Kinetics of Dispersion Polymerization of Styrene in Ethanol. 2. Model

Ind. Eng. Chem. Res. 1997, 36, 2605-2615

2605

Kinetics of Dispersion Polymerization of Styrene in Ethanol. 2. Model Validation S. Farid Ahmed and Gary W. Poehlein* School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100

Predictions of monomer conversion, polymerization rate, and evolution of particle size distribution during seeded batch and continuous dispersion polymerization obtained from simulation are compared to experimental results. An understanding of the kinetic mechanisms governing the relative prevalence of solution and microbulk polymerization has been gained. Estimates of parameters in the radical transport rate coefficient models compare favorably with values reported in the literature. 1. Introduction In the first part of this two-part series, mathematical models of seeded batch and continuous dispersion polymerization have been presented. Validation of the models by simulation of polymerization rate and particle size evolution during seeded batch and continuous polymerization experiments is presented in this part. Estimates of adjustable parameters in the mathematical models of the radical interchange process obtained by simulation are also presented. 2. Experimental Section Reagent-grade styrene monomer inhibited with 4-tertbutylcatechol was obtained from Aldrich. Monomer was vacuum distilled before use. Reagent-grade Azobis(isobutyrontrile) (AIBN) was obtained from Eastman and was recrystallized in methanol and then vacuum dried. Poly(N-vinylpyrrolidone), PVP K-90 with a nominal molecular weight of 360 000, was obtained from Sigma Chemical and used as received. Absolute Ethanol was used as the dispersion medium. Purified-grade hydroquinone was obtained from Fisher Scientific Company, while high-purity nitrogen was supplied by Holox. Seed dispersions were prepared by dispersion polymerization for subsequent use in the seeded polymerization experiments undertaken for model validation. These reactions were conducted in a 1 L reaction vessel placed in a constant-temperature bath controlled at 70 °C. The reaction vessel was equipped with a 1-7/8-in. 3-blade propellor type agitator to generate downward axial flow and horizontal mixing in order to prevent larger polymer particles from settling during the polymerization. A weighed amount of PVP was dissolved in ethanol, and the solution was charged to the reaction vessel and purged for 10 min with pure nitrogen. The water bath temperature was raised to the reaction condition, and agitation was started. Distilled monomer and initiator were weighed, and the initiator was dissolved in the monomer. This monomer solution was then added to the reaction vessel to start the polymerization. Nitrogen blanketing was maintained throughout the reaction. Polymerization was continued for 36-48 h to minimize residual initiator in the seed polymer. Seed dispersions with average diameters in the range of 1-3.5 µm were prepared. Polymerization recipe and dispersion characteristics of these seed dispersions are presented in Table 1. These colloidally stable dispersions were prepared by varying the monomer and S0888-5885(96)00506-4 CCC: $14.00

initiator concentrations in order to prepare dispersions with different average diameters. In developing a polymerization recipe for these experiments, a simple nucleation factor, κ, was found to be useful in predicting the formation of stable dispersions with narrow particle size distribution.

κ)

S0(10-4) kP[M]0x(kI/kt)x[I]0

(1)

Here S0 is the mass concentration of the stabilizer, expressed as gm/dm3 of ethanol, while [M]0 and [I]0 are the initial molar concentrations at the polymerization temperature. A κ value above 16 for the polymerization recipe was found to be necessary to ensure the formation of polystyrene particles with narrow size distribution. Batch Polymerization. Bimodal seed dispersions were prepared by combining two seed dispersions in equal volume of the total polymer as seed particles. The required amount of fresh ethanol and PVP was mixed and purged with nitrogen. Initiator was weighed and dissolved in fresh monomer. Monomer was then mixed with ethanol and the solution slowly added to the seed dispersion at 6.5 mL/min with a syringe pump. This was done to avoid localized high monomer concentrations that can lead to partial flocculation. The reaction mixture was then stored in the freezer for 12 h to allow the seed particles to swell. The reaction vessel was nitrogen purged, and the water bath was raised to the reaction temperature. The reaction mixture was charged into the vessel, and agitation was started at 80 rpm. Recirculation of the reaction mixture from the bottom of the reactor was started using a masterflex peristaltic pump in order to minimize layer formation. The initial time was recorded as soon as the reactants reached the polymerization temperature. Samples were withdrawn after every 15 min and quenched with hydroquinone solution in ethanol for gravimetric analysis. Table 2 summarizes the recipe and reaction conditions for the bimodal seeded competitive growth experiments conducted for model validation, identified as experiments F1-F4. Seed polymer, monomer, stabilizer, and initiator concentrations are in units of g/dm3(ethanol) at the reaction temperature. Experiments were conducted at 60, 70, and 80 °C. The first three experiments were conducted at similar initial rates of radical initiation in the continuous phase. Run F4 was a repeat of run F1, but at a higher temperature and at an initial rate of radical generation that was almost an order of magnitude greater than the other three experiments. © 1997 American Chemical Society

