Effects of Agitation on Oxygen Inhibition, Particle ... - ACS Publications

Ind. Eng. Chem. Res. 2004, 43, 6331-6342

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Effects of Agitation on Oxygen Inhibition, Particle Nucleation, Reaction Rates, and Molecular Weights in Emulsion Polymerization of n-Butyl Methacrylate Sitaraman Krishnan,† Andrew Klein,* Mohamed S. El-Aasser, and E. David Sudol Iacocca Hall, Department of Chemical Engineering and Emulsion Polymers Institute, Lehigh University, 111 Research Drive, Bethlehem, Pennsylvania 18015

Oxygen-free conditions are required during emulsion polymerization reactions to eliminate the inhibition effect of oxygen on the free-radical mechanism of polymerization. Results of a kinetic study of the emulsion polymerization of n-butyl methacrylate using a 1-dm3 reaction calorimeter indicate that oxygen, even in concentrations as low as 1 ppm, not only prolongs the induction period that precedes the chain propagation but also influences the particle nucleation and molecular weights. Agitation promotes the transfer of residual oxygen from the reactor headspace into the emulsion and, therefore, has an effect on the particle nucleation step and other reaction events that follow. Introduction To remove oxygen, procedures such as boiling water and cooling under nitrogen, applying freeze-degasthaw sequences, and bubbling nitrogen for extended periods are routinely used in kinetic studies of emulsion polymerization. Some of these might not be feasible when the reaction is carried out on a larger scale. Unless the reactor is evacuated and back-filled with nitrogen before the reaction ingredients are added, it might not be possible to completely remove oxygen from the headspace (gas phase of the reactor). In most cases, trace amounts of oxygen impurity in the reaction are unavoidable. In this paper, we report the agitationdependent effects of oxygen on the induction-period reaction rate, particle nucleation, and molecular weight during the emulsion polymerization of n-butyl methacrylate. Nomura et al. found that, when the nitrogen in the reactor headspace contained oxygen impurity, the induction period was longer at higher agitation speed and that the reaction rate after a longer induction period was greater than that after a shorter induction period.1,2 They proposed that the oxygen retarded the volumetric growth rate of the polymer particles during the nucleation stage of the reaction. Hence, the number of particles at the end of the nucleation stage, which is inversely proportional to the volumetric growth rate of the particles, was higher in the presence of oxygen. Following Nomura’s work, other researchers have investigated the role of oxygen and other water-soluble and monomer-soluble impurities on particle nucleation in ab initio emulsion polymerization. Cunningham et al.3 varied the initial levels of dissolved oxygen corresponding to 0, 50, 80, 90, and 100% of saturation and measured the effects on the induction period, conversion kinetics, molecular weight, and particle size in the * To whom correspondence should be addressed. Tel.: 610758-4219. Fax: 610-758-5880. E-mail: [email protected]. † Current address: Materials Science and Engineering Department, Cornell University, 214 Bard Hall, Ithaca, NY 14853. E-mail: [email protected].

emulsion polymerization of styrene. They found that the mean particle diameter decreased as the initial oxygen concentration increased, but the final molecular weight averages were not greatly influenced by the presence of oxygen early in the reaction. Also, the conversiontime data did not show significant rate differences between different levels of oxygen. This was attributed to the competing effects of higher reaction rate due to a higher number of particles and lower reaction rate due to retardation by oxygen as the initial level of dissolved oxygen increased. Kiparissides et al.4 studied the emulsion polymerization of vinyl chloride and found that, at low initial oxygen concentrations, the polymerization rate increased with increasing oxygen concentration. The particle size however exhibited a U-shaped behavior. They explained these results on the basis of the dual role of oxygen as an inhibitor and a radical generator through the formation and subsequent decomposition of vinyl polyperoxides. In the present work, the concentration of oxygen in the reactor headspace was kept constant, and the kinetics of polymerization was studied at different agitation speeds. In contrast to the behavior of the system investigated by Cunningham et al., the reaction rates and the molecular weights showed a significant dependence on the aqueous-phase concentration of oxygen, determined by the mass-transfer rate of oxygen from the headspace in to the emulsion. The induction period, the particle size, and the molecular weight all showed a sigmoidal variation with agitation speed. Materials and Methods n-Butyl methacrylate (BMA, 99%, CAS # 97-88-1, MW ) 142.20 g/mol, Sigma-Aldrich) inhibited by 10 ppm monomethyl ether of hydroquinone (MEHQ, CAS # 15076-5) was used as the monomer. The monomer was freed from the inhibitor by passing it through an inhibitorremoval column (Sigma-Aldrich). Sodium dodecyl sulfate (SDS, CAS # 151-21-3, MW ) 288.38 g/mol, ultrapure bioreagent, J. T. Baker) was used as the surfactant and potassium persulfate (KPS, CAS # 7727-

