emulsion copolymerization: kinetics model and reactor performance

Emulsion Copolymerization : Kinetics Model

and Reactor Performance* GEORGE J. QUARDERER

Applied Organics & Functional Polymers Research Dow Chemical U.S.A.

Midland, Michigan 48640

and

SANJEEV S. KATTI**

Engineering Sciences Dow Chemical U.S.A.

B-1226 Texas Operations Freeport, Texas 77541

The Dow process for producing perfluorinated ionomeric membranes includes several emulsion copolymerizations involving gaseous tetrafluoroethylene and a second liquid phase monomer. The choice of the organic phase monomer depends on the desired product. The emulsion copolymerization reactor model was developed by extending the Smith-Ewart-Gardon theory for emulsion polymerization processes. Population balance techniques and Flory-Huggins solution theory were applied. The resulting coupled partial differential equations were solved using the method of characteristics. The reactor model, with minimal adjustable parame ters, predicts most polymerization results, including molecular weight, reaction rates in the three process stages, latex particle size, polymer composition, and the composition drift as a function of reaction time. The analysis and reactor model is used in the manufacturing process to set process conditions to obtain the desired properties in the polymer product.

INTRODUCTION The Dow Process for producing bilayer perfluori-

mulsion polymerization is an industrial process E used to manufacture a variety of polymeric mate- rials such as elastomers, coatings, adhesives, and colloids (generally called latexes). The process is used to produce large molecular weight polymers at high rates (owing to the high polymer content) in a low viscosity medium (enhancing mixing, heat and mass transfer).

The main ingredients of an emulsion polymerization system include monomer, dispersant, emulsifier, and initiator. Water is commonly used as the dispersant. An organic (water-insoluble) monomer can be dispersed in water by means of an oil-in-water emulsifier and polymerized with a water-soluble initiator. The latex product is a colloidal dispersion of polymer particles that can often be used without separation.

‘Presented as a paper at the A.1.Ch.E:. Sprina National Mceling. Houston. April 1991. **To whom correspondence should be addressed.

nated ionomeric membranes includes several emulsion copolymerizations involving gaseous tetraflue roethylene (TFE) and a second liquid phase monomer. The choice of monomer depends on the desired product. All the components except TFE are added at the beginning of the reaction. TFE is fed continuously to maintain constant pressure.

QUALITATIVE DESCRIPTION

A single charge emulsion polymerization typically comprises three reaction intervals. Initially the reaction charge consists of a continuous water phase and a dispersed phase of monomer droplets. The water phase usually contains soap, a pH buffering system, and a free radical initiator. Most of the soap is present in micelles, each of which contains approximately 50 soap molecules.

During the first reaction interval, free radicals, which are generated in the water phase, oligomerize a few monomer molecules in the water phase and then

564 POLYMER €NG/NE€R/NG AND SCIENCE, MID-MAY 1993, Vol. 33, No. 9

Emulsion Copolymerization Model and Performance

either enter existing latex particles or enter micelles, thereby generating new latex particles. Equilibrium exists between the monomer droplets and the latex Darticles, which are monomer-swollen. The probabik ity that an oligomer enters an existing latex particle or a micelle is determined by the fraction of the dispersed phase surface area represented by each entity. The monomer droplets in the initial emulsion are considerably larger than Lhe polymer particles produced. The reaction does not involve the polymerization of monomer droplets (as is the case with suspension polymerization).

As the latex particles grow, their surfaces remain saturated with soap. To maintain this condition, ex- cess micelles disappear throughout the first reaction Interval. During Interval I, there is at most one growing free-radical in each latex particle. The end of Interval I coincides with the complete disappearance of micelles. All latex particles are produced during Interval I.

During Interval 11, the reaction mixture comprises monomer-swollen latex particles, monomer droplets, and an aqueous phase. However, there is no longer any micellar soap. Thus, no new particles are initiated during Interval 11. As in Interval I, free radicals are initiated and oligomerize in the water phase be- fore entering a latex particle. Each latex particle contains either zero or one growing free radical. The end of Interval I1 coincides with the complete disappearance of the monomer droplet phase.