2606 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 1. Preparation of Seed Dispersions Using PVP K-90 Stabilizer monomer concentration, g/dm3 stabilizer concentration, g/dm3 initiator concentration, g/dm3 mean diameter PDI nucleation index

C4

C5

C6

C7

C8

C9

C10

185.1 13.88 3.7 3.46 1.007 16.19

82.3 16.46 1.65 2.602 1.008 64.64

82.3 12.34 0.41 1.31 1.05 97.22

82.3 16.46 0.83 1.1 1.02 91.14

246.8 19.75 2.47 2.03 1.009 21.14

185.1 16.54 1.85 1.794 1.006 27.28

130.7 16.55 1.31 1.131 1.01 45.93

Table 2. Seeded Batch Competitive Growth Polymerization F1

F2

F3

F4

seed polymer concentration 37.6 27.8 27.4 36.5 fresh monomer concentration 150.2 157.4 155.00 145.9 stabilizer concentration 6.57 7.41 10.03 6.38 initiator concentration 3.00 0.93 0.39 2.92 -12 15.7 12.43 21.09 15.25 number density, ×10 1684 1208 1098 1684 surface coverage dm2/g temperature 60 70 80 80 2.1 2.5 3.8 28.7 initiation rate, ×107 final conversion 80.1 80.2 69.8 83

Table 3. Particle Size Evolution in Batch Competitive Growth F1 seed particle diameters seed 1 seed 2 seed volume ratio final particle diameters seed 1 standard error seed 2 standard error final volume ratio calculated conversion conversion error

1.31 3.46 18.42 2.4 0.009 4.37 0.009 6.04 81.6 1.5

F2

F3

F4

1.31 2.60 7.80

1.13 1.79 4.00

1.31 3.46 18.42

2.05 0.007 2.64 0.01 2.14 68.6 -1.2

2.42 0.009 4.49 0.027 6.39 84.9 1.9

2.58 0.01 3.59 0.03 2.69 77.1 -3.1

Table 4. Seeded Continuous Polymerization Experiments G1

G2

G3

G4

seed polymer concentration 38.9 37 36.5 48.6 fresh monomer concentration 148.1 148.1 145.90 194.6 stabilizer concentration 11.57 7.03 14.59 9.73 initiator concentration 1.48 4.443 2.92 3.89 53.53 11.43 44.96 10.37 number density, ×10-12 mean residence time 70 60 60 45 temperature 70 70 80 80 1759 1644 1238 1380 surface coverage, dm2/g steady-state conversion 46.0 40.5 45.8 38.7

Table 5. Particle Size Evolution in Continuous Polymerization seed particle diameter polydispersity index effluent particle diameter polydispersity index calculated conversion conversion error

G1

G2

G3

G4

1.1 1.02 1.402 1.08 44.2 -1.8

1.79 1.01 2.19 1.05 36.3 -4.2

1.13 1.01 1.535 1.12 50 4.2

2.03 1.009 2.522 1.06 38.4 -0.3

SEM micrographs of polymer particles after competitive growth for runs F1-F4 are shown in Figure 1. These micrographs show no evidence of larger coagulated particles, and only the presence of relatively small concentrations of secondary particles for runs F1 and F2. Table 3 shows the particle diameters and ratios of the unswollen volumes of the two particle populations before and after competitive growth. These ratios decreased by competitive growth, indicating that the smaller size seed particle population grew faster than the larger size seed particles. An important requirement for these experiments to be useful as model validation tools was that the number

density of seed polymer particles remain constant during the batch polymerization. Thus the generation of new stable polymer particles by secondary nucleation as well as coagulation of seed particles must be limited during seeded batch and continuous polymerization experiments. The conversion error, ∆Xf, represents the difference between the measured conversion and the monomer conversion calculated based on the new sizes of the seed particles after competitive growth.

