An Evahation of Molecular Weight Predictions in Emulsion Polymerization Under Conditions of Diffusion Limited Chain Transfer

by Tricia Witty

A thesis submitted to the Department of Chernical Engineering in conformity with the requirements for the degree of Master of Science (Engineering)

Queen's University Kingston, Ontario, Canada April, 2001

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The rnoIecular weight (MW) and molecular weight distribution @IWO) of polymers are extremely important properties because many end-use properties are a function of the polymer's

MW and W.Typically the MW and MWD are measured by on-line GPC, which can take up to 1 hour to generate a reading for a sample. From a control standpoint it would be desirable to be able to generate estimates on the molecular weight on the order a few minutes so that the process can be controlled more effectively.

In homogenous polymerization systerns, kinetic rnodets are well estabiished. However, in emulsion system the heterogeneity of the system complicates the process. In this work the validity of integrating a kinetic model, proposed by Gilbert et al. (1995), and a diffusion model describing the transport of a chain-transfer agent (CTA) under conditions of difision limited chain transfer, (Nomura et al., 1994), in order to generate molecular weight predictions bas been investigated. The technology exists to obtain accurate estimates of the required mode1 parameters through techniques that make this approach amenable to on-line application.

A series of styrene emulsion polyrnerizations were bedout with varying levels of

CTA, surfactant, and initiator. The data collected ivas analyzed by the Malvern Mastersizer 2000 to determine the monomer droplet and polyrner particle size, by gas chromatography (GC) to determine the CTA concentration and by gel pemeation chromatography, (GPC) to determine the molecular weight.

The results showed that our approach provides a reasonable estimate of the product's weight average molecular weight and molecular weight distribution, even under conditions of severely diffusion Iimited chain transfer. The results also demonstrate the model's sensitivity to accurate estimates of the monomer droplet size as well as the CTA partition coefficient. The data collected f?om the Malvem Mastersizer 2000 also demonstrates that in out system, monomer droplets do not disappear at the theoretid end of interval II. Ac knowledgments

1 would Iike to thank Dr. M. F. Cunningham for offering me the opportunity to work on this project. The guidance he has given me and the support he has shown has undoubtedly helped me to prepare for the many chaltenges that lie ahead.

Thanks must be given to rny fellow members of the Cunningham !ab, Jodi Smith, Karine

Tortosa and John Ma for al1 of their help support. Special thanks must also be given to John for the time he has spent helping with everything £iom getting things going in the lab, to interpreting the results,

Steve Hogdeson also deserves thanks for the countless hours he has spent helping me with the analytics involved in this project. Without his help this project tvouId not have been possible.

1 would dso like to express my thanks to the Department of Chernical Enguieeruig for the financial support 1 received whiIe working on this project.

Finally I would like to thank my fnends and fellow graduate students for providing me with the necessary distractions fiom my research and for making rny extended time at Queen's that rnuch more enjoyable. CHAPTER 1

1. Introduction 1.1 Objectives

CHAPTER 2

2. Literature Revîew 2.1 OveMew of Emulsion Polyrnerization 2-2 Polymerizaîïon Kinetics 2.3 DBkion Limited Chain T-er 2.4 Molecular Weiglit Distributions 2.4.1 MWD ModeIs

CHAPTER 3

3. Experimental 3.1 Materials 3.1.1 Monomer Purification 3 -2 Ex-perimental Apparatus 3 -3 Experïrnental Procedure 3 -3.1 Monomer Droplet Study Procedure 3 -3.2 Polymerization Procedure 3 -4 Anaiytical Procedures 3 -4.1 Gravimetric Analysis 3.4.2 Gas Chromatography 3 -4.2.1 Equipment 3 -4.2.2 Sample Preparation and Analysis 3.4.3 Gel Permeation Chromatography 3 -4.3.1 Equipment 3 -4.3 -2 GPC Calibration 3 -4.3 -3 Sample Preparation and Analysis 3 -4.3.4 Treatrnent of GPC Dam 3.4.4 Monorner Droplet and Particle Size Distributions 3-4.4.1 Equiprnent 3-4.4.2 Sample Preparation and Analysis

CHAPTER 4

4. Particle Size Mcasurements 4.1 Monomer Droplet Analysis 4.1.1 Effect of Surfactant Concentration 4.1.2 Reactor RPM 4.1.3 Malvern RPM 4.1.4 Sampling Location 4.1.5 MingTime in the Reactor 4.1.6 Effect of the Scunple Injection Metliod 4.2 Polymerization Particle Size halysis 4.2.1 Understanding the Results 4.2.2 Polymerization Particle SizeResults 4.3 Summary CHAPTER 5

5. Eaperimentd Results 5,L Conversion Data 5-2 Dodecanethiol Consumption 5.3 Number and Weight Average MoIecular Weight

CHAPTER 6

6. Resul ts 6.1 Two-Film Difhision Mode1 6.1.1 Mode1 Parameter Estimation 6-1.2 Comprison of [A,] Values 6.1.3 Twvo-Film DZhsion Mode1 Summaq 6.2 Kinetic Mode1 6.2.1 Muence of Diffiision Limitations of MW 6.2.2 Results 6.2-2-1 Evaluation of Weight Average MoIecuiar Weight Data 6.2.2.2 Cornparison of W(1ogMW) values 6.2-2.3 Filtering of Data to Improve Mode1 Predictions 6.2.2-4 Relative Peak Areas of Particles and Droplets 6.3 Summary

CHAPTER 7

7. Conclusions

CHAPTER 8

8. Recommendations for future work List of Tables

Table 2.1: Parameters contained in the S2 term of Nomura's model-., ...... 12

Table 3.1: The materials used in the project ...... ,,,,...... 18

Table 3.2: A summary of the formuIations that were investigated-...... 21

Table 3 -3: The GC program setting used to analyze the latex samples ...... 24

Table 3.4: The integration parameters used to detemine the integrated peak areas...... -.-24

Table 3 -5: Molecular weight separation ranges for the GPC colum...... 25

Table 4.1: A surnmary of the distribution characteristic for systems with varying levels of surfactant concentration...... -31

Table 4.2: A surnmary-. of monomer droplet distributions subject to various rates of agitation...... 32

TabIe 4-3: A sumrnary of the distribution charactenstics when the agitation speed of the Malvern is varied and the agitation speed of the reactor is constant (500rpm)...... 33

Table 4-4: A surnmary of the distribution characteristics when sarnples are withdrawn fiom three regions within the reactor ...... 34

Table 4.5: A surnmary of the particle size distribution information and its correspondïng conversion reported on a number basis ...... -.39

Table 6-1: A surnmary of the constants used in diffùsion mode1 for a n-DDT water system at 50°C...... 37

Table 6.2: A cornparison of the number of particles calculated from Malvern and polymerization rate data for a run containing 3 wt%, 6.658 SDS, and 2.0 g KPS...... -59

Table 6.3 (a)-(c) Monomer Droplets Observed in the Malvern Data compared to the Monomer Droplets Present in the Equilibnum Swelling Assumptioo ...... 69

Figure 6-9: Comparison of W(1ogMW) for a nui containing 3wt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals ...... 98

Figure 6.10. Cornparison of filtered and unfiltered data ...... 101

Figure 6.1 1: Monomer concentration in the polyrner particles ...... 102

Figure 6.12. MW Cornpan-son using Relative Peak Ares ...... 103

Figure 6.13. Cornparison of W(1ogMW) using relative peak areas ...... 105

Figure 6.14. Cornparison of W(1ogMW) using relative peak areas ...... 108 Nomenclature

.l chah transfer agent concentration in the polymer particleç (moVdrn3) critical micelie concentration concentration of monomer in the polymer particles (moUdm3) chah transfer agent merconstant monomer droplet diameter polymer particle diameter diaision coefficient (dds) propagation rate coefficient (dni3/mol s) tennination rate coefficient (d~n~/rnols) transfer rate coefficient to an added meragent (dm3/mol s) transfer rate coefficient to monomer(dm3/mol s) gel permcation chromatograpliy partition coefficients rnoledar tveight of the monorner (g/mol) rnolecular weight (Daltons) rnolecular weight distribution number average rnolecular weight (Daltons) weight average moIecular weight (Daitons) average number of radicaldparticIe nonnaijzation factor Avogadro's nurnber number of rnonorner droplets number of polymer particles cumulative rnolecular weight distribution instantaneous rnolecular weiglit distribution polymenzation rate (mou L s) enuy rate coefficient (s") relative response factor GPC molecular weight distribution Chapter 1

1. Introduction

Many commercial polymers are produced by emulsion polymerization, EmuIsion polymerization offers the ability to produce high molecular weight polymers at a high reaction rate under easier handling and processing conditions than conventionai bulk systems. In dl polymerization systerns the ability to predict and control the rnolecular weight of the product is of the utmost importance because many end-use properties are a function of the polymer's molecular weight (MW) and molecular weight distribution (MWD)- Currently the best method for molecular weight control is on-line GPC. However, the drawback to this technique is that it can take up to one hour to generate the molecular weight distribution of the sample. From a control standpoint, it would be desirable to be able to generate an estimate of the product's MMrD on the order of a few minutes. In homogenous systems it is relatively straightfonvard to estimate the molecuIar weight of the polymer because adequate kinetic models have been developed.

However, in emulsion systems, heterogeneity complicates the process so that reIiable on-Iine estimates of the MWD are more difficult to obtain,

Clay and Gilbert (1995) have proposed a mode1 that predicts the instantaneous molecular weight distribution of a polyrner produced in emulsion polymerization in the presence (or absence) of a chain transfer agent (CTA). in order to make this prediction the mode1 requires knowledge of the propagation and chain transfer rate constants, the CTA and monomer concentrations in the poiymer particles, as well as the entry-rate coeEcient. Thermodynarnic models allow calculation of the equilibrium monomer and CTA concentrations in the particles and the values for many of the other parameters are available in the literature. However, many authors have shown that when long-chain transfer agents, possessing vexy low water solubilities, are used, the concentration of CTA tvithui the particles wiii not be at equilibrîum for at least part of the polyrnerization due to diffusion limitations.

Nomura et al. (1994) proposed a model describing the transport of CTA under di£tùsion

Iimited conditions, which when rnanipulated, could allow estimation of the chah transfer agent concentration in the polymer particies. It is the objective of tlüs work to evaluate whether the kinetic model proposed by Clay and GiIbert and the difision mode1 proposed by Nomura can be integrated with monomer droplet and polymer partide size measurements to provide an accurate estimate of not only the molecular weight, but also the molecdar weight distribution of polymers produced under conditions of difision limited chah transfer. Previous work by Ma and

Cunningham (2000b) used Clay and Gilbert's model to predict the molecular weight distribution of seeded emulsion polymerization systems employing ndodecanethiol as a transfer agent.

However, due to the method by which the thiol concentration in the polymer particles \vas detennined, their approach kvas not suitable to on-line application.

In order to perform this study a number of styrene emulsion polymerizations were nui with varying arnounts of n-dodecanethiol, surfactant, and initiator. Samples were analyzed for particle and monomer droplet size, thiol concentration, molecular weight distribution, and conversion.

1.1 Objectives

It is the prïmary objective of this work was to assess the feasibility of integrating established kinetic and diffision models, to develop a technique capable of generating a diable moIecular weight distribution when chain transfer is difision limited. In order to meet this objective several steps were required. The following is a sumrnary of the key issues that were addressed in this study so that the pnmary objective could be met.

An understanding of the capabilities and limitations of the Malvem Mastersizer 2000 for

measunng droplet and particle size distributions \vas detennined. The [A,] estimates generated fiom Nomura's diaision mode1 were compared to those

made ushg the GPC technique outiined b y Ma and Cunningham (2000a).

The sensitivity of Nomura's model predictions to elements such as the diffusion and

partition coefficients, and monorner droplet measurements \vas investigated,

The molecular weight estirnates generated f?om the mode1 using the measured [Ap]

values were compared with experimental data.

This work represents the first method that has been developed to predict the MWD

when chain transfer is diaision limited. Although Nornura developed a model describing

transport under diffision limited conditions, without measurements of the monomer droplet and

polyrner particle sizes it could not be used in a predictive manner- For the first the measurements of monomer droplet and polyrner particle size have been used in the prediction of the MWD. Chapter 2

2, Literature Review

2.1 Ovewiew of Emulsion Polymerization

Emulsion polyrnerization is a widely used industriai process for manufacturhg polymenc matexials. The major constituents of emulsion polyrnerization systems are water, monomers, surfactants, initiators and chain transfer agents. The fiee-radical process proceeds via a senes of initiation, propagation, transfer and termination reactions in order to convert the monomer to the final polymer product.

Water acts as the continuous phase and although it is inert, plays an important role in the process. The aqueous phase allows the viscosity of the solution to remain low even at high conversions, and aIso improves the heat transfer bebveen the vanous phases in the system- The aqueous phase is also the location of chain initiation.

Upon agitation the monomers disperse within the aqueous phase to give monomer swollen micelles, surfàctant stabilized monomer dropIets, and dissolved monomer in the aqueous phase. Micelles are formed when surfactant moIecules cluster together with their hydrophobic tails oriented toward the center of the micelle and the hydrophilic end groups toward the aqueous phase, if the surfactant levels are above the critical micelle concentration (CMC) (CMC is 3.9 x

10" rnol/dm3 at 50°C for styrene (Gilbert, 1995)). The cores of the micelles are swollen with monomer. Before the polymerization is initiated the rnajority of the monorner will be present as monomer droplets. Sufictant motecules di absorb ont0 the surface of the droplets allowing them to stabilize. Many monomers, such as styrene, exhibit low water solubility,

(4.3xl0~rno~clm~at 50°C), (Gilbeh 1995) and therefore only a small fraction of the monomer is typically dissolved in the aqueous phase. The initiators used in emulsion systerns are typically water-soluble although in some cases oii-soluble initiators are also ernployed- Upon decomposition of the initiator, fiee radicals are fonned, that in turn react with the monomer dissolved in the aqueous phase.

The fiee radicals that have been generated are responsible for initiating chain growth.

This occurs through three main mechanisms; micellar, homogenous and droplet nucleation. In micellar nucleation the initiator radicals react with the monomer dissolved in the aqueous phase to forrn short-chain oligomers. The oligomers continue to propagate in the aqueous phase until they reach the critical length for entry in micelles is achieved. They then enter monomer swollen micelles and the polymerization continues, fonning monomer swollen polyrner particles. In the polymenzation system there are approximately a million times more micelles than droplets-

Therefore, the micelles have a much larger surface area available for radical capture than monomer droplets and are the primary source of particle formation. Micelles and droplets that do not capture a radical serve as reservoirs of surfàctant and monomer respectively for the growing poIyrner particles. During hornogenous nucleation radicals growing in the aqueous phase add monomer units to fom an oligomer, The oligomeric radical precipitates once it is no longer soluble to form a particle. Droplet nucleation involves radicals entenng the monomer droplets reacting to form polyrner particles.

Once particle nucleation has occurred the propagation reactions begin in the particle.

During this phase of the process the molecular weight is increased as monomer units are added to the chain until either chain transfer or termination occurs. The following set of reactions outline the typical initiation, propagation, and termination reactions involved in the process. In the reaction scheme outlined below is the initiator decomposition rate coefficient, 1- are prirnary

£?ee radicals, k, is the propagation rate coefficient, M-. and M.. are free radicals containing rn and n monomer units, k& and k,, are the temination rate coefficient for disproportionation and combination respectively, A is an added chain transfer agent and is the transfer rate coefficient.

Chah transfer agents (CTAs) are used to control the molecular weight of the polymer by terminating the growing chains and transfenùig the radical activity to the CTA. A vaiiety of mercaptans (C4-CIZ)and other compounds such as CCL can be employed for this task. In the literâture it is common to see reference to the transfer constant C,, which is defmed by:

In equation (2.7) kWVAis the transfer rate coefficient and k, is the propagation rate coefficient. It is important to note that in emulsion polyrnenzation systems A can refer to transfer to monomer, polymer or an added chain transfer agent. IdealIy the chain transfer agent should only affect the molecuiar weight of the polyrner product and not the overall rate ofthe reaction. This is generally tme in emulsion polymerization if the CTA has negligible water solubiIity (e-g. n- DDT). Ifthe CTA as appreciably soluble in the aqueous phase, desorption of the CTA raciical can reduce the average number of radicals per particle (q) and the overail fate of polyrnenzation-

One advantage emulsion systems exhibit over solution or bulk polyrnerizations is that the propagating radicals are isolated fiom one another. As a result, there are fewer biradical interactions and therefore chain tennination does not occur as fkequently. When bïradical chain termination does occur it is by combination or disproportionation mechanisms. During combination two growing chah are coupled resulting in the formation of a dead chain. During termination by disproportionation one chah absîracts a hydrogen atom fiom the other. This produces two dead polyrner chahs, one containing a saturated end group and one comprised of an unsaturated end group. The overail rate of polymenzation will decrease when biradical tennination reactions occur because the oumber of radicals present in the system decreases. in most systems termination wilt occur by both mechanisrn simultaneously resulting in t5e overall tennination rate coeff~cient,kt.

