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

Copyright O Tricia Witty, 2001

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Abstract

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 b e d out 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 d s o 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 M i n g Time 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 colu m... ........................... ..25

Table 4.1: A surnmary of the distribution characteristic for systems ...................................................... with varying levels of surfactant concentration.. -3 1

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.. 3 7

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 area s 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

m e r constant

monomer droplet diameter

polymer particle diameter

diaision coefficient ( d d s )

propagation rate coefficient (dni3/mol s)

tennination rate coefficient (d~n~/rnol s)

transfer rate coefficient to an added m e r agent (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 d l

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 d i a b l e 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 t h e

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 o f 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) kWVA is 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). If the CTA as appreciably soluble in the aqueous phase, desorption of the CTA raciical

can reduce the average number o f 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 NA is 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 a s 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, 4 x 1 0 ~ 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 lnterval II

-b lnterval III - 0.01 0

- 0.008 . - Fractional Conversion

Rate , - 0.006

O 50 100 200 Tirne (min)

Figure 2.1: The h c t i o n a l conversion and polymerization displayed as a function of time for a typical emulsion polyme~ization system. (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 t h e 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

l e s 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

dif is ion 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 o f 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 c o n f m 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 dif ision 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, d f i s i o n 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 ~ ~ O U S high 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 N d 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 \as obtained 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 t ha t 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 t h e earlier 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 a n d molecular weight averages, such as the number

average molecular weight Mn and 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 M W contains 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 a 1 the

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<uM is the rate coefncient for traosfer to monomer (dm3/mols), kW.* is

the rate- coefficient for transfer to a chain transfer agent (drn3/mols), p is the pseudofirst-order

entry rate coefficient, C, is the concentration of monomer in the polymer particles (rno~drn~), [A]

is the concentration of c h i n transfcr agent (rnoI/drn3), kp is the propagation rate

coe~cient(dm~lmols). M is the molecular weight of the polyrner , Mo is the molecular weight of

the monomer (gmol), kt is the average chain-length-dependent termination rate coefficient

(dm3/mols), NA is 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 r a c h 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 dif is ion 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

washed and distilled before use used as received used as received used as received used as received used as received filtered before use used as received used as received used as received used as received used as received used as received

Styrene 1dodecanethioI Sodium dodecyl sulfàte Potassium persuifate Sodium bicarbonate Sodium hydroxide Te trahydroft ran Hydroqu inone Ethylene glycol Calcium chloride Methanol Nitrogen Helium

Aldrich Aldrich Sigma Fisher Scientific Fisher Scientific Aldrich Aicirich Fisher Scientific Aldrich Fisher Scientific Caledon P raxair P raxair

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/L7 5.05gL (1.73 x

10-~ m o n , 3.7 1 x l~-~rnol/L., and 1.75 x 10-*mot/L respectively). These d u e s were selected

because they created systems below, near and above the critical micelle concentration (CMC =

3.9 x 1 0 " ~ and 8 x LO-~M at 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 c a r y 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. M e r 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. M e r 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 Chrornatograp hy

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 ) ' ~ ( e t h y Z e n e 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 component7s peak 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 g l a s wool, \vas placed

in the injection port of the apparatus to prevent any undissolved polymer from e n t e ~ g the

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 Ho ldTie 1

Initial Column Temp. 45°C 2 minutes Final C o l u m Temp. 250°C 2 minutes

R a m ~ 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 ( S N ) , 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 2 p pore 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

s c a t t e ~ g patterns of light as t h e 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. M e n the 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, or just 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 carrïed out using three different concentrations of SDS,

O.5&, 1.07g/L and 5 . 0 5 g L These values correspond to molar concentrations of 1.75 x IO"M,

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

3.9 x 1 O-~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 a t a value of 1 150 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 t h e s

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 t h e distribution characteristic for systems with varying Ieveis of

Peak 2 to CMC

surfactant concentration. Mean o f Peak 1 Pm

65

63

37

388

BimodaI Distribution In Region B

Yes

Yes

No

Below 1

Mean of Peak 2

Pm

200

N/A

N/A

450

N/A

Mean of Peak 1 Pm

5 3

74

55

Surfactant Level

Low 0.5ga4 Middle 1 . 0 7 ~ K Higb S.OSg/L

Below

Above

Birnodd Distribution In Region A

Yes

No

No

Table 4.1 shows that to obtain an ernulsion with a unimodal monomer droplet size the

surfàctant concentration must be above the CMC value. I f i t 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 a t rpm settings of 200,400,500, and 600 rprn. Table 4.2 surnrnarizes these results

for a system containing 5.05 g S D S L When the samples were analyzed the Malvern agitation

speed was set a t 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

The data indicates that ifthe agitation speed of the reactor is not sufficiently high a

agitation.