∆Xf ) Xf,meas. - Xf,calc.

(2)

Monomer conversion was calculated from the seed number densities and the measured average particle sizes according to eq 3.

Xf,calc. )

(NS1vP1 + NS2vP2)dP M0

(3)

Monomer conversions during and after the reactions were measured by gravimetry. The conversion errors reported in Table 3 are within reasonable limits and also include the errors associated with both the conversion measurement by gravimetry and the measurement error of particle size determination by electron microscopy. Size characterization of the seed dispersion and final polymer particles from the bimodal polymerization was done by scanning electron microscopy. Polymer dispersion samples were diluted in ethanol about 200 times, taking care to add the required amount of PVP to prevent coagulation. Polymer particles were deposited on a carbon sample holder and dried by evaporation. A gold-palladium coating was applied in a sputter coater. Several micrographs were then taken from different regions of the sample holder. The particle size distribution was obtained with a Zeiss-Endtler optical size distribution analyzer. Approximately 500-1000 particles were measured for each sample. The number-average molecular weight of the polystyrene formed by batch dispersion polymerization was found to be in the range of (3-6) × 104 g/mol. Numberaverage molecular weights of seed polymers 1 and 2 for experiment F4 were 60 600 and 33 500, with polydispersities of 2.28 and 2.78, respectively. The average molecular weight of the polymer after seeded polymerization was found to be 59 200, with a polydispersity of 2.91. Continuous Polymerization. Seeded dispersion polymerization reactions were also conducted in a continuous reactor using monomodal seed dispersions. Table 4 shows the seed dispersion recipe and polymerization conditions for the continuous polymerization experiments identified as runs G1-G4. These reactions were carried out for about eight mean residence times. As expected, steady state was reached in about four mean residence times, and significant variation of monomer conversion was not observed thereafter. Experiments G1 and G2 were conducted at 70 °C, while experiments G3 and G4 were conducted at 80 °C.

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2607

Figure 1. SEM micrographs of particles after competitive growth: (a) run F1, (b) run F2, (c) run F3, (d) run F4.

Considerable broadening of the size distribution of polymer particles in the effluent stream compared to the seed particle distribution was evident, as seen from the increase in the polydispersity index reported in Table 5. SEM micrographs of polymer particles in the effluent from the reactor are shown in Figure 2. These micrographs indicate that, except for run G1, secondary particles were not formed. Critical Chain Length. One of the parameters required for modeling of radical and primary particle

concentration in the continuous phase during dispersion polymerization is the critical chain length for homogeneous nucleation, Z. Experiments were conducted to detect the monomer concentration at which polystyrene molecular weight standards of different chain lengths precipitated from styrene-ethanol solutions by measuring the turbidity of the solution. A small quantity (approximately 10 g/dm3) of the polystyrene standard was dissolved in fresh styrene which has not been distilled to remove the inhibitor.

2608 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 2. SEM micrographs of particles after continuous polymerization: (a) run G1, (b) run G2, (c) run G3, (d) run G4.

Ethanol was then added successively and the turbidity of the solution measured. Turbidity declined as the styrene concentration of the solution decreased as a result of ethanol addition. The polystyrene chains precipitated when the monomer concentration decreased below their solubility limit and the turbidity of the solution increased drastically. The monomer volume fraction at which this change occurred was noted. Polystyrene molecular weight standards of numberaverage chain lengths of 21, 33, 36, 50, 71, and 76 were used for the tests. These tests were done at 60, 70, and

80 °C, and tests of each polystyrene standard were repeated to improve reliability. Figure 3 shows the plots of the natural log of the polystyrene chain length, Z, with the volume fraction of monomer in the ethanolstyrene solution at different temperatures. The correlations for Z, the critical chain length for homogeneous nucleation of primary particles, with δmix, the mixture solubility parameter of the continuous phase at the reaction temperatures, were obtained from regression fitting of these plots. These correlations have been used in the simulation modeling.


β* is given by the following expression:

β* ) {1 + (ktC[MT*]C + kaSNS* + kaPNP*)/ (kpC[M]C)}Z-1 [MT*]′C is the radical concentration determined in the previous solution. The simulation program is supplied with an initial estimated value of [MT*]′C given by the following relation:

[MT*]′C )

( ) RiC

1/2

ktC

The radical concentration is given by the positive root of the quadratic.