In emulsion particles, in a zero-one system, tennination usually occurs by the entry of a second radical into a particle that akeady contains a growing chain. This is by definition how a zero-one system is defined. A polymer particle cannot contain more than one growing chain.

2.2 Polymerization Kinetics

The overalI rate of emulsion poIymerization is governed b y the following equation (2.9)-

During the reaction the rate can be espected to initially increase (Interval I), remain approximately constant for a penod of tirne (Interval II) and then decrease towards the end of the reaction (Interval IU)- In equation 2.8 & refers to the polymerization rate, is the propagation rate coefficient,

C, is the concentration of monomer swelling the polyrner particles, q is the average number of

radical per particle (0.5 for zero-one systems), N, is the number of polymer particles in the system, and NAis Avogadro's number.

In the past, the process of emulsion polymerization has been typically divided into three intervals. Interval 1 is known as the nucleation penod and typically occurs from -0-10% conversion. During this time the number and size of the particles, as well as the rate of polymerization, increase. Interval LI, fiom approxirnately 10-40% conversion, begins once particle nucleation has ceased. The particle nurnber and rate of polymerization are ideally constant during interval II. In interval II enough monomer will be present in the system to swelI the polymer particles to equilibrium, therefore C,, the monomer concentration in the polymer particles, will also remain unchanged. interval III, -40-100% conversion, begins when the monomer droplets disappear. Since the monomer reservoirs have been exhausted, there is no longer a sufficient arnount of monomer present to swell the polyrner particles to equilibrium-

This results in a decrease in C,. For polyrnerization systems such as styrene, where the monomer exhibits an extrernely low water solubility, 4x10~mol/dm3 at 50°C, (Gilbert, 1995) it is assumed that the remaining monomer in the system is located within the particles. During interval III it is cornmon for the rate of polymerization to decrease due to the difision limitations that may be faced by the monomer ulthin the particles in addition to the rate decrease due to decreasing C,.

Figure 2.1 below summarizes the three stages of polymerization. n-b lnterval III - 0.010

lnterval II - 0.008 . Fractional Conversion - , - 0.006 Rate

O 50 100 200 Tirne (min)

Figure 2.1: The hctional conversion and polymerization displayed as a function of time for a typical emulsion polyme~izationsystem. (Gilbert 1995)

The recent literahire has begun to question the validity of the traditional three interval

system. Lin et al (1999 and 2000) have shown through a series of optical photographs that

monomer droplets may still be present up unfil approxhately 90% conversion has been reached.

They have also concluded that the particle nucleation occurs continuously throughout the polymerization and is not limited to interval 1 as previously believed.

2.3 Diffusion Limited Chain Transfer

Mercaptans of various chah lengths are typically used in emulsion polymerization systems to control molecular weight. Mercaptans with short chah lengths ( <6 carbons) are able to readily diffuse fiom the monomer droplets to the polymer particles without their solubility in the aqueous phase hindering their transport, However, as the number of carbon atorns is increased the soiubiiity of the mercaptan in the aqueous phase decreases significantly leading to the transport of the transfer agent becoming diffusion lirnited. This behaviour has been recognized for severai years, The eariy studies showed that in heterogeneous systems as the molecuIar weight of the rnercaptan increased the apparent transfer constant decreased, and was les than the observed value in bulk or solution systems (Smith, 1946). Koltoffand Harris

(1947) also reported that when the carbon number exceed ten the polyrner product had a higher molecular weight and appeared to be undennodified, where as modifiers with a carbon number less than 10 resulted in a Iarge arnount of low rnolecular weight product dunng the early stages of reaction and higher molecular weight polymer being produced during the later stages. This provides further evidence of diffusion limited conditions because the reactivity of radicak to mercaptans only varies slightly with the number of carbon atoms.

Dietrich (1988) also studied the chain transfer constants of mercaptans in seeded batch and semi-batch polymerizations. Again the results showed that the apparent transfer constants decreased with an increasing number of carbon atoms. Dietrich beiieved that the decrease in the apparent transfer constant is related to the difference in the mercaptans' distribution coefficients between the water phase and the monomer droplets. Although apparent transfer constants can be determined for a given set of experimental conditions they are not an effective way of handling difision limited conditions because they are sensitive to several variables in the system such as reactor scale, temperature and the concentrations of initiator and surfactant.

The efficiency of mercaptans as chah transfer agents was fùrther studied by Bamdio et al. (1998). Their work focused on achieving a better understanding of the influence that mercaptans have on the kinetics of emulsion polymerizations, They showed that a slight decrease in reaction rate occurred as the number of carbon atoms decreased fiom twelve to four, but that for dodecanethiol the decrease was minimal. The experimental results were explained by investigating the average number of radicals per particle and the desorption of radicals fiom the particles. They aiso confm that diffiision limitations exist for CTAs.

AIthough it was acknowledged for many years that the transfer of CTA fkom the monomer droplets to the polymer particles \vas diaision lirnited, the effect was not quantified until 1994. Nomura et al. (1994) used the two-film theory for mass transfer to create a model that described the transport of CTA from the monomer droplets to the polymer particles. The two- film theory developed by Nomura assumes that ttie two phases are in equilibriurn at the interface and the bamer to difision is created in thin films present on both sides of the interface, and not across the intefice itself. The mode1 takes into account several diffusional steps including diffusion to the droplet/aqueous phase interface, diffusion across the interface, transport through the bulk of the aqueous phase to the particle intefice, dfision across the particle interface and finally transport to the interior of the particle.

Nomura's model shown below in equation 2-10 was developed to predict the diffUsion and consumption rates for V~~OUShigh rnolecular weight mercaptans. It relates the actual concentration of the CTA in the particle to its equilibrium value by:

where [Ap] is the concentration of the CTA in the particle and [ApIe,is the equilibnum concentration of CTA that wouid exist if diaision iimitations did not exist, and the parameter ZZ represents the difisional resistance. Table 2.1 summarizes the parameters used in equations 2.10 and 2.11. Table 2-1: Parameters contained in the R term of Nomura's model. Variable Parameter Variable Units Represen ts DT Diffusion coefficient dm2/s (id Monomer droplet diameter dm 4 Polymer particle diarneter dm Nd Number of monomer droplets #/dm3 aqueous phase per unit volume of aqueous phase NP Nurnber of polymer particles #/dm3 aqueous phase per unit volume of aqueous phase k~ Chain transfer rate coeEcient dm3/mo1 s rl Average number of radicals per particIe m CTA partition coefficient (dropiets and aqueous phase) m' CTA partition coefficient (particles and aqueous phase)

The model \vas evaluated experimentally by Nomura by evaluating several seeded emulsion polymerization systems containing mercaptans ranging from CTC12- Nomura et al. were not able to fùlly test the model since measurements of the monomer droplet size were not available. In order to evaluate the model, experimental data was fit by manipulating the monomer droplet size. This produced reasonable results for a11 mercaptans (n-CrnCio) except n-

CL2,which resulted in a rnonomer droplet size of lpm being predicted. The authors acknowledged that this prediction is unrealistic. The predicted droplet sizes for the other mercaptans were -3-7pm. Since Nornura did not masure the size of the droplets an investigation was performed to evaluate which of the following two assurnptions provided a better fit with the data (1) that the number of monomer droplets remains constant throughout the polymerization, or

(2) that the average diameter of the droplets remains constant during the course of reaction. It

\tris concIuded that the best fit of the data \asobtained when it was assurned that until44% conversion is reached the average diameter of the monomer-CTA droplets remains constant and after this point the number of droplets does not change, which is probably not a realistic assumption. This assumption kvas made because after approximately 50% conversion an acceleration is noted in the observed data that does not match the predicted values ifit is assumed

that the diameter of the droplets remains conistant throughout the polyrnerization.

Mendoza et al- (2000) recently studied tâhe kinetics of styrene emulsion polymerizations using

ndodecyl mercaptans. They agreed with theearlier work of Nomura et al- and found that the

rate-controlling step in the process is the diffision of the CTA fiom the monomer droplets to the

aqueous phase. The concentration of CTA, :surface area of the droplets, mass-transfer and

equiIibrïum coefficients al1 influence the -port of CTA from the droplets to the aqueous

phase. They also found that increasing the agitation rate, emulsifier concentration, or pH could

increase the rate of transport. The authors ;also created a mode1 describing the system and using partition coefficients (m=4.5 x LO', mY=3.6 w IO') similar to those reported by Nomura et al.

(1 994) (m=4.9 x IO', m'=3.18 x 10') good agreement between the experimental data and the mode1 was achieved.

Ma and Cunningham (2000a and 2000b) also conducted a senes of seeded emulsion polymerizations employing n-dodecanethio:-l as a chain transfer agent. Through detailed analysis of the instantaneous rnolecular weight distrËbution, a method was developed that alIowed an estimate of [A,] to be made. The results were the first to quant* the extent to which transport of the mercaptan is limited by diffusion when n-dodecanethiol is used. It was found that values of

[A,] were on the order of 10'-10' times lower than the equilibrium values. niese results are in agreement with the findings of Nomura et al. (1994) and support the work of eariier authors.

There is an interest in being able to accuratcdy predict [A,] because it affects the molecular weight of the polymer and an accurate estimate of tthe MWD cannot be made vithout it.

2.4 Molecular Weight Distributions

The rnolecular weight distribution a[MWD) is a record of the kinetic history of the polymer. Molecular weight distributions and molecular weight averages, such as the number average molecular weight Mnand the weight average molecular weight MW are extremely important because rnany mechanicd properties of the polymer product are a fùnction of the molecular weight andior rnolecular weight distribution. The MWcontains valuable information and if the data is manipulated correctly, it can reveal important kinetic information about the process. Molecular weight distributions are typically measured by gel perrneation chromatography (GPC). The GPC provides the cumulative MWD, which is a record of a1the various chain lengths that have been produced up until the point of sampling. However, carefiil manipulation of the GPC data cm provide an estimate of the pseudo-instantaneous MWD, which is a record of the various chain lengths that have been formed in a srnall conversion interval. This idormation is valuable because it gives information about the dominant mode of chain stopping reactions over the course of reaction, which for ernulsion systems, rnay change through the course of the polymerization.

2.4.1 MWD Models

The ability to accurately describe and mode1 the behaviour of ernulsion polymerization systerns has been of interest for many years. Early work in this area \vas camïed out by Katz et al.

(1969). Their work resulted in a set of coupled partial differential equations fiom which in theory the MWD could be obtained- The solutions to these equations required extensive numencal cornputation and were lirnited to the lower moments of the molecular weight distribution. The proposed models did provide a starting point for work in this area aIîhough they failed to account for termination by disproportionation and transfer to monomer and chain transfer agent.

Lichti et al. (1980) improved upon the work of Katz and others by generating a set of ordinary differential equations that describe the evolution of the number rnolecular weight distribution by accounting for radical entry and exit Fom polymer particles, bimolecular termination, and chain transfer, The solutions to these equations are applicable to emuIsion polymerizations systems during interval II and can be solved analyticaIly* Litchi et al* did not test the validity of the model but did discuss a method by which this could be accomplished. Their work predicted that ifthe dominant mode of chah termination is chain transfer then the MWD wilI be a monotonically decreasing fùnction. The model also suggests that having bimolecular termination as the dominant terrnination rnechanism will yield a MWD with a single maximum-

However, this mode1 does not account for the &ct that the termination rate coefficients are dependent upon the chah length of the radicals involved.

A complete set of rate equations that describe the kinetics of fiee-radical polymerization in bulk, solution and emulsion were generated and tested by Russell et al. (1992, 1993). This set of equations represented a significant step fonvard because for the first tirne termination rate coefficients were allowed to depend on chain length, This work provided the basis for the work conducted by Clay and Gilbert (1995). In their work Gilbert et al. developed equations, presented below, that allow the instantaneous MWD to be calculated for polymerizations in pseudo-bulk and zero-one systems. Pseudo-bulk kinetics exist when the average number of radicals/particle exceeds 0.7 while in zero-one systems the average number of radicals/particle is typically 0.5.

zero - one kinelics In the above rnodels I

(dm3/mols), NAis Avogadro's number and V, is the swollen volume of the latex particle (dm3).

Clay and Gilbert's (1995) mode1 for zero-one kinetics, and the ability to generate estirnates of its parameters using on-Iine techniques, will form the basis for the kinetic modeling in the present work.

Mendoza et al. (2000) have also modeled styrene emulsion polymenzations using a dodecyl mercaptan as a CTA. They developed a mathematical model of the process that produces estirnates of monomer conversion, particle diameter, number of polyrner particles, and number and weight average molecular weights as outputs. The authors were able to achieve good agreement between the model and experimental data by using the data to fit the parameters of the model.

Ma and Cunningham (2000b) used the kinetic models presented by Gilbert et al. to predict the cumulative molecular distributions of emulsion systerns following zero-one and pseudo-bulk kinetics, by relating the instantaneous and cumulative distributions through:

The largest challenge this work presented was obtaining an accurate estimate of the [Ap] value that would be used in Gilbert et al.'s model. Since the transport of dodecanethiol is diffûsion limiteci, [A,] does not rach its equilibrium value. In this study values of [A,] were obtained fiom Uistantaneous molecular weight distributions as outlined by Ma and Cunningham. The results produced by the model provided a reasonable approximation to the molecular weight distributions that were generated by GPC. However, two discrepancies were consistentiy noted bettveen results obtained from the model and the GPC. The distributions that were predicted by

Gilbert et d.'s model tend to be narrower than the GPC distributions- The mode1 aIso does not predict the presence of the very Iow molecular weight material that is seen in the GPC trace. Ma and Cunningham attnbuted this to insufficient sampling during the early stages of polyrnerization when the rnajority of the low molecular weight material is being produced. It is also noted that since generatîng an estimate of [A,] involved deconvolution of the molecular weight data, this approach is not suitable for industrial on-Iine application, However, it \vas proposed by Ma and

Cunningham that the diffision model proposed by Nomura in Equation 2.4, may be capable of generating estimates of [A,], in a manner that is suitable for on-Iine application if on-line GC and particle size measurements are avaiIable. This would involve using the [A,] values predicted by

Nomura's diffirsion model in Clay and Gilbert's kinetic model to generate predicted MWDs under conditions of difision limited chah transfer. The feasibility of tfiis new approach is evaluated in this work by investigating several unseeded styrene emulsion polymerization systerns. Chapter 3

3. Experimental

Sty-rene emulsion polymerïzations were run using various concentrations of chain transfer

agent, surfactant and uiitiator. The following sections give a detailed description of the

materiais, expenmental techniques, apparatus and analytical procedures that were employed to

carry out the experiments and analyze the sarnples.

3.1 Materials

Table 3.1 : The materials used during the course of the project. 1 Material Purity Supplier Additional Comments Styrene Aldrich washed and distilled before use 1dodecanethioI Aldrich used as received Sodium dodecyl sulfàte Sigma used as received Potassium persuifate Fisher Scientific used as received Sodium bicarbonate Fisher Scientific used as received Sodium hydroxide Aldrich used as received Tetrahydroft ran Aicirich filtered before use Hydroqu inone Fisher Scientific used as received Ethylene glycol Aldrich used as received Calcium chloride Fisher Scientific used as received Methanol Caledon used as received Nitrogen P raxair used as received Helium P raxair used as received

3.1.1 Monomer Purification

The styrene monomer is inhibited with 10-15 ppm of 4-tert-butylcatechol and requires

purification before it can be used. in order to accomplish this, the styrene was washed three times

with a 2 wt% NaOH solution. The volume of the NaOH solution used equaled the volume of

styrene being washed- To ensure that no residual NaOH remained in the styrene it was washed

three additional times with an equal volume of distilled water. To ensure that residual water \vas removed the styrene was placed in a beaker containing calcium chlonde petIets and refngerated

overnight. The styrene was then distilled under vacuum prior to use.

3.2 Experimental Apparatus

The experiments were carried out in a 1-litre glas reaction vesse1 contained in a 50°C

water bath- The reactor contents were agitated using a six pitched-blade (45") irnpeller- The

irnpeller was connected to a variable speed motor, thus allowing the desired rprn value (-500rprn) to be achieved. The three additional ports on the top of the vesse1 contained a thennometer to monitor the temperature of the reaction mixture, a condenser, and a sarnpling port- Pnor to the start of the reaction the sarnpling port was used to purge the reactor with nitrogen gas to displace any oxygen that was present. Throughout the course of the reaction a nitrogen blanket was maintained through a nitrogen port on the condenser. Figure 3.1 illustrates the experimentai apparatus that \vas used.