During Interval 111, there is no free monomer droplet phase. Reaction occumng during this interval results in deswelling of the existing latex particles. Because the mobility of a free radical within a latex particle is strongly dependent upon the degree to which the particle is swollen, the assumption, stated earlier, that each particle contains either zero or one growing free radical can break down during Interval 111.

For an excellent description of the basic theory and mechanism of emulsion polymerization, the reader is referred to a series of papers by Gardon (1-7). A comprehensive simulation model of batch emulsion polymerization has been developed by Min and Ray (8).

High volume products are often produced by continuous emulsion polymerization. Continuous emulsion polymerization processes have some unique fea- tures, such as sustained oscillations (limit cycles) in conversion, particle number, and free emulsifier concentration under isothermal conditions (9- 1 1). Multi- ple steady states have also been observed (12). Reac- tor modeling, dynamics, and control aspects of continuous emulsion polymerization are discussed else- where (13-15). The article (16) by Poehlein and Schork gives a general overview of emulsion polymerization.

ASSUMPTIONS

The following assumptions are used in the analysis:

1. Isothermal reaction.

POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, Vol. 33, NO. 9

2. No mass transfer limitations. 3. Only a small fraction of the initiator decomposes

during the entire polymerization process and thus the rate of initiation is constant throughout the polymerization.

4. Each latex particle contains either 0 or 1 growing free radical, i.e., if there are two free radicals growing within a particle, they rapidly combine and quench each other.

5. Secondaly monomer reactions are neglected.

ANALYSIS AND MODEL

Initiation Rate

The rate of free radical formation is given by:

R, = 2 NA kdC,

The chain transfer agent, in addition to its role as such, also competes with monomers for the sulfate radical anion in the water phase. The net effect of this competition is a reduction in the effective initiation rate:

Ro R =

(I+-)

Soap Surface Area

lize the emulsion is given by: The surface area of soap that is available to stabi-

Reaction Stoichiometry

The definitions of an, p ) and an, p ) given in the nomenclature are repeated here for clarity: n, p ) = number of non-growing (dead) particles with n reacted units of monomer 1 and p polymer chains at time t per volume of water; and an, p ) = number of growing particles with n reacted units of monomer 1 and p polymer chains at time t per volume of water.

In each case, n is the number of reacted monomer 1 mers in the particle. The number of reacted monomer 2 mers is obtained from the relative rate of reactions of monomer 1 and monomer 2. This relative rate is given by:

moles of monomer 2 reacted ' = moles of monomer 1 reacted

Literature data suggest that the monomers of inter- est undergo ideal copolymerizations, that is, the reactivity ratios are related by:

r 1 x r 2 = l

For this case

565

George J. Quarderer a n d Sanjeev S. Katti

The reaction stoichiometry, for particles containing n reacted monomer 1 units and p polymer chains is abbreviated as follows:

R + D( n, p - 1) --+ G( n, p) R + G( n, p ) -+ D( n, p )

kl M , + G( n, p ) - G ( n + 1, p )

kT A + G(n, p ) - G(n, p + 1)

Adding a chain transfer agent (denoted by A in the last equation) to the polymerization charge reduces the melt viscosity and the molecular weight of the resultant polymer.

Surface Area Calculations

The probability that an oligomer enters an existing latex particle or a micelle is determined by the fraction of the dispersed phase surface area represented by each entity.

The surface area associated with a monomer-swollen particle containing n reacted monomer 1 units, i.e., a an, p) or an, p) particle, is:

The total dispersed phase surface area during In- terval I is just the surface area of soap that is available to stabilize the emulsion:

During Interval 11, S, is equal to the sum of the surface areas of all the individual particles:

2 z

x n2/3(D( n, p ) + G( n. p)} p = l n = O

In actuality n only takes on discrete values, i.e., n = 1,2,3.. . However, since n ranges from zero to approximately 100.000, there is little error intro- duced by treating it as a continuous variable.

x 5 ( n z / 3 { D ( n, p ) + G( n, p)} dn p = 1

Material Balance Equations

are given by: The accumulations of D( n, p) and G( n, p) particles

+ kTy c.4( G( n* P - ) - G( n* P))

Here y denotes the partition coefficient for the chain transfer agent A between the monomer phase and the water phase.

