymer

composition. In the previous two sections, models have been developed to predict the

monomer mole fraction in the polymer phase for a given monomer-water-polymer mixture

at both saturation and partial swelling. Using the models for saturation and partial swelling

a computer program has been written to predict the course of emulsion copolymerization.

A flow diagram of this program is presented in Figure 6.1.

Based on the homo-monomer saturation values of monomers i and j in the polymer

([M;]p.salh), [M1]p,sa,(h)) and aqueous ([M;].,,m(h), [MJ.,, • .(h)) phases it can be determined in

a quite straightforward way whether the model for saturation or partial swelling should be

applied to a given monomer-water-polymer mixture (V., VP, M11, and M;J. From the water

solubility and maximum polymer swellability values combined with recipe conditions, the

monomer mole fractions can be calculated using eqs 6.2-6.8 in the case of saturation

swelling, and eqs 6.9-6.19 and repeated iteration in the case of partial swelling. The

instantaneous copolymerization equation 18•19 (eq 2.2; fp; instead of f;) will give the

copolymer composition in mole fraction of monomer i (F;) as a function of the reactivity

ratios and the mole fraction of monomer i in the polymer particle phase.

Assuming that monomer partitioning equilibrium is maintained despite

polymerization, complete emulsion polymerization can be predicted in the following manner,

provided that small successive conversion steps are taken until complete conversion. The

conversion steps taken need to be small enough to ensure a nearly constant mole fraction

of monomer i in the polymer, and as a consequence an also almost constant copolymer

composition during this conversion step. As a result of polymerization the total monomer

(M;., MJt) and polymer (V po) quantities will change slightly during each conversion step. The

monomer mole fraction in the polymer phase at the next small conversion step can then be

calculated with slightly different monomer and polymer concentrations, again using eqs 6.2-

6.8 for saturation swelling and eqs 6. 9-6.10 for partial swelling. Based on this approach,

prediction is possible of inter alia, fP;' F" [M;]., and [Mj]P as a function of conversion.

74

X:= X +0.01

YES

recalculate Mit , MJ1 , V po for x: = x + 0.01 using eq 2.2

x: =X+ 0.01

NO

recalculate M;1 , Mjt , V po for x: = x + 0.01 using eq 2.2

if x:= I then prediction of emulsion copolymerization as

function of x is complete

Chapter 6

Gpi,in: = qpi,in • C2

Figure 6. 1: Flow diagram of the program used for predictions of emulsion copolymerization. Tol stands for a small tolerance value, CJ and C2 are constants, x is conversion, and qp;,,.1, qP'·"' and qpi,caii· are the mole ratios of monomer i at the end of saturation swelling, and the start value and resulting value of consecutive conversions steps at partial swelling, respectively.


The use of the models presented herein for saturation swelling and partial swelling

only require that the homo-monomer saturation values in the polymer and aqueous phases

are known for a given monomer-water-polymer mixture. Predictions of monomer partitioning

experiments for a given monomer-water-polymer mixture in terms of mole fraction of

monomer i in the polymer phase and based on this predictions of complete emulsion

copolymerizations as a function of conversion now can be made quite easily.


Monomer partitioning in latex systems at partial swelling with one or two monomers

can be described by eq 6.18 as can be concluded from Figure 6.2 where monomer

partitioning predictions are successfully compared with experimental results for homo-MA

and MA-V Ac combinations if the experimental error resulting from gas chromatography

is taken into account. Furthermore, from Figure 6.2, it can be concluded that at partial

swelling the aqueous phase is closer to saturation than the polymer phase, i.e. F sat. > F sat p·

Thus, for monomers with a relatively high but limited water solubility a considerable amount

of the monomer can be located in the aqueous phase. Note that the curvature of lines

predicted with eq 6.18 depends upon the volume fraction of polymer at saturation swelling

and therefore also on the maximum swellabilities of monomer in polymer. However, the

difference in volume fraction of polymer at saturation swelling for homo-monomer swelling

of MA compared with V Ac is relatively small (0.3 7 for MA and 0.44 for V Ac ), and

therefore all monomer partitioning results for homo-monomer as well as for co-monomer

experiments can be compared with one theoretical line.

1.00

= .g, 0.80

~ ~ 0.60 0 Q,

~ 0.40 .I :: 0.20

0.00 l!t-:........--r-~--.-~--r--~-.--~-. 0.00 0.20 0.40 0.60 0.80 1.00

% saturation aqueous phase Figure 6. 2: Comparison of the predictions of eq 6.18 (line) with experiments for homo-saturation of MA (D), and two monomer (MA-VAc) experiments at several overall monomer fractions forMA (.1) and VAc (o).

76 Chapter 6

6.3.1 General monomer partitioning considerations.

In this thesis monomer i has been chosen to be the monomer with the higher water

solub~lity. Adding more water to a certain monomer-water-polymer mixture will especially

withdraw monomer i from the polymer phase into the aqueous phase leading to lower values

of the mole fraction of monomer i in the polymer phase. In general this means that by

choosing a monomer-to-water ratio or polymer volume one is able to control the monomer

composition in the polymer particle phase. This is the main issue in the following section.

Two extreme monomer partitioning situations may occur in emulsion polymerization

resulting in a maximum and a minimum value for the mole fraction of monomer i in the

polymer particle phase.

The maximum value of the mole fraction of monomer i in the polymer phase is

reached if all monomer is located in the monomer droplet and polymer particle phases. In

this case, the mole fraction of monomer i in the polymer phase equals the overall mole

fraction of monomer i, i.e., fJ>i,max f01• This will occur at saturation swelling when the

amount of monomer dissolved in the aqueous phase is negligible as compared with the total

amount of monomer (large monomer droplet and polymer particle phases as compared with

aqueous phase) or if the water phase concentration is too low to significantly affect the

monomer amounts within the monomer droplet and polymer particle phases.

The minimum value for the mole fraction of monomer i in the polymer particle phase

is reached when all monomer is dissolved in the aqueous phase. In this case the mole

fraction of monomer i in the aqueous phase equals the overall mole fraction of this

monomer, fa~ = f01• From this mole fraction of monomer i in the aqueous phase, the minimum

mole fraction of monomer i within a hypothetical polymer phase, fpi,min• can be determined

with eqs 6.4a-c if the ratio of the water solubilities of monomer j over monomer i, i.e., if

a = [Mj].,, .. (h)/[M J.,,.,(h) is known. In the absence of polymer the minimum mole fraction

of monomer i in the polymer phase is only a hypothetical quantity. However, if there would

be a small amount of polymer in the monomer-water-polymer mixture, with a negligible

effect on monomer partitioning, the mole fraction in the polymer phase would be very close

to the hypothetical minimum mole fraction. The value of fpi,min strongly depends upon the

a-value as can be seen in Figure 6.3 where it is clearly shown that the difference between

fpi,max and fpl,min is larger for smaller a-values. This fpi.min can be reached only if the monomers

have high water solubilities, if the monomer-to-water ratio is low and if the amount of

polymer phase is too small to affect monomer partitioning.

Model development

1.0

-C+-40. 0.5

0.0 0.0 0.5 1.0

Figure 6.3: The extreme values of the mole fraction of monomer i in the polymer phase (t;,) are given by the maximum, J;,,,max (all monomers in the polymer porticle and monomer droplet phases), and the minimum, J;,;,mm (all monomers in the aqueous phase) monomer mole fraction in the polymer phase for several values of a = [M}a.salh)I[MJa..mlh), a = 0.5; 0.267 and 0.005.

77

For a nonpolymerizing monomer partitioning experiment with an arbitrary monomer

water-polymer mixture, the value of the mole fraction of monomer i in the polymer phase

can be calculated using the relationships presented in the "Theory" section of this chapter

for saturation or partial swelling. Depending on mixture conditions, e.g., monomer-to-water

ratio (M/W) and the polymer volumes (V po), the value for the mole fraction of monomer

i in the polymer phase will vary between fP'·"""' and fp;,min· From Figure 6.3, we can conclude

that the effect of different monomer-water-polymer mixture conditions on monomer

partitioning is the largest for small values of a. Furthermore, in Figure 6.3 the effect of

overall monomer mole feed fractions (f01), on fp;,max and fpl,min and the maximum difference

between this maximum and minimum value for the mole fraction of monomer i in the

polymer phase, i.e., fp;,m"" - fpl,min• can be seen. Note that if a= I there will be no effect of

different monomer-to-water ratios and polymer volumes on the mole fraction of monomer

i in the polymer phase, i.e., fp;,mll>< fpi,min· However, if a= 1, and if the monomer amount

is kept constant, the volume of the droplet phase will decrease with increasing water amount

(i.e., decreasing monomer-to-water ratio) or increasing polymer volume at saturation

swelling. At partial swelling the absolute concentrations of monomers in both the polymer

78 Chapter 6

particle and aqueous phase will decrease with increasing water content (decreasing monomer

to-water ratio} and increasing polymer volume due to dilution effects.

6.3.2 Monomer partitioning of MA-VAc monomer systems.

The effect of different monomer-water-polymer mixture conditions, e.g., the

monomer-to-water ratio and the polymer volume, upon the monomer mole fractions in the

polymer phase can be predicted by the models developed herein. In the MA-V Ac monomer

system, MA will be the monomer with higher water solubility resulting in a ratio of water

solubilities of V Ac and MA of 0.5. The extreme values of the monomer mole fractions in

the polymer phase for MA-VAc with an overall monomer mole fraction ofMA equal to 0.5,

are fp;,max=O.S and fp;,min=0.333 as can be seen in Figure 6.3. For the MA-VAc monomer

system the effect of increasing monomer-to-water ratio in the absence and presence of

polymer at an overall monomer mole fraction of 0.5 was investigated.

If there is no polymer phase present at an overall monomer mole fraction of 0.5 and

if the aqueous phase is kept constant at a volume of V w = I dm3, the effect of different

monomer-to-water ratios on the mole fraction of MA in the hypothetical polymer phase

is the largest, i.e., going from the hypothetical minimum monomer mole fraction at low

monomer-to-water ratios (f~.min

monomer-to-water ratios (f~ ...... )

o.so

0.45

.._.'& 0.40

0.35

0.33) to the maximum monomer mole fraction at high

0.5, as shown in Figure 6.4.

saturation

0.30 '-~-~--.---.....--.--....----....-....--....----. 0.00 0.20 0.40 0.60 0.80 1.00

M/W (gjg)

Figure 6.4: Predictions for saturation and partial swelling of the mole fraction of MA in the polymer phase if;,AvJ as a jUnction of the monomer-to-water ratio (MIW) for the MA-VAc monomer combination at an overall monomer mole fraction of /,,MA = 0.5 in the absence of polymer.


At similar overall monomer mole fractions of 0.5, in the presence of polymer with

a volume of V PO that can swell with MA and V Ac, the minimum value for the mole fraction

·of MA in the polymer phase, ~ 0.33, will not be reached at similar values for the

aqueous phase volume (V w) and the monomer-to-water ratio, due to monomer partitioning

between the polymer and aqueous phase. In Figure 6.5 (Vw = 1 dm3, VPO = 0.05 dm3,

varying M/W) one can see that in the presence of a polymer with volume V PO 0.05 L, the

lowest value for the monomer mole fraction of MA in the polymer phase is indeed higher

than fpMA,min 0.33. The presence of polymer makes the maximum difference in mole fraction

of MA in the polymer phase (t;,i,max - fpi,min) smaller. Furthermore, the saturation swelling

region will start at higher monomer-to-water ratios (Figure 6.4 as compared with Figure 6.5)

in the presence of polymer.

0.50

0.45

..._., 0.40 saturation

0.3S

0.30 L...--+--.----.....----..-----.r-----. 0.00 0.20 0.40 0.60 0.80 1.00

MfW (gig)

Figure 6.5: Comparison of model predictions (line) with experimental (o) values of the mole fraction of MA in the polymer phase (f,uJ for partial and saturation swelling as a function of the monomer-to-water. ratio (MIW) for the MA-VAc monomer combination at overall fractions of MA of /.,MA 0.5, in the presence of polymer with a volume of 50 cm3 polymer I dm1 water.

The effects of different monomer-water-polymer mixtures, i.e., different monomer-to

water ratios and polymer volumes, on the monomer mole fraction in the polymer phase, are

based on withdrawing monomer from the monomer droplet and polymer particle phase into

the aqueous phase. Therefore, changing of these monomer-water-polymer mixture conditions

will have the largest effect on the monomer mole fraction in the polymer if only one of the

monomers has a relatively high but limited homo-monomer saturation concentration in the

aqueous phase. For monomer systems in which monomer i is the more water soluble

monomer, the effects of increasing monomer (at constant volumes of polymer and water),

polymer (at constant volumes of water and monomer) and water (at constant volumes of

80 Chapter 6

monomer and polymer) volumes on the mole fraction of monomer i in the polymer phase

at constant overall monomer mole fractions are combined in Table 6.1. The increasing,

decreasing, or constant mole fraction of monomer i in the polymer phase as a result of

different water (V w), polymer (V po) and monomer (M11 and M.J are represented in Table 6.1

by +,, • and o respectively.

Table 6.1 The efficts of increasing water, polymer or monomer volumes on J;,,; - = decrease, + = increase and o = no effect (constant fo)

constant fo; at saturation swelling partial swelling

increasing volume of: fpi,sal fpi

water: Vw -/o monomer: M;t, M;t + + polymer: V po 0 +

It is trivial that increasing the volume of the aqueous phase at partial swelling in the absence

of polymer in the monomer-water-polymer mixture will have no effect on the, in this case

hypothetical mole fraction of monomer i in the polymer phase (see also Figure 6.4}, while

in the presence of polymer a decrease in the mole fraction of monomer i in the polymer

phase will appear for an increased volume of the aqueous phase (see also Figure 6.5).

Furthermore, in Table 6.1 it is shown that increasing the polymer volume at saturation

swelling will lead to more saturated polymer phase and a smaller volume of monomer

droplet phase leaving the mole fraction of monomer i in the polymer phase unaffected.

However, one should realize that, starting at saturation swelling, a large increase in polymer

volume will lead to a shift from saturation towards partial swelling resulting in a constant

mole fraction of monomer i in the polymer phase at saturation swelling followed by an

increase in mole fraction of monomer i in the polymer phase at partial swelling. Using the

results represented in Table 6. I one can see the effects on the mole fraction of monomer

i in the polymer phase of different monomer, polymer, and water volumes and combinations

of these quantities such as monomer-to-water ratios at constant overall monomer mole

fractions. Knowing whether the mole fraction of monomer i in the polymer phase will

increase or decrease, predictions of monomer concentrations in the polymer phase and

aqueous phase can be made using eqs 6.2a-b and 6.3a-b at saturation swelling and 6.14a-b

and 6.15a-b at partial swelling.

The models developed in this chapter for saturation and partial swelling are compared


with experimental monomer partitioning results for MA-VAc in Figure 6.5. From the good

agreement between predictions and experiments it can be concluded that the models are

. capable of correctly predicting monomer mole fractions in the polymer phase for static

monomer partitioning experiments including a certain polymer volume.