Figure 3.1 Reactor Schematic (a) condenser column, (b) nitrogen port, (c) agitator shaft, (d) sparging tube, (e) sarnpling and nitrogen sparging port, (0 impeiler, (g) water bath 3.3 Experimental Procedure

3.3.1 Monomer Droplet Study Procedure

Pnor to performing poIyrnerizations an initial study was camed out to investigate the effect that the surfactant concentration, the location of sampling, the reactor agitator rpm, and the rpm setting of the Malvern Mastersizer 2000 internal agitator, had on the measured monomer droplet distribution. Three surfactant levels were investigated, 0.5g/LY 1.07g/L75.05gL (1.73 x

10-~mon, 3.7 1 x l~-~rnol/L.,and 1.75 x 10-*mot/Lrespectively). These dueswere selected because they created systems below, near and above the critical micelle concentration (CMC =

3.9 x 10"~and 8 x LO-~Mat 50°C and 25°C respectively). Samples were withdrawn from three regions within the reactor. Samples were taken fiom Region 1, near the surface of the reactor,

Region 2, halfivay betveen the surface and the tip of the impeller, and Region 3, near the tip of the impeller at a radial distance midway behveen the center of the vesse1 and the wall. Various reactor agitation speeds were also investigated during this study- Experirnents were camed out with reactor rpm values of 200, 400, 500, and 600. The effect of the Malvern internal agitator rprn kvas evaluated by maintainhg a constant reactor rpm setting and varying the Malvem rpm setting that was used during anaiysis. With a constant reactor rpm of 500, Maivern settings of

500, 1000, 1500 and 2000 rpm were investigated.

In order to cany out these experiments 183g of styrene, 43 Ig of DI water, 0.75g of

NaHC03 and the required amount of surfactant were added to the reaction vessel outlined in

Figure 3.1. The reaction vessel \vas placed in the water bath, the mixture was agitated for 20 minutes and then samples were withdrawn and analyzed. A detaiIed description of the Malvern operation is provided in section 3 -4.4.2. 3.3.2 Polymerization Procedure

Systems with various arnounts of dodecanethiol, surfàctant and initiator were used. Table 3 -2 summarizes the various formulations that were investigated. These three parameters were varied to create a wide range of conditions over which to assess the reliability of the technique. Varying these three elements wiii ultimately affect the rate of polyrnerization by generating systerns wïth varying numbers of particles, thus creating different rates of reaction and diffusion limitations.

Table 3-2:A summary of the formulations that were investigated. - Experiment Styrene . DI H20 CTA KPS SDS NaHC03

styrene) A 183 43 1 1 4.0 6 -65 0 -75 B 183 43 1 1 4.0 3 .O0 O -75 C 183 43 1 2 2.0 3 .O0 O -75 D 183 43 1 2 2.0 6.65 0.75 E 183 43 1 2 4.0 6.65 0.75 F 183 43 1 2 4.0 3 .O0 0.75 G 183 43 1 3 2.0 3 .O0 0.75 H 183 43 1 3 2.0 6.65 0.75 1 183 43 1 3 4 .O 3 .O0 0.75 J 183 43 1 3 4.0 6.65 O -75 -

In order to cary out the experirnents, the required amount of deionized water was weighed out and lOOrnL kvas set aside to later dissolve the KPS while the rernaining DI water was added to the 1L reaction vessei. The required arnounts of SDS and NaHCO, were then added to the vessel.

The reactor was pIaced on a stir pIate and agitated until the surfactant and bicarbonate had dissoived- The reactor was then transferred back to the balance and the styrene and the chain transfer agent were added. At this point the reactor was sealed, the therrnometer and condenser were attached and the vessel was placed in the water bath. The contents of the reactor were stirred at 500 rpm and allowed to reach 50°C. Once the contents of the reactor reached 50°C they were purged with Nz for 20 min to displace dissolved Oz. The KPS was added to the DI water that had been set aside and was stirred and heated on a hot plate until it reached approximately

50°C. At this time a nitrogen blank vas created in the reactor by attaching the N2 line to the port on the condenser and a tirne zero sample was taken to be analyzed for thiol concentration as well as monomer droplet size. The initiator soIution \vas then added through the sarnpling port and subsequent sarnptes were withdrawn every IO min for the first hour and every 30 min for the remaining hour.

3.4 Analytical Procedures

In order to compare our experirnental results to those results generated by the mode1 developed by Clay and Gilbert (1995) several analytical techniques including gravimetric analysis, gas chromatography, gel permeation chromatography, and particle size rneasurement techniques were employed. The following sections describe the various techniques and equipment, as wetl the procedures and parameter settings that were used.

3.4.1 Gravimetric AnaIysis

Gravimetric analysis \vas used to determine the amount of styrene that had been converted to polystyrene in each latex sample. Prior to the start of each experiment a glass via1

\vas weighed and a hown mass of a 1 \vt% hydroquinone solution was added to each via1 so that the reaction would stop immediately once a sarnple was added to the vial. Mer a sample had been added to the vial it \vas weighed again and then transferred to the refrigerator. In order to detennine the amount of polymer present in the latex, after each sample had cooled, a known amount of the latex was added &op-wise to 75 mL of rnethanol to break the emulsion. This solution \vas stirred occasionally and alIowed to stand for 20 min. After 20 min, 10 rnL of a 2 wt% NaOH solution was added to coaguiate the polymer that had precipitated. Mer an additional 10 min, a piece of pre-weighed fine porosity filter paper was used to filter the solution.

Once the solution was filtered and the polymer had been collected, the polyrner \vas placed in a vacuum oven (25 psig) at 70°C overnight to remove the remaining volatile components. The dry polymer sample was weighed and the conversion was determined. 3.4.2 Gas Chrornatography

Gas chromatography was used to determine the concentration of the chah transfer agent, n-dodecanethiol, at each sampling time. The method of interna1 standards \vas used to relate the integrated area of the L-dodecanethiol peak to the corresponding thiol concentration. Ethylene glycol was employed as the intemal standard as it gave distinct peaks that did not interfere with the elution of the n-dodecanethiol. The following relationship allowed the concentration of the n- dodecanethiol to be determined-

concentration of the thioC thiol peak nrea concentrafion of the ethylene glycol )'~(ethyZene gylcoZ peok mea

In order to use the above relation the GC first had to be calibrateci so that the relative response factor, RRF, could be determined. Standards were prepared by adding known arnounts of n-dodecanethiol and ethylene glycol to tetrahydrofuran, THF, that was being used as a solvent.

This \vas done for a series of concentration ratios and the samples were then injected into the GC-

As output the GC gave a list of integrated peak areas that correspond to the arnount of each cornponent that is present in the sample being injected. A plot of the concentration ratio versus the ratio of the component7speak areas alIows the RRF to be easily determined. The calibration produced a relative response factor of 0.124. This value is a hnction of not only the two components, but also the equipment and its settings. The equipment and settings remained constant throughout the duration of the experiment and an RRF value of 0-124 was used to analyze the thiol concentration in al1 subsequent latex samples. 3,4,2.1 Equipment

A Varian 3400 gas chrornatograph was used to determine the concentration of 1-

dodecanethiol. The unit was equipped with a DB-FFAP column 30m in length with an D=0-32

Fm (J & W ScientSc) and a flarne ionization detector (FW), A guard column (Chromatographic

Specialists) \vas also installed. The system utilized helium as a canier gas at a pressure of 15

psig, that corresponds to a gas flow rate of approximately 3 rnL per minute. A splitless recessed

gooseneck (2 mm) glass insert (Chrornatographic Specialists), filled with glas wool, \vas placed

in the injection port of the apparatus to prevent any undissolved polymer from ente~gthe

colum- Several settings needed to be specified for the unit, Table 3.3 surnmarizes the program

settings that were developed by Ma (1998) and used again in this situation to achieve the

separation.

Table 3 -3: The GC program setting used to analyze the latex samples. 1 GC Settine Value HoldTie 1

Initial Column Temp. 45°C 2 minutes Final Colum Temp. 250°C 2 minutes

Ram~ 40°C/min Oven Temperature 250°C Injector Temperature 250°C Attenuation 4 Range 10

Star Chromatography data acquisition software was used to collect the data and analyze

the results. In order for the peak areas to be calculated the signai to noise ratio (SN), initial peak

width and the tangent height % had to be specified. Table 3.4 outlines the values that were used-

Table 3 -4: The integration parameters used to determine the integrated peak areas.

1 Intemation Parameter Value 1 SM Ratio 5 Initial Peak Width Tangent Heieht % 10 3.4-2.2 Sample Preparation and Analysis

Pt-ior to the start of each experiment a viai \vas prepared for each sample to be taken

during the reaction. (8 mL of THF and 100 pL, of ethylene glycol) The vials were placed in the

refi-igerator until needed. At each sampling time approximately 4 rnL of the latex was removed

fiorn the reactor for GC andysis and placed in an empty glass vid. This sample was immediately

capped and shaken vigorously for 5-10 sec, An Eppendorfpipette kvas then used to quickly

transfer 2 mL of the sarnple to a via1 containhg the THF and glycol. The polymer \vas allowed to

dissoIve and then 0.5 pi., of the sarnple was injected into the GC. Once the glycol and thiol peak

areas were obtained the thiol concentration kvas determined using the RRF as outlined above.

3-4-3 Gel Permeation Chrornatography

3.4.3.1 Equipment

A Waters 2960 Separations Module was used to obtain the molecular weight distributions

for the samples obtained from each experiment. The unit contained a Waters 410 Differential

Refiactometer as well as an on-line degasser. Four Waters Styragel columns (HR0.5, HR 1.0, HR

3.0 and HR 5.0) where used to separate the samples based on their respective moIecu1ar weights.

Table 3.5 sumrnarizes the molecular weight ranges for the four columns used.

Table 3 -5: Molecular weight separation ranges for the GPC columns.

1 Column Molecular Weight Range ( (Daltons) HR 0.5 0-1000 3.4.3.2 GPC Calibration

The GPC had to be calibrated before it could be used to analyze polymer samples. To accornplish this a series of polystyrene standards were analyzed and the data was fitted to a fourth order polynomial-

3.4.3.3 Sample Preparation and Analysis

GPC samples were prepared using the dried polymer sarnples obtained from the gravimetric analysis. For each sarnple 8-12mg of dned polymer was weighed out and then dissolved in lOrnL of filtered THF. Once the poIymer had cornpletely dissolved in the THF the samples were filtered using a nylon filter with a 2ppore size to ensure that no solids entered the

GPC. After filtenng the sarnples were placed in the GPC autosampler. The samples were then run and their molecular weights were detennined.

3.4.3.4 Treatment of GPC Data

The raw data obtained from the GPC is a trace of the detector's response to the sample and therefore, the conversion, and the concentration of the sample influence it. The cumulative

GPC distribution, W(logMW), can be obtained by from the raw GPC data through the following relationship :

w (log MW ) = - G (V N d (log MW ) l dY

In equation 3.1 G(V) is the detector response, d(logMW)/dV is the slope of the GPC calibration curve, and N is the nomalization factor that accounts for the conversion and sarnple concentration. The nomalization factor is found by dividing the fractional conversion of the sarnple by the GPC peak area. The cumulative number rnolecular weight distribution is related to the cumulative GPC

distribution by:

Once the normalized cumulative number distributions has been obtained for each sample,

an estimate of the instantaneous number moiecular distribution can be made b y subtracting

successive cumulative number distributions as outlined below. The distinction should be made

that these distributions are not true instantaneous distributions, but rather pseudo-instantaneous

distributions as they are generated over srnall, not instantaneous time intervals. However, for the

remainder of this work they will be referred to as estimates of the instantaneous distribution.

Number and weight average molecular weights can then be estimated fiorn:

3.4.4 Monomer Droplet and Particle Size Distributions

3.4.4.1 Equipment

The Malvern Mastersizer 2000 with the Hydro 2000s opticai unit was used to evaluate the monomer droplet and poIymer particle size distributions. The unit operates by capturing the scatte~gpatterns of light as the sample is passed through the optical unit. Sarnples are added to the optical unit and circulated through the system using water as a dispersant phase- To ensure

that the size of the monomer droplets and polyrner particles were not aItered by the fâct that slight

solubility of styrene in water, the water being used as the dispersant was saturated with styrene

pnor to use.

3.4.4.2 Sample Preparation and Analysis

At each sarnpling point a small amount of latex kvas removed fkom the reactor for particle

size rneasurements and transferred to a gIass and irnmediately added to the Malvern using a disposable gIass pipette- When adding the sample it \vas important to add it as srnoothly and quickly as possible and avoid dropwise addition of the sample- The effect that this has is discussed further in Chapter 4. In order to rninimize the coagulation of the particles it \vas also important that the samples were added to the Matvern immediateiy upon removal from the reactor-

The Malvern requires the user to create a Standard Operating Procedure (SOP) file for each type of sampIe that is analyzed, Within this file the user specifies the settings the machine will operate at as well as the parameters that will be used to analyze the information that is collected- When analyzing the latex samples a rehctive index of 1.59 was used for the latex and

1.33 for dispersant phase which was water. The agitation speed \vas set at a value of 1438 rprn.

This value \vas determined from a study that was perfonned on the effect that agitation speed has on monorner droplet distributions (see Chapter 4). Within the SOP it \vas specified that the measurement time would be 12 seconds and that 12 000 snaps \vould be taken in that time- Four measurements were to be taken on each aliquot with a delay of 10 seconds between measurements. However, only the first measurernent \vas used in subsequent calculations due to tlie apparent coalescence of droplets that \vas observed. The Malvem also offers the user the option to sonicate samples whiIe they are being analyzed. However, since samples were analyzed immediately upon removal fiom the reactor this feature was not activated within the SOP. Within the SOP cleaning instructions are also given. The Malvem was flushed and cleaned between each sample. Menthe Maivern was not in use the opticai unit was filled will Micron 90 cleaning solution circulating at 1500 rpm-

The results of each run are displayed in a graphical format as a distribution of the various particle sizes detected by the Malvern. Depending upon the degree of conversion rnonomer droplets, monomer droplets and polyrner particles, orjust polyrner particles may be detected.

One of the draw backs to the Malvern Mastersizer 2000 is that it is not able to detect the polymer particles in the presence of rnonomer droplets until approximately 30% conversion has been reached, This can be explained by considering the way in wiiich the Maivern operates- The

Malvern passes laser light through an optical unit and based upon the way the light is scattered can deduce the size of the partides that are present. However during the early stages of polymerization the monomer droplets are significantly larger that the particles- A typical monomer droplet is approximately 5 pm, while a polymer particle is -0-06 p. Once approximately 30% conversion has been reached the monomer droplets have become smaU enough to alIow the particles to be detected. The effect that this has on the overall results of this study will be discussed in more detail in Chapter 4.

The raw data that the Malvem obtains can be analyzed in three ways. The particle size distributions can be presented on a volume, surface, or number basis. The number based results were used for the monomer droplets. The effect of using the number distribution compared to the volume distributions will be discussed in further detail in Chapter 4. Chapter 4

4. Particle Size Measurernents

Tbe Mahem Mastersizer 2000 was used to perforrn the particle size measurements required for this work. Prior to perfonning any poIymerizations an initial study \vas carried out in order to ensure that the conditions selected for the subsequent polymerizations and the mode of the equipment operation allowed a reliable monomer droplet distribution measurement to be achieved

(Le. a uniform distribution within the reactor). In order for this to be accomplished, the effect that the surfactant concentration, the Iocation of sampling, the reactor rpm value, and the rpm setting of the Malvem had on the distribution were evaluated. This section of the report summarizes those findings and contains a surnmary of the particIe size measurements that were obtained during the polymerizations.

4.1 Monomer Droplet Analysis

4.1.1 Effect of Surfactant Concentration

Sodium dodecyl sulfate (SDS)was used as the surfactant during this study as well as during the polymerizations. Trials were carrïedout using three different concentrations of SDS,

O.5&, 1.07g/L and 5.05gL These values correspond to molar concentrations of 1.75 x IO"M,

3.5 x loJ~and 1.75 x IO-'M.SDS has a critical micelle concentration (CMC) of 8 x ~o-~Mand

3.9 x 1O-~M at 25°C and 50°C respectively in pure water (Gilbert, 1995). By using these three concentrations the system could be analyted above, near and below the CMC. During these trials the reactor agitator speed was held constant at 400rpm. When the samples are added to the

Malvern they are agitated in a small vesse1 and circulated through the optical unit. The agitation speed of the Malvem was set ata value of 1150 rprn- This value of the Maivern agitation speed was chosen to ensure the maximum rate of shear in the reactor and the Malvem was equal. The maximum rate of shear is proportionai to tip speed as outlined below.

Maximum Rate of Shear oc Tip Speed Maximum Rate of Shear oc N x D

Where N is the agitation speed L(rprn) and D is the impeller diameter. The diameters of the irnpellers were measured to be 5.75cm in the reactor and 2.0cm in the Malvern. Based on these rneasurements it kvas detennined that agitation speed in the Maivem needs to be 2.875 thes greater than that of the reactor.