unifonn mixture of monomer droplets will not be created. Therefore it was concluded that the

Mean of Peak2

prn 675

433

N/A

N/A

Mean of Peak 1

pm 102

53

47

54

Mean of Peak2 pm 400

3 83

NIA

NIA

Reactor Rpm

200

400

500

600

Mean of Peak 1

pm 56

54

43

56

Bimodal Region 3

Yes

Yes

No

No

BirnodaI Region 1

Yes

Yes

No

No

Mean of Peak2 pm 367

3 58

N/A

N/A

BimodaI Region 2

Yes

Yes

No

No

Mean of Peak 1

prn 56

50

46

52

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 c m

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 s u e distribution. A system contaking 5,OSg S D S L 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

500

Based on the results it Table 4.3 it can be concluded that the rate of shear in the Malvem

2000

relative to the rate of shear in the reactor wïll not alter the results, since bimodal monomer droplet

No

distributions were not detected. The mean particle size does vary slightly fiom 38-43 pm over

No

the range of rpm values investigated. The mean partide size is constant at 4 3 p fiom 1000-

pm 40

1SOOrpm. For a reactor rpm setting of 500, a Malvem rpm setting of 1438 will ensure that the

Exceeded in the Malvern No

3 8

maximum rate of shear remains constant. Since this vaIue lies between 1000-1500 rpm al1

Yes

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 S D S L

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.

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

Region 1

Region 2

Rcgion 3 No

Standard Deviation

4.4 1

3 -70

Bimodal Distribution

No

No

Samplc Mean p u 53

4 3

45 3.43

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 Number -1

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. D u ~ g the 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 t h e h m e .

4.1.5 Effect of the Sample Injection Method

D u ~ g the course of the sample analysis an important trend was noted. In some

instances it kvas noted that a very smaU arnount of large particles (= 2 0 0 ~ ) 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 a t 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 s h c e basis. 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 s c a t t e ~ g patterns 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 ba i s 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 ~proceeds the 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 h a s been reached al1 o f 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 t b e poIymerization proceeds and

the monomer dropIet size decreases and the light scattered by t h e 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 r u n 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 1 O 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)

~irfide She 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% f i e r 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 concent rations 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 ~ n s carried 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, a t 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 dif is ion 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 f ic t ion 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 Mn and 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 - 2 O

- O 0 . 8 - C

* g 0 - 7 - g 0 . 6 -

E * *

0 0 . 5 - - 0 - 4 - O

O 0.3 - 4

- 0 . 2 - O 0-1 - *

O r 9

O 2 0 4 0 6 0 8 0 1 0 0 1 2 0

R e a c t i o n T i m e (m i n )

o l w t % CTA m 2 w t % CTA a 3 w t % CTA

O 2 0 40 6 0 8 0 1 O0 1 2 0

R e a c t i o n T i m e (rn i n )

e 2 w t % C T A m 3 w t % CTA

R e a c t i o n T i m e (m i n )

e 2 w t % CTA m 3 w t % CTA

(cl Figure 5.1: .Conversion vs. T h e (a) Run conraining 9.6xCMC: 4.0g KPS (b) Run containing 4SxCMC: 2.0g KPS (c) Run containhg 9.6xCMC: 2.0g KPS

R e a c t i o n T i m e (rn i n )

-3 w t % C T A mm2 wtOh C T A al wt% C T A

Figure 5.1: Conversiom us. Time (d) Run containhg 4.5xCMC: 4.0g KPS

F r a c t i o n a l C o n v e r s i o n

4 6 . 6 5 9 S D S , 4 .0g K P S ~6.659 S O S , 2-09 K P S

O 0.2 0.4 0.6 0 -8

F r a c t i o n a l Convers ion

1113.09 S D S , 2.0g K P S m3,Og S D S , 4.0g K P S

F r a c t i o n a l C o n v e r s i o n

a6.659 S D S , 4-09 K P S ~ 6 , 6 5 9 S D S , 2.09 K P S

(cl Figure 5.2: CTA consumption. (a) Runs containing 3w1% thioI@) R w containhg 3wvt% thiol (c) Runs containing 2\vt% thiol