In the preceding formula, the concentration of monomer 1 in the swollen latex particles is given by the ratio 41/Vl. Since n is treated as a continuous variable, the equation can be rewritten as:

Equations 1 and 2 describe the changing population of latex particles throughout the polymerization. The parameter grouping RS,/ST, which comprises the initiation rate, the total dispersed phase surface area, and the surface area of a particle containing n reacted monomer 1 units, is the average number of free radicals that enter an n-particle per second.

Three boundary conditions are needed for the two material balance equations. Two of these are o b tained directly:

D ( n , p ) = O at t = O ( O s n s = , O < p < = ) G ( n , p ) = O at t = O ( O s n r = , O j p < = )

The third boundary condition describes the initiation of new latex particles by the interaction of water phase free radicals with soap micelles and the subse- quent growth of these particles. The reaction stoichiometry for these steps is abbreviated as:

R --+ G(O.1) (initiation) M + G ( 0 , l ) -+ G( 1, l)(growth)

The amount of micellar soap surface area that is available to catch radicals is given by Ssf, where:

f, = 1 - s,/ss

In terms off, the material balance for G O , 1) is

This equation is the required third boundary condition. I t can be used in its present form. Since the average time for a growing particle to react with a monomer unit is much smaller than the total reaction time (approx. 10,000 s), it is more convenient to use the Bodenstein stationary-state hypothesis.

566 POLYMER ENGINEERINGAND SCIENCE, MID-MAY 1993, YO/. 33, NO. 9


Hence: appropriate set of reference quantities is:

Rf*Vl a t 4lkl

= 0 and G(O.1) = - aG(0.1)

In addition, it is not possible to have latex particles with more than one polymer chain but no reacted monomer units; thus:

G(0, i) = 0 for i = 2,3,4, . .

Transitions Between Intervals

As described earlier, the transition from Interval I to Interval I1 occurs when the surface area of the particles equals the surface area of the soap that is available to stabilize the emulsion, i.e.,

s, = s,

For calculating the transition between Interval I1 and Interval 111, it is assumed that monomer 1 is charged batchwise at the beginning of the reaction and that monomer 2 is added as a gas throughout the reaction. At the transition point, the amount of monomer 1 reacted plus the amount of monomer 1 absorbed into the latex particles equals the amount of monomer 1 charged:

d,[l- 41 - 421 Wdl

N A G m = - [ vl +

x ’Ex knmaXn(G( n, p ) + D( n, p ) } dn p = 1

The two terms within the first set of brackets repre- sent the amount of monomer 1 reacted and the amount of monomer 1 absorbed, respectively.

Dedimensionalization of the Model

To generalize the results, it is convenient to dedi- mensionalize the model equations by introducing reference quantities such as Go, Do, to, and %. The dimensionless variables are given by:

,

The reference quantities are chosen to simplify the problem and to remove dimensional parameters from the governing equations. It can be shown that an

RVI Go=Do=- kl@ 1

Calculation of the Reaction Rate

In terms of the population density of growing latex particles, an, p ) . the rate of reaction of monomer 2 (TFE) is given by:

Dedimensionalizing this equation gives

Ra x~

R a = - = /‘&(A, p ) dfi Ra, p = l 0

where the reference rate of reaction is

1 WQ [ 3 6 ~ ] ’ / ~ dw

Ra, =

Molecular Weight

culated directly from the population balances: The number average molecular weight can be cal-

Dedimensionalizing this equation gives

5 CA{G( A, p ) + D( A, p ) ) d A

p/’{G( A, p) + D( A, p ) } dA

n MN p = l M =-=

MNo p = l 0

where the reference molecular weight is given by:

567 POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, VOl. 33, NO. 9

George J. Quarderer a n d S a y e e v S. Katti

Particle Size Information The population balances can be used to calculate

average particle size and particle size distribution data as a function of reaction time either in the monomer-swollen condition or in the dry state. The approach for doing this is illustrated for the Sauter mean diameter, [D32] . The swollen diameter of an n-particle is given by:

while the unswollen diameter is given by:

D,(unswollen) = -

The Sauter mean diameter is calculated as:

and:

D32( unswollen)

Dedimensionalizing these equations gives: -,

1 , p) + D( A, p ) } d A - u32 = - -

Do i X r iz, p) + 6( A, p ) ) dfi p= 1 p J o L ‘ L .

where the reference particle size is given by:

(swollen) 6 E, s, k l 4 1

Do= [ r2RV1NA(1 - 4 , - 42)dp

or by:

Solution of the Model

The set of governing partial differential equations was solved using the method of characteristics on a

digital computer. In this method, each partial differential equation is solved along a series of characteris- tic curves or lines, which are uniquely defined by the form of the partial differential equations (17, 18).

A solution of the model gives the dimensionless population density functions G( n, p ) and n, p ) as a function of dimensionless time. Once these quantities are known, quantities like reaction rate, molecular weight, and particle size can be calculated directly.

RESULTS

Figure 1 shows dimensionless reaction rate as a function of dimensionless time. The limiting reaction rate as t becomes large is given by:

R a = 0.5173

Figure 2 shows dimensionless particle size as a function of dimensionless time with each variable being in dimensionless form. Alternatively, the surface area can be plotted vs. dimensionless time (Fig. 3). Figure 4 shows molecular weight as a function of reaction time and as a function of the dimensionless

; O ’

0 2

0.1 O i

O I ~ , , , , , , , , , , , , , , / , , , 0 2 4 6 8 10 12 14 16 18

DIMENSIONLESS TIME

Rg. 1 . Reaction rate as afunction of time.

EMULSION POLYMERIZATION FATE OF REACTION

EM U LS ION PO LY M ER I ZATI ON SAUTER U W DUMETER

2 2 , 2

I 8

16

1 4

1 2

1

0.8

0.6

01

0 2

- MODEL

- PPPROXIMATIDN 4 6

0 2 4 6 8 10 12 1 1 16 18 20

DIMENSIONLESS TIME

Fg. 2. Particle size (Sauter mean diameter) us. time.

568 POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, Vol. 33, No. 9


EM U LS I0 N POLYMER I ZATlO N SURFACE AREA OF UTEY PmncLEs

5 I

0 2 4 6 8

TlME-(2/3)

Fg. 3. Surfae area of particles us. time.

MOLECUIAR WEIG3T VS. REACTI0P.I TIME

I K :O

~

~

(1.7 -

I 1

K7 = I 1

! 1 ! --I

0 2 4

DIMENSIONLESS VME

Fg. 4. Molecular weight us. time with chain transfer coeffr cient as a parameter.

chain transfer parameter, k,. As shown for the individual curves, the limiting molecular weight as t becomes large is given by:

1 M - N-

Solubility of TFE in Monomers (Organic Phase)

In order to apply the emulsion polymerization model to the copolymerizations, the phase equilibria for the individual systems must be calculated. The proce- dure used was developed originally by Prausnitz and Shair (19), and is described in Prausnitz's book (20).

1. The calculation of the fugacity of TFE in the gas phase at reaction temperature and pressure;

2. The estimation of hypothetical liquid phase fugacity of TFE at reaction temperature and one atmo- sphere pressure using the correlation developed by Shair;

3. Correcting this estimate to reaction pressure using the Poynting correction, which accounts for the compression of the liquid phase; and

The calculations involve the following steps:

4. The use of regular solution theory and solubility parameters to estimate the activity coefficient of TFE in the monomer phase.

where:

and f$' is the standard state liquid fugacity at 1 atm for component 2 and was obtained from Fig. 8.9 of Ref. 20.

Solubility of Mixed Monomers in the Polymer

In the polymer particle phase, TFE and the organic monomer are assumed to be in equilibrium with the polymer. The relative volume fractions of the three components were calculated using the method of Flow and Schultz (21), who analyzed the thermodynamics of a ternary polymer system with two solvents. The chemical potentials for the two solvents are given by:

VZ +( x2l@l +x23@3)(@1+@3) - x 1 3 ~ @ 1 @ 3

where the x are the Flory-Huggins parameters for the indicated interactions.