The results from the trials performed with the vanous surfactant concentrations are summarïzed in Table 4.1. Samples were taken fiom two regions within the reactor. (Region A corresponds to the area near the tip of the irnpeller and Region B corresponds to the area near the bottom of the reactor.) The sampIes were a11 taken at an equal radial position, approximateiy the midway point between the centeir and the \val1 of the reaction vessel. Al1 of the values reported in

Table 4.1 were obtained by anaHyzing the data on a volume basis-

Table 4.1 : A sumrnary of thedistribution characteristic for systems with varying Ieveis of surfactant concentration. Surfactant Birnodd Mean of Mean of BimodaI Mean of Level Distribution Peak 1 Peak 2 Distribution Peak 1 Peak 2 to CMC In Region A Pm Pm In Region B Pm

Low Yes 5 3 200 Yes 65 388 Below

0.5ga4 1 Middle No 74 N/A Yes 63 450 Below 1.07~K Higb No 55 N/A No 37 N/A Above S.OSg/L Table 4.1 shows that to obtain an ernulsion with a unimodal monomer droplet size the

surfàctant concentration must be above the CMC value. Ifit is not, the system wiii exhibit a

bimodd monomer droplet size distribution in some or possibly al1 regions, This is undesirable

because it suggests that a high level of coalescence rnay be occurrïng in the system and it will be

difficult to obtain a reproducibIe droplet size distribution. If the monomer droplet size varies with

location obtaining a reliable and meaningfùl measurement of it will be difficult. Based on these

results al1 fiirther investigations in this study were peiformed with 5.05g SDSIL.

4.1.2 Reactor RPM

The influence that the reaction vesse1 agitation speed had on the monomer droplet size

\vas evaluated at rpm settings of 200,400,500, and 600 rprn. Table 4.2 surnrnarizes these results

for a system containing 5.05 g SDSL When the samples were analyzed the Malvern agitation

speed was set at a value such tbat the maximum rate of shear was the same in the reactor and the

Malvern. in Table 4.2, Region 1 corresponds to the region just beIow the surface of the mixture,

Region 2 is approximately the midpoint between the surface and the tip of the impelIer and

Region 3 is at the same height as the impeller. Al1 of the results sumrnarized in TabIe 4.2 were obtained by analyzing the data on a volume basis.

Table 4.2: A summary of monomer droplet distributions subject to various rates of agitation. Reactor BirnodaI Mean of Mean of BimodaI Mean of Mean of Bimodal Mean of Mean of Rpm Region 1 Peak 1 Peak2 Region 2 Peak 1 Peak2 Region 3 Peak 1 Peak2 pm pm prn pm pm prn 200 Yes 56 367 Yes 56 400 Yes 102 675

400 Yes 54 3 58 Yes 50 3 83 Yes 53 433

500 No 43 N/A No 46 NIA No 47 N/A

600 No 56 N/A No 52 NIA No 54 N/A

The data indicates that ifthe agitation speed of the reactor is not sufficiently high a unifonn mixture of monomer droplets will not be created. Therefore it was concluded that the reactor wouid be operated at or above 500 rpm. Figures 4.1 a and b contain the droplet size distributions obtained fiom a sample in Region 1 when the reactor rpm kvas set at values of 200 and 600 respectively. These plots clearly show the bimodal nature of the distribution that cm exist at Iow rpm vaIues or surfactant Ievels.

4.1.3 Malvern RPM

Up to this point the rpm speed of the Malvern agitation has been set at the value which allowed the maximum rate of shear to remain the same as in the reactor. During this stage of the investigation the reactor rpm was held constant and the Malvern agitation speed was varied.

Information gained fiom this study ensureci that the interna1 agitation rate would not affect the measured dropfet sue distribution. A system contaking 5,OSg SDSL was agitated at 500 rpm within the reactor. The -;dume based results are sumrnarized below in Table 4-3.

Table 4.3: A summary of the distribution characteristics when the agitation speed of the Malvem is varied and the agitation speed of the reactor is constant (500rpm). Malvern mm 1 Bimodal Distribution 1 Mean of Peak 1 1 Maximum Rate of Shear pm Exceeded in the Malvern 500 No 40 No

2000 No 3 8 Yes

Based on the results it Table 4.3 it can be concluded that the rate of shear in the Malvem relative to the rate of shear in the reactor wïll not alter the results, since bimodal monomer droplet distributions were not detected. The mean particle size does vary slightly fiom 38-43 pm over the range of rpm values investigated. The mean partide size is constant at 43pfiom 1000-

1SOOrpm. For a reactor rpm setting of 500, a Malvem rpm setting of 1438 will ensure that the maximum rate of shear remains constant. Since this vaIue lies between 1000-1500 rpm al1 further analysis were carried out maintaining an equal rate of shear in the reactor and the particle size analyzer.

4.1.4 Sampling Location

In order to obtaùl a measurement of the reliability and consistency of the Malvem measurements the effect that the sampling Iocation had on the size of monomer droplets kvas investigated. Ten sampfes were taken fiom each region of a mixture containing 5.05g SDSL

The system was being agitated at 500 rpm within the reactor, and when the samples were analyzed the MaIvern agitation speed ensured that the maximum tip speed remained constant.

Table 4-4 sumrnarizes the volume based results.

Table 4.4: A summary of the distribution characteristics when samples are withdrawn fkom three regions within the reactor. Bimodal Samplc Mean Standard Deviation Distribution pu Region 1 No 53 4.4 1

Region 2 No 4 3 3 -70

Rcgion 3 No 45 3.43

An ANOVA test was used to determine whether the difference between the three mean values \vas significant. The test indicated that a significant difference does exist between Region

1, just below the surface, Region 2, half way behveen the surface and the impeller, and Region 3, near the tip of the impeller. Therefore, a11 of the data should not be cornbined. This difference can be attnbuted to the fkct a somewhat stagnant zone may be created near the surface of the mixture, thus allowing the droplets to coalesce. This would create the Iarger droplets that are detected in Region 1. The test was preformed a second time using only regions 2 and 3. The results fiom this suggest that there is not a significant difference behveen the data collected fiom these 2 regions and it is acceptable to combine the data and treat them as one area. Based on these results when samples were withdrawn for analysis durhg polymerïzations they were taken from Region 3.

4.1.5 Mixing Time in the Reactor

The effectThat mixing time had on the rnonomer droplet size \vas studied to ensure that the monomer droplet distribution equilibriurn was attauied quickly and that it did not Vary with time. It is important to determine whether the length of time the mixture was in the reaction vesse1 influenced the size of the monomer droplets. The ten samples wittidrawn fiom Region 1 in the above section were used to perform the evaluation. Figure 4.2 is a plot of the mean droplet size vs. sample number.

- - M onomer Droplet Stability Over Time

Sample -1 Number Figure 4.2: Monomer Droplet Stability Over Time

As shown by the random distribution of droplet sizes in Figure 4.2 the size of the monomer droplets is not correlated with the tirne at which they were sampled. Du~gthe trials that produced this data samples were typically withdrawn every 6-8 minutes. The mixture was agitated for approximately 20 minutes before the first sample was withdrawn. Therefore this figure illustrates the size of droplets present within a mixture between the 20-80 min thehme. 4.1.5 Effect of the Sample Injection Method

Du~gthe course of the sample analysis an important trend was noted. In some instances it kvas noted that a very smaU arnount of large particles (= 200~)were present in some, but not all, of the of the simples fiom conditions that consistentiy produced distinct one peak distributions. Upon firther examination of the sample injection technique it \vas determined that adding the sample slowly, &op-wise, to the Malvem increased the occurrence of these large peaks- Ifthe sample was injected quickly, in a smooth fashion, the larger peaks were not detected, This is illustrated in Figure 4.3.

Figure 4.3 shows the Malvem particle distribution plots for bvo samples that were withdrawn from the same reaction mixture with a high level of surfactant and operating at a reactor rpm value 600- The distribution shown in Figure (a) vm.s created fiom a sample that \.vas added drop-wise to the MaIvem and therefore contains a small cluster of larger droplets, while

Figure (b) was injected a smooth fashion and thus the trace amount of larger particles has been eliminated.

4.2 Polymerization Particle Size Analysis

Ln order to be able to evaluate the mode1 proposed by Clay and Gilbert (1995) that allows a prediction of the motecular weight of zero-one polyrnerization systems, information is required about the particle size of the polyrner latex. In order to obtained this information the Mastersizer

2000 kvas used to evaluate the size of the polyrner particies and monomer droplets that were present at each sarnpling time. The information that was collected fiom the preliminary monomer droplet investigation, with regard to smpling location and injection technique, aided the analysis of the latex sarnples. 4.2.1 Understanding the Results

The Malvern Mastersizer 2000 analyzes the Iight scattering pattern and typically reports the data to the user on a volume basis, However, the software also enables the user to transform the results by having the data analyzed on either a number or shcebasis. In many cases analyzing the data on a volume basis is sufficient however the user must be aware of the advantages and disadvantages to each form of analysis. When the results are reported on a volume basis it is quite easy for a few larger particles to mask the existence of several smaller ones, thus altering the overall depiction of the results- This occurs because the Malvem assumes each particle is a sphere and therefore a size difference of 10 fold transiates into a volume difference of 1000 fold due to volume's cubic dependence on radius.

When the results are converteci to a number basis the bias that the size différence created no longer exists because now each sphere that is detected by the scattering of Iight is weighted equally. This therefore allows the presence of a significant number of srnall particles to be detected even if they constitute an extremely small portion of the total particle volume.

A third option that is presented to the user is analyzing the light scatte~gpatterns on a surface basis. This means that the particles with the greatest surface are weighted most heavily.

This would cause a 10 fold difference in particle size to translate into a 100 fold difference in particle surface area due to the squared dependence of surface area on radius. Although the effect wouId not be as pronounced as on a volume bais using this setting can still cause smaller particles to appear less significant. In Figure 4.4 the effect of selecting either a surface, number or volume-based analysis arc presented. Analyzing the same light scattering pattern using the three techniques generated the three plots. When the three options of data analysis were evaluated it \vas determined that the most meaningful results for the monomer droplets were those reported on a number basis. It shouid be noted that in spite of this the data in Figure 4.1,4.3, and

4.5 have been presented on a volume basis. This was done because the volume-based plots are better able to illustrate the issues being presented. The corresponiding nurnber bas& plots have been included in Appendix B,

4.2.2 Polymerization Particle Size Results

At the start of each experiment, before the addition of Gtiator, a time zero sample was taken and anaiyzed- Subsequent samples were taken at 10 min imtervaIs for the first hour and at

30 min intervals dunng the second hour. As the poIyrnerization ~proceedsthe sbift in particle size from a system containing only monomer droplets, to a system camtaining monomer droplets and polymer particles, and finally to a system in interval III, comprissed only of polyrner particles, can be seen. From time zero until appro.xirnately 30% conversion has been reached al1 of the particles detected by the Maivem were greater than 1pm, thus suggesting; that only monomer droplets and not polymer particles, (CIpm), were present. This cannot be accurate because in order to obtain a conversion of 30% polymer particles must be present. In order Ito explain this behaviour the way in which the MaIvern generates the particle size distributions muta be esamined. The particle size distributions that the Malvern creates are based upon the light scattering patterns that are detected. Since dut-kg the early stages of polymerization the newly forrning polymer particles are extremely smalI, the amount of light they scatter when compared to the much larger monomer droplets is negligible, and therefore they are not detected. As tbe poIymerization proceeds and the monomer dropIet size decreases and the light scattered by the particles begins to be detected at approxlmately 30% conversion. This is shown in Figures 4-55 (ad) that contains the Malvern particle distribution plots, displayed on a volume basis, for a run from time equak 50 min. when the particles were first detected to the end of the polymerization at 120min. Table 4.6 sumrnarizes the information in Figure 4.5 and includes the conwersion at each sampling point. Table 4-5 A surnmary of the particle size distribution information and the corresponding conversion reported on a number basis. (Tt is believed the droplet measurement at 60 min is an outIier.) Tirne Conversion Monomer Droplet Polymer Particle Size (pm) (min) (W S ize (pm)

In order to accurately estimate of the molecular weight using Clay and Gilbert's mathematical model, the polymer particle size must be known at each sampling point. This problem was overcome by using the conversion data and perfoming a simple mass balance and is discussed fûrther is Chapter 5.

4.3 Summary

Preliminary monomer droplet studies were perfonned using the Mastersizer 2000 to determine the reliability of the instrument and the best set of conditions under which to run the polyrnerization- It \vas determined that the reactor rpm would be 500 rpm and that the interna1 agitator in the Malvem would be set at value that aIlowed the maximum rate of shear to remain constant- The monomer droplets appear to reach equitibrium in the reactor after 20 minutes of agitation and it was determined that samples would subsequently be withdrawn near îhe tip of the impeiler. After reviewing the three rnethods of analysis, volume, surface and number it was decided that results would be reported on a number basis. Problems detecting small particles in the presence of large monomer droplets was addressed and the method chosen to solve Ùiis problem will be discussed further in Chapter 5. i-

Figure 4. l: (a) Parride size distribution @ 2OOrpm. @) Particle size distribution @ 600rpm. Partide Sue- @un)

3-01 0.1 1 10 100 1000 Particte Size (jm)

Figure 4.3: (a) Particle sizc distribution when the sample was injected dropwke. @) Particle size distribution when sample was ddded in a smooth fashion. 1 10 100 1000 Particle Sue @rn)

3-01 0.1 1 1O 100 1000 -\ Particle- Size (pm) Figure 4.4: (a) Particle sire distribution analyzed on a number basis. (b) Particle size distribution analyzed on a volume basis. (c) Particle size distribution analyzed on surface basis. '6.01 0.1 1 10 100 1000 Particle Size (pn)

'b.01 0.1 1 10 100 1000 Particle Size (pm)

~irfideShe Distribution

(c) Y Particle Size @in) - Figure 4.5: (a) Particle size distribution @ t=50 min. (b) Particle size distribution (c) Particle size distribution @ e90 min. t Figure 4.5: (d) Particle size distribution @ t=120 min. Chapter 5

5. Experimental Results

The data coIIected fiorn the experirnents are presented by plotting styrene conversion as a fimction of reaction tirne, and rnolecular weight (Mn and MW)and the n-DDT consurnption as a firnction of conversion. This data forms the basis to wbich the modeling work presented in subsequent chapters will be compared.

5.1 Conversion Data

The conversion data are presented in Figure 5.1 (a)-(d). The data have been grouped and plotted so that runs performed with the same amount of surfactant and initiator can be cornpared and the influence that the wt% CTA has on conversion can be seen. When the data in Figure 5-1 are exarnined, the rate of reaction and degree of polymerization do not appear to be strongly influenced by the wt% of CTA in the system. AIthough stight deviations are seen, al1 runs performed with a given arnount of surfactant and initiator appear to proceed at approxirnately the same rate and reach approxirnately the sarne final conversion,

In Figure 5.1 a high level of conversion was reached under al1 expenmental conditions, a minimum of approximately 80% fier two hours, although the rate of reaction did vary depending upon the experimental conditions. The slope of the linear region of the conversion-time plot is an indication of the rate of reaction. Figure 5.1 (a) demonstrates the fastest reaction rate. This is expected since t hese three systems contained the highest concentrations of initiator and surfactant. Figure 5-1 (b) appears to have the slowest rate of reaction, which is in accordance with the low concentrations of both surfactant and initiator- By comparing Figure 5.1 (c) and (d) it is evident the increased amount of surfactant caused a larger increase in reaction rate than the addition of more initiator. This occurs because the additional surfactant will create more micelles in the aqueous phase and subsequently more poIymer particIes wilI be formed. Therefore, the reaction can occur more quickly.

5.2 Dodecanethiol Consumption

The percentage of DDT that was consumed at each sampling point is presented as a function of conversion for each run in Figure 5.2. The DDT concentrations were determined by GC as outlined in Chapter 3. The data have been grouped and presented so that ~nscarried out with the same wt% of CTA can be compared. Under al1 experimental conditions, alrnost 100% of the transfer agent was consumed by the end of the reaction. The runs performed with 2 and 3 \vt% thiol consurned approximately 80% of the thiol in the system wben conversions of -80-90% had been achieved. The experiments performed with 1 wt% thiol were able to consume 80% of the thiol slightly sooner, at approximately 6575% conversion.

In general, Figure 5.2 shows that the thiol in the systern is consumed slowly until approximately 40-45% conversion, the end of traditional Interval II, has been reached. After this point, there theoretically should no Ionger be rnonomer droplets present in the system and hence the banier to the difision of DDT no longer exists. During Interval III it is assumed that any transfer agent that rernains is located in die polymer particles, and therefore it is expected that the rate of consumption, represented by the slope of the curve, should increase. The exception to the generally slow consumption of CTA at lower conversions is seen when the data associated with the runs containing 3 .O g of SDS and 2.0 g of KPS is examined- During these runs the CTA appears to be consumed much faster during the early stages of reaction. This can be explained because these mns are proceeding at a slower rate, as illustrated in Figure 5.1. Since the rate of reaction has been reduced it takes longer to reach a given conversion and ttierefore the CTA has been given more time to diffuse to the particles. It should be noted that at certain points in Figure

5.2 the % of CTA consumed appears to decrease, thus suggesting that thiol has been added to the reactor. This is obviously not possible and the apparent decrease in consumption is likely caused by sample preparation errors. 5.3 Number and Weight Average Molecular Weight The number average molecular weight, Mn, and weight average molecular weight, MW, are displayed as a fiction of conversion in Figures 5.3 and 5-4 respectively. The data have been presented so that nuis containing the same wt % thiol can be compared (Figure 5.3 and 5 -4 (a)-

(e)) and so that the effect that increasing the arnount of thiol in the system has on a given surfàctant and initiator level can be seen (Figure 5.3 and 5.4 (f)).