F r a c t i o n a l Convers ion

e 4 . 5 x C M C . 2-09 K P S -4.SxCMC, 4.09 K P S

O 0.2 0 -4 0.6 0.8 1

F r a c t i o n a l C o n v e r s i o n

-6.659 S D S , 4-09 K P S m3.0g S D S , 4.09 K P S

Figure 5.2: C ï A Consumption (d) Runs containing 2wt% thiol (e) Runs containing lwt% thiol

46.659 S D S , 4-09 K P S ~6.659 S D S , 2.09 K P S

40000

35000 - 30000 - 25000 - ; 20000 -

15000 - 10000 - 5000 -

O ,

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

F r a c t i o n a l C o n v e r s i o n

A * * A *

A A

A * A** A

m3-0g S D S , 2-09 K P S 03-09 S D S . 4.09 K P S

O 0 -2 0 -4 0.6 0 -8 1

F r a c t i o n a l C o n v e r s i o n

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

F r a c t i o n a l C o n v e r s i o n

e 3 . 0 g S D S , 4-09 K P S ~6.659 S D S , 2-0g K P S

(cl Figure 5.3: Number Average Molecular Weight (a) Runs containing 3wt% (Iuol (b) Runs containhg 3wt% tliiol (c) Runs containing 2wt%thiol

F r a c t l o n a I C o n v e r s i o n

m3.09 S D S , 2.0g K P S e 3 . 0 9 S D S , 4.09 K P S

0 - 4 0 -6 0.8 -

F r a c t i o n a l C o n ve rs ion

e 6 . 6 5 9 S D S , 4 - 0 9 K P S m3.09 S D S , 4 -09 K P S

O - 4 0.6 0 - 8

F r a c t i o n a l C o n v e r s i o n

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

F r a c t i o n a l C o n v e r s i o n

a 6 . 6 5 g S D S . 4 . 0 9 K P S a6.65g S O S , 2-09 K P S

O 0.2 O. 4 0.6 0 - 8 1

F r a c t i o n a I Conversion

~ 3 . 0 9 SDS, 2 . 0 g K P S 03.0g S D S , 4-09 KPS

e 6 . 6 5 g S D S , 4-09 K P S a6.65g S D S , 2.09 K P S

120000

100000 -

80000 -

60000 -

40000 -

20000 -

O

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

54

* * . A A A *

A * A -

A AA

-- O 0.2 0 .4 0.6 O . 8 1

F r a c t i o n a l C o n v e r s i o n

F r a c t i o n a l C o n v e r s i o n

03-09 S D S , 2 -09 K P S m 3 - 0 g S D S , 4 - 0 9 K P S

0 -2 0 .4 0 -6 0 -8

F r a c t i o n a l C o n v e r s i o n

e 6 . 6 5 g S D S , 4 -09 K P S rp3,Og S D S , 4 .09 K P S

F r a c t i o n a l C o n v e r s i o n

( 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 f i c t i o n 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 s h o w 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 d f i s i o n 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 Value Source ---*---___-__.._. _ _ _ _ - . CI_I---.-- -_-..- - -----_____-------- -- 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 1 0 ~ 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 par t i~ 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 dficul ty detecting the

presence of small polymer particles when Iarger monomer droplets are present in the system. A s

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 a t a

value of 0.5 for all calculations. Rp was detennined for each run fkom the slope of the linear

region of the conversion vs, t h e plot, 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) Np Predicted d, Measured d, Measured Np Predicted 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) ~ a t e / d m ~ 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 dif is ion 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 b y 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 Cio or 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 MW values 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 m7 tenn 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 d 7 s exmpoIated 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 1 0-'-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 LM Cp 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 rnodeIYs ability 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 MW values 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-

Mwim values 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 modelys ability

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 h m the

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 b a i s al1 further predictions \.vil1 be inaccurate (overestimated) because this data point

is included in the caiculations performed a t each subsequent sarnpling point, as d l be 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 MW plot 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 es thate 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 MW predictions to exceed the calculated GPC values. When

the corresponding instantaneous MW plot 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 M W ,,

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 d l is 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-* r n o ~ d m ~ SDS. -

Conversion % CTA Should Droplets Are Droplets Droplet Size Consumed be Theoretidly Observed?