From chapter 5 we known that the monomer mole fraction is equal in the polymer

and monomer droplet phase, fpi,sat = fdi,sat· The maximum swellability of monomer in the

polymer is determined by an equilibrium between the interfacial tension and the mixing of

monomer with polymer. Nomura et a/.20 found that the maximum swellabilities were

independent of copolymer composition for MMA-S. However, Maxwell et a/. 14 and van

Doremaele et a/. 4 showed that copolymer composition does have an effect on the homo

monomer swellabilities of monomer in the polymer phase for MA-S. Van Doremaele4

concludes, however, that this small effect of copolymer composition on homo-monomer

saturation values is negligible in practical situations. Furthermore, Maxwell et a/.21 pointed

out that temperature effects upon monomer partitioning are within experimental error for

MA-S in the temperature range from 20-45°C. However, it is known that water phase

concentrations of monomers are temperature dependent. From model predictions and theory

it can be concluded that at partial swelling the water solubilities (i.e., homo-monomer

saturation concentrations in the aqueous phase), the ratio of the water solubilities of both

monomers (a-value), the maximum swellabilities in the polymer phase (homo-monomer

saturation concentrations in the polymer phase) of monomers i and j, and the presence and

volume of polymer, will affect the monomer mole fraction in the particle phase. The point

where saturation swelling should be used instead of partial swelling depends on the same

parameters - namely the water solubilities, the maximum swellabilities, and the polymer

volume. At saturation swelling, the water solubility of the monomers and the ratio of these

water solubilities (a-value) affect the monomer mole fraction in the polymer phase, while

the maximum swellabilities of monomer in the polymer phase will only affect the absolute

concentrations of monomers i and j in the polymer phase and the volume of the monomer

droplet phase, leaving the monomer mole fraction in the polymer phase unchanged. Since

equal monomer mole fractions are found in the monomer droplet and polymer particle phase

at saturation swelling, i.e., fp; = fd;• the use of polymer volume in the case of saturation

swelling only affects the volume of the polymer and the monomer droplet phases and

certainly not the monomer mole fraction in the polymer phase. This result, already

represented in Table 6.1 is also illustrated by the similarity between Figures 6.4 and 6.5 at

saturation swelling.

82 Chapter 6

6.3.3 Prediction of emulsion copolymerization composition.

To predict the course of emulsion polymerizations using the models for saturation

and partial swelling presented herein, the homo-monomer saturation values in the polymer

and aqueous phases and the reactivity ratios for the chosen monomer system must be known.

For the MA-V Ac monomer combination, the reactivity ratios can be found in the

literature22 (r~ = 6.3 ± 0.4, rvAc = 0.031 ± 0.006). The homo-monomer saturation values

in the polymer and aqueous phase are listed in Table 3.5. In predictions of complete

emulsion copolymerization reactions, it is important to have accurate data on homo-monomer

saturation data and reactivity ratios since the calculations are sensitive to the values of these

quantities. Typical confidence intervals for homo-monomer saturation swelling are in the

range of 5-10% accuracy, while the accuracy in reactivity values strongly depends on the

calculation method used23 in combination with the number of experiments, and also on the

accuracy of the experimental method used. The influence of deviations in model parameters

will be discussed in the sensitivity analysis presented in the appendix.

For reactions with high monomer-to-water ratios starting in interval II, the homo

monomer saturation concentrations in the polymer phase only affect the absolute monomer

concentrations in the polymer phase leaving the monomer mole fraction in the polymer phase

(fp; . ..J unaffected. The large effect of the o:-value can be taken into account when using

homo-monomer saturation values in the aqueous phase determined at reaction temperature

(values are listed in Table 3.5). Predictions of the course of emulsion polymerization in

terms of monomer mole fractions in the polymer phase as a function of conversion, or

numbers of mole of monomers i and j as a function of conversion result in important

composition drift data. Since gas chromatography of reaction samples will give overall

values of the mole fraction of monomer i, experimental values for this overall monomer

mole fraction as a function of conversion will be compared with model predictions.

For the MA-V Ac ·monomer system experimental and predicted results of the overall

monomer mole fraction as a function of conversion are compared in Figure 6.6 (initial

reaction recipe is shown in Table 6.2). As can be seen by the strong decrease in the overall

monomer mole fraction with increasing conversion, there is strong composition drift. This

could be expected since the reactivity values in MA-V Ac copolymerizations are very far

apart (by a factor of200). Gas chromatography yields, as well as the overall monomer mole

fractions, the total moles in the reaction mixture, i.e., MMA.< and MvAc.1, as a function of

conversion. The number of moles as a function of conversion are presented in Figure 6.7.

Again a strong composition drift occurs leading to faster reaction ofMA (stronger decrease)


due to the higher reactivity ratio of MA Table 6.2 MA-VAc recipe for a kinetic batch

(rMA = 0.63) as compared with VAc (rvAc polymerization with a monomer-to-water ratio (MIW) of 0.1.

= 0.03). At 70% conversion the MA has

completely disappeared resulting m

homopolymerization of V Ac.

From the good agreement shown

in Figures 6.6 and 6.7 between model

predictions and experimental results for

the overall monomer mole fraction (f0MA)

and the numbers of moles (MMA,t and

Ingredients (g)

MA

VAc

Water

NaPS

SDS

Na2C03

Kinetic run

45

45

917.4

0.219

1.313 0.098

M_,,) as a function of conversion, it can be concluded that the relationships used to predict

the monomer mole fractions in the polymer phase are indeed capable of correctly predicting

the course of emulsion polymerization for saturation swelling and partial swelling. Note that

the reactivity ratios and the homo-monomer saturation values used for model predictions

are accurate enough to obtain good agreement between experimental results and model

predictions.

Comparison of model predictions of emulsion copolymerization composition as a

function of conversion with experimental results for the MA-Ind monomer system show

good agreement as can be seen in Figure 7.7 (initial reaction recipes are shown in Table 7.1).

From this, it can be concluded that the above described approach can be used not only for

MA-V Ac, but also for other monomer systems. The reactivity ratios of the monomer system

MA-Ind (rMA = 0.92 and r100 = 0.086) are less far apart than those of MA-VAc (a factor of

10 for MA-Ind as compared with a factor of200 for MA-VAc) leading to less composition

drift. The large effect of different monomer-to-water ratios on composition drift shown in ,._ Figure 7.7 is typical for a system like MA-Ind where one of the monomers (MA) is very

water soluble. This effect will be discussed in more detail in chapter 7.

From the good agreement shown in Figures 6.6, 6.7 and 7.7 between experimental

results and model predictions it can be concluded that the models for saturation and partial

swelling developed in this chapter provide a good description of the course of emulsion

copolymerization. Furthermore, it can be concluded that the reactivity ratios (Table 3.7) and

homo-monomer saturation values (Table 3 .5) used in the model predictions of MA-V Ac and

MA-Ind emulsion copolymerizations were determined accurately enough to obtain good

agreement between predicted and experimental results.

84

0.60

o.so

0.40

~0.30 ..... 0.20

0.10

0.00 1--.----,,.-------.---....-'+-<,..... ...... ~~ 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Chapter 6

Figure 6. 6: Comparison of predictions (line) with experimentally determined values (o) of the overall mole fraction of MA (f~ as a function of conversion for the monomer system MA-VAc (Initial recipe: MIW 0.1, Vpo = O,f.MA = 0.5).

::::: 0

0.60

o.so

a o.4o .._

-~ 0.30 :I ,0.20

0.10

0.00 L-~-...----.-----...__;:--------4P 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 6. 7: Comparison of predictions for the number of moles of MA and VAc (lines) with experimentally determined results for MA (o) and VAc (D) as a function of conversion (Initial batch recipe: MIW = 0.1, V"', = 0, f.,MA 0.5).

6.4 Conelusions

Combining thermodynamically-based monomer partitioning relationships for

saturation14 and partial swelling 15 with mass balance equations results in a model for

saturation and a model for partial swelling, in either case predicting the mole fraction of a

certain monomer i in the polymer phase. The effect of monomer-to-water ratio and polymer

volume on the monomer mole fraction in the polymer phase can be well predicted with the


relationships described in this chapter.

The ratio of homo-monomer saturation concentrations in the aqueous phase of

monomer j over monomer i (monomer i being the more water soluble monomer) has shown

to play a key role in determining the resulting mole fraction of monomer i in the polymer

phase.

With the models presented in this chapter it is possible to predict emulsion

copolymerization in terms of monomer mole fractions within the particle phase (composition

drift) and absolute monomer concentrations as a function of conversion. Predicted emulsion

polymerization behaviour compares quite acceptably with experimental results forMA-V Ac

and MA-Ind especially when considering that these predictions were made without any

adjustable parameters. The approach presented in this chapter is valid for all monomer

systems that have equal monomer mole fractions in the polymer and droplet phase at

saturation swelling. It has been shown experimentally 14•15 and theoretically17 that this

condition is met for several monomer systems. Possible exceptions are monomers that do

not swell their polymer and monomers that are fully miscible with water. It must be realized

that the approach presented here is very convenient since it only requires the homo-monomer

saturation values in the polymer and aqueous phase, which can easily be obtained from

experiments. This means, the copolymer composition in a batch emulsion copolymeriza!ion

can be predicted, a priori, without the use of any adjustable parameters!

86 Chapter 6

Appendix: sensitivity analysis

A-6.1 Introduction

In chapter 6 a model has been developed capable of predicting absolute monomer

concentrations and their ratios in the polymer, aqueous, and monomer droplet phases as a

function of conversion in batch emulsion copolymerizations. This model will be referred

at as "the model" in the rest of this thesis. In this appendix the sensitivity of model

predictions of composition drift toward deviations up to 1 0% in all model parameters is

estimated using the monomer combination MMA-S as an example.

Assuming the formation of homogeneous particles, model predictions can be

performed if the reactivity ratios, water solubilities, maximum swellabilities, monomer and

polymer densities, and the recipe conditions (monomer amounts and water volume) are

known. Although the model has been shown to give good agreement between theory and

experiments,24 it is of great importance to know the sensitivity of the model predictions

to the various parameters. For this reason, this appendix investigates the effects of deviations

in water solubilities, swellabilities, reactivity ratios, and monomer and polymer densities on

the predicted course of emulsion copolymerization in terms of composition drift and absolute

monomer concentrations. The effect on copolymer composition can be seen by studying the

change of the monomer mole fraction in the polymer phase for different parameter values

as a function of conversion. Note that any effects of model parameters on the monomer mole

fraction in the polymer phase can be linked directly with copolymer composition by the well

known instantaneous copolymer equation (eq 2.2). 18'19 The MMA-S monomer system was

selected since it has been the subject of several investigations, l,20.2S,l6.27

•28

•29

·3ti.JI.32

resulting in many known parameters.

For model predictions of MMA-S, amongst others, the maximum swellability and

water solubility need to be known. Comparing results of Nomura et al. 20 who found that

the maximum swellabilities of S and MMA in the copolymer MMA-S were independent

of the copolymer composition at so•c, with results of other investigators 33•4 indicates that

maximum swellabilities are temperature independent in the range of20-so•c. Based on these

data we adopted for the present sensitivity analysis the copolymer independent maximum

swellabilities: [MMA]p.sat 6.3 ± 0.6 mol/dm3 and [S]p.sat 5.5 ± 0.6 mol/dm3• These values

were validized by Noel et a!. by comparing monomer partitioning results with conductivity

Appendix: sensitivity analysis 87

measurements.24 All other model parameter values were either found in the literature or have

been determined experimentally at 40"C by using densimetry for density values and gas

chromatography analysis of monomer-saturated water for the determination of the water

solubility of MMA. 24 All standard parameters used for model predictions are listed in Table

A-6.1.

The sensitivity of model predictions is estimated for deviations up to I 0% in the

model parameters shown in Table A-6.1 (total deviation is 20%). The 10% deviation in

model parameters is selected since it represents the estimated precision in some of the model

parameters. For convenience this 10% deviation has been used for all model parameters that

have been the subject of this sensitivity analysis.

Table A-6.1: Model parameters used for model predictions of MMA-S copolymerizations at 4(J'C

model parameter MMA s swellability (mol/dm 3) 6.3 5.5

water solubility (mol/dm3) 0.12. 3.8•10'3 b

monomer density (kg/dm3) 0.918. 0.887<

polymer density (kg/dm3) l.l49" 1.046c

reactivity ratiosd 0.46 0.523

A-6.2 Results and discussion

a these values were determined experimentally by densimetry or gas chromatography. b value determined by Lane et al. 34

c values determined by Patnode et al.Js d values determined by Fukuda et a/. 26

On behalf of the sensitivity analysis, a standard recipe was adopted for the model

predictions of MMA-S copolymerizations with a monomer-to-water ratio of 0.2 and an

overall monomer mole fraction of fo,MMA = 0.5 (SM4: Tables A-6.2 and A-6.3). All possible

deviations in model predictions resulting from the use of other model parameters were

compared with this standard recipe. The deviating model parameters are shown in Tables

~-6.2 and A-6.3. Deviations in changing homo-monomer saturation concentrations and

reactivity ratios are expected to depend on the monomer-to-water ratio. For this reason, the

effects of deviations in model parameters on the mole fraction of MMA in the polymer

phase, fp.MMA> is also studied as a function of changing monomer-to-water ratios (SMI-SM6}.