Figures 5 -3 and 5.4 (a)-(e) show that regardless of the wt% thiol in the system the Mnand MW values follow the same general behaviour. During the initial nucleation period (Interval 1) the Mn and MW increase slightly and remain stable throughout hterval II, Once -40-45% conversion has been reached, Interval iT ends, and the molecular weight begins to steadily decrease until the end of the reaction- However, the decrease is more evident in the Mn than M,values- The molecular weight decreases towards the end of the reaction because the largest banïer to the CTA transport, the monomer droplet interface, is theoretically no longer present in the system beyond Interval II-

It is assumed that the remaining transfer agent is located in the polymer particles where it can react more readily, thus causing the MW to decrease,

Figures 5.3 and 5.4 (f) illustrate that as the amount of CTA present in the system is increased, the MW of polyrner decreases, as expected. 1 0.9 - O -O 0.8 - 2 C * g 0-7 - E * g 0.6 - * -0 0.5 - 0-4 - O O 0.3 - 4 - 0.2 - O 0-1 - * O r 9 O 20 40 60 80 100 120 Reaction Tim e (m in)

olwt% CTA m2wt% CTA a3wt% CTA

O 2 0 40 60 80 1 O0 120 Reaction Tim e (rn in)

e2wt% CTA m3wt% CTA

Reaction Tim e (m in)

e2wt% CTA m3wt% CTA (cl Figure 5.1: .Conversion vs. The(a) Run conraining 9.6xCMC: 4.0g KPS (b) Run containing 4SxCMC: 2.0g KPS (c) Run containhg 9.6xCMC: 2.0g KPS Reaction Tim e (rn in)

-3 wt% CTA mm2 wtOh CTA al wt% CTA

Figure 5.1: Conversiom us. Time (d) Run containhg 4.5xCMC: 4.0g KPS Fractional Conversion 46.659 SDS, 4.0g KPS ~6.659SOS, 2-09 KPS

O 0.2 0.4 0.6 0 -8 Fractional Conversion

1113.09 SDS, 2.0g KPS m3,Og SDS, 4.0g KPS

Fractional Conversion a6.659 SDS, 4-09 KPS ~6,659SDS, 2.09 KPS (cl Figure 5.2: CTA consumption. (a) Runs containing 3w1% thioI@) Rwcontainhg 3wvt% thiol (c)Runs containing 2\vt% thiol Fractional Conversion e4.5xCMC. 2-09 KPS -4.SxCMC, 4.09 KPS

O 0.2 0 -4 0.6 0.8 1 Fractional Conversion

-6.659 SDS, 4-09 KPS m3.0g SDS,4.09 KPS

Figure 5.2: CïA Consumption (d) Runs containing 2wt% thiol (e) Runs containing lwt% thiol 40000 35000 - A * 30000 - * A * 25000 - A A ;20000 - A * A** A 15000 - 10000 - 5000 - O, O 0 -2 0 -4 0.6 0 -8 1 Fractional Conversion

46.659 SDS, 4-09 KPS ~6.659SDS, 2.09 KPS

O O -2 0 -4 0 -6 0 -8 1 Fractional Conversion

m3-0g SDS, 2-09 KPS 03-09 SDS. 4.09 KPS

O 0 -2 0 -4 O -6 0.8 1 Fractional Conversion

e3.0g SDS, 4-09 KPS ~6.659SDS, 2-0g KPS (cl Figure 5.3: Number Average Molecular Weight (a) Runs containing 3wt% (Iuol (b) Runs containhg 3wt% tliiol (c) Runs containing 2wt%thiol Fractlona I Conversion

m3.09 SDS, 2.0g KPS e3.09 SDS, 4.09 KPS

0 -4 0 -6 0.8 - Fractional Con version

e6.659 SDS, 4-09 KPS m3.09 SDS, 4-09 KPS

O -4 0.6 0 -8 Fractional Conversion

(f) Figure 5.3 : Nurnber Average Molecular Weight (d) Runs containhg 2wt% thiol (e) Rucontaining lW%o thiol (f) Runs containing 6.65g SDS,4.0g KPS Fractional Conversion

a6.65g SDS. 4.09 KPS a6.65g SOS, 2-09 KPS

O 0.2 O. 4 0.6 0 - 8 1 Fractiona I Conversion

~3.09SDS, 2.0g KPS 03.0g SDS, 4-09 KPS

120000 100000 - * * A . A A * 80000 - A * A A - 60000 - AA 40000 - 20000 - -- O -- O 0.2 0.4 0.6 O. 8 1 Fractional Conversion

e6.65g SDS, 4-09 KPS a6.65g SDS,2.09 KPS

Figure 5.4: Weiglit Average Molecular Weight (a) Runs coniaining 3wt% thiol@) Runs containing 3wtY0 thiol (c) Runs containing 2wtY0thiol

54 Fractional Conversion

03-09 SDS, 2-09 KPS m3-0g SDS, 4-09 KPS

0 -2 0.4 0 -6 0 -8 Fractional Conversion

e6.65g SDS, 4-09 KPS rp3,Og SDS, 4.09 KPS

Fractional Conversion

(f) Figure 5.4: Weiglit Average Molecular Weight (d) Runs containing 2wv% thiol (e)Runs contaidg lwt% thiol (f)Runs containing 6.65g SDS.4.0g KPS. Chapter 6

GPC provides a reliable method of determining the average MWs and MWD of a polymer sample, which are important parameten because many end-use properties are a fiction of the polymer's MW and MWD. However, the drawback of GPC is that it can take up to one hour to generate data for a sample. Cunningham and Ma (2000a) have show that when the transfer agent concentration in the particles is known under diffusion lirnited conditions, the kinetic model presented by Clay and Gilbert (1995) gives a reasonable prediction of the MWD of the sample.

Ma and Cunningham (2000a) have also shown that under difision luiiited conditions the concentration of dodecanethiol in the particles, [A,], can be estimated by generating pseudo- instantaneous moIecular weight distributions fiom the cumulative GPC distribution. However, this technique cannot be used in conjunction with a kinetic rnodel to estimate molecular weight on-line. In this section, [AJ values predicted fiom the two-film dinusion model, that has the potential to be applied on-line, (Nomura et al. (1994)) are presented and discussed. The problems associated with the technique are outlined and the [A,] values are compared to those generated by the method developed by Ma and Cunningham. The sensitivity of the predicted [A,] predictions to parameters such as the dfision and partition coefficients is also addressed. These [Ap] predictions are then incorporatecl in Clay and Gilbert's kinetic rnodel so that validity of integating the two models to generate estimates of molecular weight under diffusion limited conditions can be addressed. 6.1 Two-Film Diffusion Mode1

The results of the mode1 developed by Nomura et al. (1994) are surnmarized below in

Equations 6.1 and 6.2. It reIates the actud concentration of the CTA in the particles to its

equilibrium value through a lumped parameter C2 that represents the difisional resistance. The

resistance to diffusion is a fùnction of the size and number ofdroplets and particles, and is largeiy

influenced by the partitioning of the CTA between the aqueous and organic phases as well as the

rate at which it is able to diaise through the aqueous phase.

Table 6-1: A summary of the constants used in diffùsion mode1 for a n-DDT water system at 50°C.

--- Parameter---*---___-__.._. Constant_ ___-. CI_I---.-- Value -_-..------_____------Source -- Partition coefficent m 4.9 10' Nomura et al. (1994) Partition coefficient m/m7 1.54 Nomura et al. (1994) ratio Difision coefficient Dr 6.0 x 10~drn2/s Nomura et al. (1994) Chain transfer rate kt, 3 744 drn3/mol s Hutchinson et al. coefficient (1995) (G=l5-6) Average number of rl 0.5

In order for the mode1 to be evaluated accurate estimates of the size and number of

droplets and particles (cid, d,, Na, and Np)needed to be obtained. The number of droplets and

particles were determined by combining knowledge of conversion, equiiibrium swelling of the particles with monomer, and individuai particle and droplet volumes. Ideally the number of polyrner particles could be caiculated at each sampling point by using the following relationship:

vol. of styrene in the parti~le~(m) + vol of PS NI the sysfem(m3 ) Np = 43nr3

The volume of polysiyrene, (PS), can be deterrnined fiom conversion data and the volume of styrene swelling the polymer can be determined by assuming that equilibrium swelling occurs so that the concentration of styrene in the particles is 5.5 mol of styrene/dm3 (Gilbert,

1995) as long as monomer droplets exist (Interval II). The volume of each particle can be easily calculated fkom the rneasured diameter. However, the Malvern has dficulty detecting the presence of small polymer particles when Iarger monomer droplets are present in the system. As a result, the polyrner particles are not detected during the early stages of the reaction. Since the particles are not detected, an estirnate of the number of particles cannot be made using the technique oudined above. In order to overcome thLs problem an estimate of the number of particles was made by assurning that the number of particles is constant during Interval II. Frorn a plot of conversion vs. tirne, the polymerization rate can be detennined fiom the slope of the curve during Intervai II and thus Np, can be calculated as follows.

In Equation 6.4 & is the rate of polyrnerization, and Cp is the concentration of monomer swelling the polymer. Since the system was deterrnined to follow zero-one kinetics q was set at a value of 0.5 for all calculations. Rpwas detennined for each run fkom the slope of the linear region of the conversion vs, theplot, when the systern was in Interval 11. Once the number of polyrner particles has been estimated the average size can be determined by Equation 6.3.

Iri order to evaluate whether the method outlined above in Equation 6.4 gave a reasonable estimate of the nurnber of particles the cafculation was also performed on samples for which particles were detected by the Mahern, A sarnple of these results is presented below:

Table 6.2: A cornparison of the nurnber of particles calcuiated fiom Maivern and polymerization rate data for a run containing 3 wt% CTA, 6.65g SDS,and 2.9g KPS. Time (min) NpPredicted d, Measured d, Measured NpPredicted dp Estimated from Particle by Maivern on by Malvern on from From Rate Size /dm3 H20 a Volume a Nurnber Polymerization Data Basis (pm) Basis (pm) ~ate/dm~HzO (pm) 10 N/A N/A N/A 8.87E+17 0.070

S ince the results presented in Table 6-2 indicate that calculating the number of particles fiom the rate equation gave an acceptable estimate of particle size, for each run the nurnber of polymer particles used in Nomura's mode1 \vas set at the value detemined by the rate equation in

Interval II.

Correctiy interpreting the monomer droplet data fiom the Malvern also presented challenges. It was noted in several of the runs that material with a particle size greater than ljun was detected by the Malvern at points in the reaction beyond which thermodynamic relationships suggest monomer droplets should exist. It is possible that particles coalesced, or since n- dodecanethiol is a strong swetling agent it is not unreasonable that a small arnoiint of residual monomer remained in the system in the droplets. It has been reported in the literature by Lin et al. (1999 and 200 1) that monorner droplets do not disappear at the end of interval 11 and in fact they may be present until approximately 90% conversion has been reached. They believe that this occurs because a small arnount of polymer or oligomer may fonn inside the droplet either by thermal poIyrnerization or by the droplet capturing a radical, The presence of the hydrophobic polyrner may inhibit the difision of monomer. in our systern it is believed that the DDT in the system cause similar conditions to be created in the droplets and thus retards monomer diftùsion as well. The presence of droplets beyond the end of theoretical Interval II presents a problem, due to the manner in which the number of monomer droplets was calculated. The number of monomer droplets \vas detennined by calculating the amount of monorner rernaining in the systern fiom conversion data, and then subtracting the volume of monomer that the equilibrium swelling assumption dictates must reside within the particles. The diameter measured by the

Malvem \vas then used to estimate the volume of one droplet, and subsequently the number of droplets was calculated. If our theoretical understanding of Interval II is in fact correct, not including the residual monomer droplets in the mode1 will cause the bamer to diffùsion to be underestimated, therefore adding error to the [A,] prediction. There will also be error associated with the estimate of [C,], since the system is not truly in interva1 III (Le. a11 rernaining monomer is located within the particles). These two sources of error will cause the mode1 predictions to deviated from the calculated GPC values beyond Interval II.

6.1.1 Mode1 Parameter Estimation

The sources of the model's parameters are outlined in Table 6.1. Nornura et al. (1994) directly detennined the partition coefficients for mercaptans con!ziining up to 9 carbon atorns fiom water solubility data but acknowledge that no data is available for Cioor CI:! chains. These values were then extrapolated fkom the existing data. Later in his work Nornura concludes that the only data point that deviated £Yom the theoretical predictions involves the Ci*mercaptan, thus casting doubt onto the validity of the extrapolation. The partition coefficient, m., presented by Nomura was used as a starting point in this work however, the [A,] values that were predicted were far below those obtained from the technique outlined by Ma and Cunningham, and subsequently lead to the MW being overestimated. Therefore, the partition coefficient was adjusted to give the best fit between the MWvalues obtained fiom GPC and the predictions generated by Clay and Gilbert's kinetic rnodel over the time that monomer droplets were detected in the systems. It should be noted that within the mode1 the partition coefficient m will cancel as it appears in both the numerator and the denominator of the equation. Therefore by keep the ratio of dm' constant and manipulating the value of m the effect that the m7tenn has on the model estirnates is being illustrated.

Nomura et al- calculated the diffùsion coefficient fiom a semiempirical correlation presented by Wilke and Chang (1955). The vaIue reported by Nornura et al. kvas used for al1 of the calculations although it is acknowledged that since it is a measure of the diffùsion through water at 25°C and the polyrnerization system contains a mixture of surfactant, monomer and CTA at 50°C, it is not unreasonable that this estimated diffision coefficient rnay be quite unreliable.

6.1.2 Comparison of [Ap] Values

The estirnates of [A,] made using the difision model were compared to the estimates that were generated using Ma and Cunningham's GPC technique as well as those generated by the mode1 once the value of the partition coefficient was adjusted, The results for the runs containing 1, 2 and 3wt% thiol are shown in Figures 6.1 (a)-(j). In the figure the data labeled as the GPC series refers to the estimates made using Ma and Cunningham's method. A detailed description of the technique they developed is available in Ma, 1998. It will be noticed in the figure that occasionally an estirnate is not available fiom the GPC technique. When samplss are taken over short time intervals a large amount of noise may be present in the instantaneous distribution, and this prevents an estimate of [A,] fiom being available. In Figure 6.1 the partition coefficient has been adjusted so that the best fit is achieved for each individual set of data (Le. a Werent coefficient value was used in each case). It is acknowledged that the coefficient must have one value that applies to al1 cases but the data have been reported in this manner because the fitting of the data set did not produce one exact value. Figure 6.2 again shows the CTA concentration in the particles predicted by Nornura et al's model as a fhction of conversion. [n Figure 6.2 a cornmon value for the partition coeficient (2.82 x 10') was used in the model for four of the experimental nins (b, c, $ g). These nuis were selected because they provided the most data points before 40% (the onset of the traditional Interval II)- The partition coentcient value of 2-82 x 10' represents the average value for the four mns.

From Figure 6.1 it can be seen that using Nomura et d7sexmpoIated partition coefficient (m=4.9 x 10')' the concentration of dodecanethiol in the polyrner particles is consistently underestimated when droplets are present in the system, Once the droplets disappear, the model is able to give a reasonable estimate of the CTA concentration in the particles. However, since the theory behind the mode1 states that the Iargest barrier to diffùsion is across the monomer droplet interface it is important to focus on the results that are obtained during Interval II before the droplets, in theory, disappear.

It is important to have an accurate estimate of the concentration of CTA in the particles because it cvill have a direct influence on the molecular weight of the polymer. Therefore in order to improve upon the estimates generated by Nomura et ale's mode1 the partition coefficient \vas adjusted for reasons outlined in section 6.1.1. In order to produce reasonable estirnates of Mw fiom Clay and Gilbert's kinetic model it was found that the partition coefficient had to typicdly be adjusted by a factor of 10-'-105. The exact factor that was applied to each set of data is indicated in Figure 6.1.

By adjusting the partition coefficient we are able to obîain more accurate estimates of the

CTA concentration in the particles. From Figure 6.1 it can be seen that using Nomura's partition coefficient value of 4.9 x 10' the model significantly underestimates the CTA concentrations when monomer droplets are present in the systern. Applying a factor of 10" to IO", as indicated in each Figure, to Nomura's value irnproves the estimates. However, the model does appear to deviate fiom the GPC values during the latter stages of the reaction. The model predictions appear to deviate from the GPC values once the monomer droplets are no longer accounted for in the model, and the system appears to be enterhg the traditional Interval III (monomer droplets have disappeared and al1 remaining monomer in the system resides in the polymer particles). Our measurements indicate, in agreement with the findings of Lin et al. (1999, 200 1) that monomer droplets do in fact exist beyond the theoretical limits of Interval II. If monomer droplets were still in the system the difisional resistance is greater than wtiat is currently being predicted by

Nomura's model thus, accounting for the overestimate of the of the transfer agent concentration in the particles once the monomer droplets are no longer accounted for in the model. In some cases the mode1 predictions also deviated durlng the early stages of reaction. It is believed that this is caused by the number of polymer particles in the system being overestirnated, since the system has not yet reached interval II and nucleation is still occurring. An overesthnate of the number of polyrner particles would cause the total difisional resistance, !2, to be overestimated and therefore underestimate estimate the concentration of CTA in the particles. This would cause the molecuIar weight to be overestimated while nuckation is occunng.