[MT*]C ) [(R2 + 8γktC)1/2 - R]/4ktC Figure 3. Critical chain length for precipitation of polystyrene oligomers in ethanol-styrene.

Similarly, making the quasi-steady-state assumption regarding the primary particle concentration in the continuous phase, eq 6 in part 1 may be rewritten as

60 °C: Ln(Z) ((1.1) ) 24.433 ((1.71) 1.693 ((0.14)δmix 70 °C: Ln(Z) ((1.1) ) 21.772 ((2.30) 1.460 ((0.19)δmix 80 °C: Ln(Z) ((1.1) ) 21.319 ((1.98) 1.412 ((0.16)δmix δmix is defined by the following relation:

kfPNP*2 + 2ψNP* - ξ ) 0

δm and δs are the Hildebrand solubility parameters of monomer and solvent in units of (cal/cm3)1/2. Batch Simulation. Simultaneous solution of differential equations describing the change of [MT*]C and NP* with time along with the particle growth equations (eqs 5, 6 and 27, 28 of Part 1) produces a very stiff system that does not solve easily. To facilitate solution, a modified procedure has been adopted that allows calculation of these quantities from algebraic equations. Making the quasi-steady-state assumption regarding the total radical concentration in the continuous phase, eq 5 (in Part 1) may be written as 2

2ktC [MT*]C + R[MT*]C + γ ) 0

(6)

where

ψ ) kCSNS* -

j VCkdn β

and

ξ)

δmix ) {φMCδm2 + φSCδs2}1/2

(5)

2VCRiC β

Equation 6 may also be transformed into a quadratic equation by replacing β with β0, where β0 is given by the expression

β0 ) {1 + (ktC[MT*]C + kaSNS* + kaPN ˜ P*)/ (kpC[M]C)}Z-1 N ˜ P* is the molar concentration of primary particles determined at the previous solution of eq 6 in the simulation. The positive root of the quadratic gives the primary particle concentration.

NP* ) [(ψ2 + kfPξ)1/2 - ψ]/kfP

(7)

(4)

where

R ) kaSNS* + kaPNP* j )(1 - 1/β) γ ) (RiC + kdNpn and

β ) {1 + (ktC[MT*]C + kaSNS* + kaPNP*)/ (kpC[M]C)}Z-1 The last term in eq 4 is a higher order function of [MT*]C if Z g 4, which is the case for dispersion polymerization of styrene in ethanol. Equation 4 may be transformed into a quadratic equation by replacing β with β*, where

The simulation program is supplied with an initial estimated value of N ˜ P*. Kinetic rate coefficients and parameters in the rate coefficient models are summarized in Table 6, while parameters in the radical transport rate coefficient models are given in Table 7. Three parameters describing the radical transport processes between the continuous phase and primary and seed particles have been used as adjustable parameters: n j , the average number of radicals per primary particle; DC, the effective mean diffusion coefficient for radical capture from the continuous phase; and δ, the ratio of continuous-phase resistance to particle-phase resistance to desorption of monomeric radicals from primary particles. The best fit of polymerization rate, the final volume ratio of the two seed particle populations, and monomer

2610 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 6. Values of Parameters in Kinetic Rate Coefficient Models parameter kI kpo kto Cm fo A B D Vfc1 Vfc2 Crd

value

reference

1.58 × 1015 exp(-15500/RT) 1.4218 × 107 exp(-30084/RT) 8.2 × 109 exp(-15525/RT) 0.2 exp(-5400/RT) 0.58 0.465 1.0 10-3 0.11 0.036 135

Van Hook and Tobolsky, 1958 Deady et al., 1993 Soh and Sundberg, 1982 Tobolsky and Offenbach, 1955 Tobolsky and Baysal, 1953 Vivaldo-Lima et al., 1994 Vivaldo-Lima et al., 1994 Vivaldo-Lima et al., 1994 Vivaldo-Lima et al., 1994 Vivaldo-Lima et al., 1994 Vivaldo-Lima et al., 1994

Table 7. Values of Parameters in Radical Transport Rate Coefficient Models parameter

value

reference

Dw md Wpp WPS rp

1× 1.0 1.0 103 2.5 × 10-8

Hansen and Ugelstad, 1978 this work Gilmore et al., 1993 this work Gilmore et al., 1993

10-8

Figure 4. Simulation of monomer conversion for batch polymerization.