P resent? -----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 O bserved? (Po

Present? -.---------.--.- ---- - ------ -a-----p--- ---..-- 0,079 20 -47 Yes Yes 2-48 0-1 82 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 U S , 1.75 s 1 0 - ~ movdrn3 SDS.

Conversion % CTA Should Dropiets Are Droplets Droplet Size Consumed be TheoreticaIIy O bserved? (P)

Present? -.-----.---.--.--------------- 0-1 22 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 r u s , (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 MW predictions 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

d u ~ g the early stages of the reaction when the concentration of CTA in the polymer p d c l e s is

changing rapidly. D u ~ g thïs 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 o f 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 dif is ion 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 MW predictions 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 M W 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 quan t e 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 p a t e r 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 MW estirnates 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 modeIYs ability 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 a l . 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 1 while

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 d u ~ g Interval 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

C o n v e r s i o n I e Diffusion M o d e l Nomura 's m r Diffusion M ode1 A d j u s t e d m A G P 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

Convers ion 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 G P C

(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

Convers ion m D i f f u s i o n M o d e l Nomura's m m D i f f u s i o n M o d e l A d j u s t e d rn A G P C

C o n v e r s i o n + Diffusion Mode l Nomura's m m Diffusion M ode1 Adjusted m A G P C

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

--

C o n v e r s i o n e Diffusion M o d e l N o m urams rn m Diffusion M o d e l Adjusted m A G P C

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

C o n v e r s i o n

Individually Adjusted rn e Common Adjusted rn A G P C D a t a

Co n v e rsio n

O Individually Adjusted rn rn Corn m o n Adjus ted m A G P C D a t a

C o n v e r s i o n

e lndividually Adjusted rn rn Common Adjusted rn A G P C 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

Convers ion

e Individually A d j u s t e d m rn Common A d j u s t e d m A G P C D a t a

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

Co n v e rsio n

e P redicted M W if C T A is at Equilibrium i GP C Data

0.40 0 . 6 0 Co n ve rsio n

* Predicted M W if CTAis a t Equi l ibr ium G P C 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: 3-08 SDS: 4.0g KPS

Predicted ar GPC Data

Conversion

C o n v e r s i o n 6 P r e d i c t e d m G P C D a t a

O - 2 0 O - 4 0 O - 6 0 C o n v e r s i o n

e P r e d i c t e d m G P C D a t a

(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

C o n ve rsio n

e p r e d i c t e d m G P C Data

C o n v e r s i o n

e p r e d i c t e d m G P C D a t a

0 .O O 0 -20 0-40 0.60 0.80 1 .O0 C o n v e r s i o n

e K i n e t i c M o d e 1 m G P C D a t a - - -

(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

* P r e d i c t e d m G P C D a t a

2500000

- 2000000 - VI E O 1 s o o o o o - 0 E 1000000 - 2 I

500000 -

O

C o n v e r s i o n

i

* * * * * *

a rn 9 R R - rn gl I L 1 I 1

e P r e d c i t e d ppiG P C D a t a

0.00 0 -2 0 0 - 4 0 0.60 0.80 1 .O0

C o n v e r s i o n

Conversion

+ Kinetic Mode l 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

C o n v e r s i o n e K i n e t i c M ode1 G P C Data

Figure 6.4: MW- cornparison. 0) Run contaùiing 3wt% thiol: 3.0g SDS: 4-0g KPS

e P redicted MI G P C D a t a

0.20 0.40 0.60 0.80

Conversion

* Kinet ic Model m GPC Data

P

3000000

2500000 - V)

8 2000000 - C - m 0 1500000 - - . = 1000000 - 2

500000 -

C o n v e r s i o n

4 *

O

e P r e d i c t e d m G P C D a t a

O

Figure 6-5: MW kt 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

m 1 a I 1 I T

0 .O 0 0 -20 O -40 0-60 0-80 1 .O0

C o n v e r s i o n

C o n v e r s i o n

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

C o n v e r s i o n

e P redicted m G P C Data

0.00 0.20 0.40 O -6 0 0 - 8 O 1-00

C o n v e r s i o n

6 Kinetic M ode1 m G P C D a t a

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

C o n v e r s i o n

* P r e d i c t e d i G P C D a t a

0.00 0.20 0.40 0.60 0.80 1 .O0

C o n v e r s i o n

e P r e d i c t e d ~ I G P C D a t a

0.00 0.20 O -4 O 0 -6 O 0.80 1 .O0 Conversion

h

150000 - O = m P_ 100000 - -

C - & soooo -

O

e Kinetic M ode1 m GP C Data

*

* PP

m m I m I I

rn e

e e * * T I l 1

(il Figure 6.5: MW htcornparison (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 i lndividually 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: MW k,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 i lndividually Adjusted rn A GPC Data