6.1.3 Two-Film Diffusion Mode1 Surnmary

The concentration of n-dodecanethiol in the polymer particles is an important parameter in the kinetic model proposed by Clay and Gilbert for estirnating instantaneous molecular weight.

The concentrations of n-dodecanethiol in the polymer particles were determined using a two-film diffiision model. These values were then compared to the [A,] obtained fkom the dope of the instantaneous GPC distributions using the method outlined b y Ma and Cunningham and values generated from Nomura's model after the partition coefficient had been adjusted. Our approach was able to accurately predict the CTA concentration when the system was in the traditional

Interval II. However, an overestimate of the nurnber of particles dunng the early stages lead to an underestimate during the nucleation pen'od. Since the residual monomers that appear to be

present during the Iater stages of the reaction (Interval III) could not be accounted for in the

model, our approach overestirnates the CTA concentration at high conversions. In the following

sections of this Chapter, the calculated [Ap] values are used in CIay and Gilbert's kinetic model to

generate predicted values of MW.

6.2 Kinetic Mode1

The kinetic model, for zero-one systems, proposed by Clay and Gilbert is presented in

equation 6.5- Within the model the term l~ti,~[A]dominates and hence the entry rate coefficient

as well as LMCp can be neglected- The model predicts the probability of producing a chain of a

given MW at any instant in the polymerization given the concentration of monorner and transfer

agent in the particles and their respective rate coefficients. In order to generate MWD predictions

the rnodel \vas evaluated over a MW range equal to the MW range of the GPC calibration (3000-

4 167160 Daltons), and P,, (cumulative molecular weight distribution) \vas estimated from Pi,,

(instantaneous molecular weight distribution) as outlined in equation 3 -3. This allowed estimates

of MW, and MW.- to be made at each sampling point. The MW ,, and Mwi,estimates are

compared to the values obtained by GPC analysis and are presented in Figures 6-4 and 6.5 (a)-G)-

zero - one kinetics (6.5)

The results were also compared by generating plots of W(log(MW) vs- IogCMW) using

equations 3.1 and 3.2 so that the rnodeIYsability to predict the GPC distribution could be assessed. The area under al1 W(1ogMW) curves (those generated fiom the model and the GPC

data) \vas normalized to 1 so that the results could be compared. The results are presented in

Figures 6.7-6-9 and wi11 be discussed later in section 6.2.2.2. 6.2.1 Influence of Diffusion Limitations of MW

The effect that diffiision limitations have on the moIecular weight was investigated by

comparing the molecuIar weight estimates generated by the kinetic model using equilibrium CTA concentrations that would exist in the absence of difision limitations to GPC data. This analysis was camied out for two runs (b) and (f) whose behaviour will be described by Case 1 in section

6.2.2.1. These nins were selected because monorner droplet rneasurements were considered

reliable- The results of the cumulative MW comparison are presented in Figure 6.3.

The results show that when the equilibtium CTA concentrations are used in the kinetic model the molecular weight estimates are dways significantly lower than the value measured by the GPC. When it is assumed the CTA concentration is at equilibrium the GPC MWvalues are approximately 4-5 time greater than the model predictions. This resuIt is important because it fiirther quantifies the effect that the diffUsion limitations faced by the transfer agent have on the molecular weight and illustrates the importance of understanding the transport of DDT in the systern.

6.2.2 Results

The predictions made by Clay and Gilbert's (1995) kinetic model have been compared to the actual GPC values in three ways: using MW i,, MW,, and W(1ogMW) values. When these predictions were generated the adjusted coefficients were used in Nornura's model to generate the estimates of the CTA concentrations in the particles. In Figures 6.4 and 6.5 the individually adjusted partition coefficients were used to in Nomura's mode1 where as in Figure 6.6 the average partition coefficient of 2.82 x 10' was used to generate the estimate of CTA concentration in the particles. Of these three methods of comparison, M,,,and W(1ogMW) are important, as they illustrate the model's ability to predict the moments of the distribution as well as its overail shape-

Mwimvalues are valuable because they offer more mechanistic insight. They have been included because if the model makes one poor prediction on a cumulative basis, dl subsequent predictions also deviate fiom the GPC values. By examining the instantaneous values, greater insight into the model's ability to rnake accurate predictions during the later stages of reaction can be aquired.

6.2.2.1 Evaiuation of Weight Average MoIecular Weight Data

When the data was evaluated it became apparent that the model predictions deviated from the GPC values at different tirnes during the reaction for different reasons. Tt is believed that the discrepancies between the measured and predicted values occurred for three main reasons: an inaccurate monomer droplet measurement fforn the Malvem, an unreliable estimate of the thiol concentration fiorn the GC, or due to the fact that the equilibrium swelling assumption is not valid as the end of theoretical Interval II (-40% conversion) is approached-

In order to demonstrate the influence that the accuracy of the monomer droplet rneasurements have on the molecular weight predictions the runs have been groüped together according to the following three cases.

Case 1: The Malvem data gave apparently accurate monomer droplet rneasurements

until the theoretical end of Interval Il (al1 monomer droplets were - 2-5pm with no

obvious outIiers). This lead to reasonable MW predictions for most of the

esperiment and the data only begun to deviate substantially at conversion that

approached the theoretical end of interval II. This is illustrated in Figure 6.4 @), (c),

(f), (hl mKl(i) -

Case 2: The Malvern data produced one questionable monorner dropIet size part way

through the reaction (e.g. -20pm), which is believed to be inaccurate, and therefore

causes the MW predictions to be exqrernely high at all subsequent points when the

data is exarnined on a cumulative basis. This is evident in Figure 6.4 (g). Case 3: The monomer droplet size reported at the first sampling point is believed to

be inaccurate (-20pm), thus causing the cumulative predictions to deviate fiom the

GPC values fiom the start of the experiment. This case is shown in Figure 6.4 (a),

(d) (el-

The data described in Case 1 provides support for the ability of the diaision and kinetic

models to be integrated in order to give accurate estirnates of MW. The di&sion modelysability

to produce accurate estirnates of the CTA concentration in the particles allows the kinetic model

to be used to make reasonable MW predictions. The model predictions begin to deviate hmthe

GPC data beyond approximately 35% conversion- It is believed that this occurs because the

system is approaching the end of the theoretical Interval II, the point at which the equilibnum

swelling assurnption dictates monomer droplets cease to exist in the system. However, the data

clearfy indicates the esistence of monomer droplets until much higher conversions. Since dodecanethiol is a strong swelling agent, the equilibnum swelling assumption may no longer be

valid and more monomer than expected may be residing in the droplets. More evidence of this is provided in Table 6-3. Due to the manner in which the number of droplets was calculated, overestimating the amount of monomer in the particles (by erroneously assurning an end to

Interval II) tvould cause the estimated number of rnonomer droplets in the system be Iow, thus

increasing the estimated diffisional resistance. An increase in the diaisional resistance would cause the MW to be overestimated, as seen in the Figures- Once an overestirnate is made on a cumulative bais al1 further predictions \.vil1be inaccurate (overestimated) because this data point

is included in the caiculations performed at each subsequent sarnpling point, as dlbe seen when

Case 2 is examined. This explains the subsequent deviations on a cumulative basis. When the

nuis described by Case 1 are examined on an instantaneous basis it seen the overestimates only occur up until the theoretical end of Interval II, after this point the model values are less than those measured by the GPC. When the data described by Case 2 are closely examined it also provides support for the ability of the two models to be integrated and generate accurate estimates of the MW, although when the cumulative MWplot of Figure 6.4 (g) is first exarnined large deviations are evident.

These are caused by one of the monorner droplet measurements made by the Malvern apparently being incorrect. A Table containing the measured droplet size at each sampling point can be found in Appendix A. In Figure (g) this occurs at the third sampling point. An overestimate of the diameter by a factor of 10 results in the dropIet volume esthate being off by a factor of 1000, due to volume's cubic dependence on radius. This ultimately causes the diffùsional resistance to be overestimated and therefore the MWpredictions to exceed the calculated GPC values. When the corresponding instantaneous MWplot is examined (Figure 6.5 (c)) it becomes evident that only the prediction made in association with the poor Malvem measurement that deviates substantiaiiy. The remaining data points illustrate the sarne behaviour that was previously described in Case 1.

Although the data associated with Case 3 does not generate mode1 predictions of MW ,, that agree well with the data, it provides additional support for the conclusion that monomer droplet measurements that appear to be inaccurate, or c'outliers" should be filtered fiom the cdculation as they do not represent the situation in the reactor and tàey will affect all subsequent predictions. When the data is evaluated on an instantaneous MW basis it displays the same results as Case 2 samples, the largest deviations are seen at points when large monomer droplets are detected. Figure 6.5 (e) contains inaccurate monomer droplet measurements at al1 sampling points, while Figures (a) and (d) contain inaccurate droplet estimates at the first sampling point.

The fact that the mode1 cannot account for monomer in the system beyond the theoretical end of Interval 11, affects the ability to generate accurate molecular weight predictions under ali conditions. Beyond -40% conversion the mode1 underestimates the molecular weight ofthe polymer because the assumption of equilibrium monomer swelling based on literature data

"forces" al1 the CTA to be in the particles. However, droplets (presumably containing DDT) clearly exist beyond this point. It should be noted that this effect can only be seen in the

instantaneous plots because other errors are influencing the cumulative predictions. Tbe problem

arises because the monomer droplets are no longer incorporated into the model, even though

experirnentally we see tbere dlis a residuai amount of Iarge droplet/particles (>1 p)detected

by the Malvem- If the residud monomer couId be accounted for, more accurate difisional

resistance would improve our ability to predict the MW during the latter stages of reaction- Table

6.3 surnmarizes the discrepancy between the theoretical disappearance of monomer droplets at

-40% conversion and the Malvern measurements. Data has been presented for three mm, (b),

(f) and (i) which were classified as Case 1 above- It should be noted that at higher conversion

although droplets are observed an estimate of their size is not always available- This is due to the

fact the Malvern plots no longer give a narrow bel1 shaped droplet distribution. The plots appear

broader and in some cases distorted in shape, which makes it difficult to obtain an accurate

estirnate of the droplet diameter, even though the material is being detected. The fact that

monomer droplets remain in the system until 100% of the CTA is consumed in Table 6-3 (a)

provides fiirther evidence that the DDT may be acting as a swelhg agent inhibiting the difision

of monomer from the dropIets to the particles.

Table 6.3 (a) Tracking rnonomer droplets in a system containing lwt% CTA, 4.0g KPS, 1.75 s 10-* rno~dm~SDS. - Conversion % CTA Should Droplets Are Droplets Droplet Size Consumed be Theoretidly Observed? P resent? -----a------a------*--.----.------..-*-- 0.081 3.05 Yes Yes 2.94 0.1 67 56.82 Yes Yes 1.91 0.298 65.29 Yes Yes 1.95 0.440 46.50 No Yes 2-00 0.497 66 -67 No Yes 1.86 0.542 68.81 No Yes 2.76 0.655 92.1 3 No Yes N/A 0.734 100.00 No Table 6.3 (b) Tracking rnonomer droplets in a system containing 2wt% CTA, 4.0g KPS, 1.75 x IO**moI/drn3 SDS. Conversion % CTA Should Droplets Are Droptets Droplet Size Consumed be Theoretically Observed? (Po Present? -.------.--.------a-----p------..-- 0,079 20 -47 Yes Yes 2-48 0-182 30-59 Yes Yes 1-70 0,300 54.14 Yes Yes 1.92 0,400 33.60 No Yes 1-89 0,483 50.22 No Yes 1.91 0,556 55-67 No Yes 1.94 0-796 59.95 No Yes NIA 0.794 85.96 No Yes NIA

Table 6.3 (c) Tracking monomer droplets in a system containing 3wt% CTA, 4.0g US,1.75 s 10-~movdrn3 SDS. Conversion % CTA Should Dropiets Are Droplets Droplet Size Consumed be TheoreticaIIy O bserved? (P) Present?-.-----.---.--.------0-122 54.22 Yes Yes 1.70 0.21 3 57.87 Yes Yes 3 -22 0.339 70.02 Yes Yes 2.0 1 0.433 64.39 No Yes 1-95 0.541 66 -62 No Yes 2.00 0.609 78.65 No Yes 1.99 0.741 82.00 No Yes NIA 0.832 98.29 No Yes N/A

6.2.2.2 Cornparison of W(1ogMW) values

For three of the rus, (b), (f) and (h), that were classified as Case 1 above, the GPC data

has been compared to the predictions made by the kinetic mode1 by generating plots of

W(1ogMW) as a function of log(MW). These plots cari be found in Figures 6.7-6.9. The

comparison behveen the GPC data and the predictions generated by the kinetic mode1 show that

the mode1 is able to accurately predict W(1ogMW) during the middle portion of the reaction but

deviates during the early and latter stages of reaction (towards the end of traditional Interval II).

This result is expected since the MWpredictions deviated over the same intervals. During the

early stages of reaction the mode1 is generally narrower that the GPC distribution and appears to

have difficulty predicting the large amount of low molecular weight polyrner produced.

Cunningham and Ma (20006) also reported this effect and attributed it to insufficient sarnpling du~gthe early stages of the reaction when the concentration of CTA in the polymer pdcles is changing rapidly. Du~gthïs work samples were withdrawn more frequentry and an irnprovement in the fit of the data was seen, providing support for the Cunningham and Ma's conclusion- The mode1 also deviates during the latter stages of reaction, with the model predictions generating a broader distribution, shifted to the right indicating that the mode1 is predicting that polymer of a higher molecular weight is being forrned. As discussed previously in section 6-3.1 it is believed this occurs because of dodecanthiol's ability to act as a strong swelling agent, thus causing the equilibrium swelling assumption to be invalid and ieading to an overestimate of the diffusional resistance in the system. The fact that the model continues to deviate fiom the GPC data beyond Interval LI is due to the fact that the results are presented on a cumulative basis.

6.2.2.3 Filtering of Data to Improve Mode1 Predictions

In order to fùrther assess the vaIidity of combining the difision and kinetic models the the data from run (g) described by Case 2 above, \vas reanalyzed negating the sample for which it is believed that the monomer droplet size was overestirnated. This was done to show that if this system were being used in an on-line application, upon detection of a monomer droplet rneasurement outside a specified range, the system could choose to filter the data point and would then be capable of making accurate predictions on a cumulative basis at subsequent points in the reaction. The effect of filtering the larger monomer droplet out of the model can be seen if Figure

6.10 where the MWpredictions with and without the overestimated droplet are compared to the

GPC data as a fünction of conversion.

From Figure 6.10, it is evident that upon filtration of the overestimated monomer droplets the model is able to make more reliable MW,, estimates. Once the data was filtered the system behaved like those described by Case 1 in which overestirnates were seen towards the end of behaved like those descnbed by Case 1 in which overestimates were seen towards the end of traditional Intervai II. This result reiterates the validity of combining the difision and kinetic models to obtain estimates of the MW and the MWD.

6.2.2.4 Relative Peak Areas of Particles and Droplets

While it is believed that a solid qualitative understanding of the system has been obtained it is dif33cult to quanti.@the theory that monomer droplets remain in the system beyond the end of the traditionai Interval II (40% conversion) and are responsible for the deviations observed in the model. Data obtained fiom the Malvern (Le. the relative peak areas of the particles and droplets) has been used in an attempt to quante this theory. In addition to particle size the

Malvem outputs the vol % of the sample below a given size, and thus ailows an estimate of the volume of residual monomer, Three distinct peaks were typicaily observed in the Maivern plots, on below 1 pm, one between 1-100 Pm, and beyond 100 p.For this analysis it was assurned that ;inv material less than 1 pm \vas a polymer particle and anything fiom 1- 100 prn was monomer droplets. Particle sizes pater than 100 pm were a assumed to be either monorner droplets or polymer particles that had coagulated due to the fact the concentration of SDS drops significantly when the sample is added to the Malvern. The relative areas of the particle and droplet peaks are then assumed to represent the relative amounts of each. Once an estimate of the volume of monomer droplets was obtained it was used to predicted the number of monomer droplets present in each system beyond the end of Interval II, assurning the droplet diameter remained constant at the last measured value before -40% conversion. The degree to which the system deviates fkom the equilibriurn swelling assumption is illustrated as a plot of Cp as a fiinction of conversion in Figure 6.11. There will be error associated with these measurements because the amount of monomer that constituted material greater than lOOpm could not be determined, and subsequently some monomer was eliminated fiom the calculation. However it the data clearly illustrated the system vas not following equilibrium swelling behaviour.