These complex equations can be simplified with the following reasonable assumptions

1. xI2 = x21 = 0 (ideal solution) 2. Molar volume ratio of polymer to TFE (component

2) and organic monomer is very large, tending to infinity, i.e.,

VI/V3 = vz/v3 = 0

3. x13=x23 = x (solvents have same solubility parameter)

The resulting simplified equations are:

POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, Vol. 33, No. 9 569

George J. Quarderer and Sanjeev S. Katti

900 -

The Flory-Huggins Parameter ,y was obtained from binary solvent-polymer swelling data.

As long as there is a separate mixed monomer phase (i.e., system is in regime I and I1 described earlier), the chemical potentials of the two monomers will be constant and can be evaluated from the earlier solubility analysis. For the binary monomer phase:

POLYMER MA EOUIVALENT WEIGHT VS. TFE PRESSURE

Vl -- -In(@,) + (1 - @ I ) - -B2 P1- P(:

RT v2

t 4 Boo-

: k

E 3 7 0 0 . U

U 6 0 0 -

500 -

When these chemical potential values and the ,y parameter are substituted into the simplified Flory- Huggins equations above for a ternary polymer system with two solvents, the individual volume fractions can be calculated by trial and error.

After the transition from Interval I1 to Interval 111, there is no free monomer phase and the chemical potential of the organic monomer in the particle phase, and correspondingly its volume fraction, gradually decrease.

Copolymerization Reactivity Ratios

ization of two monomers: The Alfrey-Price equation describes the copolymer-

4 M 2 1 [M21 r2[Mzl +[M11 4 M I l [MI] [ % I + f-l[Mll -=-

The reactivity ratios rl and r2 are given by:

kl 1 k,, k12 k2 1

rl = - and r2 = -

where k , is the second order rate constant for the addition of a j type monomer to a polymer chain whose growing end is an i type monomer unit.

A copolymerization system is deemed “ideal” when two radicals show the same preference for adding one of the monomers over the other, i.e., kl , /k l2= k21/k22. Equivalently, rl = l / r2 or rl * r2 = 1. It was found to be reasonable to assume that the present systems are ideal and that r, = 7. During polymerization Intervals I and 11, the relative rates of incorpora- tion of TFE and organic monomer into the polymer are given by:

d[TFE] [TFE] r2 - -=

4 MI [ MI

Equivalent Weight

The equivalent weight is an important and measur- able characterization of the polymer. I t is defined as the weight of the polymer per functional group that is on the organic monomer. Thus the equivalent weight can be calculated from the relative reactivities and component concentrations obtained from the equilib rium calculations described earlier.

Initial Equivalent Weight The equivalent weight remains constant during In-

tervals I and 11, since the activities (or concentrations) of TFE and the organic monomer remain constant. The initial equivalent weights to be expected during Intervals I and I1 have been calculated for several sets of reaction conditions. The calculated values for the copolymerizations of TFE with monomer MA, and with monomer MB are shown in Figs. 5 and 6 as a function of reactor pressure and temperature The trends predicted by the model are in excellent agreement with measured trends. The agreement on absolute values is reasonable.

Composition Drift During Interval 111, the amount of each of the

monomers in the swollen polymer gradually d e creases. The chemical activity of TFE is determined by the reaction pressure and temperature and thus does not change during Interval 111. However, the chemical activity of organic monomer decreases with decreasing volume fraction in the polymer:

TFE PRESSURE. PSIG

Rg. 5. Initial equivalent weight as a function of reactor tern perature and pressure (copolymer MA).

POLYMER M B EOUIVALENT WEIGHT VS. TFE PRESSURE

TFE PRESSURE. PSIG

Flg. 6. Initial equivalent weight as a function of reactor tern perature and pressure (copolymer MB).

570 POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, VOl. 33, NO. 9


where the superscript “0” denotes the standard state ,hosen to be pure liquid at reaction temperature and pressure.