10.1021/ie049796r CCC: $27.50 © 2004 American Chemical Society Published on Web 09/04/2004

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Ind. Eng. Chem. Res., Vol. 43, No. 20, 2004

21-1, >99%, MW ) 270.33 g/mol, ACS reagent, SigmaAldrich) as the initiator. Sodium bicarbonate (CAS # 144-55-8, MW ) 84.01 g/mol, Mallinckrodt Baker, Inc.) was used as the buffer. Deionized water (DI water) was obtained from Barnstead NANOpure II and had a conductivity of below 0.8 µS. The nitrogen gas (Zero Grade 0.5, minimum purity 99.998%, oxygen < 0.5 ppm) was obtained from Airgas. Tetrahydrofuran (THF, CAS # 109-99-9, MW ) 72.11 g/mol) obtained from J. T. Baker (“Baker Analyzed” HPLC solvent) was used as the eluant for gel permeation chromatography. All chemicals except BMA were used as received. The Mettler RC1 reaction calorimeter consisted of a 1-dm3 medium-pressure (1 MPa) glass reactor with a cylindrical body and a hemispherical base. The metallic lid of the reactor was maintained at the reaction temperature by a flow of water to minimize heat loss by condensation. The agitator speed was varied between 300 and 800 rpm by means of the magnetic drive of the reactor. In the case of the emulsion polymerization recipe used, agitation speeds lower than 300 rpm resulted in phase separation. Silicone oil flowing through the jacket surrounding the reactor at a high flow rate (2 dm3/s) acted as the heat-transfer fluid. The total height of the reactor (from the lid to the inside bottom) was ca. 22 cm, and the inside diameter was 8.2 cm. A stainless steel (SS), flat-blade Rushton turbine with six blades (tip-to-tip diameter of 5 cm, blade width of 1.2 cm, and blade height of 0.9 cm) was used as the agitator. The agitator was attached to a stainless steel shaft at a position ca. 20 cm below the reactor lid. A SS baffle, 14 cm long and 1.5 cm wide, was also attached to the reactor lid. The height of 0.6 dm3 of water in the reactor was ca. 12 cm. Nitrogen flow through the reactor was maintained at a constant volumetric flow rate using a gas flowmeter (F&P tube no. FP-1/8-09-G-3/61, Fischer & Porter Co.). Kinetic investigations using reaction calorimetry involve the determination of the instantaneous rates of heat evolution, Qr (J/s), as a function of reaction time. The rate of heat evolution during the exothermic polymerization reaction is directly proportional to the rate of polymerization, Rp (mol‚dm-3‚s-1)

Qr ) Rp∆HpVw

(1)

where ∆Hp (J/mol) is the molar heat of polymerization of the monomer and Vw (dm3) is the volume of aqueous phase in the reactor. The term Vw in the product arises from the fact that the rate of polymerization Rp is customarily expressed in terms of moles of monomer reacting per unit time per unit volume of aqueous phase. Because both ∆Hp and Vw are constants for a particular monomer and for a batch reaction (where there is no addition of water to the reactor during reaction), the experimentally determined heat evolution rate can be converted to the polymerization rate, which is of kinetic interest. In typical kinetic studies on emulsion polymerization, samples of latexes are withdrawn at different times during the reaction, and the mass of polymer formed, or the mass of unreacted monomer, is determined by techniques such as gravimetry, gas chromatography, or spectroscopy. The data are then represented in terms of monomer conversion, x, as a function

of time, t. The profile of the heat evolution rate versus time can also be used to determine x by

x)

∫0tQr dt ∫0TQr dt

xT

(2)