The cumulative and uistantaneous MWestirnates that were generated once the monomer droplets were included in the model are presented Figure 6.12. Figures 6.13 and 6.14 contain comparisons of the W(1ogMW) values generated fiom the GPC and fiorn the mode1 with the rnonomer droplet estimates beyond Interval II included.

From Figure 6.12 it can be seen that the modeIYsability to predict the MW of the polymer is irnproved once the remaining monomer droplets are included. The instantaneous and cumulative are consistently more accurate than those made foIiowing the equilibriurn swelling assumption. Once the monomer droplets are incorporated into the mode1 the predictions are no longer consistently over or under estimating the MW, thus preventing any further conclusion about the relative amounts of monomer and polymer that constitute the material greater than

100 prn detected by the Malvem. It should be noted that in Figure 6.12 (a) and (b) the mode1 predictions at high conversions have not been shown on the Figure. This is because the GC did not detect any thiol in the systern at the last sarnpling, thus causing the MW estimate to be extremely higb At the second last sampling point the CTA concentration reported by the GC

\.vas extrernely low. This also Iead to an extremely high MW estimate. (The actual GC measurements are available in Appendix A) These two data points are believed to be outliers and therefore were etiminated.

Figures 6.13and 6.14 contain the W(1ogMW) values presented as a fùnction of 1ogOMW)-

When the data presented in these Figures is compared to Figures 6.7 and 6.8 (the corresponding runs without the monomer droplet present in the model beyond Interval II), in can been seen that including thc monomer droplets estimates ftom thc Malvcrn data improves the predictions obtained fiom the kinetic model at higher conversions.

The data shown in Figures 6.12, 6.13 and 6.14 shows that monorner droplets in the systern beyond the end of the traditional Interval II need to be incorporated into the diffusion model. The MW estimates generated once the monomer droplets have been incmporated are in good agreement with GPC values. Smali deviations are still evident between the GPC values and the rnodel predictions. It is believed that this is partly caused by the coagulatiorir of the droplets/particles in the Malvern introduces additionai error into the calculation. The volume of the monomer droplets and polymer particles that constituted the larger matenal a>100 pn) could not be determined. The way in which the larger material was removed i5om the calculation resulted in the assumption that droplets and particles coagulated at the same ratio as they are present in the system. This may not be true and thus introduce error into the calculation of how much monomer esists in the droplets. 6.3 Summary

The validity of integating the diffusion model proposed by Nomura et al. with the kinetic model proposed by Clay and Gilbert in order to produce reliable estirnates of the MW and MWD distribution has been assessed. The influence the partition coefficient vaiue has on the model's ability to generate accurate estimates has been addressed and it is clear that a more accurate measurement of the coeficient is required for dodecanethiol. It has been shown -that with reliable particle and droplet size measurements we can now predict the M,and MWD even under conditions of difision limited chah transfer. The importance of an accurate particle number measurement has been demonstrated, This \vil1 be most dif5cuIt during Interval 1while nuckation is still occurring. Our results have also shocvn the monomer droplets exkt past the theoretical end of Interval II, and it has been recognized that the amount of monorner present in the droplets needs to be quantified in order to obtain accurate MW predictions du~gInterval III-

The influence that a single erroneous measurement (either GC or PSD) can have on al1 subsequent predictions has also been seen, Therefore, care must be taken to ensure that these points are "filtered" fiom the model. Conversion

Diffusion Model Adjusted m r Diffusion Mode1 Nomura's rn A GPC

Conversion I e Diffusion Model Nomura's m r Diffusion M ode1 Adjusted m A GP C

Conversion Diffision Model Nom ura's m rn Diffusion Model Adjusted m A GP C (cl Figure 6.1: [Ap] value cornparison. (a) Run containing Lwt% thïol: 6.65g SDS: 4.0g KPS (b) Run contauiing 1wt% tliiol: 3.0g SDS: 4.0g KPS (c) Run containing 2wt%thial:3.0g SDS: 2.0g KPS Conversion + Diffusion Model Nornura's rn œ Difision Model Adjusted rn A GPC

Conversion e Diffusion Model Nornura's rn r Diffusion Model Adjusted m A GPC

Conversion Diffusion Model Nomura's rn I Diffusion Model Adjusted rn A GPC (0 Figure 6.1: [Ap] value cornparison. (d) Run containing 2wt% thiol: 6.65g SDS: 2.0g KPS (e) Run containing 2wt% thiol: 6.65g SDS: 4.Og KPS (f) Run containing 2wt%thiol: 3.0g SDS : 4.0g KPS I Conversion I + Diffision Model Nomura's rn Diffision Model Adjusted rn A GPC

Conversion m Diffusion Model Nomura's m m Diffusion Model Adjusted rn AGPC

Conversion + Diffusion Model Nomura's m m Diffusion M ode1 Adjusted m A GPC

Figure 6.1 : [Ap] value cornparison. (g) Run containing 3 w& tluol: 3.0g SDS : 2.0g KPS 01)Run containing 3wt% thiol: 6.65g SDS: 2.0g KPS (i) Run containing 3wtY0thioI: 3.0g SDS: 4.0g KPS -- Conversion e Diffusion Model Nom uramsrn m Diffusion Model Adjusted m AGP C

Figure 6.1: [Ap] value cornparison. (j)Run containing 3~%thiol: 3.0g SDS: 4.0g KPS Conversion

Individually Adjusted rn e Common Adjusted rn A GPC Data

Co n ve rsio n

O Individually Adjusted rn rn Corn mon Adjusted m AGPC Data

Conversion

e lndividually Adjusted rn rn Common Adjusted rn AGPC Data

Figure 6.2: [A,] cornparison. (a) Run containing lwt% thiol:3.0g SDS: 4.0g KPS (b) Run contauiing 2wt% thiol: 3.0g: 2.0g KPS (c) Run containing 2wt%thiol: 3.0g SDS: 4.0g KPS Conversion

e Individually Adjusted m rn Common Adjusted m AGP C Data

Figure 6.2: [A,] cornparison. (d) Run containhg 3\vt% thiol: 3.0g SDS :2.0g KI'S Co n ve rsio n

e P redicted MW if CTA is at Equilibrium iGP C Data

0.40 0.60 Co n ve rsio n

* Predicted MW if CTAis at Equilibrium GPC Data

Figure 6.3: The effect of diffusion limitations on MW. (a) A nin containing 2 wt% thiol: 3.0g SDS: 4.0g KPS (b) A nrn containing 1 wt% fhiol: 3-08SDS: 4.0g KPS Conversion Predicted ar GPC Data

Conversion 6 P redicted m G P C Data

O -20 O -40 O -60 Conversion e P redicted m G P C Data (cl Figure 6.4: M,,,comparison (a) Run containing lwt% thiol:6.65g SDS: 4.0g KPS (b) Run containing lwt% thiol:3.0g SDS: 4.Og KPS (c) Run containing 2wt%ùuol: 3.0g SDS: 2.0g KPS 0.00 0 -20 O -4 O O -60 0.80 1 .O0 Con ve rsio n epredicted mGPC Data

Conversion

epredicted mGPC Data

0 .O O 0 -20 0-40 0.60 0.80 1 .O0 Conversion

eKinetic Mode1 mGPC Data

-- - (f) Figure 6.4: MW,, cornparison. (d) Run containing 2wt% thiol: 6.65g SDS: 2.0g KPS (e) Run containing 2wtY0 thiok6.65g SDS: 4.0g KPS (f) Run containing 2wt%thiol: 3.0g SDS: 4.0g KPS 2500000 i 2000000 - * -VI E *** * * O 1sooooo - 0 2E 1000000 - I 500000 -

a rn 9 RR- rn gl O I L 1 I 1 0.00 0 -20 0 -40 0.60 0.80 1 .O0 Conversion

* P redicted m G P C Data

Conversion

ePredcited ppiG PC Data

Conversion + Kinetic Model GPC Data (0 Figure 6.4: MW- cornparison. (g) Run contauung 3wt% thiol: 3.0g SDS: 2.0g ECPS (h) Run containhg 3wt% thiol: 6.65g SDS: 2.0g KPS (i) Run containing 3wt%thiol: 3.0g SDS: 4.0g KPS 3 60000 r g SOOOO lu 0 40000

0 .O0 O .20 O -40 O .60 0.80 1 .O0 Conversion eKinetic M ode1 GPC Data

Figure 6.4: MW- cornparison. 0) Run contaùiing 3wt% thiol: 3.0g SDS: 4-0g KPS 3000000 2500000 - * 4 P V) 8 2000000 - C -m 0-. 1500000 - O = 1000000 - 2 500000 - m 1 a I O 1 I T 0.O 0 0-20 O -40 0-60 0-80 1 .O0 Conversion

e P redicted MI G P C Data

0.20 0.40 0.60 0.80 Conversion * Kinetic Model m GPC Data

Conversion

ePredicted mGPC Data

Figure 6-5: MWkt cornparison (a) Run containing lwt%thiol: 6.65g SDS: 4.0g KPS (b) Run containing 11vWo thiol: 3.0g SDS: 4.0g KPS (c) Ru.containing 2wt%thiol: 3.0g SDS: 2.0g KPS Conversion

e P redicted e G P C Data

350000 300000 250000 200000 150000 100000 SOOOO O 0.00 0 -20 0 -40 0.60 0.80 1 .O0 1-20 Conversion

e P redicted m G P C Data

0.00 0.20 0.40 O -60 0 -8O 1-00 Conversion

6 Kinetic M ode1 m G P C Data

Figure 6.5: MW,,cornparison. (d) Run contahing 2wt% ihiol: 6.65g SDS: 2.0g KPS (e) Run containhg 2wt% thiol: 6.65g SDS: 4,Og KPS (f) Run containing 2wt%thïol: 3.0g SDS: 4.0g KPS .O0 0-20 0-40 0-60 0.80 1 .O0 Conversion

* Predicted iGPC Data

0.00 0.20 0.40 0.60 0.80 1 .O0 Conversion

ePredicted ~IGPC Data

h * 150000 - O =m P_- 100000 - * PP -C mm I m I I & soooo - rn e e e* * O T I l 1 0.00 0.20 O -4 O 0 -6 O 0.80 1 .O0 Conversion

e Kinetic M ode1 m GP C Data (il Figure 6.5: MWhtcornparison (g) Run containing 3wt% thiol: 3.0g SDS: 2.0g KPS (h) Run containing 3wt0& thiol: 6.65g SDS: 2.0g KPS (i) Run containing 3wt%thiol: 3.0g SDS: 4.0g KPS Conversion

e Kinetic M ode1 m GPC Data

Figure 6.5: MWhcomparison (j) Run containing 3wt% thiol: 3.0g SDS: 4.0g KPS Conversion

Common Adjusted rn ilndividually Adjusted rn r GPC Data

0.00 0.20 0.40 0.60 0.80 1-00 Conversion

Common Adjusted rn Individuatly Adjusted m A GPC Data

0.00 0.20 0.40 0.60 0.80 1 .O0 Conversion

6 Com mon Adjusted m lndividually Adjusted rn A GPC Data (cl Figure 6.6: MWk,comparison. (a) Run containuig lm% thiol:3.0g SDS: 4.0g KPS (b) Run containkg 2wt% thiol: 3.0g: 2.0g KPS (c) Run containing 2wt%thioI: 3.0g SDS: 4.0g KPS 0.40 0.60 Conversion

Common Adjusted rn ilndividually Adjusted rn A GPC Data

Figure 6.6: MW ktcornparison (g) Run containing 3wt% thiol: 3.0g SDS: 2.0g KPS - Kinetic M ode1 - - -

- GPC Data

-

- Kinetic M ode1 - - - GPC Data - -

0.00E+00 +

Figure 6.7: Cornparison of W(1ogMW) values: (a)-(g) Run containing .1~%thiol: 3.0g SDS: 4-08KPS at increasing conversion intervais (a) x=0.081 (b)x=O. 167 (c)x=0.298 - Kinetic M ode1 GPC Data

-

- -

- - GPC Data - Kinetic M ode1 - - -

- - GPC Data - - Kinetic M ode1 - -

Figure 6.7: Cornparison of W(1ogMW) values: (a)-@) Run containhg lwt% tiuol: 3.0g SDS: 4.0g KPS at increasing conversion intervals (d) x=0.440 (e)x=0,497 (f)x=0.542 Figure 6.7: Cornparison of W(1ogMW) values: (a)-(g) Run containhg fwt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion in tervals (g) x=0.655 Kinetic M ode1

GPC Data -

GPC Da

Kinetic M ode1

1.4OE+OO

1.20E+00 - GPC Data 1.00E+00 - $5 8.00E-O1 - -O 6.00E-01 - Kinetic M ode1 rY 4.00E-01 -

2.OOE-O1 -

0.00E+00 , I ,

Figure 6.8: Cornparison of W(1ogMW) values: (a)-@) Run containing 2wt% tiuol: 3 .Og SDS: 4.0g KFS at hcreasing conversion intervals (a) x~û.079(b)x=0.182 (c)x=0.300 - Kinetic M ode1 - GPC Data - - -

- Kinetic M ode1 - GPC Dat

- -

Figure 6.8: Cornparison of W(1ogMW) vahes: (a)-@) Run containing 2wt% mol: 3.0g SDS: 4.0g KPS at increasing conversion in tervals (d) x=0.400 (e) ~0,483(f)x=OS 56 Figure 6.8: Cornparison of W(1ogMW) values: (a)-@) Run containhg 2wt% thiol: 3 -0gSDS :4.0g KPS at increasing conversion intervals. (g)x=0.796 (h)x=0.794 1.4OE+OO

1.20€+00 - GP C Data

1.00€+00 Kinetic Model ' 8-OOE-O1 A - 6.OOE-01 - z 4.OOE-O1 - 2.00E-01 -

0.00E+00 0-00 1-00 2-00 3.00 4 -0O 5.00 6.00 7 .O0 log(MW 1

GPC Data

Kinetic M ode1

Figure 6.9: Cornparison of W(iogMW) values: (a)+) Run containhg 3wt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals. (a)x=û. 122 @)x=0.213 (c)x=O.33 9 GPC Data .-> - - Kinetic M ode1 -

- I

Figure 6.9: Cornparison of W(1ogMW) values: (a)+) Run containing 3wt% tliiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals. (d)=0.433 (e).x=0.541 (f)x=0.609 GPC Data n

Figure 6.9: Cornparison of W(logMW) values: (a)-@) Run containhg 3wt% thiol: 3.0g SDS: 4.0g KPS at hcreasing conversion intervals. (g)x=0.741 (h)x=O.83 2 Conversion

4FiItered Data AGPC Data m Unfiltered Data

Figure 6.10: Cornparison of filtered and unfiltered data, (a) Run containing 3wt% thiol: 3.0g SDS: 2.0g KPS @lot (g) in Figure 6.3-6.4) 0.00 0.20 0.40 0.60 0.80 1-00 Conversion

Figure 6.1 1 Monomer concentration in the poIymer particles detemiined using reIative peak areas for a rtm containing lrvt% CTA, 3.0g SDS, 4.0g KPS. Conversion eUsing Relative Peak Areas mGPC Data ~FollowingEquilibrium Swelling

0.20 O, 4 0 Conversion

e Using Relative Peak Areas m GPC Data r Following Equilibrium Swelling

Figure 6.12: MWcompatison using MaIvem volume estimates. (a) MW,, for run containing I wt% thiol: 3.0g SDS: 4.0g KPS (b) M,-,for run containing IwiO/o thiol:3.0g SDS: 4.0g KPS O .O0 0 -20 O -40 0.60 0 -80 1 .O0 Conversion

Using Relative Peak Areas ps GPC Data A FolIowing Equilibrium Swelling

O -40 0 -6O Conversion

eUsing Relative Peak Areas E GPC Data A FolIowing Equilibriurn Swelling

Figure 6.12: MW cornparison using Malvern votume estirnates. (c) MW,, for nin containing 2\vt% thiol: 3.0g SDS: 4.0g KPS (d) Mwbtfor run containhg 2wt% thiol:3.0g SDS: 4.0g KPS Kinetic M ode1

GPC Data 7

Kinetic Model -. /IC\

------. -- -- -

- Kinetic M ode1 GPC Data

- - - - - i

Figure 6.13:Compaxison of WOogMW) values for a case using relative peak areas. (a)-@) Run containhg lwt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals (a) ~0.081 (b) x-O. 167 (c)~0.298 - Kinetic M ode1 GPC Data - -

- -

L (f) Figure 6.13 :Cornparison of W(1ogMW) values for a case using relative peak areas. (a)-(g) Run containhg iwt% thiol: 3.0g SDS: 4.0g KPS at inmeashg conversion intervals Cd) x=0.440 (e) ~0.497(f) ~0.542 Figure 6.13:Comparison of W(1ogMW) values for a case using relative peak areas. (a)-(g) Run containing lwt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals (g) ~0.655 Kinetic M ode1

GPC Data

- 8 I

GPC Data

Kinetic M ode1

Cc) Figure 6.14:Comparison of W(1ogMW) values for a case using relative peak areas. (a)-(g) Run containhg 2wWo thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals (a) x=0.079 @) x-O. 182 (c) ~û.300 Kinetic M ode1

GPC Data

-

GPC Data . fi Kinetiç Model

0 Figure 6.14:Cornparison of W(1ogMW) values for a case using relative peak areas. (a)-(@ Run contaùung 2wt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervals (d) x=0.400 (e) ~0.483(f) ~0.556 Figure 6.14:Comparison of W(1ogMW) values (a)-(g) for a case using relative peak areas. Run containing 2wt% thiol: 3.0g SDS: 4.0g KPS at increasing conversion intervais (g) x=0.796 (h) .-O-793 Chapter 7

7. Conclusions

A senes of styrene ernulsion polymerization were performed in order to assess the validity of

integratïng the diffiision mode1 proposed by Nomura et al. (1995) with the kinetic mode1

proposed by Clay and Gilbert (1994) to generate accurate estimates of the MW and MWD of

polymers produced under diffision limited conditions, in a marner that would be amenable to on-

line application. The data coliected fiom the experiments were analyzed by GC to deterrnine the

CTA concentration, by the Malvern Mastersizer 2000, to evaluate the sizes of the polymer particles and monomer droplets, and by GPC to rneasure the molecular weight of the sample. The

data were then incorporated into the respective models so an evaiuation could be made and the

objectives outlined in Chapter 1 could be addressed- The work that \vas performed led to the

following conclusions:

(i) With reliable polymer particle and monomer droplet size rneasurements we can

now fit the mode1 predictions to the experimental data even under conditions of

strong diffusion iimited chain tranfer-

(ii) The Malvern Mastersizer 2000, although it is a valuable tooI for assessing

particle size distributions, presented several challenges in this work. rt is not able

to detect the presence of small polymer particle during the early stages of

reaction, when a large number of monomer droplets also exist in the system.