Table 8. Values of Adjustable Parameters Obtained From Simulation of Batch Competitive Growth Experiments. parameter run ID

temp (°C)

DC

δ

n j

F1 F2 F3 F4

60 70 80 80

2.86 × 10-10 2.86 × 10-10 2.86 × 10-11 2.86 × 10-11

0.06 0.07 0.08 0.08

0.35 0.30 0.30 0.05

conversion with reaction time were obtained with values of the adjustable parameters given in Table 8. The value of DC at 60 °C was adopted from Hansen and Ugelstad (1978) for styrene emulsion polymerization. Values of n j and δ were then varied to obtain good fits of conversion and final size ratio. At 80 °C, an order of magnitude decrease of the DC value was necessary to obtain good fit of experimental data with reasonable values of the other two parameters. Results of simulation of monomer conversion during batch competitive growth reactions are shown in Figure 4. The points in these figures represent the experimental conversion data, while the solid lines are the predicted conversions. Simulations of rates of polymerization in both polymerization loci and the total rates are shown in Figures 5-8. The solid lines are the experimental polymerization rate curves obtained by differentiating the polynomial fit of the conversion data. Reasonable fit of experimental conversion data was obtained from the simulation. Examination of polymerization rates versus monomer conversion curves for runs F1, F2, and F3, which were carried out with similar rates of initiation but at increasing temperature levels, shows that solution phase polymerization becomes more important at higher temperature. In all cases, the relative contribution from polymerization inside particles increases with conversion, and at 60 °C, this is the dominant polymerization loci. At 80 °C, the continuous phase is the dominant polymerization loci almost throughout the reaction. The increase in contribution from the continuous phase can be attributed to two causes. The increase in the critical chain length for precipitation of growing oligomers from the solution

Figure 5. Simulation of polymerization rate for batch run F1.

increases the radical concentration in the continuous phase. A decrease of the mean diffusion coefficient for radical absorption, and hence the coefficient for radical capture by seed particles, also increases the radical concentration in the continuous phase. However, when the initiator concentration is increased from 0.39 to 2.92 g/dm3 (experiment F4), polymerization in the disperse phase becomes dominant once again. Table 9 shows the experimental ratio of seed particle volumes before and after competitive growth along with the ratio of seed particle volumes at the end of the reaction as predicted by the simulation modeling. The predictions of final ratio of particle volumes are reasonably close to the experimental values, except for run F4. Continuous Polymerization Simulation. Simulation of polymerization rate and particle size distribution in continuous polymerization was done based on the mathematical model developed in part 1. The steadystate concentrations of monomer in the continuous phase and inside the particles were first calculated from the thermodynamic equilibrium relations at the measured steady-state monomer conversion. All particles


Figure 8. Simulation of polymerization rate for batch run F4. Figure 6. Simulation of polymerization rate for batch run F2.

Table 9. Results of Simulation of Size Evolution of Seed Particles through Competitive Growth run ID initial ratio final ratio experimental simulation

Figure 7. Simulation of polymerization rate for batch run F3.

were assumed to have the same monomer concentration, as the effect of particle diameter on the monomer partitioning is very small for particles of such large diameters and in a system with low interfacial surface tension. Steady-state concentrations of initiator in the continuous and disperse phases were calculated from eq 8.

[I]C ) [I]D )

I0 (VD + VC)(1 + θkI)

(8)

The total free-radical and primary particle concentrations in the continuous phase, [MT*]C and NP*, are then determined by an optimization procedure, solving eqs 5 and 7 simultaneously. The radical flux into polymer particles by absorption and by heterocoagulation of primary particles and the radical flux out of the primary particles by desorption are determined by using the adjustable parameters DC, n j and δ and the measured average particle size at steady state. The experimentally determined particle size distribution at steady state is then utilized to calculate the number density,