where xT is the monomer conversion in the latex, determined gravimetrically, at time T. In this paper, both Qr versus time and monomer conversion versus time profiles are presented. The particle diameters in the final latexes were determined by dynamic light scattering (DLS) using a Nicomp 370 submicron particle analyzer. Molecular weight distributions were measured by gel permeation chromatography using a Waters 515 HPLC pump, Waters Styragel columns (HR3, HR4, and HR6) at 35 °C, and a Waters 410 differential refractometer detector. THF was used as the eluant at a flow rate of 1 cm3/ min. Narrow-molecular-weight polystyrene standards with molecular weights ranging from 580 to 3800000 g/mol were used for calibration. Results and Discussion The recipe used for this study consisted of 30.00 g of BMA, 570.00 g of DI water, 0.6575 g of SDS, 0.4622 g of KPS, and 0.4622 g of NaHCO3. Thus, the weight fraction of monomer was ca. 5%; the surfactant concentration was 4 mM based on water; and the KPS and NaHCO3 concentrations were 3 and 9.65 mM, respectively. A low concentration of surfactant was used because we were interested in studying the effects of agitation when the surfactant concentration was below the critical micelle concentration. Latexes are usually sensitive to shear-induced coagulation (and possibly diffusion-induced coagulation) at low surfactant concentrations if the solids content is high. Coagulation would make the interpretation of kinetic results, especially those on particle concentration and molecular weight, difficult. Hence, a recipe with low solids content was chosen. The reactions were carried out at agitation speeds of 300, 400, 500, 600, and 800 rpm,and at a temperature of 50 °C. Nitrogen was bubbled through ca. 1 dm3 of DI water in a conical flask for about 30 min at a flow rate of 8 cm3/s, and this water was used for preparing the emulsion. DI water (451.58 g), 100.00 g of SDS solution (prepared by dissolving 1.3237 g of SDS in 200.00 g of water), and 30.00 g of BMA were added to the reactor. The stirrer speed was set to 300 rpm (in all experiments), and nitrogen was passed through the reactor headspace for ca. 30 min. After the nitrogen flow had been stopped, the following actions were taken: (i) the agitator speed was raised to the experimental value, (ii) a calibration for the heat-transfer coefficient was performed, (iii) the temperature was ramped to 50 °C, (iv) another calibration was performed at the reaction temperature and agitation speed, (v) 20.00 g of the initiator solution (prepared by dissolving 2.4231 g of KPS and 2.4231 g of NaHCO3 in 100.00 g of DI water) was injected into the reactor using a needle and a syringe, (vi) 3 mL of 1 wt % hydroquinone solution was injected into the reactor ca. 60 min after the addition of initiator, and (vii) a final calibration was performed to determine the heat-transfer coefficient of the final latex. Each calibration procedure lasted for ca. 30 min,

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Figure 1. Variation of the heat-transfer coefficient with agitation speed.

Figure 3. Dependence of the duration of the induction period on agitation speed. The dashed curve is drawn as a guide to the eye.

Figure 2. Heat evolution rate vs time for the reaction performed at 300 rpm agitation speed. Qr values were recorded at 6-s intervals. Time t1 corresponds to the addition of the initiator solution; t2 corresponds to the end of induction period, characterized by sharply increasing Qr; and t3 corresponds to the addition of hydroquinone solution. In subsequent figures, t2 is arbitrarily set to zero. The negative spikes in Qr at t1 and t3 are because of the endothermic effect of injecting solutions at room temperature into the reaction fluid that is at 50 °C. The duration of the induction period is given by (t2 - t1).

Figure 4. Effect of agitation on Qr vs time profiles; t ) 0 corresponds to the end of the induction period (t2 in Figure 2).

and the time required for the temperature to increase to 50 °C and stabilize was ca. 30 min. Figure 1 shows the variation of the overall heat-transfer coefficient (of the initial emulsion) with agitation speed. The heattransfer coefficient of the final latex was determined to be almost the same as that of the initial emulsion. As seen in Figure 2, the heat evolution rate, Qr, did not rise immediately upon injection of the initiator solution. The start of each reaction was preceded by an induction period, the duration of which depended on the agitation speed. The induction period was determined as the difference between t2 and t1 (cf. Figure 2). It is also seen that the heat evolution during the induction period was almost zero. Figure 3 shows the variation of the induction period with the agitation speed. For the reactions at higher agitation speeds (600 and 800 rpm), the induction period lasted for an hour or more. Figure 4 shows the rate of heat evolution with time for polymerizations carried out at different agitation speeds. As discussed before, the rate of polymerization, Rp, is directly proportional to the heat evolution rate, Qr. It can be seen that the maximum in the rate of heat evolution, Qr,max, is higher at a higher agitation speed. The Qr curves for lower agitation speeds (300 and 400