Figure 6.6: MW kt cornparison (g) Run containing 3wt% thiol: 3.0g SDS: 2.0g KPS

- K i n e t i c M o d e 1 -

-

- - G P C D a t a

-

- K i n e t i c M o d e 1

-

- -

G P C D a t a -

-

0 . 0 0 E + 0 0 +

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

K i n e t i c M o d e 1 - G P C D a t a

-

-

-

- G P C D a t a

- -

K i n e t i c M o d e 1 - - -

-

G P C D a t a -

-

Kinet ic M o d e 1 -

-

-

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

Kinet ic M ode1

G P C D a t a

-

G P C D a

K i n e t i c M ode1

1 .4OE+OO

1 . 2 0 E + 0 0 - G P C D a t a

1 . 0 0 E + 0 0 - $ 8 . 0 0 E - O 1 - 5 O - 6 . 0 0 E - 0 1 - K i n e t i c M o d e 1 rY

4 . 0 0 E - 0 1 -

2.OOE-O1 -

0 . 0 0 E + 0 0 , 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

Kinet ic M o d e 1 - G P C D a t a -

- -

-

K i n e t i c M o d e 1 - G P C D a t -

-

-

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 -0g SDS : 4.0g KPS at increasing conversion intervals. (g)x=0.796 (h)x=0.794

1.4OE+OO

1 . 2 0 € + 0 0 - G P C D a t a

1 . 0 0 € + 0 0 Kinetic M o d e l ' 8-OOE-O1 A - 6.OOE-01 - z

4.OOE-O1 -

2.00E-01 -

0 . 0 0 E + 0 0 0-00 1-00 2-0 0 3.00 4 -0 O 5.00 6 .00 7 .O0

l o g ( M W 1

G P C D a t a

Kine t i c M o d e 1

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=0.2 13 (c)x=O.33 9

G P C D a t a .-> -

- Kinet ic 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

G P C D a t a 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=0.74 1 (h)x=O.83 2

C o n v e r s i o n

4 F i I t e r e d D a t a A G P C D a t a m Unf i l t e red D a t a

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 e U s i n g Relative Peak Areas m G P C Data ~ F o l l o w i n g Equilibrium Swelling

0.20 O, 4 0

Conversion

e Using Relative P e a k Areas m GPC Data r Following Equilibrium Swelling

Figure 6.12: MW compatison 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 P e a k A r e a s ps GPC Data A FolIowing Equilibrium Swelling

O -40 0 -6 O

Convers ion

e U s i n g Relative P e a k A r e a s E G P C 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

G P C Da ta 7

Kinetic M o d e l -. /IC\

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

- Kinet ic M o d e 1 G P C D a t a

-

-

- -

- 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) ~0.08 1 (b) x-O. 167 (c) ~ 0 . 2 9 8

Kinet ic M o d e 1 - G P C D a t a

-

-

- -

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 . 4 9 7 (f) ~ 0 . 5 4 2

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 . 6 5 5

Kinet ic M ode1

G P C D a t a

- 8 I

G P C D a t a

K i n e t i c M o d e 1

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

Kinet ic M ode1

G P C D a t a

-

G P C D a t a . f i Kinetiç M o d e l

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 . 4 8 3 (f) ~ 0 . 5 5 6

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 k v a s 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-DDT partition 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 o f h tu re 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 \ d l be df icu l t 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 m a s u r e 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 M W C U ~ 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 1,91 E-04 1,73E-06 151 7531 151 7531 2343025 2343025 126870 7.49E-07 2.1 3E-05 2.47E-05 1 149450 91 2362 201 7403 1668545 1 16479 104432 9.10E-07 2.22E-03 1023603 19981 201 3088 33220.72 102482 65774 9.60E-07 1,58E-03 955891 19783 201 0323 32837,22 90682 36644 9,70E-07 3,65E-04 91 881 7 44948 2006487 83639.66 91 867 123709 9.9OE-O7 2.44E-04 9071 92 54374 2004953 102952.8 96526 126389 6.4OE-07 8.34E-05 875443 77975 1998629 150647,6 86389 64053 7.70E-07 0,OOEtOO 102901 3 1601 340 21 35990 241 5853