Since the activity of the organic monomer is decreasing while the activity of WE remains constant, the composition of the polymer produced will change. Figure 7 shows a typical predicted instantaneous and average equivalent weight drift as a function of the organic monomer conversion. The calculated drift in equivalent weight is in reasonable agreement with the limited experimental data available. It may be noted at this point that the goal is to minimize the composition drift in the polymer product.

The Possibility of Slow Termination

An assumption made at the outset of this paper is that bimolecular free radical termination is a rapid process and as a result each latex particle contains either 0 or 1 growing free radicals. If the assumption were to fail, it would do so during the latter stages of Interval 111 when the volume fractions of monomer have decreased and the Trommsdorf effect slows the rate of termination. Assuming this to be the case, the average number of free radicals in each latex particle would increase with increasing conversion and there would be corresponding increases in reaction rate and molecular weight.

The experimental data for the present systems showed no increase in reaction rate with increasing conversion and support the original assumption of 0 or 1 growing free radicals per latex particle.

APPLICATIONS OF THE MODEL A mathematical model provides a mechanism for

understanding the interrelationships that exist between dependent and controllable variables. Thus it can be used to more fully understand what has been done and why things worked out the way they did.

However, a more valuable use of a model is to provide direction for future work. A whole series of “what if’ questions can be posed and answered without exhaustive and expensive laboratory studies. Only

0.7 I I

cumu1.uvc €?UCTIONAL COWnRSlON

- In.(mt.neou.

Fig. 7. Instantaneous and average equivalent weight drii for copolymer MA.

the most promising leads are pursued experimen- tally. Thus the model has been used to answer questions like, “What should the process variables be to produce a polymer with the same equivalent weight and 40% less molecular weight? How can the equivalent weight drift be reduced?”

CONCLUSIONS

An emulsion copolymerization reactor model was developed by extending the Smith-Ewart-Gardon theory for emulsion polymerization processes. Popula- tion balance techniques and the Flory-Huggins solution theory were applied. The resulting coupled partial differential equations were solved using the method of characteristics.

The reactor model, with minimal adjustable parameters, predicts most polymerization results, including molecular weight, reaction rates in the three process stages, latex particle size, polymer composition, and the composition drift as a function of reaction time. The model also predicts the time of transition between successive reaction intervals. The analysis and reactor model is used in the manufacturing process to set process conditions to obtain the desired properties in the polymer product.

NOMENCLATURE

= Surface area covered by a single soap molecule, cm2.

= Initiator concentration in the water phase, gmol/cm3.

= Soap concentration in water phase, gmol/cm3 H,O.

= Critical micelle concentration of the soap, gmol/cm3 H 2 0 .

= Polymer density, g/cm3. =Water density, g/cm3. = Number of non-growing (dead) particles

with n reacted units of monomer 1, p polymer chains, at time t per unit volume of water.

= Dimensional reference quantity for a n , p ) , number/cm3 H,O.

= Sauter mean diameter, cm. = Equivalent weight of polymer per gram

= Fraction of water phase free radicals

= Fugacity of monomers 1 and 2, psia. = Dimensional reference quantity for

= Number of growing particles with n

monomer 1 reacted, gm/gmol.

intercepted by micelles.

a n , p ) , number/cm3 H 2 0 .

reacted units of monomer I, p polymer chains, at time t per unit volume of water.

= Second order rate constant for quenching of radical by the chain transfer agent, cm3/gmol-s.

= First order rate constant for initiator decomposition, s-

POLYMER ENGINEERING AND SCIENCE, MID-MAY 1993, VOl. 33, NO. 9 571

George J. Quarderer and Sanjeev S. Katti

k ,

kT

KT

kl

kij

= Second order rate constant for oligomerization, cm3/gmol-s.

= Rate constant for chain transfer, cm3/gmol-s.

= Dimensionless chain transfer rate constant.

= Polymerization rate constant for monomer 1, cm3/gmol-s.