Accurate particle number estimates are especially important during the

nucleation penod to ensure that mode1 produces reliable MW predictions.

Ensuring that the droplets were stabilized and did not coagulate within the

sarnpling loop also presented a challenge because within the Malvern the concentration of surfactant would no Ionger be capable of stabifizing the dropiets.

In light of these factors this study was able to determine an optimum set of

operating conditions under which the Malvern Mastersizer 2000 can be used to

assess the monomer droplet and poIyrner particle size distributions of polymer

latexes.

(iii) When the predictions of the CTA concentrations in the particles predicted by

Nomura's mode1 (1995) were first compared to the values generated by the GPC

technique presented by Ma and Cunningham (2000b) large deviations existed, as

Nomura's model underestimated the CTA concentration when the monomer

droplets were present in the system. Upon fürther examination of Nomura's

work the CTA partition coefficient for dodecanethiol was adjusted to provide a

betîer fit of the data. When this value was adjusted by a factor of -IO", an

improvement kvas seen in the model's ability to predict the CTA concentration in

the polymer particles and subsequently the MW of the polymer. It should be

noted that although only the value of the partition coefficient \vas adjusted it is

believed that there may be error associated with the diffüsion coefficient reported

by Nomura as well, since it is based on a semi-empirical correIation and therefore

subject to error. However, due to the structure of the model the partition and

difision coefficients cannot be evaluated independently- A more accurate

measure of the n-DDTpartition coefficient and diffusivity would be helphl.

(iv) Monomer droplets exist beyond the theoretical end of interval II. There is a need

to accurately quanti% experimentally how much monomer is in the droplets in

order to obtain accurate MW predictions during Intervai III. Chapter 8

8. Recomrnendations for future work

The study that was performed produced valuable information on the validity of integrating the diEusion and kinetic models in order to estimate rnolecular tveight. The information that \vas gathered during this study has allowed the following areas of hture work to be identified so that the accuracy of the molecular weight predictions generated by the kinetic mode1 as well as the understanding of the ernulsion polyrnerization systems can be improved.

(i) In this work, the lack of confidence in the literature values for the partition and

difision coefficients for long-chain transfer agents (dodecanethiol) has been

highlighted. Ideally, it would be desirable to obtain a more accurate estimate of

these values. However, it is acknowledged that this is a âifEcult task due to the

extremely low water solubility of Iong-chain transfer agents. Since these materials

are at best sparingly soluble, it \dl be dficult to differentiate betsveen the

measured values and the "noise" associated with the measurements-

(ii) The data collected by the Maivem Mastersiter 2000 indicates that monomer

droplets are be present in the system beyond points in the reaction where traditional

thermodynarnic relationships suggest that they should exist. The behaviour of

monamer at conversions greater than approximately 40% is essential for a detailed

understanding of diffùsion limited chain-transfer. Being able to quant@ the

concentrations of monomer in the particle and droplet phases at late stages of

reaction not oniy enables better predictions to be made fkom the diffirsion and kinetic modeIs but has the potential to have a rnuch broader impact on the generai

study of emulsion systems,

(iii) In this work it has been ilhstrated that the limitations of the Maivern Mastersizer

2000 prevented particles fkom being detected during the early stages of reaction.

This Iead to the number of particles in the system being estimated fiom conversion

data and subsequently was a source of error in the model. It would be desirable to

devetop a technique that allows the particle size to be measured fkom the first

sampling point- This may be able to be achieved by introducing another piece of

particle size equipment (such as a CHDF) to strictly masure the polymer particle

size, while the monomer droplets continue to be measured by the Mastersizer. (a) Run containing Iwt% CTA, 6.659 SDS, 4.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDT] Mncum Mninst MWCU~Mwlnrt Diameter Diameter [DDTJ Mncum Mninn NIwcum Mwint (min) molldm3 (dm) (dm) molldm3 10 0.1 03 1.06E-02 47972 47972 92681 92681 7.55E-07 1,91E-04 1,73E-06 1517531 1517531 2343025 2343025 126870 7.49E-07 2.1 3E-05 2.47E-05 1 149450 91 2362 2017403 1668545 116479 104432 9.10E-07 2.22E-03 1023603 19981 2013088 33220.72 102482 65774 9.60E-07 1,58E-03 955891 19783 2010323 32837,22 90682 36644 9,70E-07 3,65E-04 91881 7 44948 2006487 83639.66 91867 123709 9.9OE-O7 2.44E-04 907192 54374 2004953 102952.8 96526 126389 6.4OE-07 8.34E-05 875443 77975 1998629 150647,6 86389 64053 7.70E-07 0,OOEtOO 1029013 1601340 21 35990 241 5853 Jb) Run containing 1 wt% CTA, 3.0~SDS, 4.0g KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion 1DDT.J MWn Diameter Diameter [DDTJ (min) mol/dm3 (dm) (dm) molldm3 10 0.081 8.83E-03 118876 7.75E-07 2.94E-05 6.36E-04 20 0.167 3.93E-03 186887 7.98E-07 1.91 E-05 5.49E-04 30 0.298 3,16E-03 191902 9.40E-07 1,95E-05 1.63E-04 40 0.440 4.87E-03 159172 9.50E-07 2.00E-03 50 0.497 3.03E-03 123460 8.90E-07 1 .19E-03 60 0.542 2.84E-03 133308 8.40E-07 1 .12E-O3 90 0.655 7,16E-04 43683 8.40E-07 2,82E-04 120 0.734 0.00E+00 61316 7,70E-07 0,OOEtOO (c) Run containing 2 wt% CTA, 3.09 SDS, 4,Og KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDTJ MW,,, Diameter Diameter [DDT,,] (min) molldm3 (dm) (dm) molldm3 10 0.018 2,58E-02 17441 2,43E-05 5,61 E-07 3,12E-03 20 0,038 2.17E-02 19625 1.56E-05 5.65E-07 4.29E-03 30 O, 114 1.82E-02 701 94 3,46E-05 5,80E-07 9,97E-04 40 0.234 1.19E-02 87560 1.88E-05 6.03E-07 1,Il E-03 50 0.349 1.17E-02 83694 2.08E-05 6.30E-07 2.86E-04 60 0.442 7.26E-03 6.30E-07 2,85E-03 90 0.676 9.05E-03 65984 7.70E-07 3,56E-03 120 0,809 9.20E-04 7.70E-07 5.57E-04

Appendix A (d) Run containing 2 wt% CTA, 6.659 SDS, 2.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDT] Mncum Mnn Mwcum Mwlnst Diameter Diameter [DDTp] Mn,", Mn~nst Mwcum Mwinst (min) mol/dm3 (dm) (dm) molldm3 IO O. 165 1,82E-02 34053 34053 90824 90824 6,66E-07 1,55E-04 9.59E-05 342040 342040 673562 673562 20 0.361 1.80E-02 43179 97728 94501 97728 7.05E-07 2,42E-05 4.68E-04 253832 79420 61891 2 153540 30 0.513 1.57E-02 39436 89638 92920 89638 7,33E-07 6.38E-03 219984 9545 615270 13232 40 0.674 1,26E-02 47156 72914 74096 72914 7,60E-07 4.96E-03 192623 1O1 49 61 II42 14353 50 0.663 9.34E-03 34670 84467 82514 84467 9.50E-07 3,68E-03 192623 12870 61 1142 19501 60 0,770 1,09E-02 27857 25627 72746 25627 9.10E-07 4,30E-03 178925 8252 609085 10873 90 0.896 3.84E-03 22601 33763 65835 33763 8.60E-07 1.51E-03 165004 8736 606498 11749 120 0.915 2.72E-03 19913 44493 63065 44493 7.80E-07 1.65E-03 163288 7391 606204 935 1 (e) Run containing 2 wt% CTA, 6.659 SDS, 4.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDTJ Mncum Mnina MW,", Diameter Diameter [DDT,] Mn Mn MW,., MWl,, (min) mol/dm3 (dm) (dm) molldm3 10 (3.1 85 1.74E-02 28828 28828 98386 98386 6,12E-07 1,45E-04 2.1 3E-04 166371 166371 325699 325699 20 0.435 1.83E-02 40379 105865 105907 105865 6.56E-07 5.94E-03 109862 9789 315665 13684 30 0.700 1.33E-02 41 155 101457 93392 101457 9.50E-07 5.25E-03 82621 9087 306649 12388 40 0.828 9.42E-03 30605 53217 84486 53217 9.50E-07 3.87E-03 74814 7197 303685 9014 50 0.895 5.71 E-03 21 139 105332 8.70E-07 2,25E-03 71384 7104 302199 8853 60 90 0.949 1,77E-03 23886 72821 78300 72821 8.20E-07 6,99E-04 68585 8715 300550 11711 120 0.953 9.85E-04 22551 105749 77953 105749 7,70E-07 5.97E-04 68408 9146 300435 12497 (f) Run containing 2 wt% CTA, 3.09 SDS, 4.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDTJ Mncum Ml MW,,, NIwlnst Diameter Diameter [DDTp] Mn,., Mnlnst Mwcum MWlnd (min) molldm3 (dm) (dm) molldm3 IO 0.079 1,56E-02 22396 22396 65054 65054 8.00E-07 2,48E-05 8,01 E-04 4801 5 4801 5 89937 89937 20 0.1 82 1.36E-02 30869 84441 73448 84441 8.27E-07 1,70E-05 9,90E-04 43405 39649 81287 72751 30 0.300 9.01 E-03 31 909 81 181 76227 81 181 6.70E-07 1 .92E-05 3,21 E-04 77577 1131 58 180835 220593 40 0.400 1.30E-02 33319 93402 79951 93402 8.90E-07 4,88E-03 65328 II 123 175667 16180 5 O 0.483 9.78E-03 33897 63096 72610 63096 9.50E-07 3,85E-O3 58275 23132 170927 20003 60 0.556 8,71E-03 33296 68525 71024 68525 8.90E-07 3,42E-03 53464 14295 166578 22235 90 0,796 7.87E-03 27571 54852 65567 54852 8.40E-07 3.09E-O3 42788 9161 158630 12524 120 0.794 2.76E-03 30803 133073 66882 133073 9.3OE-07 1.67E-03 42788 14024 158630 21713

Appendix A (g) Run containing 3 wt% CTA, 3,Og SDS, 2,Og KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDT] Mncum Mnlnn Mwcum Mwinn Diameter Diameter [DDT,,] Mncum Mn MW,, MwlM (min) molldm3 (dm) (dm) molldm3 10 0.070 2.74E-02 25087 25087 70399 70399 7,89E-07 3.25E-05 7.27E-04 52533 52533 99191 99292 20 0.159 2.48E-02 34768 90277 80142 90277 8.13E-07 2.14E-05 9,37E-04 46606 41677 88317 76919 30 0.250 1.88E-02 36349 168189 113754 168189 6.40E-07 1.53E-04 1.OSE-05 964706 1237571 2046841 2068762 40 0.357 1.08E-02 37669 93090 91435 93090 9.40E-07 2.01 E-05 9.23E-05 775372 351964 1856980 693218 50 0.436 1.25E-02 36880 107202 94765 107202 9.50E-07 4.92E-03 730999 Il070 1855361 16081 60 0.523 1.43E-02 38806 106767 861 75 106767 9.50E-07 4.32E-03 686331 12096 1853349 18025 90 0.709 8.19E-O3 35867 54400 73461 54400 8.70E-O7 3.22E-03 608080 12143 1849095 18115 120 0.822 6.07E-03 31205 63628 71681 63628 7,90E-07 3.67E-03 574673 7545 1847752 9619 (h) Run containing 3 wt% CTA, 6,659SDS, 2-09 KPS GPC GPC Particle Droplet Predicted Predicted 1 Time Conversion MnDiameter Diameter {DDTJ (min) (dm) (dm) molldm3 -10 58470 6.96E-O7 2.22E-05 1.17E-03 20 42583 7.41 E-07 2.02E-05 2.46E-04 30 25431 6.70E-07 1.1 5E-02 40 1101 3 9.60E-07 1,07E-02 5 0 16099 9.50E-07 9.63E-03 60 46437 8.7OE-07 7.01 E-03 90 8587 7,90E-07 3.34E-O3 120 0.928 5,21E-03 16990 10135 46517 10135 7,70E-O7 3.15E-O3 71219 5178 258034 5753 (i) Run containing 3 wt% CTA, 3,O g SDS, 4.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversiorr [Dili] MlDiameter Diameter [DDTJ (min) molldm3 (dm) (dm) molldm3 10 0.1 22 3.21 E-02 62974 7,8l E-07 1,70E-05 2.21 E-03 20 0,213 2.95E-02 30 0.339 2.1 OE-02 40 0.433 2.49E-02 5 0 0.541 2.34E-02 60 0,609 1.49E-02 90 0.741 1.26E-O2 120 0.832 1.20E-03

Appendix A ÿ) Run containing 3 wt% CTA, 6.65 g SDS, 4.09 KPS GPC GPC Particle Droplet Predicted Predicted Time Conversion [DDT] Mn,,, MnlnSt MW,," MW,,, Diameter Diameter [DDTJ Mn Mn M,,,, (min) molldm3 (dm) (dm) molldm3 IO 0.207 3,37E-02 28949 28949 71095 71095 6.37E-07 2,46E-05 9.81E-04 39990 39990 73453 73453 20 0.443 3.49E-02 32615 75285 72828 75285 6,40E-07 1.14E-02 25929 6814 66202 8358 30 0.658 2.16E-02 28764 51193 65184 51193 9.60E-07 8.49E-O3 20527 7711 59933 991O 40 0.801 1.32E-02 2401 9 461 36 60944 461 36 9,50E-07 7.06E-03 18549 5926 57637 6897 50 0.866 1.32E-02 21225 61 51 7 59490 61 51 7 9.50E-07 5.1 9E-O3 17861 5550 56794 6310 60 0.897 1.1 1E-O2 19904 45052 55206 45052 9.7OE-07 4.37E-03 17573 5294 56442 5924 90 0,932 5.60E-O3 17492 39056 49936 39056 8,OOE-07 2,20E-03 17232 5767 55961 6645 120 0,954 1.54E-03 17005 103523 50623 103523 7,80E-07 9,33E-04 17020 7097 55550 8842

Appendix A Partide Size (pm)

Particfe Size (pm)

Figure B.1: (a) Particle size distribution @ 200rpm. @) Particle size distribution @ 6OOrpm.

APPENDIX B Particle Size (pm)

3-01 0.1 1 10 100 1000 Particle Size (pm)

Figure B.2: (a) Particle size distribution when the sample \vas injected dropwise. (b) Particle size distribution when sarnple was added in a smooth fashion. Partiels Size Okbibution . . . .

Paeicle Size (~m)

Particle Size (pm)

Figure B.3: (a) Particle size distribution @ t=SO min. @) Particle size distribution @ t=60 min. (c) Particle size distribution @ t=90 min.

APPENDIX B Particie Size (ml

Figure B.3: (d) Particle size distribution @ t=120 min,

APPENDIX B Refereaces

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