88 Chapter 6

Table A-6.2: Standard (SM4) and deviating model parameters (SM1-SM12) used to perform a sensitivity analysis of the theoretical batch emulsion copolymerization model: the sensitivity ofhomo-monomer saturation concentrations, monomer-to-water ratios and overall monomer mole fractions are tested All other parameters as in Table A-6.1.

name MJW fo,MMA [MMA].,,.,(h) [SJ .... ,(h) ( ·1 o·3) [MMA]p,sat(h) [ s ]p,sat(h)

SM1 0.02 0.5 0.12 3.8 6.3 5.5 SM2 0.05 0.5 0.12 3.8 6.3 5.5 SM3 0.1 0.5 0.12 3.8 6.3 5.5 SM4 0.2 0.5 0.12 3.8 6.3 5.5 SM5 0.4 0.5 0.12 3.8 6.3 5.5

SM6 1.0 0.5 0.12 3.8 6.3 5.5

SM7 0.2 0.5 0.132 3.4 6.3 5.5 SM8 0.2 0.5 0.108 4.2 6.3 5.5

SM9 0.2 0.5 0.12 3.8 6.93 6.05

SMIO 0.2 0.5 0.12 3.8 5.67 4.95

SM11 0.2 0.25 0.12 3.8 6.3 5.5 SM12 0.2 0.75 0.12 3.8 6.3 5.5

Table A-6.3: Standard (SM4) and deviating model prediction parameters (SM13-SM18) used to perform a sensitivity analysis of the theoretical model: the sensitivity of reactivity ratios (rMMA and r.J and monomer and polymer densities (SM13-SM18) are tested All other parameters as in Table A-6.1.

name rMMA rs PMMA,m Ps,m PMMA,p Ps,m

SM4 0.46 0.523 0.918 0.886 1.149 1.046

SM13 0.506 0.471 0.918 0.886 1.149 1.046

SM14 0.414 0.575 0.918 0.886 1.149 1.046 SM15 0.46 0.523 0.826 0.797 1.149 1.046

SM16 0.46 0.523 1.010 0.975 1.149 1.046

SM17 0.46 0.523 0.918 0.886 1.264 1.151

SM18 0.46 0.523 0.918 0.886 1.034 0.941

A-6.2.1 Homo-monomer saturation concentrations

The effects of deviations up to 10% in homo-monomer saturation concentrations in

both the aqueous phase (water solubility) and the polymer phase (swellability) were

investigated by comparing model predictions with deviating model parameters with the

standard prediction (SM4). For this purpose the water solubility of both monomers was

varied separately and also simultaneously. The predictions leading to the strongest deviations


in composition drift and/or absolute monomer concentrations are depicted in Table A-6.2

(SM7 and SM8). A similar approach was adopted for deviations in the maximum

swellabilities of monomer in the polymer phase (Table A-6.2: SM9 and SMIO). The

predictions of the monomer mole fraction in the polymer phase do not noticeably depend

on the 10% deviation in homo-monomer saturation concentrations in both the polymer and

the aqueous phase (all predicted curves coincide; SM4, SM7, SM8, SM9, and SMIO). The

effects of changing homo-monomer saturation concentrations (both aqueous and polymer

particle phases) on the absolute monomer concentration can be seen in Figure A-6.1.

7 1------'~t.!Wt.-.,._

61----.....::::; .......

s J 4

! 3

2

0 ~----r-----r-----~----~--~ 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure A-6.1: The absolute monomer concentration in the polymer phase is depicted as a function of conversion for model predictions in which the water solubility and the maximum swellabi/ity was changed (SM4 and SM7-SMJO: the model parameters can be seen in Table A-6.2).

Water solubility: The negligible effect of changing water solubility values on the

predictions of monomer mole fractions and total monomer concentration in the polymer

phase as a function of conversion is a result of the negligible amount of monomer located

in the aqueous phase ( 6 g) as compared to the total monomer amount (200 g). Increasing

the water solubility value of the more water soluble monomer will lead to an increase of

the total amount of monomer dissolved in the aqueous phase. However, the maximum

experimental difference of 10% will not make the amount of monomer located in the

aqueous phase considerable compared to the total amount of monomer present in the

predicted reaction.

Swellability: The effects of varying swellabilities on model predictions of composition drift

and absolute monomer concentrations in the polymer phase (Figure A-6.1) can be described

by dividing the model prediction into a saturated interval II region and an unsaturated

interval III region. Since the monomer mole fractions in the polymer particle phase and

90 Chapter 6

monomer droplet phase are equal, changing swellability values will only affect the total

monomer concentration in the polymer phase and the amount of monomer droplet phase at

saturation swelling. This results in monomer mole fractions in the polymer phase totally

independent of the swellability values of both monomers in the polymer phase at saturation

swelling.33 In other words, at saturation swelling composition drift is not at all influenced

by maximum swellability values.

At partial swelling it has been shown that monomer partitioning between the polymer

particle and aqueous phases depends only on the maximum swellability of the monomers

in the polymer phase. Different maximum swellabilities will affect the curvature of the

relationship between the degree of saturation of the aqueous and polymer phases. In Figure

A-6.2, the relation between the degree of saturation in the aqueous and polymer phases is

presented for several maximum swellability values, illustrating that even the largest

deviations in maximum swellability have only a small effect on the curvature of the line.

Furthermore, the different curvature can lead to deviating monomer mole fractions only if

the amount of monomer in the aqueous phase cannot be neglected compared to the total

monomer amount. For MMA-S predictions with monomer-to-water ratios of MIW = 0.2,

the amount of monomer in the aqueous phase is negligible as compared with the total

amount of monomer (6 g to 200 g). From this it can also be concluded that at partial

swelling the maximum swellability has a negligible effect on composition drift.

1.00

0.80

... 0.60

J 0.40

0.20

0.00 0.00 0.20 0.40 0.60 0.80 1.00

F .... Figure A-6.2: The degree of saturation in the polymer (F,01 ,) is depicted as a function of the degree of saturation in the aqueous phase (F sm J. The lines depict the maximum swellability of MMA (6.3 molldm3

), S (5.5 molldm3), and the

minimum and maximum swellabilities on the MMA and S (minimum: 4.95 mol!dm3 and maximum: 6.93 molldm3

) taking 10% deviation into account.

From Figure A-6.1 it can be seen that the maximum swellability of monomers in the

polymer phase will affect the absolute monomer concentration in the polymer particle phase


at saturation swelling. Although the absolute monomer concentrations are quantities that are

not important for composition drift (only the mole fraction in the polymer is relevant), it

is an important parameter affecting polymerization rates at saturation swelling. As can be

seen in Figure A-6.1, the disappearance of droplets at the end of interval II is strongly

affected by the maximum swell ability. At partial swelling, the monomer concentration in

the polymer particle decreases with conversion in an approximately linear relationship. At

partial swelling the use of different swellability values does not lead to large differences

between the absolute monomer concentrations in the polymer phase as a function of

conversion.

It should be noted that the deviations in monomer mole fraction and absolute

monomer concentrations in the polymer phase depend on the monomer-t~rwater ratio and

on the water solubility of the selected monomer combination. In case the amount of

monomer in the aqueous phase is not negligible as compared with the total amount of

monomer, the monomer mole fraction in the polymer phase will deviate more from the

standard prediction. This implies directly that, for monomer combinations with lower water

solubility values as compared with MMA (< 0.12 mol/dm3), the effect of water solubility

on composition drift can be neglected. Furthermore, it can be expected that, for monomers

with higher water solubility values than MMA, the monomer amount in the aqueous phase

may no longer be negligible as compared to the total monomer amount. In these cases the

effect of water solubility on composition drift may be significant even at higher monomer-ttr

water ratios.

5

""' * 4 ._,

j 3

8 8 2

'::1 .l!l > &

Figure A -6. 3: The predicted maximum deviations in the monomer mole fraction in the polymer phase resulting from different water solubility (top line) and swellability (lower line) values are depicted as a function of the monomer-towater ratio.

92 Chapter 6

For the monomer combination MMA-S the deviations in monomer mole fraction and

absolute monomer concentrations in the polymer phase as a function of the monomer-to

water ratio are estimated by comparison between predictions with standard model parameters

and deviating parameters. From Figure A-6.3 it can be seen that the maximum deviations

in predicted monomer mole fractions are larger at low monomer-to-water ratios. Note that

the effect of deviations in the maximum swellability can be neglected even at low monomer

to-water ratios, while the effect of deviations in water solubility can no longer be neglected

for monomer-to-water ratios below MIW = 0.02.

Comparing standard with deviating model parameters results in large, significant

deviations in the absolute monomer concentrations in the polymer phase at saturation

swelling, as can be seen in Figure A-6.4. Note, however, that these large deviations in

monomer concentration in the polymer phase are only present at saturation swelling. At the

end of interval II these deviations will quickly reduce to negligible effects of maximum

swellability values on the maximum concentrations in the polymer phase. The deviations

in monomer concentrations in the polymer phase caused by deviating water solubilities

increase with decreasing monomer-to-water ratios (Figure A-6.4). At monomer-to-water

ratios lower then MIW = 0.1 these deviations can no longer be neglected.

10

€ 8 ! ~ 6

8 c:l 0

4 ·= .. ·;;: 2 0

Q

M/W

Figure A-6.4: The predicted maximum deviations in the absolute monomer concentration in the polymer phase resulting from diffirent water solubility (lower line) and swellability (top line) values are depicted as a function of the monomer-to-water ratio.

The most important conclusions from the above discussion about the effect of

deviating homo-monomer saturation concentrations on model predictions are:

In MMA-S copolymerization reactions the effect of changing water solubilities on

the monomer mole fraction in the polymer phase, i.e, on composition drift and


copolymer composition distributions, is limited to low monomer-to-water ratios (MIW

< 0.02), since in these cases the amount of monomer located in the aqueous phase

is not negligible compared to the total amount of monomer.

2 Composition drift in copolymerization reactions is virtually independent of the

maximum swellability of monomer in polymer for monomer systems in which the

monomer mole fractions in the polymer and monomer droplet phase at saturation

swelling are equal.

3 In MMA-S copolymerizations, the effect of deviations in water solubility on the

absolute monomer concentrations is limited to low monomer-to-water ratios (MIW

< 0.1).

4 The maximum swellability will have a large effect on the absolute monomer

concentrations in the polymer phase.

The most important aim of the model described in Chapter 6 is the prediction of composition

drift occurring in batch emulsion copolymerization reactions. Taking this into account, it

should be noted that conclusions 3 and 4 are not relevant since the absolute monomer

concentrations will only affect the polymerization rate, leaving composition drift unchanged.

A-6.2.2 Reactivity ratios

The effect of deviations up to 1 0% in reactivity ratios on the predicted monomer mole

fraction increases with increasing conversion, as can be seen in Figure A-6.5.

0.80

0.70

~ 0.60 ,J

0.40 '-------..,,....-----.---....----.---~ 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure A -6.5: The monomer mole fraction in the polymer phase is depicted as a function of conversion for several reactivity ratios. The model parameters of the reactions represented SM4, SM13 and SM14 can be seen in Table A-6.3.

94 Chapter 6

Due to small deviations in consecutive conversion steps (of 1%) taken in the model

prediction, accumulation of the deviation occurs leading to the largest deviations at 1 00%

conversion. Note that although larger conversion steps would reduce the accumulation of

small deviations, this would make the approximation of constant monomer and copolymer

composition during that conversion step dubious. Changes of 1 0% in only one of the

reactivity ratios will already lead to deviations of 5% at 90% conversion and to deviations

of l 0% at I 00% conversion. Deviations in both reactivity ratios may even double the

deviations in monomer mole fractions in the polymer phase. The reactivity ratios are,

therefore, the most important parameters for model predictions of composition drift. This

is in sharp contrast with the negligible effect of deviations in reactivity ratios on the total

monomer concentration in the polymer phase(< 2%). This is probably due to the relatively

small difference in maximum swellability values of MMA and S. Performing similar model

predictions -at different overall monomer mole fractions results in approximately the same

deviations in monomer mole fractions and absolute monomer concentrations in the polymer

phase, as could be expected since the reactivity ratios are an intrinsic property of the

copolymer system.

A-6.2.3 Monomer and polymer densities

Recipe conditions, such as the amount of monomers and the volume of the aqueous

phase, are known within small deviations of I%. A sensitivity analysis shows that both

composition drift and absolute monomer concentrations in the polymer phase are not

significantly affected by these small deviations, leading to experimentally inobservable

differences. Other important parameters needed for model predictions are the density values

of both monomers and homo-polymers participating in the simulated batch emulsion

polymerization. These density values are often known in the literature within a small

reliability interval of approximately I%. A sensitivity analysis of small errors of I% on both

the monomer and polymer densities showed that here also predictions of composition drift

and absolute monomer concentrations are within experimental error. For monomers of which

the monomer and polymer densities are not known, a rough estimation of both values already

results in reliable predictions of composition drift. This was concluded from model

predictions in which first the monomer and then the polymer densities were changed with

10"/o (Table A-6.3: SM15-SM18), resulting in almost identical monomer mole fractions as

a function of conversion. The effects of changing monomer and polymer densities on the

absolute monomer concentrations in the polymer phase can be seen in Figure A-6.6,


indicating that the predicted end of interval II is influenced by the monomer and polymer

densities. The maximum deviations in the absolute monomer concentrations in the polymer

phase resulting from different monomer and polymer density values are approximately 6%

(at ca. 40% conversion) and 8% (at 100% conversion) for deviating monomer and polymer

densities respectively.

7

61----~"""""./

s ! 4

!3 2

1

0~--~----~----~--~----~

0.00 0.20 0.40 0.60 0.80 1.00 Conversion

Figure A-6.6: The absolute monomer concentration in the polymer phase is depicted as a jUnction of conversion for model predictions performed with deviating monomer and polymer density values. The model parameters of the reactions represented SM4 and SMJ5 to SM18 can be seen in Table A-6.3.

A-6.3 Conclusions

From the sensitivity analysis it can be concluded that composition drift predicted in

the modelling of batch emulsion copolymerizations strongly depends on the reactivity ratios.

Due to accumulation of small deviations in consecutive conversion steps, the final deviation

at high conversion (> 90%) then can no longer be neglected. The effect of water solubility

of the monomers on composition drift is significant only when the amount of monomer

dissolved in the aqueous phase cannot be neglected as compared with the total monomer

amount. For the monomer combination MMA-S, this effect becomes important only at very

low monomer-to-water ratios (< 0.02). For monomer combinations with water solubilities

lower than MMA ( < 0.12 mol/L) this effect of water solubility on composition drift can be

neglected, whereas this effect may be significant even at higher monomer-to-water ratios,

for monomers with higher water solubility values. The effects of maximum swellability

values and monomer and polymer densities on composition drift can usually be neglected.

96 References

1. M. Nomura, K. Fujita, Macromol. Chern., Suppl., 10/11, 25 (1985) 2. M. Nomura, I. Horie, M. Kubo, K. Fujita, J. Appl. Polym. Sci., 37, 1029 (1989) 3. G.H.J. van Doremaele, A.H. van Herk, A.L. German, Polym. Int., 27, 95 (1992) 4. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,

Polymer, 33, 1914 (1992) 5. G.H.J. van Doremaele, H.A.S. Schoonbrood, J. Kurja, A.L. German, J. Appl. Polym.

Sci., 45, 957 (1992) 6. M.J. Ballard, D.H. Napper, R.G.Gilbert, J. Polym. Sci., Polym. Chern. Ed., 19, 939

(1981) 7. J. Guillot, Makromol. Chern., Suppl, 10/11 235 (1985) 8. J. Forcada, J. M. Asua, J. Polym. Sci., Polym. Chern. Ed, 28, 987 (1990) 9. M. Morton, S. Kaizermann, M.W. Altier, J Colloid Sci., 9, 300 (1954) 10. J.L. Gardon, J. Polym. Sci., Polym. Chern. Ed, 6, 2859 (1968) 11. J. Ugelstad, P.C. Mork, H.R. Mfutakamba, E. Soleimany, I. Nordhuus, R. Schmid,

A. Berge, T. Ellingsen, 0. Aune, K. Nustad, in Science and Techno/ow o(Polymer Colloids, Vol.l, G.W. Poehlein, R.H. Ottewill, J.W. Goodwin, Eds., NATO ASI Series, 1983

12. J. Guillot, Acta Polym., 32, 593 (1981) 13. C.M. Tseng, M.S. El-Aasser, J.W. Vanderhoff, Org. Coat. Plast. Chern., 45, 373

(1981) 14. I.A. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chern., 193,

2065 (1992) 15. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 16. L.F.J. Noel, W.J.M. van Well, A.L. German, to be submitted 17. I.A. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol.