F1

F2

F3

F4

18.40

7.80

4.00

18.40

6.04 6.76

2.69 2.94

2.14 1.92

6.39 9.29

NSj, and the radical concentration, [MT*]Dj, in each particle population. The dimensionless age at which a seed particle, starting from the mean size of the ith class, grows to the limiting size of successive jth classes of the effluent size distribution was determined from the particle growth equation. The rate of growth for each size class j was considered constant, as the reaction environment at steady state remains constant, and only the radical concentration varies due to the dependence of radical flux into particles on the particle diameter. However, the dimensionless ages at which seed particles of different mean size will grow to the successive particle size classes are not the same. The predicted size distributions for each seed size class, Ui(vp,i), were then calculated from the age distribution. The overall size distribution was obtained from these individual distributions using eq 33 in part 1. Numerical values of adjustable parameters in the mathematical models describing the polymerization kinetics, thermodynamic equilibrium, and radical transport and the adjustable parameters obtained from the batch simulation were used without any change for the simulations of the continuous polymerization reactions. However, as noted before, the mean effective diffusion coefficient, DC, and the average number of radicals per primary particle, n j , do not remain constant with monomer conversion and change as the batch reaction progresses. Thus, the values obtained from the batch simulation are average values of these parameters over the entire conversion range. The monomer concentration in the continuous phase, and hence the critical length of oligomer for homogeneous nucleation, Z, decreases as monomer conversion increases. The change in the concentration of monomer in the continuous medium, as the total monomer conversion goes from 20 to 70-80% during batch polymerization experiments F1-F4, was quite large. Hence, the change in the


Figure 9. Optimization of PSD fitting for continuous run G1. Figure 11. Optimization of PSD fitting for continuous run G3.

Figure 10. Optimization of PSD fitting for continuous run G2.

instantaneous value of DC over the course of the batch polymerization is expected to be quite large. However, for the continuous polymerization experiments, the critical length Z and hence the mean effective diffusion coefficient do not change with time. The primary particle number density and the total radical concentration in the continuous phase were found to change only slowly with monomer conversion during the batch polymerization experiments. Hence, n j , the average number of radicals per primary particle, is not expected to undergo a large change in value. Prediction of particle size distribution for the continuous polymerization experiments was optimized by searching for the minimum deviation from the experimental particle size distribution for values of n j close to those obtained from batch simulation and for a wide range of DC values. The closeness of fit between predicted and experimental PSD’s was determined by minimizing the sum of error, Ev, as defined by eq 9. l

EV )

∑ |g′q - gq|

(9)

q)1

where g′q and gq are the relative fractions of the predicted and experimental particle volume distributions. Figures 9-12 show the response surfaces for the sum of errors of the PSD prediction for continuous polymerization runs G1-G4. A relatively narrow range of DC values yields the best fit of experimental PSD from the seeded continuous polymerization runs. Assuming an j value of 0.30, as obtained from the batch simulation result (run F2) at the same temperature and similar rate of initiation in the continuous phase, the lowest value of the sum of errors occurs at DC value of 1.0 × 10-10 dm2/s. In Figure 10 for run G2, the best fit of

Figure 12. Optimization of PSD fitting for continuous run G4.

experimental PSD at n j value of 0.30 occurs at a DC value of 2.5 × 10-10 dm2/s. Figure 11 for run G3 also shows a similar response surface for the sum of errors of the PSD fit. This experiment was conducted at a higher temperature (80 °C) than the previous two experiments. As seen from the batch simulation of runs F3 and F4 at this temperature, the n j value varies from 0.30 to 0.05 at the same temperature but with about an 8-fold increase in the rate of initiation in the continuous phase. The steadystate rate of initiation in the continuous phase for run G3 was 1.62 × 10-6 mol/dm3‚s. This value lies closer to that for run F4. The average number of radicals per primary particle for this experimental condition was thus assumed to be between 0.05 and 0.10, giving DC values of 7.25 × 10-10 and 5.50 × 10-10 dm2/s, respectively. Figure 12 shows the response surface for the sum of errors of the PSD fit for experiment G4. Values of DC obtained from the best fit of experimental PSD at n j values of 0.05 and 0.10 were 4.75 × 10-10 and 1.75 × 10-10 dm2/s, respectively. The rate of radical initiation in the continuous phase for this run was 2.25 × 10-6 mol/dm3‚s. Similar to runs G1 and G2, the differences in the sum of errors for the best PSD fit at the two values of n j considered for runs G3 and G4 were also very small. Hence, the mean effective diffusion coefficient values for these experiments were considered to be within these limits. A comparison of mean effective diffusion coefficient values indicates the close agreement between values obtained from simulation of batch and continuous polymerization. Figures 13-16 show the reasonable agreement of predicted particle size distributions for experiments G1-G4, respectively, to the experimental distributions.