Jb) Run containing 1 wt% CTA, 3 . 0 ~ SDS, 4.0g KPS GPC GPC Particle Droplet Predicted Predicted

Time (min)

10 20 30 40 50 60 90 120

Conversion 1DDT.J mol/dm3

0.081 8.83E-03 0.167 3.93E-03 0.298 3,16E-03 0.440 4.87E-03 0.497 3.03E-03 0.542 2.84E-03 0.655 7,16E-04 0.734 0.00E+00

M W n Diameter Diameter [DDTJ (dm) (dm) molldm3

1 18876 7.75E-07 2.94E-05 6.36E-04 186887 7.98E-07 1.91 E-05 5.49E-04 191 902 9.40E-07 1,95E-05 1.63E-04 1591 72 9.50E-07 2.00E-03 123460 8.90E-07 1 .19E-03 133308 8.40E-07 1 .12E-O3 43683 8.40E-07 2,82E-04 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 (min)

10 20 30 40 50 60 90 120

Conversion [DDTJ molldm3

0.018 2,58E-02 0,038 2.17E-02 O, 1 14 1.82E-02 0.234 1.19E-02 0.349 1.1 7E-02 0.442 7.26E-03 0.676 9.05E-03 0,809 9.20E-04

MW,,, Diameter Diameter [DDT,,]

(dm) (dm) molldm3 17441 2,43E-05 5,61 E-07 3,12E-03 19625 1.56E-05 5.65E-07 4.29E-03 701 94 3,46E-05 5,80E-07 9,97E-04 87560 1.88E-05 6.03E-07 1 ,Il E-03 83694 2.08E-05 6.30E-07 2.86E-04

6.30E-07 2,85E-03 65984 7.70E-07 3,56E-03

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 M n n Mwcum Mwlnst Diameter Diameter [DDTp] Mn,", Mn~nst Mwcum Mwinst (min) mol/dm3 (dm) (dm) molldm3

I O 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-02 431 79 97728 94501 97728 7.05E-07 2,42E-05 4.68E-04 253832 79420 61 891 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 1 O1 49 61 II 42 14353 50 0.663 9.34E-03 34670 84467 82514 84467 9.50E-07 3,68E-03 1 92623 12870 61 1 142 1 9501 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,] M n M n 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 1 05865 105907 1 05865 6.56E-07 5.94E-03 109862 9789 315665 13684 30 0.700 1.33E-02 41 155 101 457 93392 101 457 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 901 4 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 M l MW,,, NIwlnst Diameter Diameter [DDTp] Mn,., Mnlnst Mwcum MWlnd (min ) molldm3 (dm) (dm) molldm3

I O 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 1 131 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 M n 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 1681 89 11 3754 1681 89 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 351 964 1856980 69321 8 50 0.436 1 .25E-02 36880 107202 94765 107202 9.50E-07 4.92E-03 730999 Il 070 1855361 16081 60 0.523 1.43E-02 38806 1 06767 861 75 1 06767 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 181 15 1 20 0.822 6.07E-03 31205 63628 71681 63628 7,90E-07 3.67E-03 574673 7545 1847752 961 9

(h) Run containing 3 wt% CTA, 6,659 SDS, 2-09 KPS GPC GPC Particle Droplet Predicted Predicted

Time (min) -

10 20 30 40 5 0 60 90

Conversion 1

M n Diameter Diameter {DDTJ (dm) (dm) molldm3

58470 6.96E-O7 2.22E-05 1.1 7E-03 42583 7.41 E-07 2.02E-05 2.46E-04 25431 6.70E-07 1.1 5E-02 11 01 3 9.60E-07 1,07E-02 16099 9.50E-07 9.63E-03 46437 8.7OE-07 7.01 E-03 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 (min)

10 20 30 40 5 0 60 90 120

Conversiorr [Dili] molldm3

0.1 22 3.21 E-02 0,213 2.95E-02 0.339 2.1 OE-02 0.433 2.49E-02 0.541 2.34E-02 0,609 1.49E-02 0.741 1.26E-O2 0.832 1.20E-03

M l Diameter Diameter [DDT J

(dm) (dm) molldm3 62974 7,8l E-07 1,70E-05 2.21 E-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 M n M n M,,,, (min) molldm3 (dm) (dm) molldm3

I O 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 991 O 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 21 225 61 51 7 59490 61 51 7 9.50E-07 5.1 9E-O3 17861 5550 56794 631 0 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

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