Chern., Theory Simul., 2, 269 (1992) 18. T. Alfrey, G. Goldfmger, J Chern. Phys., 12, 205 (1944) 19. F.R. Mayo, F.M. Lewis, JAm. Chern. Soc., 66, 1594 (1944) 20. M. Nomura, K. Yamamoto, I. Horie, K. Fujita, M. Harada, J. Appl. Polym. Sci., 27,

2483 (1982) 21. I.A. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison,

Makromol. Chern, 193, 2049 (1992) 22. N.G. Kulkarni, N. Krishnamurti, P.C. Chatterjee, M.A. Sivasamban, Makromol.

Chern., 139, 165 (1970) 23. F.L.M. Hautus, H.N. Linssen, A.L. German, J Polym. Sci., Polym. Chern. Ed, 22,

3487 (1984) 24. L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.L. German, to be submitted 25. H.K. Mahabadi, K.F. O'Driscoll, J Macromol. Sci, Chern. Ed, Al1(5), 967 (1977) 26. T. Fukuda, Y -D Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 27. T. Fukuda, Y-D rna, H. Inagaki, Makromol. Chern., Rapid Commun., 8, 495 (1987) 28. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, J Polym. Sci., Polym. Letters,

27, 181 (1989) 29. K. O'Driscoll, J. Huang, Eur. Polym. J, 7/8, 629 (1989) 30. T.P. Davis, Polym. Comm., 31, 442 (1990) 31. I.A. Maxwell, A.M. Aerdts, A.L. German, Macromolecules, 26, 1956 (l993) 32. J. Schweer, Makromol. Chern., Theory Simul., 2, 485 (1993) 33. A.M. Aerdts, M.M.W.A. Boei, A.L. German, Polymer, 34, 574 (1993) 34. W.H. Lane, Ind. Eng. Chern. Anal. Ed., 18, 295 (1946) 35. W. Patnode, W.J. Schreiber, J Am. Chern. Soc., 61, 3449 (1939)

Monomer-to-water ratios as a tool 97

Chapter 7 Monomer-to-water ratios as a tool

in controlling emulsion copolymer composition

The methyl acrylate-indene system

Abstract: Most copolymerizations typically exhibit drifting copolymer composition as a function of conversion. Reducing this so-called composition drift will lead to a decrease in chemical heterogeneity of the copolymers formed. For monomer systems in which the more water soluble monomer is also the more reactive one, theory predicts that composition drift in batch emulsion copolymerization can be reduced or even minimized by optimizing the monomerto-water ratio. To verify these theoretical considerations, emulsion copolymerizations have been performed with varying monomer-to-water ratios, for the monomer combination MA-Ind. This monomer combination bas been chosen as the model system since it meets the basic requirements needed to obtain minimum composition drift. From the good agreement between experiments and theoretical predictions for MA-Ind, it was concluded that control and even minimization of composition drift in batch emulsion copolymerization for monomer systems in which the more water soluble monomer is also the more reactive is indeed possible by adjusting the initial monomer-to-water ratio of the reaction mixture.

7.1 Introduction

Composition drift occurring in batch emulsion copolymerization will lead to

chemically heterogeneous copolymers. To control composition drift, semi-continuous

emulsion copolymerization processes have been developed. The various addition strategies

used in semi-continuous processes include (1) the addition of a given monomer mixture at

a constant rate lower than the polymerization rate (starved conditions) '·v·4•5

•6

•7

•8

•9 and

(2) the addition of monomer(s) at an optimal addition profile with addition rates higher than

the polymerization rate (flooded conditions). 10•11

•12

•13

•14 Disadvantages of these

98 Chapter 7

strategies are the relatively long reaction times, especially under starved conditions, and the

time consuming determination of the optimal addition profile or rate coefficients (in case

a theoretical model is used), which, furthermore, requires an immediate start of reaction since

inhibition hampers the addition procedure. For monomer systems in which at least one of

the monomers has a relatively high but limited water solubility, a different approach can

be used to influence composition drift. When a monomer has a relatively high but still

limited water solubility, a certain amount of that monomer will be located in the aqueous

phase, thus influencing the monomer ratio and concentrations within the polymer particle

phase. Since this polymer particle phase is considered to be the main locus of reaction, the

monomer ratio and monomer concentrations within the polymer phase control both,

copolymer composition and polymerization rate. Depending on the amount of water in the

reaction mixture, i.e., depending on the monomer-to-water ratio (MIW), more or less

monomer will be dissolved in the aqueous phase. It should be noted that efforts to raise the

final solids content of a latex will change the monomer-to-water ratio and thus, in many

cases, the copolymer composition of the product. By adding more water to the reaction

mixture, the more water soluble monomer can be withdrawn from the particles and thus from

reaction. If the monomer with the higher water solubility is also the less reactive one,

composition drift can be enhanced by decreasing the monomer-to-water ratio. A system that

illustrates this is the system MA-8. 15 In principle it should be possible to lower or even

minimize composition drift for monomer combinations where the more water soluble

monomer also is the more reactive one. Since the water solubilities of the monomers MA

and indene (Ind) differ by two orders of magnitude and since MA is not only the more water

soluble but also the more reactive monomer, the somewhat unusual monomer combination

MA-Ind is chosen as an example to show that minimization of composition drift is indeed

possible just by changing monomer-to-water ratios (M/W). The structural formula of indene

(CqH8) is shown in Figure 7.1. Note that although the monomer system MA-lnd is an ideal

monomer combination to verify theoretical predictions other monomer combinations in which

the more water soluble monomer is also the more reactive one also comply with the theory.

However, it is important to realise that for reactivity ratios that are far apart composition

drift can only be minimized if the water solubility of the monomers is also very far apart.

Otherwise unrealistic and impractical monomer-to-water ratios will be required or, in

extreme situations, minimum composition drift cannot be achieved in batch emulsion

copolymerization by simply changing the monomer-to-water ratio.

In this chapter, effects of increasing both the initiator and surfactant concentrations

upon the MA-Ind conversion-time curves are discussed. Based on homo-monomer saturation

Monomer-to-water ratios as a tool

concentrations and reactivity ratios

(Chapter 3) model predictions of

minimum composition drift are

performed for the monomer system

MA-Ind using the theory and model

presented in this thesis. In this way the

effect of changing monomer-to-water

ratios in ab initio batch emulsion

copolymerizations with similar initial

overall monomer mole feed ratios can

be studied. Theoretical predictions of

99

Figure 7.1: The structural formula of the monomer indene.

minimum composition drift will be compared with experimental results for the monomer

combination MA-Ind.

7.2 Theory

The copolymerization equation (eq 2.2) relates the instantaneous copolymer

composition with the reactivity ratios and monomer feed composition for solution and bulk

polymerizations. 16•17 In solution and bulk copolymerization of a given monomer system

i-j with reactivity ratios lower than unity, conditions can be reached where the monomer

mole fraction equals the copolymer composition of the instantaneously formed copolymer

(f; = F;). At these so-called azeotropic conditions, there will be no composition drift, i.e.,

the instantaneous copolymer composition remains constant during conversion.

If there is a separate aqueous phase present as in emulsion copolymerization, the

simple theory predicting azeotropic conditions becomes complicated. For monomers with

relatively high, but still limited water solubility, a considerable amount of the monomer can

be dissolved in the aqueous phase. This will affect the monomer mole fractions in the

particle phase. In these emulsion copolymerizations, the copolymerization equation (eq 2.2)

can still be used, but instead of the overall monomer mole fraction, f0 ;. the monomer mole

fraction in the polymer phase, fp;• should be used. For monomer combinations in which at

least one of the monomers has a relatively high, but still limited water solubility,

composition drift will occur with increasing conversion, even if conditions are chosen in

which the pre-requisite for azeotropic conditions, i.e., instantaneous copolymer composition

equals the overall monomer mole composition, is met. The reason that azeotropic conditions

cannot be maintained over a wide range of conversion in emulsion copolymerization is

100 Chapter 7

caused by the effect of changing monomer-to-water ratios and increasing polymer volumes

on the monomer mole fraction in the polymer particles as conversion increases. In emulsion

copolymerizations, where at least one of the monomers in the selected monomer combination

has a relatively high, but limited water solubility, composition drift cannot be avoided; it

can only be minimized. Theoretically, this minimum composition drift can be obtained for

several overall monomer mole fractions by using the heterogeneity of the emulsion system.

This is in contrast with solution or bulk polymerization, where azeotropic conditions can

only be obtained at one overall monomer mole fraction. Exact azeotropic behaviour in

emulsion copolymerization can be obtained only in the following cases: (I) if both

monomers in the chosen monomer combination have low water solubility, leading to

negligible amounts of monomer in the aqueous phase as compared to the amount of

monomers in the organic (monomer droplet and polymer particle) phase, or, (2) if the ratio

of the water solubilities is equal to unity, leading to identical monomer mole ratios in the

aqueous phase and in the polymer particle phase. Note that in the above cases changing the

monomer-to-water ratios has no effect on the course of emulsion polymerization.

As stated above, theoretically, it should be possible to control and minimize

composition drift for monomer combinations where the more water soluble monomer also

is the more reactive one. Based on the water solubility of the monomers, an amount of

monomer is withdrawn from the monomer droplets and polymer particles, thus affecting the

monomer ratio within the polymer phase and therefore having an effect on the copolymer

formed. If monomer i is chosen to be the monomer with the highest water solubility, the

mole fraction of monomer i in the copolymer will reach a maximum value when all the

monomer is located in the polymer particle and monomer droplet phase (comparable with

solution and bulk polymerizations), and it will reach a minimum value when all monomer

is located in the aqueous phase. The value for the minimum mole fraction of monomer i

strongly depends upon the ratio of the water solubility of monomer j over the water

solubility of monomer i, denoted as the a-value. It has been shown in Chapter 6 that the

difference between maximum and minimum monomer mole fractions will be the largest for

small a-values. In such cases, changing the monomer-to-water ratio or polymer volume will

have the strongest effect upon the monomer mole fraction in the polymer phase. It is in these

cases that, for monomer systems in which the more reactive monomer is also the more water

soluble one, minimum composition drift can be obtained by changing the monomer-to-water

ratio.


7.3 Experimental

The emulsion copolymerizations described in this chapter can be divided into two

categories: 1) polymerizations to determine optimum concentrations of surfactant (Ant C0-

990) and initiator (NaPS) resulting in stable latices and reasonable polymerization rates, and

2) polymerizations to study composition drift .

. Emulsion copolymerizations to determine optimum concentrations of surfactant and

initiator were carried out in 100 ml reactors thermostated at 1o•c and mixed with a magnetic

stirrer. Since our main interest was obtaining reasonable polymerization rates, these reactions

were followed by gravimetry only. For the MA-Ind copolymerization high initiator

concentrations were needed to give reasonable polymerization rates, resulting in unstable

latices. The use of non-ionic Ant C0-990 instead ofSDS gave satisfying results. The recipes

used to determine optimum concentrations for the emulsion copolymerizations are shown

in Table 7.1

Table 7.1: MA -Ind copolymerization recipes to achieve optimum reaction conditions (optimize) and to study the effict of monomer-to-water ratio on composition drift (MIW = 0.4, 0.3 and 0.1).

Ingredients optimize MIW = 0.4 MIW = 0.3 MIW 0.1

MA (g) 3.8 165.47 144.87 62.09 Ind (g) 5.2 74.41 64.46 27.83

Water (g) 90 600.1 700.3 898.8 NPS (l o-3 molldmw3

) 10-25 26.31 25.05 24.90 Ant C0-990 (10'3 molldmw3

) 2.5-12.5 7.449 7.498 7.539

Na:zC0 3 (10'3 mol/rlmw3) 10 9.968 9.916 10.035

Emulsion polymerizations to study composition drift were performed as described

in Chapter 3 and Figure 3.1. The recipes for these emulsion copolymerizations, which were

performed using the same overall monomer mole fraction of foMA 0.75 and varying

monomer-to-water ratios are given in Table 7.1. All reactions concerning composition drift

were monitored by gravimetry, yielding conversion-time curves, and by GC providing the

overall monomer fractions as a function of time. An indication of the accuracy of data

analyses was obtained by adding known amounts of n-butanol as internal standard to the

GC samples in order to obtain extra conversion-time data. Combining both data gives the

overall conversion of both monomers at each moment during the reaction.

102 Chapter 7


7.4.1 Optimization of recipe conditions

To achieve reasonable polymerization rates in MA-Ind emulsion copolymerization

reactions, high initiator concentrations were needed. Reactions performed with surfactant

SDS, frequently used in emulsion polymerization, did not result in colloidally stable latices

for any SDS concentration (going from 10·10·3 to 75·10"3 mol/dm3). The use of the non

ionic surfactant Ant C0-990 instead of SDS resulted in colloidally stable latices. The

surfactant and initiator concentrations were optimized resulting in concentrations of 7.5·10·3

and 10·10'3 mol/dm\ respectively.

Some typical conversion-time curves for the emulsion copolymerization of MA-Ind

can be seen in Figure 7.2 for several initiator (NaPS) concentrations. From Figure 7.2 it can

be concluded that the overall polymerization rate increases with increasing NaPS

concentrations as can be expected from emulsion polymerization theory.

1.00 0 0

0 0 0 0

0.75 0 0 0 _..... 0 0 . 0 0 0 '-'

c:l 0

·~ 0 D 0 l>

l>

0.50 D 0 l> 0 l> ., 0 l>

> D l> c:l

0 0 0 l> <.1 0.25 D

0 l> 0 €l "

l>

0.00 0 3 6 9

time (hours)

Figure 7. 2: Conversion-time curves of MA -Ind emulsion copolymerizations for initiator (NaPS) concentrations of 10·}()"3 (il), 15 ·J0·3 (o), 20 ·10·3 (D), and 25 ·10·3 molldm,/ ( 0 ).

Experiments performed with increasing surfactant (Ant C0-990) concentrations showed a

slight increase in polymerization rate. Particle size analysis by dynamic light scattering

(Malvern Autosizer lie) showed that the particle size decreased with increasing initiator and

surfactant concentrations. This behaviour is typical of emulsion polymerization, 18 since by

using more surfactant, more particle surface can be stabilized. Increasing the initiator

concentration leads to higher radical concentrations in the beginning of the reaction and,


·therefore, more particles can be nucleated.