Figure 13. Simulation of particle size distribution for continuous run G1.



From Figure 13, it is seen that the PSD simulation overpredicts the volume distribution for the smaller seed size segments and underpredicts the distribution for the largest segments. This can be attributed to limited coagulation of seed particles during the polymerization. Figure 14 also shows overprediction of intermediate size segments and underprediction of largest size segments. Figure 15 for run G3, on the other hand, shows underprediction of the distribution at the smaller size segments and overprediction of intermediate size segments. Figure 16 again shows some overprediction of smallest size segments and underprediction of intermediate and largest sizes. Some of the differences in the experimental and simulated distribution may also be attributed to sampling error in the experimental distributions. Sensitivity Analysis. Sensitivity of the effluent particle size distribution prediction to parameter values


Figure 17. Sensitivity of predicted PSD to desorption rate parameter δ.

used for simulation of polymerization rate and particle growth for the continuous runs have been investigated. Values of δ, the ratio of mass-transfer resistance to desorption of monomeric radicals from the continuous phase, have been obtained from the batch polymerization simulations. The critical chain length for homogeneous nucleation of growing radicals in the continuous phase, Z, was calculated based on the correlations obtained from solubility studies and described earlier. Sensitivity of the effluent PSD predictions to an increase or decrease in the estimation of these parameter values is described in the following paragraphs. Figure 17 shows the PSD predictions at δ values that are double and half of the value obtained from simulation of batch polymerization at 80 °C. These simulations were done at n j and DC values of 0.05 and 4.75 × 10-10, respectively. The PSD predictions were not found to be very sensitive to this parameter value as the sum of errors were 0.149 and 0.143, respectively, as against a value of 0.142 for the standard parameter value. However, the lower value tended to increase the overprediction of the distribution for smallest size segments and underprediction for largest size segments while decreasing the underprediction of the intermediate segments. Using a larger value for this parameter increased the calculated steady-state concentration of primary particles and total radicals in the continuous phase and the total rate of polymerization, while using the smaller value decreased the calculated concentrations and polymerization rate. This was because a larger value of δ increases the rate coefficient for desorption of monomeric radicals from primary particles, kd, as defined by eq 19 in part 1.


Figure 18. Sensitivity of predicted PSD to critical chain length for oligomer precipitation.

Figure 18 shows the PSD predictions for values of the critical chain length, Z, that are 25% more or less than that obtained from the correlations. The critical chain length at the steady-state monomer concentration for experiment G4 was found to be 52 from the correlation. Simulation of the continuous polymerization rate and effluent particle size distributions was done assuming values for the critical length at 65 and 39. The standard error of the solubility correlation was approximately 7%. Thus, the actual value of this parameter could be considered to lie within (25% with a confidence level above 99%. The sum of errors for the Z values of 65 and 39 were 0.149 and 0.163, respectively, indicating the more pronounced impact of the lower estimate. The overprediction of the distribution at the lowest size segments and the underprediction at the largest size segments were also more pronounced for the lower value, although prediction of intermediate size segments was improved. At a Z value of 39, the calculated primary particle concentration was higher than that for a value of 52, while the total radical concentration was lower. The total polymerization rate was decreased, increasing the offset from measured polymerization rate. The calculated polymerization rate was closer to the experimental value for the higher critical length estimate. Discussion. The effect of solvency of the continuous medium for the polymer on the dominant locus of dispersion polymerization was demonstrated by Lok and Ober (1985) and Williamson et al. (1987). These were extreme examples of polymerization conditions which favored either the solution polymerization in the continuous phase or particle phase polymerization with a strong gel effect. Dispersion polymerization of styrene in ethanol represents an intermediate situation in which polymerizations in both loci are important. This presents an interesting opportunity for studying the effect of reaction variables on the polymerization locus and radical transport. The discernible effect of initiator concentration and temperature on the average molecular weight (Chen and Yang, 1992) in the styrene-ethanol system pointed to the importance of these variables in moderating the kinetic competition between the two polymerization loci. Through the modeling of polymerization rate during seeded batch polymerization, these observations regarding the influence of initiator concentration and temperature have been confirmed. An order-of-magnitude decrease in the average value of the mean diffusion coefficient for radical capture by the seed particles at 80 °C from that at 70 °C was identified as the mechanism that governs the effect of