= Rate constant for addition of a j type monomer to a polymer chain whose growing end is an i type monomer unit, cm3/gmol-s.

m M, M,, M2 = Monomer, monomer 1, and monomer 2,

[ M,], [ M,] = Concentrations of monomer 1 and

= Monomer 1 charged to reactor, g.

respectively.

monomer 2 respectively, gmol/cm3. = Number average molecular weight. = Reference quantity for MN. = Number of reacted monomer 1 units in

= Reference quantity for n. = Avogadro’s number, 6.02252 X =Number of polymer chains in a latex

= Moles monomer 2 reacted per mole of

= Reactivity ratios. = Effective initiation rate, radicals/cm3

= Initiation rate, radicals/cm3 H20-s . = Reaction rate, gmoltmonomer 2)/sec-

cm3 H 2 0 . = Reference quantity for Ra, gmol/s-cm3

H 2 0 . = Surface area of a swollen latex particle

with n reacted monomer 1 units, cm2. = Sum of surface area of particles,

cm2/cm3 H 2 0 . = Surface area of soap available to stabilize

emulsion, cm2/cm3 H20. = Total dispersed phase surface area,

cm2/cm3 H 2 0 . = Reaction time, s. = Reference quantity for t , s. = Temperature, K. = Molar volumes of monomer 1 and

=Water charged to reactor, g. = Mole fraction of monomer 1 and

monomer 2, respectively.

a latex particle.

particle.

monomer 1 reacted.

H2O-S.

monomer 2 respectively, cm3/gmol.

Greek Symbols, Subscripts and Superscripts

S 1, 6, , 6,

P = Density, g/cm3.

= Solubility parameters of monomer 1, monomer 2, and polymer (Cal/cc) 1/2.

= Monomer 1 and monomer 2 volume fractions in a swollen latex particle.

= Polymer volume fraction in a swollen latex particle.

p l . p 2 = Chemical potential of monomer 1 and monomer 2, cal/gmol.

py, p; = Chemical potentials of monomers in standard state.

X = Nonspecific Flory-Huggins parameter defined in text.

= Parameter in Flory-Huggins solution model that describes interactions between component i and component j.

= Superscript denotes liquid state.

= Superscript denotes gaseous state.

= Denotes a dimensionless variable.

4 1 9 42

43

X i j

L G

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177 (1974). 9. D. B. Gershberg and J. E. Longfield, 45th AIChE Meet-

ing, Paper 10, New York (1961). 10. M. Nomura and M. Narada, “On the Optimal Reactor

Type and Operations for Continuous Emulsion Polymer- ization,” in Emulsion Polymers and Emulsion Polymer- ization, D. R. Bassett and A. E. Hamielec. eds., Ameri- can Chemical Society, Washington, D.C. (1981).

11. R. K. Grene, R. A. Gonzalez, and G. W. Poehlein, in Emulsion Polymerization, I. Piirma and J. Gardon, eds.. American Chemical Society, Washington, D.C. (1976).

12. F. J. Schork and W. H. Ray. J . AppL Polym Sci., 34, 1259 (1987).

13. C. Kiparissides, J. F. MacGregor. and A. E. Hamielec, Can. J . C h e n Eng., 58. 56 (1980).

14. K. W. Leffew and P. B. Deshpande, in Emulsion Poly mers and Emulsion Polymerization D. R. Bassett and A. E. Hamielec, eds., American Chemical Society, Washing- ton, D.C. (1981).

15. C. Kiparissides, J . F. MacGregor. and A. E. Hamielec, AIChEJ., 27, 13 (1981).

16. G. W. Poehlein and F. J. Schork, Polymer News, 13, 231 (1988).

17. L. Lapidus and G. F. Pinder, Numerical Solution of PDE’s in Science and Engineering, Wiley Interscience, New York (1982).

18. R. Aris and N. R. Amundson, Mathematical Methods in Chemical Engineering, Vol. 2, Prentice-Hall, Englewood Cliffs, N.J. (1973).

19. J . M. Prausnitz and F. H. Shair, AIChE J., 7 , 682 (196 1).

20. J. M. Prausnitz, Molecular Thermodynamics of Fluid- Phase Equilibria, Ch. 8, Prentice-Hall. Englewood Cliffs, N.J. (1969).

21. P. J . Flory and J. M. Schultz, J. Am. C h e m Soc., 75, 5618 (1953).

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emulsion copolymerization: kinetics model and reactor performance

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