Comparison of gravimetry and GC results is shown in Figure 7.3 for the MA-Ind

reaction at a monomer-to-water ratio of 0.1 kg/kg (recipe: Table 7.1). For the reaction

depicted in Figure 7.3 it can be concluded that the polymerization rate of Ind is higher than

the polymerization rate of MA, resulting in a copolymer composition that is more Ind-rich

in the beginning and more MA-rich towards the end of the polymerization as compared with

the initial overall monomer mole fraction. The accuracy of the experimental results is

illustrated by the good agreement when comparing the total conversion-time curves obtained

from gravimetry with the data obtained from GC analysis using an internal standard,

enabling the determination of not only monomer ratios but also conversion data of the

separate monomers. Note that the internal standard was added afterwards to samples taken

from the reaction since, otherwise, monomer partitioning during reaction would have been

affected by the internal standard. All MA-Ind emulsion copolymerization experiments

performed to study composition drift behaviour were analyzed in the above manner.

1.00 lJ. B ~ Q a lJ.

~ lJ. ~

,..... 0.1S '

lJ. 8 0

0 lJ. ~ ...... 0

d .5! o.so lJ.

"' 0 .. 0 4) 0 > d 6

~ 0

0 tJ. ~ B ... 0.2S tJ.8 ~@

0.00 0 2 4 6

time (hours)

Figure 7.3: Experimental conversion-time results for MA-lnd emulsion copolymerization at MIW = 0.1 and foMA = 0. 7 5. The total conversion was determined by gravimetry ( 0) and GC (o); the partial conversion of both monomers was determined by GC (MA: D ; !nd .t.}.

7.4.2 Model parameters

Predictions of the course of emulsion copolymerizations can be made by using the

model described in Chapter 6. The use of this model is very convenient since it only requires

the reactivity ratios and the homo-saturation values of the monomers in the aqueous and

104 Chapter 7

polymer phase to be known. For this reason these model parameters have been determined

experimentally for the current work. The determination procedure and the results are

described in full detail in Chapter 3.

Although the absolute concentrations of monomers in the particle phase strongly

depend upon the homo-saturation concentrations of the monomers in the polymer particle

phase, it has been shown in previous sections that the monomer ratio within the polymer

phase is independent of the maximum swellability of both monomers in the polymer phase,

i.e., independent of the copolymer composition at saturation swelling. Therefore, it can be

concluded that changing copolymer composition as a function of conversion occurring at

saturation swelling, may affect the rate of polymerization (changing absolute concentrations)

but certainly not the composition drift (constant monomer ratio within the particles).

At partial swelling monomer partitioning between the aqueous and polymer phase

depends upon the volume fraction of polymer (eq 6.18), i.e., depends on the maximum

swellability in the polymer of the monomers. The change in maximum swellability as a

function of copolymer composition has been shown to be negligible 19•20 for several

monomer systems. The effect of changing monomer composition on the (maximum) volume

fractions of polymer is taken into account in model predictions in eq 6.2a-b, whereas the

effect of changing copolymer composition can be estimated using eq 6.18 by assuming

maximum swellabilities of a monomer mixture (50% MA-50% Ind; normal swellability of

5 mol/dm3) in the homopolymer-Ind of 4 mol/dm3 and in the homopolymer-MA of 6

mol/dm3• From Figure 7.4 where the degree of saturation in the polymer phase is depicted

as a function of the degree of saturation in the aqueous phase, it can be concluded directly

that the effects of changing copolymer composition going from poly-Ind to poly-MA has

a relatively small influence on monomer partitioning at partial swelling. These results agree

very well with the results of the sensitivity analysis presented in the appendix of Chapter

6. In practical situations, all effects of changing maximum swellabilities will even be smaller

since the change in copolymer composition is less drastic than presented in Figure 7.4.

Based on the above discussion, all effects of changing maximum swellabilities of

monomer in the polymer phase as a result of changing copolymer composition are neglected

for saturation and partial swelling. All model predictions are carried out using one set of

homo-saturation concentrations of MA and ]nd that have been determined by monomer

partitioning experiments in a 50% MA-50% Ind seed (Chapter 3).

As shown in the sensitivity analysis, the water solubility of both monomers in the

aqueous phase may have a large effect on monomer partitioning in cases where the absolute

monomer amount in the aqueous phase cannot be neglected compared to the total amount


of monomers. For some of the reactions presented in this Chapter the amount of monomer

(MA has a relatively high water solubility) in the aqueous phase cannot be neglected. For

this reason, accurate water solubility values of the both monomers in the aqueous phase at

reaction temperature have been determined (Chapters 3 and 4).

0.75

Qo

r:s.ti 0.50

0.25

0.00 w::;_ _________ ___J

0.00 0.25 o.so 0.75 1.00

Figure 7. 4: Model predictions of the degree of saturation in the polymer phase, F,at P' as a fimction of the degree of saturation in the aqueous phase, F sat, using eq 6. 18 with maximum swellabilities of monomer in the polymer phase of 4 and 6 molldm3

•

7.4.3. Composition drift in emulsion copolymerization of MA-Ind

The monomer mole fraction in the polymer phase is determined by monomer

partitioning. Changing the monomer-to-water ratio or the polymer volume in a monomer

water-polymer mixture will lead to different monomer mole fractions in the polymer phase.

This effect will be especially large if one of the monomers has a relatively high but still

limited water solubility, as, for instance, MA.

Assuming monomer i to be the more water soluble monomer, two extreme values

for the monomer mole fraction in the polymer phase can be obtained, i.e., a maximum value

fpi.max which is reached if all monomer is located in the polymer phase and a minimum value

fp;,min which is reached if all monomer is dissolved in the aqueous phase. As was shown in

Chapter 6, the value of fp;,min strongly depends upon the a-value leading to larger differences

between fp;,max and fpi,min for smaller a-values (see eq 6.4a). This t;,;,min can be reached only

if at least one of the monomers has a relatively high water solubility and if the monomer-to

water ratio is low and if the amount of polymer phase is too small to affect monomer

106 Chapter 7

partitioning. It is important to realise that although the minimum monomer mole fraction

in the polymer only depends on the ratio of the water solubilities, a, the absolute water

solubility values are determining the monomer-to-water ratio needed to obtain this minimum

monomer mole fraction in the polymer phase. This is illustrated by the following example:

if a = 0.1 and the water solubilities are 0.5 and 0.05 mol/dm3 then less water is needed to

dissolve all these monomers than in case of water solubilities of 0.05 and 0.005 moVdm3•

This obviously results in different monomer-to-water ratios needed to obtain a minimum

monomer mole fraction in the polymer phase.

Depending on recipe conditions, like monomer-to-water ratio (MIW) and polymer

volumes (V po), the value for the mole fraction of monomer i in the polymer phase will vary

between fp;,max and fpi,min· In Figure 7.5 the maximum and minimum values for the monomer

mole fraction in the polymer phase as a function of the overall monomer mole fraction are

given for the monomer system MA-Ind in which a 0.0053. Due to the large difference

in water solubility of MA as compared with Ind, expressed in the low a-value, the monomer

mole fraction in the polymer phase is strongly affected by changing monomer-to-water

ratios. This effect of MIW on the mole fraction of monomer i in the polymer phase in the

absence of polymer is also clearly shown in this Figure 7.5.

1.00

i 0.50 '-"<

0.25

0.016

0.25 0.50 0. 75 1.00 fo.MA

Figure 7.5: Monomer mole fractions in the polymer phase, J;,.MA• as a function oft he overall monomer male fraction for the monomer system MA-Ind: minimum (min), maximum (max) and monomer-to-water ratio dependent (MIW = 0.0/, 0.02, 0.05, 0.1. 0.3).

Monomer-to-water ratios as a tool

1.00 ,..----------~

0.78 ~~----------£.-' 0.75

rs..i o.so

0.25

0.00 0.00 0.25 o.so 0. 75 1.00

fo,MA

Figure 7. 6: Monomer mole fractions in the copolymer, F MA• (resulting from J;,MA data presented in Figure 7.5) as afimction of the overall monomer mole fraction, f.MA, for the monomer system MA-Ind: instantaneous copolymer compositions resulting from the minimum (min), maximum (max) and MIW dependent mole fractions (MIW = 0.0/, 0.02, 0.05, 0./, 0.3).

107

The copolymer composition resulting from the maximum and minimum values for

the monomer mole fraction in the polymer phase can be calculated with the instantaneous

copolymer equation (eq 2.2) using the reactivity values rMA = 0.92 and r1nd = 0.086 (Chapter

3). These copolymer compositions, which are typical of each monomer system with given

a.-value and reactivity ratios, are depicted in Figure 7.6 together with the diagonal line

representing azeotropic conditions, i.e., overall monomer mole fraction equal to instantaneous

copolymer composition. From Figure 7.6 one can see directly the minimum and maximum

instantaneous copolymer compositions obtainable when starting from a given overall

monomer mole fraction in an emulsion copolymerization of MA-Ind. The strong effect of

varying monomer-to-water ratios on the instantaneous copolymer composition is also

depicted in Figure 7.6. To illustrate the minimum and maximum mole fractions of monomer

i and the resulting instantaneous copolymer compositions an example is shown in Figures

7.5 and 7.6 for an overall monomer mole fraction offoMA 0.75. For low monomer-to-water

ratios without polymer (almost all monomers located in the aqueous phase), one can see that

the minimum monomer mole fraction in the polymer phase is reached, fpMA,min = 0.016,

(Figure 7.5) resulting in a copolymer composition ofF MA 0.13 (Figure 7.6), whereas at

high monomer-to-water ratios, the maximum monomer mole fraction is reached, fpMA.max =

0.75 (Figure 7.5), resulting in a copolymer composition ofFMA = 0.78 (Figure 7.6). We have

108 Chapter 7

already seen that azeotropic conditions occur only if the instantaneous copolymer

composition equals the overall monomer mole fraction. Knowing this, one can see in Figure

7.6 that the intersection of the lines representing minimum, maximum and MIW-dependent

values for the instantaneous copolymer composition with the diagonal gives the conditions

needed to obtain azeotropic conditions, i.e., instantaneous copolymer composition equals

overall monomer mole fraction. Calculation shows that these azeotropic conditions can be

found by varying the MIW ratio for fllM4 values between 0 and 0.91 at low conversion.

However, the aim of this work is to achieve minimum composition drift over a wider range

of conversion, and is not restricted to low conversion. Therefore, the overall monomer mole

fraction needed for minimum composition drift over the entire range of conversion may

deviate slightly from the conditions represented by the intersections of the diagonal and the

copolymer compositions shown in Figure 7.6.

Experimental results of emulsion copolymerization composition as a function of

conversion have been compared with predictions of the model presented in Chapter 6 for

MA-Ind systems. The large effect of different monomer-to-water ratios on the system MA

Ind, with a relatively water soluble monomer like MA, can be seen in Figure 7.7 where

theory and experiment are compared resulting in very good agreement (initial reaction

recipes are shown in Table 7.1). To enlighten the maximum span of composition drift, a

theoretical prediction of extreme high monomer-to-water ratios (MIW oo) is depicted in

Figure 7.7.

1.00

0.90

0.80

0.60

oo

/9/' M/W •0.1 9-

MfW- 00

solution, bulk

o.so '---~-...,-----...--~--,--~---,-~__._, 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 7. 7: Comparison of predicted and experimentally determined overall mole fractions for the monomer system MA-lnd, with initial overall monomer mole fraction off,,MA 0. 75 and different monomer-to-water ratios (MIW) ofO.J, 0.3 and 0.4 (predictions lines, experiments symbols).


Note that the composition drift behaviour in this extreme case is equal to the composition

drift behaviour in homogeneous systems as bulk and solution (i.e., fP = f.) for similar initial

mole fractions. Note furthermore that increasing the monomer-to-water ratios to extreme

high values may result in phase inversion. However, this phenomenon is not discussed here.

In case of MA-Ind emulsion copolymerizations more of the more water soluble MA will

be buffered in the aqueous phase at lower monomer-to-water ratios as compared with higher

monomer-to-water ratios. As can be seen in Figure 7.7, minimum or even reversed

composition drift can be achieved by simply changing the monomer-to-water ratio in a batch

emulsion copolymerization of MA-Ind.

J

1.00

0.90

0.80

0.60

0

0 M/W•O.l

o.so L..---..----..----..------~__;;..__._, 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 7.8: Comparison of model prediction (lines) with experimental results (symbols) of the mole fraction of MA in the polymer phase as a function of conversion, with an initial overall monomer mole fraction of /.,MA 0. 75 and different MIW ratios.

What exactly happens in the emulsion copolymerizations of MA-Ind at an overall

monomer ratio of MA with varying monomer-to-water ratios is depicted more clearly in

Figure 7.8, where theoretical and experimental mole fractions ofMA in the polymer phase

are compared. In case of MA-Ind emulsion copolymerizations, a larger part of the more

water soluble MA will be buffered in the aqueous phase at lower monomer-to-water ratios,

resulting in lower mole fractions of MA in the polymer phase at the beginning of the

reaction. Composition drift at low M/W ratios (Figure 7.8, foMA = 0.75, MIW = 0.1) shifts

from instantaneous copolymer compositions with higher Ind contents than the initial overall

feed in the beginning of the reaction, to instantaneous copolymer compositions with higher

MA contents than the initial overall feed at the end of the reaction. At higher monomer-to

water ratios (Figure 7.8, t;,A-M = 0.75, M/W = 0.4 to oo) less MA is buffered in the aqueous

110 Chapter 7

phase, leading to composition drift shifting from higher mole fractions ofMA in the polymer

phase in the beginning of the reaction {higher MA content in instantaneous copolymer than

in the initial overall feed) to lower mole fractions of MA in the end of the reaction {higher

Ind content in the instantaneous copolymer than in the initial overall feed). From Figures

7. 7 and 7 .8, we can conclude that composition drift can indeed be minimized by varying

the monomer-to-water ratio in MA-Ind emulsion polymerization. For overall mole fractions

of MA of foAM = 0. 75 minimum composition drift is achieved for monomer-to-water ratios

ofMJW = 0.3.

The course of emulsion copolymerization at minimum composition drift is shown

in more detail in Figure 7.9, where model predictions of fpAM and foMA and resulting from

this the mole fraction of MAin the copolymer {FMA) are compared with experiments (fpMA

and F AM are calculated from foMA and overall conversion using monomer partitioning

relationships and the instantaneous copolymer equation). As could be expected at minimum

composition drift conditions, all three compositions, fpMA, foMA, and F MA are more or less

constant as a function of conversion. Another important result of Figure 7.9 is that the

prerequisite for minimum composition drift, i.e., f.MA equal to FA« (see Figure 7.6), is

apparently approximated during reaction. In Figures 7.5 and 7.6, it is illustrated that by

simply changing initial reaction conditions like the monomer-to-water ratio, one can reach

minimum composition drift, if desired. In case the occurrence of composition drift is desired,

one can change the monomer-to-water ratio in such a way as to achieve composition drift

in the desired direction and to the desired extent.

1.00

0.90

f;l,i 0.80

J fp,MA

J 0.70

0.60

0.50 L----.....---.....-~-.--~---,.--~--. 0.00 0.20 0.40 0.60 0.80 1.00

Conversion

Figure 7. 9: Comparison of model predictions (lines) and experimental results (symbols) of!;..~« (o), /,,.~« (0) and F.~« (!J.) as a function of conversion for the emulsion copolymerization of MA-Ind with MIW = 0.3 andf.MA = 0. 75, resulting in minimum composition drift.