Figure 19. Effective diffusion coefficient values from continuous polymerization.

temperature on the relative importance of the two polymerization loci. This decrease in coefficient value can be related to an increase in the critical length of oligomer chains for precipitation. The critical length Z increases, as solvency of the monomer-ethanol mixture for the oligomers increases with temperature. The maximum length of oligomers in solution, and thus the concentration average length, also increases. This effect is qualitatively demonstrated from a plot of DC against the steady-state value of Z during the continuous polymerization experiments in Figure 19. The increase in the value of DC due to an increase in temperature, but with a comparable value of Z, is significantly offset by an increase of Z at the same temperature. Lange et al. (1991) obtained values of 8.5 × 10-11 and 6.6 × 10-11 dm2/s for the mean effective diffusion coefficient for seed particles of radius 425 and 245 nm in the emulsifier-free seeded competitive growth emulsion polymerization of vinyl acetate at 60 °C. Higher mean diffusion coefficient for particles of larger size used in this study is in general agreement with the increase in mean diffusion coefficient observed by Lange et al. Values of δ obtained from this study are also close to the value of 0.02 obtained by Nomura and Fujita (1994) for the emulsion polymerization of MMA at 50 °C. Increasing the initiator concentration does not appreciably increase the radical concentration in the continuous phase. However, the rate of primary particle formation is greatly increased, with a consequent increase in the rate of primary particle homocoagulation. Particle-phase polymerization is greatly increased due to an increase in the rate of radical generation inside the particles. The rate of polymerization was observed to increase with a 0.3 power of initiator concentration at high levels of initiator (Lu, 1988). Increased rate of radical extinction through homocoagulation of the primary particle population explains this observation and is confirmed by a low value of n j for experiment F4. The mathematical models of seeded batch and continuous dispersion polymerization, based on the mechanistic picture presented in part 1 of this paper, and models of monomer partitioning, bulk and solution polymerization kinetics, and rates of radical interchange developed by several investigators have been successful in predicting the polymerization kinetics over a range of temperature and initiator concentrations. In the process, an understanding of the mechanism governing the kinetic competition between solution polymerization


in the continuous phase and microbulk polymrization inside the polymer particles has been gained. Acknowledgment Support of the National Science Foundation (Grant No. CTS 9417306) and Georgia Institute of Technology is gratefully acknowledged.

Lok, K. P.; Ober, C. K. Can J. Chem. 1985, 63, 209. Lu, Y. Y. Ph.D. Dissertation, Lehigh University, Bethlehem, PA, 1988. Nomura, M.; Fujita, K. Polym. React. Eng. 1994, 2, 317. Soh, S. K.; Sundberg, D. C. J. Polym. Sci., Polym. Chem. Ed. 1982, 20, 1345. Vivaldo-Lima, E.; Hamielec, A. E.; Wood, P. E. Polym. React. Eng. 1994, 2, 17. Williamson, B.; Lukas, R.; Winnik, M. A.; Croucher, M. D. J. Colloid Interface Sci. 1987, 119 (2), 559.

Literature Cited Chen, Y.; Yang, H. W. J. Polym. Sci., Polym. Chem. 1992, 30, 2765. Deady, M.; Mau, A. W. H.; Moad, G.; Spurling, T. H. Makromol. Chem. 1993, 194, 1691. Gilmore, C. M.; Poehlein, G. W.; Schork, F. J. J. Appl. Polym. Sci. 1993, 48, 1461. Hansen, F. K.; Ugelstad, J. J. Polym. Sci., Polym. Chem. 1978, 16, 1953. Lange, D. M.; Poehlein, G. W.; Hayashi, S.; Komatsu, A.; Hirai, T. J. Polym. Sci., Polym. Chem. 1991, 29, 785.

Received for review August 14, 1996 Revised manuscript received April 10, 1997 Accepted April 11, 1997X IE960506J

Abstract published in Advance ACS Abstracts, June 1, 1997. X

Kinetics of Dispersion Polymerization of Styrene in Ethanol. 2. Model

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