As can be seen in Figure 7.6, minimum composition drift conditions can also be

achieved for other overall monomer mole fractions. From the good agreement between

predictions and experimental results shown in Figure 7.7, it can be concluded that the model

used to predict the course of emulsion copolymerization can provide good simulations of

copolymer composition in emulsion copolymerization, even under conditions as critical as

those leading to minimum composition drift. Therefore, the presented model can be used,

in combination with the experimentally determined homo-monomer saturation values and

reactivity ratios, to predict the monomer-to-water ratio needed to achieve minimum

composition drift for several overall monomer mole fractions for the monomer system MA

Ind. The monomer-to-water ratios needed to obtain this minimum composition drift at given

overall monomer mole fractions in MA-Ind emulsion copolymerization are shown in Figure

7.10. From these predicted results, we can conclude that minimum composition drift indeed

can be achieved for other overall monomer mole fractions as welL Note, however, that

realistic monomer-to-water ratios for batch emulsion copolymerizations normally are between

0.1 < MIW < 2.

1.00

]1 ~ 0.75

~ 0.50

.I 0.25 8

0.00 0.00 0.25 0.50 0.75 1.00

fo,MA (-)

Figure 7.10: Model prediction of the monomer-to-water ratio as a .function of the overall mole fraction of MA needed to achieve minimum composition drift. The parameters used in the model predictions are listed in Tables 3.2 and 3.5.

Note also that the assumption of negligible polymerization in the aqueous phase may not

longer be valid at low monomer-to-water ratios. In this case, a considerable percentage of

the polymerization might occur in the aqueous phase. One way to avoid this from happening

might be the use of an oil soluble initiator in combination with an aqueous phase free radical

scavenger or retarder as an alternative of the water soluble initiator NaPS.

112 Chapter 7

It is important to realise that minimizing composition drift in MA-Ind reactions is

possible due to the moderate difference in reactivity values of the monomers (a factor of

10) combined with a large difference in homo-monomer saturation concentrations (factor

a. 0.05). In this case, the water phase can buffer a sufficient amount of the more reactive

monomer to minimize composition drift.

The intrinsic possibility of achieving minimum composition drift in batch emulsion

copolymerization for other monomer systems can be determined directly when the water

solubilities of the monomers (a.) and the reactivity values are known for a given monomer

system. The maximum monomer mole fraction in the polymer phase always equals the

overall monomer mole fraction. If the reactivity ratios of the chosen monomer systems are

known, the copolymer composition resulting from the maximum monomer mole fraction

in the polymer phase can be calculated with eq 2.2. It was shown that the minimum

monomer mole fraction in the polymer phase is reached when the monomer mole fraction

in the aqueous phase was equal to the overall monomer mole fraction. From this monomer

mole fraction in the aqueous phase, the minimum monomer mole fraction in the polymer

phase can be calculated directly with eq 6.4a if the ratio of the water solubilities of the

monomers, the a.-value, is known for the chosen monomer system. The copolymer

composition resulting from this minimum monomer mole fraction in the polymer phase again

can be calculated using eq 2.2 if the reactivity ratios are known. If the copolymer

compositions resulting from the minimum and maximum monomer mole fractions in the

polymer phase are higher and lower, respectively, than the overall monomer mole fraction,

the prerequisite for minimum composition drift, i.e., equal overall monomer mole fraction

to instantaneous copolymer composition, can be achieved for the selected overall monomer

mole fraction. The approach presented in this Chapter will always give information about

the span of control of the composition drift even in those cases where minimum composition

drift carmot be achieved. The procedure described here can be used for any monomer system

at every desired overall monomer mole fraction, giving similar results as shown in Figures

7.5 and 7.6 for MA-Ind emulsion copolymerizations.

7.5 Conclusions

Theoretical considerations are leading to the concept that for monomer systems in

which the water solubility of the monomers is sufficiently far apart (low a-values) minimum

composition drift can be achieved by properly adjusting the initial monomer-to-water ratio

in a batch emulsion copolymerization in which the more reactive monomer is also the more


water soluble one. Experimental verification of this prediction has shown that minimum

composition drift could be achieved for the monomer system MA-Ind where MA is the more

reactive as well as the more water soluble monomer. Model predictions show that

composition drift can be minimized for MA-Ind emulsion copolymerization over a wide

range of initial monomer feed fractions, simply by choosing different initial monomer-to

water ratios.

114 Chapter 7

1. K. Chujo, Y. Harada, S. Tokuhara, K. Tanaka, J. Polym. Sci., Part C, 27, 321 (1969) 2. J. Snuparek, Angew. Makromol. Chern., 25, 113 (1972) 3. R.A. Wessling, D.S. Gibbs, J. Macromol. Sci., Chern., A-7, 647 (1973) 4. J. Snup;irek, F. Krska, J. Appl. Polym. Sci., 20, 1753 (1976) 5. J. Snuparek, F. Krska, J. Appl. Polym. Sci., 21, 2253 (1977) 6. J. Snuparek, K. Ka5par, J. Appl. Polym. Sci., 26, 4081 (1981) 7. M.S. El-Aasser, T. Makgawinita, J.W. Vanderhoff, J. Polym. Sci., Polym. Chern. Ed,

21, 2363 (1983) 8. S.C. Misra, C. Pichot, M.S. El-Aasser, J.W. Vanderhoff, J. Polym. Sci., Polym. Chern.

Ed, 21, 2383 (1983) 9. T. Makgawinata, M.S. El-Aasser, A. Klein, J.W. Vanderhoff, J. Dispersion Sci.

Techno/., 5, 301 (1984) 10. G. Arzamendi, J.M. Asua, J. Appl. Polym. Sci., 38, 2019 (1989) 11. G. Arzamendi, J.M. Asua, Makromol. Chern., Macromol. Symp., 35/36, 249 (1990) 12. G. Arzamendi, J.M. Asua, Ind Eng. Chern. Res., 30, 1342 (1991) 13. G.H.J. van Doremaele, H.A.S. Schoonbrood, J. Kurja, A.L. German, J. Appl. Polym.

Sci., 45, 957 (1992) 14. G. Arzamendi, J.C. de Ia Cal, J.M. Asua, Angew. Makromol. Chern., 194, 47 (1992) 15. G.H.J. van Doremaele, Ph.D. Thesis, Eindhoven University of Technology,

Eindhoven, the Netherlands (1990) 16. T. Alfrey, G. Goldfinger, J. Chern. Phys., 12, 205 (1944) 17. F.R. Mayo, F.M. Lewis, J. Am. Chern. Soc., 66, 1594 (1944) 18. R.M. Fitch, C.H. Tsai, Polymer Colloids, Plenum, New York, 1971 19. G.H.J. van Dorernaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,

Polymer, 33, 1914 (1992) 20. M. Nomura, K. Yarnarnoto, I. Horie, K. Fujita, J. Appl. Polym. Sci., 27,2483 (1982)

The effect of water solubility on composition drift

Chapter 8 Tbe effect of water solubility of tbe monomers on

composition drift on metbyl acrylate-vinyl ester combinations

115

Abstract: It has been shown theoretically that composition drift mainly depends on reactivity ratios and water solubilities. Minimum composition drift can be obtained by lowering the monomer-to-water ratio in monomer systems where the more reactive monomer is also the more water soluble one. Investigating the effect of water solubility on composition drift while keeping the reactivity ratios constant can elucidate the importance of the water solubility. The monomer combinations methyl acrylate-vinyl acetate (MA-V Ac), methyl acrylate-vinyl 2,2-dimethylpropanoate (MA-VPV), and methyl acrylate-vinyl 2-ethylhexanoate (MA-V2EH) are ideal monomer combinations for studying the effect of water solubility on composition drift since the reactivity ratios for this series of monomer systems are approximately equal. Solution copolymerizations are performed to elucidate maximum composition drift at extremely high monomerto-water ratios. From comparing theoretical predictions with experimental results it could be concluded that composition drift for the monomer combination MA-V Ac could only be reduced since the difference in water solubility was not large enough to compensate the effects of the large difference in reactivity ratios. However, for the monomer combinations MA-VPV and MAV2EH the difference in water solubility was large enough to make minimum composition drift possible for low monomer-to-water ratios even for monomer combinations with reactivity ratios as far apart as in the MA-vinyl ester case.

8.1 Introduction

Vinyl acetate copolymers are widely used in interior architectural waterborne

coatings. Due to the poor hydrolytic stability of these copolymers, their use as exterior

coatings is limited. Vinyl ester monomers of the C9-Cll versatic acids, as produced by

Shell, have been available in Europe for about 25 years. 1•2

·3 As a result of recently

116 Chapter 8

developed large scale transvinylation methods, new vinyl ester monomers also have been

produced by the Union Carbide Corporation.4 Due to neighbouring group steric effects, the

use of these monomers in emulsion copolymerization results in improved hydrolytic stability

and water resistance when compared with vinyl acetate. 1•2

•3 Furthermore, glass transition

temperatures of (co)polymers will strongly depend on the vinyl ester used. In this way

copolymers can be designed over a wide range of glass transition temperatures.

Next to resistance against hydrolysis and glass transition temperatures, the product

properties are also determined by the heterogeneity of the copolymer. In the sensitivity

analysis (appendix chapter 6) it was shown that the course of composition drift in

copolymerization reactions is mainly determined by the water solubility of the contributing

monomers and their reactivity ratios. 5 For the monomers VAc, VPV, and V2EH the

reactivity ratios with MA have been determined by nonlinear optimisation6•7 of monomer

feed-copolymer composition data, indicating that for practical purposes the three MA-VEst

monomer systems can be described with one set of reactivity data (chapter 3: rMA = 6.1 ±

0.6 and rvEst = 8.7·10-3 ± 23·10-3).

8 An advantage of the approximately equal reactivity

ratios for VAc, VPV, and V2EH in MA-VEst monomer systems is that these systems can

be used as a tool in studying the important effect of the monomer solubility in water on the

course of emulsion copolymerization reactions of MA-VEst, especially as a function of the

monomer-to-water ratio.

As described in chapter 7,9 minimum composition drift can be obtained for monomer

combinations in which the more water soluble monomer is also the more reactive monomer.

In this chapter it will be discussed whether or not this statement still holds for monomer

combinations with reactivity ratios as far apart as in the MA-VEst case (where they differ

by a factor of 700!). Intuitively one can see that minimum composition drift in these cases

can only be reached if the monomer-to-water ratio is very low and if the difference between

the water solubility of the monomers is large enough to counteract the difference in the

reactivity ratios. Based on homo-monomer saturation concentrations and reactivity ratios

(Chapter 3) model predictions of minimum composition drift are performed for the monomer

systems MA-VEst using the theory and model presented in this thesis. In this way the effect

of changing monomer-to-water ratios in ab initio batch emulsion copolymerizations with

similar initial overall monomer mole ratios can be predicted for a series of monomer

combination with approximately equal reactivity ratios and covering a wide range of water

solubilities (listed in Tables 3.2 and 3.5). Some of the predictions of composition drift will

be compared with experimental results to validate the theoretical model for the MA-VEst

monomer systems.

The effect of water solubility on composition drift 117

8.2 Theory

As stated above, theoretically it should be possible to control and minimize

composition drift for monomer combinations where the more water soluble monomer also

is the more reactive one. As described in chapter 7, the mole fraction of the better water

soluble monomer i in the copolymer will reach a maximum value when all the monomer

is located in the polymer particle and monomer droplet phase, and it will reach a minimum

value when all monomer is located in the aqueous phase. The value for the minimum mole

fraction of monomer i strongly depends upon the a-value, i.e., the ratio of the water

solubility of monomer j over the water solubility of monomer i according to eq. 6.4a. For

the three monomer combinations at hand the minimum mole fractions can be calculated

using the water solubility values listed in Table 3.2 resulting in a-values of 51·10·2, 13 ·10-3,

and 0.41·10·3 for the monomer combinations MA-VAc, MA-VPV, and MA-V2EH,

respectively. Using other vinyl ester monomers as for instance vinyl propionate (VP),

different a-values will be found (a= 0.11). Although the MA-VP monomer combination

has not been studied here, its a-value will be used to show the effect of different a-values /

on the minimum mole fraction in the polymer phase. The minimum and maximum mole

fraction MA in the polymer particle phase is depicted in Figure 8.la as a function the overall

mole fraction MA for the monomer combinations MA-VAc, MA-VP, MA-VPV, and MA

V2EH. Using the instantaneous copolymer equation (eq 2.2)10•11 in combination with the

reactivity ratios of rMA = 6.1 and rve,1 = 8.7·10·3, the resulting copolymer composition can

be calculated. The minimum and maximum copolymer composition resulting from these

mole fractions are elucidated as a function of overall monomer mole fraction in Figure 8.1 b.

Note that for the calculation of the instantaneous copolymer composition from the mole

fraction MA in the polymer phase the same reactivity ratios are used for the monomer

combination MA-VP as for the other MA-VEst combinations. From Figure 8.lb we can see

directly that composition drift can not be suppressed completely by lowering the monomer

to-water ratio for MA-V Ac as a result of the a-value which is too close to l (the water

solubilities are too close together). From Figure 8.1 b we can also see that for MA-VP (a

= 0.11) and MA-VPV (a = 13 ·10'3), composition drift theoretically can be minimized for

overall mole fraction of MA ranging from 0.65 to 1 and 0.28 to 1, respectively. For the

monomer combination MA-V2EH (a 0.41·10.3) minimum composition drift can be

obtained over the whole range of overall monomer mole fractions going from 0 to I. Note

that although it is theoretically possible to obtain minimum composition drift, very low (i.e.,

118 Chapter 8

impractical) monomer-to-water ratios may have to be used.

A

0.80

0.60

0.40

0.20

0.00 Wi:O.o::::;::::;...-==;;.,_.....;o.a

0.00 0.20 0.40 0.60 0.80 1.00

0.80

0.60

0.40

0.20

0.00 !!:.---..===--....:.:....-=..;.~~ 0.00 0.20 0.40 0.60 0.80 1.00

Figure 8.1 (A) Maximum ff;,,,.d and a-value dependent mmtmum mole fractions of MA in the polymer phase, and (B) instantaneous copolymer composition resulting from these mole fractions MA in the polymer phase, as a jUnction of the overall mole fraction of MA. The a values correspond with the monomer combinations MA-VAc (0.51), MA-VP (0.11), MA-VPV (0.013), and MA-V2EH (0.00041), respectively.

8.3 Experimental

The emulsion copolymerizations to study composition drift were performed as

described in Chapter 3 at a temperature of 50°C. The recipes for these emulsion

copolymerizations, which were performed using the same overall monomer mole fraction

of foMA 0.75 and varying monomer-to-water ratios are collected in Table 8.1.

Solution polymerizations of MA-V Ac and MA-V2EH were performed at 70"C and

of MA-VPV at 60°C in the same reactor as the emulsion polymerization reactions (Figure

3.1). The initial overall mole fraction of MA was similar to the emulsion situation (fo,AM =

0.75), toluene was used as solvent, and AIBN was used as initiator. The recipes of the

solution copolymerizations are collected in Table 8.2. Note that the temperature of the

solution copolymerizations was higher than for the emulsion copolymerization reactions in

order to obtain reasonable polymerization rates. It has been assumed that the reactivity ratios

do not significantly vary with temperature, within the range of 50-70°C. This assumption

will be discussed in more detail in the light of the experimental results.

All reactions concerning composition drift were monitored by gravimetry, yielding

conversion-time curves and by gas chromatography providing the overall monomer fractions


as a function of time. Combining both data gives the overall conversion of both monomers

at each moment during the reaction.

Table 8.1 Emulsion copolymerization recipes for MA-VEst reactions with varying monomer-to-water ratios at 50"C. All masses are in grams.

I VAc VPV V2EH

MIW 0.02 0.3 0.02 0.02 0.1 0.3 0.02 0.02 0.1 0.3

MA 13.50 202.4 12.03 11.91 59.90 180.4 10.81 10.78 53.79 162.6 VAc 4.50 67.43

VPV 6.04 5.91 30.01 89.52

V2EH 7.12 7.11 35.47 107.2

water 895 900 900 901 897 901 899 900 907 900 SDS 1.31 1.30 1.30 1.30 2.58 7.77 1.30 1.32 2.61 7.79

NaPS 0.20 0.21 0.12 1.07 1.06 1.06 1.06 0.12 0.48 1.07

N~~:zC03 0.10 0.10 0.48 0.48 0.42 0.47 0.48 0.49 0.20 0.48

Table 8.2 Solution copolymerization reactions of MA-VAc and MA-V2EH at 7fJ'C and MA-VPV at 6(f'C.

Ingredients (g)

MA

VAc

VPV

V2EH

AIBN

toluene


MA-VAc

75.53

24.92

0.99

891

MA-VPV

66.36

32.90

0.99

904

MA-V2EH

60.03

40.72

1.00

900

Using the reactivity ratios and water solubility values of the monomers given in

chapter 3, the course of composition drift in emulsion copolymerizations can be predicted

with the model described in chapter 6. Note that it was shown in the sensitivity analysis that

the maximum swel!ability of monomer in polymer has a negligible effect on composition

drift. Therefore, model predictions can be performed using rather rough determinations of

swellability values. These estimations were determined by monomer partitioning experiments

similar to the ones described in chapter 3. However, instead of determining the amount of

water (and monomer dissolved in it), in the polymer-monomer samples only the solids

120 Chapter 8

content was calculated. From this the maximum swellability of monomer in polymer was

determined. The results of these estimations are listed in Table 3.2.

The large effect of different monomer-to-water ratios on the monomer mole fraction

in the polymer phase and as a result of this on the instantaneous copolymer composition

can be seen in Figure 8.2 where the monomer combination MA-VPV is used as an example.

Similar results are obtained for the monomer combination MA-V2EH. As a result of the

high a-value of the MA-VAc monomer system only a small influence of the monomer-to

water ratio on the monomer composition in the polymer particle phase and thus on the

instantaneous copolymer composition has been observed.

~ ......

1.00 1.00 A B

M/W. 0.1 0.75 0.75

0.50 J 0.50

0.25 0.25

0.00 0.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75

fo,MA fo,MA

Figure 8.2 (A) Influence of the monomer-to-water ratio on the mole fraction of MA in the polymer phase, and (B) instantaneous copolymer composition resulting from these mole fractions MA, both as a function of the overall mole fraction of MA for the MA-VPV monomer combination (ex = 0.013).

1.00

The results of the reactions with varying M/W ratios are depicted in Figures 8.3-8.5

for the three monomer combinations. The maximum possible span of control in emulsion

copolymerization can be obtained when comparing very high monomer-to-water ratios with

very low ones. The high-limit case will exhibit composition drift behaviour equal to that

in reactions performed in homogeneous systems (bulk or solution copolymerizations). In

order to study this maximum monomer-to-water situation, solution copolymerizations were

performed using toluene as solvent. Note that the assumption is made that the reactivity

ratios are independent of the solvent toluene. The theoretical and experimental results of

these reactions are also depicted in Figures 8.3 to 8.5. Note that in solution

copolymerizations the reactivity ratios are the only determining model parameters. Therefore,

it can be concluded from the agreement between predicted and experimental solution

copolymerization results that the reactivity ratios which were determined by low conversion


bulk polymerization at 50°C are also valid in solution polymerization using toluene as

solvent at temperatures up to 70°C. In other words, the reactivity ratios seem to be rather

temperature independent in the range of 50-70°C. In the low monomer-to-water situations

more of the better water soluble MA will be buffered in the aqueous phase leading to

different composition drift behaviour since MA is partly and temporarily withdrawn from

reaction. For the monomer combination MA-V Ac the effect of varying the monomer-to

water ratio is relatively small even for low monomer-to-water ratios as a result of the small

difference in water solubility between MA and VAc (a= 0.5).

1.00

0.80

~ ...: 0.60

0.40

0.20

0.00 0.00 0.20 0.40 0.60 0.80 1.00

conversion Figure 8.3 Overall MA mole fraction as a function of conversion for MA-VAc solution (o) and emulsion copolymerization reactions with monomer-to-water ratios of0.02 (~>)and 0.3 (D).

1.00

0.80

.. 0.60

j 0.40

0.20

0.00 0.00 0.20 0.40 0.60 0.80 1.00

conversion

Figure 8.4 Overall MA mole fraction as a function of conversion for MA-VPV emulsion copolymerization reactions with monomer-to-water ratios of0.02 (with initiator concentrations of0.13 gdm/ (o), and 1.2 gdm.,·3

(•)}, 0.1 (D), and 0.3 (6).

122 Chapter 8

1.00

0

j 0.40

0.20

0.00 L---.----.------,.------,__.l...!ll....~ 0.00 0.20 0.40 0.60 0.80 1.00

conversion

Figure 8.5 Overall MA mole fraction as a function of conversion forMAV2EH solution ( 11.) and emulsion copolymerization reactions with monomer-towater ratios of0.02 (with initiator concentrations of 1.2 grlmw-3 (.i), and 0.13 grlm,._3 (v)), 0.1 (D), and 0.3 (o).

From Figures 8.4 and 8.5 it becomes clear that the ratio of the water solubilities of both

monomers indeed has a large effect on composition drift in MA-VPV and MA-V2EH

monomer systems as was expected from the theoretical predictions depicted in Figure 8.1-

8.2. Furthermore, from Figures 8.3-8.5 it becomes clear that there is reasonable agreement

between experimental results of emulsion copolymerization reactions and theoretical

predictions of the overall monomer mole fraction as a function of conversion for monomer

to-water ratios larger than approximately 0.1.

It is important to realise that minimizing composition drift in MA-VPV and MA

V2EH reactions is only possible due to the large difference in water solubility values of the

monomers (a factor of 80 and 2400, respectively) which is necessary to counteract the large

difference in reactivity ratios (factor 700). In this case the water phase can buffer a sufficient

amount of the more reactive monomer to minimize composition drift.

The deviations observed between theory and experiment for low monomer-to-water

ratios may have two possible causes: 1) water phase polymerization of the better water

soluble MA can not be neglected, and 2) the model predictions are sensitive towards

deviations in model parameters for low monomer-to-water ratios, where the amount of

monomer in the aqueous phase cannot be neglected as compared with the total amount of

monomer.

The water phase polymerization has been examined by performing two reactions

differing only in initiator concentration. In those cases where water phase polymerization

plays an important role, more MA-rich oligomers will be formed in the aqueous phase at


higher concentrations of the water soluble initiator. It is expected that, as a result of more

homogeneous nucleation, the MA will disappear faster as a function of conversion at higher

initiator concentrations. However, the composition drift behaviour in the two reactions is

equal within experimental error (see Figures 8.4 and 8.5), strongly suggesting that the

discrepancy between theory and experiment cannot be explained by water phase

polymerization alone. The occurrence of insignificant aqueous phase polymerization of MA

in the MA-VPV reactions was confirmed by 1H-NMR and HPLC analyses. The 1H-NMR

analyses of low conversion samples showed that the overall copolymer composition was

equal to the theoretically predicted copolymer composition within experimental error, while

in HPLC analysis no homo-polymer of MA was found.

For the MA-V2EH reactions significant deviations were found between the

theoretically predicted (pred) and experimentally (exp) determined copolymer compositions

(M/W = 0.02, 1H-NM~red = 0.73, 1H-NMI\xp = 0.87; M/W 0.3, 1H-NM~ = 0.94, 1H

NMR,xp = 0.98). Furthermore, some homopolymer of MA was found with HPLC in this

case, indicating that water phase polymerization has occurred in the MA-V2EH emulsion

copolymerizations.

The effect of intentionally imposed deviations in the model parameters on

composition drift has been discussed in detail in the appendix of chapter 6 for MMA-S,

indicating that the effect of deviations only can be neglected if the amount of monomer in

the aqueous phase is negligible as compared with the total monomer amount. In the MA

VEst polymerizations with low monomer-to-water ratios, the amount of monomer located

in the aqueous phase cannot be neglected. Therefore, the (in)accuracy of the model

parameters may lead to deviations between experimental results and model predictions. As

can be seen in Figures 8.4 and 8.5, in the present cases the deviations indeed are larger for

low monomer-to-water ratios. Performing model predictions with different parameters for

the MA-VPV combination at low monomer-to-water ratios of 0.02 (see Table 8.3; 10%

deviation on reactivity ratios, water solubility, and swellability of polymer with monomer)

indicates that predictions in these low monomer-to-water cases indeed are sensitive towards

deviations in model parameters (Figure 8.6).

Summarizing the above discussion on water phase polymerization and the sensitivity

of predictions towards the accuracy of model parameters, the following can be concluded:

1) Accurate model predictions at low monomer-to-water ratios in both MA-VPV and MA

V2EH emulsion copolymerization are prohibited by the sensitivity of predictions towards

(in)accuracies of the model parameters.

2) The discrepancy between theory and experiment in the MA-VPV copolymerization can

124 Chapter 8

solely be attributed to (in)accuracy of the model parameters, since in that case no significant

water phase polymerization has occurred.

3) The discrepancy between theory and experiment of the MA-V2EH copolymerizations is

most probably caused by both, inaccuracy of the model parameters and aqueous phase

polymerization.

Table 8.3 Standard parameters (VPVJ) and intentionally introduced deviating parameters (VPV2-4), used in MA-VPV model predictions at 5(J'C. All concentrations are in mol/dm3

•

fMA

fypy

VPVl VPV2 VPV3 VPV4

6.7 1-10'5

[MA].,sat(h) [VPV] .. ,01(h)

[MA]p,sat(h) [VPV)p,sat(h)

6.1 8.7·10'3

0.55

7.3•10'3

7.05

4.0

6.7 1•10'5

0.55 7.3•10'3

7.05

4.0

6.7 1·10"5

0.49 8·10"3

7.05

4.0

0.49 8·10'3

7.7

4.4

VPVl

0.40 VPV4

0.20

0.00 '-----.,-----..-----..-----..,..---0.00 0.20 0.40 0.60 0.80 1.00

conversion

Figure 8. 6 Model predictions of the overall MA mole fraction as a jUnction of conversion using the series of model parameters listed in Table 8.3 for a MAVPV copolymerization (MIW 0.02), and comparison with experimental data (o).

8.5 Conclusions

Theory predicts that for monomer systems in which the water solubility of the


monomers is very far apart (low a-values) the effect of differences in reactivity ratios on

copolymer heterogeneity can be compensated. In principle, composition drift can be reduced

by changing the initial monomer-to-water ratio in batch emulsion copolymerizations in which

the more reactive monomer is also the more water soluble one. Experimental verification

of this concept has shown that minimum composition drift could be achieved for the

monomer system MA-VPV and MA-V2EH, where MA is the more reactive and more water

soluble monomer. For the monomer combination MA-V Ac composition drift could only be

slightly reduced by lowering the monomer-to-water ratios since the difference in water

solubility of the two monomers is too small in this system.

An important conclusion that can be drawn when comparing the composition drift

behaviour of the three MA-VEst monomer combinations is that, although the reactivity ratios

are approximately equal for the three systems, the chemical composition distribution of each

of the resulting copolymers will definitely change if one vinyl ester monomer is replaced

by another one, as a result of their differing water solubilities. Such a replacement would

therefore also immediately affect copolymer heterogeneity and hence properties.

126 Chapter 8

1. H.P.H. Scholten, J. Vermeulen, "A new versatile building Block for HighPerformance Polymeric Binders", XIX Fatipec Conference, Aachen, 18-24, 1988

2. W.C. Aten, "Effect of Composition and Molecular Weight on the Performance of Latices Based on Vinyl Ester of Versatile Acid in Modern Emulsion Paints", XVIIth Fatipec Congress, Lugano, 1984 .

3. M.M.C.P. Slinckx, H.P.H. Scholten, "Veova 9/(Meth) acrylates, A new Class of Emulsion Copolymers", 19th Water-Borne, Higher Solids and Powder Coating Symposium, New Orleans, La., 1992

4. R.E. Murray, US 4, 981, 973 to Union Carbide, 1991 5. L.F.J. Noel, LA. Maxwell, W.J.M. van Well, A.L. German, J Polym. Sci., Polym.

Chem. Ed., 32, 2161 (1994) 6. F.L.M. Hautus, H.N. Linssen, A.L. German, J Polym. Sci., Polym. Chem. Ed., 22,

3487, 3661 (1984) 7. M. Dube, R. Amin Sanayei, A. Penlidis, K.F. O'Driscoll, P.M. Reilly, J. Polym. Sci.,

Polym. Chem., 29, 703 (1991) 8. L.F.J. Noel, J.L. van Altveer, M.D.F. Timmennans, A.L. German, in press by J

Polym. Sci., Polym. Chem. Ed., xx, xx (1994) 9. L.F.J. Noel, J.M.A.M. van Zon, A.L. German, J Appl. Polym. Sci., 51, 2073 (1994) 10. F.R. Mayo, F.M. Lewis, J Am. Chem. Soc., 66, 1594 (1944) 11. T. Alfrey, G. Goldfinger, J Chem. Phys., 12, 205 (1944)

Epilogue 127

Epilogue

The primary goal of the research described in this thesis was gaining basic insight in

copolymerization taking place in heterogeneous media, in particular emulsion copolymerization.

It was hoped that these insights, combined with the development of enhanced methods

of on-line process monitoring, would contribute to a better control of composition drift in

emulsion copolymerization, and hence to the preparation of well-defined emulsion copolymers.

In order to reach this goal, the following more specific aims were formulated:

(1) Development of a reliable and simple model to describe monomer partitioning of two

monomers with limited water solubility, in such a way as to avoid the use of interaction

parameters that are experimentally difficult to access and theoretically rather vague.

(2) Investigation and evaluation of the (theoretical) concept that minimum composition drift

could be obtained by adjusting the monomer-to-water ratio for those monomer combinations

in which the more water soluble monomer is also the more reactive one.

(3) Development and evaluation of reaction monitoring techniques that provide a large

number of high-quality· data over the entire conversion range.

In the following a summary will be given of the strategies followed to reach these aims,

and some selected results will be shortly highlighted:

ad(1) Based on earlier work an extended model has been developed capable of describing

monomer partitioning at partial swelling oflatex particles by two monomers with limited water

solubility. The most important and striking feature of this partitioning model is that the only

parameters required are the individual homo-saturation values of the monomers in the polymer

particles and the aqueous phase, which are readily accessible. Experimental verification of the

model predictions for the monomer combination methyl acrylate-vinyl acetate shows excellent

agreement.

The availability of the present model solves one of the major problems in modelling

emulsion copolymerization, and allows the prediction of i.a. the compositional heterogeneity

of emulsion copolymers.

128 Epilogue

In addition, the present model also allows prediction of the absolute monomer

concentrations in the particle phase, which det~rmine the rate of (co)polymerization. This is

of great importance in determining optimal addition rate profiles, needed when preparing

compositionally homogeneous copolymers in semi-continuous processes. The latter, however,

is beyond the scope of this thesis.

ad(2) The reactivity-solubility concept was first tested for the emulsion copolymerization of

methyl acrylate-indene, where methyl acrylate is the more reactive as well as the more water

soluble monomer. It appears, when starting from any initial value within a wide range of

monomer feed compositions, that indeed the composition drift can be minimised (almost zero)

over the entire conversion range, simply by adjusting the monomer-to-water ratio.

A most rigorous test of the validity of the above concept is performed in a study of

the effect of the monomer-to-water ratio on the copolymerization of methyl acrylate with a

series of vinyl esters of strongly varying water solubility. The large difference in reactivity

(for all these systems a factor of ca. 700), cannot be compensated by the small difference in

water solubility between methyl acrylate and vinyl acetate, but it can be compensated by the

larger difference in water solubility between methyl acrylate and the other (more hydrophobic)

vinyl esters. The results clearly show that in essence the concept remains valid: i.e., in all cases

the composition drift is suppressed when decreasing the monomer-to-water ratio. Depending

on the specific monomer combination some intrinsic or practical limitations may occur,

however, preventing the composition drift to become (almost) zero.

These investigations provide and allow the utilization of a new handle on the

compositional control in emulsion copolymerization; a tool that is unique in the sense that it

does not exist in homogeneous (bulk or solution) copolymerization.

The present findings on the effects of monomer-to-water ratio and of monomer

solubility in water are having important practical implications as well. For example, in those

cases where the solids content in the reactor is changed, or where one of the monomers in the

recipe is replaced (even by an equimolar amount of another monomer of equal reactivity), a

copolymer product of different heterogeneity and thus different properties can be expected.

ad(3) The accurate and rapid determination of the partial conversion of the separate monomers

is of key importance to understanding, modelling, and controlling emulsion copolymerization.

The physical complexity of the systems (e.g., the heterogeneity leading to monomer

Epilogue 129

partitioning), calls for the combination of two on-line techniques: densimetry yielding the

overall weight conversion, and gas chromatography providing the overall ratios of the residual

monomers. Combination of these two data sets allows the calculation of the partial conversion

of each monomer as a function of time, most importantly, without the need of an internal

standard.

Adequate solutions have been proposed for non-ideal behaviour, as observed e.g. in

the system methyl acrylate-vinyl acetate, where the specific volume of the monomers in the

aqueous phase is different from that in the mono~er droplet phase.

Even for this rather complex, non-ideal system comparison of the on-line data with

off-line results and theoretical predictions gave satisfactory agreement, which validates this

powerful combination of techniques, indispensable in monitoring emulsion copolymerization.

The method developed is certainly not restricted to the present systems, but could be

applied, in principle, to any monomer combination. Extension of the method to monitor

terpolymerization seems quite well feasible. Future developments also may include the

instantaneous control of monomer addition, based on on-line measurements of monomer

conversion data, allowing the preparation of tailor made copolymers in a single run. For

example, the composition drift could be controlled in any desired manner by on-line

measurement of the instantaneous monomer concentrations, and feed-back control of the

addition rate of the more reactive monomer.

130

symbol

A

B

DS(t)

List of symbols

temperature dependent densimeter instrument constant

temperature dependent densimeter instrument constant

dry solids content at time t determined by weighing the latex mass

of a sample before and after drying

mole fraction of monomer i

copolymer composition in mole fraction of monomer i

degree of saturation of the polymer phase

F sat. degree of saturation of the aqueous phase

propagation rate coefficient

average propagation rate coefficient

propagation rate constant of the propagation step between radical i

and monomer j

number average molecular weight

List of symbols

units

%

-I%

--1%

dm3mol"l-s·l

dm3 mol"1 -s·1

dm3mol"1-s"1

gmol"1

mass of the non-polymerizable and non-evaporative components in emulsion

mass of the initially added monomers to an emulsion

g

g

g

g

total mass of the emulsion mixture

initial mass of monomers i at the beginning of the reaction

m9 ratio of the molar volumes of monomers i and}, (my = VmfVm}

Mx,t total moles of monomer x in the system

N.. avogadro's number

N number of particles per litre water

ii average number of radicals per particle

P. number-average degree of polymerization

R gas constant

%''·' overall ratio of monomer j over i at time t

r1 reactivity ratio of monomer i defined as r, = k;/k1i

ri reactivity ratio of monomer j defined as ri = kjki1

unswollen radius of the latex particle

rate of polymerization

List of symbols

t time

T temperature

T period of oscillation of the sample tube

xto.Ct) total overall conversion determined by gravimetry

x,,, partial conversion of monomer i at time t

X mass fraction, subscripts m, p and s stand for monomer, polymer

and serum (the aqueous phase), respectively

vpo polymer volume

vp volumes of the monomer swollen polymer phase (the volume of the

polymer+ monomer in the saturated polymer)

v. volume of the saturated aqueous phase (the volume of water+ monomer

dissolved in it)

vw volume of the aqueous phase (without monomer)

vd volume of the monomer droplet phase

vmx molar volume monomer x

v specific volume

Greek symbols

p

ratio of the water solubilities of monomer j over monomer i

density, subscripts l, p, and s represent the density of the total

diluted latex, the (co)polymer and the serum, respectively

A~ partial molar Gibbs free energy or chemical potential

v P volume fraction of polymer in the latex particles

vx_vCz) volume fraction in phase x of monomer y at homo saturation swelling

(z=h) or at a certain monomer ratio (z=r), at saturation swelling

subscript 'sat' is added

x Flory-Huggins interaction parameter

xii interaction parameter between monomers i and j

X;p. x1P interaction parameters between each of the respective monomers

i and j and the polymer

y particle-water interfacial tension

131

s

K

s

--I%

--1%

--fOAl

dm3

dm3

dm3

dm3

dm3

dm3mo1"1

dm3-Jcg-l

132

Concentrations

[M] monomer concentration

[M]p,i concentration of monomer i in the polymer phase

[M] • .; concentration of monomer i in the aqueous phase

[M •] free radical concentration

Subscripts, superscripts, and abbreviations

o start of the reaction

at 1 00% conversion

a aqueous phase

e total emulsion

List of symbols

mol-dm-3

mol-dm-3

mol-dm"3

mol-dm-3

h homo saturation swelling; saturation concentration of monomer in the absence of other

monomers

monomer i

j monomerj

m monomer droplet phase

MIW monomer to water ratio

p polymer particle phase

r mole ratio of monomers i and j

sat saturated

timet

Acknowledgement 133

Acknowledgement

The work presented in this thesis has been carried out in the Polymer Chemistry Group

of Prof. A.L. German. I wish to express my gratitude towards the members of this group, who

have contributed to this thesis.

More specifically I thank my first promoter Ton German, for his confidence in me and

for his pleasant way of coaching. My copromoter, Ian Maxwell (Memtec Limited, Sydney,

Australia), is gratefully acknowledged for his invaluable contributions to and discussions on

this work especially in the field of thermodynamics and modelling, and for the correction of

papers and this thesis. Alex van Herk is acknowledged for his contributions in the discussions,

especially on the on-line measurements.

I wish to thank all students who contributed with experimental work and useful

discussions: Jan van Zon, Menno Timmermans, Dirk van Wasbeek, Frank Riswick, Eric

Brouwer, Willy van Well, Erwin Goosen, and Jeroen van Altveer. I also like to thank Herman

Ladan (TEM), Wieb Kingma (GC), Alfons Franken and Paul Cools (HPLC).

Of the people outside the polymer group who have helped me during my Ph.D. work,

wish to thank my second promoter, Prof. J.M. Asua (San Sebastian, Spain) for our

discussions and his comments on the manuscript of this thesis. Denis Heymans (Shell Research

S.A., Louvain-la-Neuve, Belgium), and David R. Bassett and Martha J. Collins (Union Carbide

Corporation, South Charleston, USA) are gratefully acknowledged for supplying me with

samples of the vinyl ester monomers.

The investigations were supported by the Netherlands Foundation for Chemical

Research (SON) with financial aid from the Netherlands Organization for Scientific Research

(NWO). Further financial contributions from the Foundation ofEmulsion Polymerization (SEP)

and Shell Nederland B.V. are also gratefully acknowledged.

Finally I wish to express my gratitude towards everybody who has shown interest in

me and my Ph.D.-work.

134 Currieulum vitae

Currieulum vitae

Lilian Verdurmen-Noel was born in Weert, The Netherlands, on the lllh of August,

1965. After graduation from secondary school at the Philips van Horne Scholen Gemeenschap

in 1985 she started her academic study in chemistry and chemical technology at the Eindhoven

University ofTechnology. She graduated (ir-diploma) on August 28, 1990 on a project entitled:

duplex stability and protein degradation of natural and fosforothioate DNA, in the group of

Prof.Dr. H.M. Buck of the organic chemistry department.

In the same year she started her Ph.D. project on monomer partitioning and composition

drift in emulsion copolymerization in the polymer chemistry group ofProf.dr.ir. A.L. German.

Stellingen

behorende bij het proefschrift

Monomer partitioning and composition drift

in emulsion copolymerization

van

Elisabeth, Franr,:ois, Johanna Verdurmen-Noel

1. Thermodynamische evenwichtsrelaties kunnen, ondanks sterke vereenvoudiging door

het gebruik van rigoureuze aannamen, leiden tot nauwkeurige voorspellingen van de

verdeling van monomeren over de verschillende fasen in emulsies. I.A. Maxwell, J. KU1ja, G.H.J. van Doremaele, A.L. German, Makromol. Chem., 193, 2065 (1992);

I.A. Maxwell, L.F:J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol. Chem., Theory and

Simulation, 2, 269 (1993); Hoofdstuk 5 uit dit proefschrift.

2. De bewering van Ballard et a/. dat het einde van interval II in

emulsiecopolymerisaties voor de twee afzonderlijke monomeren bij verschillende

overall conversies zou liggen, duidt op een gebrek aan inzicht in de

monomeerverdeling in emulsiecopolymerisatie. M.J. Ballard. D.H. Napper, RG. Gilbert, J. Polym. Sci .. Polym. Chem. Ed., 19, 939 (1983)

3. Conversie in emulsiepolymerisatie kan met behulp van on-line dichtheidsmetingen

nauwkeurig bepaald worden, ondanks grote afwijkingen tussen afgelezen dichtheid

en absolute dichtheid. P.D. Gossen, J.F: MacGregor, J. Colloid 1nter, Sci., 160, 24 (1993); S. Canegallo, G. Storti, M.

Morbidelli, S. Carra, J. Appl. Polym. Sci., 47, 961 (1993); Hoofdstuk 4 uit dit proefschrift.

4. In de literatuur beschreven bepalingen van de reactiviteitsverhoudingen met behulp

van achterhaalde, onjuiste en onnauwkeurige methoden, blijven een onnodig en

hardnekkig verschijnsel.

M. Charreyre. V, Razaftndrakoto, L. Veron, T. Delair, C. Pichot, Macromol. Chem. Phys .. 195, 2141

(1994); B. Suthar, J. Joshi, J. Indian Chem. Soc., 70, 180 (1993); M. Ada/, P. Flodin, E. Gottberg

Klingskog, K. Holmberg, Tenside Surf Det., 31, 9 (1994).

5. Vergeleken met traditionele monomeerverdelingsevenwichtsexperimenten is het

verrichten van geleidbaarheidsmetingen aan emulsiepolymerisaties een relatief

simpele en directe methode om maximale zwelbaarheden van polymeer met

monomeer te bepalen.

R.Q.F. Janssen. A.M. van Herk, AL German, Surface Coatings International (JOCCA), 76(11), 455

(!993); L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.M. van Herk, A.L. German, to be submitted

6. Het gebrek aan experimented bepaalde kinetische parameters van copolymerisaties

verhindert vooralsnog de experimentele verificatie van theoretische modellen voor

emulsiecopolymerisaties.

L.F.J. Noel, W.J.M. van Well, A.L. German, to be submitted

7. Het in 1994 publiceren van een uitgebreide beschrijving van de reeds in 1950

gepubliceerde Finemann-Ross methode om reactiviteitsverhoudingen te bepalen is

overbodig, ongewenst en duidt op een kritiekloze houding van de referees.

M. Ada/, P. Flodin, E. Gottberg-Klingskog, K. Holmberg, Tenside Surf Det., 31, 9 (1994).

8. Het aanduiden van een land (Nederland) met de naam van een van de provincies

(Holland) dient vermeden te worden onder andere omdat het kan leiden tot

verwarring en verkeerde statistieken betreffende aantallen deelnemers en hun land

van herkomst. Conference book, 8'• International Conference on Surface and Colloid Science, Adelaide, South

Australia, /3-/8 February 1994

9. Het vermelden dat uiteindelijke conclusies ondanks redeneerfouten toch geldig zijn

is eerder lachwekkend dan wetenschappelijk overtuigend.

H. Akisada, J. Colloid Interface Sci., 97, 105 (1985); Handout bij poster "CMC and Micellar

Composition of Ionic surfactant, Nonionic that, and Salt System" gepresenteerd door H. Akisada

tijdens: "8'" International Conference on Surface and Colloid Science'~ Adelaide, South Australia,

13-18 February 1994

10. De verdraagzaamheid van buren kan op eenvoudige wijze getest worden door het

nemen van een kat.

11. Aangezien het idee van nieuwbouw voor de faculteit Scheikundige Technologic al

bijna twintig jaar geleden werd geopperd, zou bij een snelle besluitvorming de dan

tot stand gekomen "nieuw"-bouw nu al weer sterk verouderd zijn.

Eindhoven, 29 november 1994

monomer partitioning and composition drift in emulsion ...monomer partitioning and composition drift...

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