rpm) have different shapes compared to those for higher agitation speeds (600 and 800 rpm). For the sake of clarity, these two sets of heat profiles are shown separately in Figure 5. In the former case, Qr rises rapidly to ca. 5 J/s (cf. Figure 5a). The gradual rise to the value of ca. 7 J/s is preceded by a slight dip in the Qr curve. In the case of the 600 and 800 rpm agitation speeds, the initial increase in Qr is less steep (cf. Figure 5b). The integral of Qr (J/s) over the entire reaction time was almost the same for all agitation speeds, with an average value of 12.657 kJ and a standard deviation of 0.075 kJ, which corresponds to a heat of polymerization of 60.0 ( 0.4 kJ/mol. Although Qr,max was higher at higher agitation speeds, the rate during the initial stages of the reaction was lower at higher agitation speeds. Figure 6 shows the rate during the first 2 min of the reaction, where the retardation effect of oxygen is clearly evident. The transfer rate of oxygen from the headspace into the emulsion is lower at the lower agitation speeds (300 and 400 rpm), thus resulting in a lower number of termination events, a higher concentration of growing free radicals, and an overall higher reaction rate. However, between 2 and 5 min of reaction, the reaction rate at the higher agitation speeds overtakes that at the lower speeds. This can be attributed to the nucleation of a higher number of particles at the higher agitation speed. Figure 7 shows the intensity-average diameter of the polymer particles obtained by dynamic light scattering (Nicomp 370). The particle diameter in the final latex decreased with increasing agitation speed. The concentrations of the polymer particles in the final latexes were

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Figure 7. Variation of the particle diameter in the final latex with agitation speed. The intensity-average particle diameter was determined by DLS. The standard deviation of the particle size distribution was less than 10% of the mean and did not show a definite trend with agitation speed. Comparison of the particle diameters determined by transmission electron microscopy and DLS of monodisperse standard polystyrene particles shows that the actual particle diameter is ca. 91% of that determined by DLS. This correction was applied in calculating the particle concentrations in the final latexes. The particle diameters were confirmed by capillary hydrodynamic fractionation. The dashed curve is drawn as a guide to the eye.

Figure 5. Effect of agitation on Qr vs time profiles.

Figure 8. Kinetics of polymerization at different agitation speeds: monomer conversion vs time profiles.

Figure 6. Effect of agitation on Qr vs time profiles during the initial stages of polymerization.

6.95 × 1016 and 6.93 × 1016 (dm of water)-3 at 300 and 400 rpm, respectively; (7.82 ( 0.48) × 1016 (dm of water)-3 at 500 rpm; and 9.66 × 1016 and 9.87 × 1016 (dm of water)-3 at 600 and 800 rpm, respectively. Thus, the number of particles in the latex prepared using 800 rpm is higher than that at 300 rpm by a factor of ca. 1.4. The Qr,max values for the agitation speeds of 800 and 300 rpm are ca. 10.2 and 7.2 J/s, respectively, which also differ by a factor of ca. 1.4. Thus, the difference in the maximum values of Qr can be attributed to the difference in the number of polymer particles present during the reaction. Figure 8 shows the kinetic results in terms of monomer conversion vs time, typical of the data obtained from other methods such as gravimetry or dilatometry. A clear distinction is seen between the two sets of agitation speeds (300 and 400 rpm vs 600 and 800 rpm). However, much of the detail seen in the original Qr vs time profiles is lost. This brings out the importance of

techniques such as reaction calorimetry that measure the reaction rate directly in comparison to techniques that measure monomer conversion with time and obtain the reaction rate by differentiation. As a control experiment, a reaction was also performed in the RC1 reactor where nitrogen was continuously purged throughout the reaction. The agitation speed was 300 rpm. The water was boiled and cooled under nitrogen using an ice-batch. As before, 451.58 g of DI water, 100.00 g of the SDS solution, and 30.00 g of BMA were added to the reactor. Nitrogen was bubbled (sparged) through the emulsion at a flow rate of 8 cm3/s for ca. 45 min until the start of the first calibration. After this, the sparging was stopped, and nitrogen was passed through the reactor headspace at a flow rate of 2 cm3/s until the end of the reaction. Thus, nitrogen flowed through the reactor headspace for more than 2 h before the initiator was added (compared to 30 min previously). In this case, the polymerization started immediately upon addition of the initiator solution, and there was no induction period. Figure 9 compares the kinetics of this reaction and the reaction in which there was no nitrogen flow. The time t ) 0 in Figure 9 corresponds to the addition of the initiator solution. For


Figure 9. Comparison of the kinetics at 300 rpm agitation speed with and without an induction period. Table 1. Molecular Weight Averages for Polymers in Latexes Prepared under Different Agitation Speeds agitation speed (rpm)

Mn/106 (g/mol)

Mw/106 (g/mol)

PDI ) Mw/Mn

300 400 500 600 800 300a

1.06 0.93 0.59 0.55 0.57 1.20

6.91 6.35 4.53 4.28 3.77 4.60

6.52 6.86 7.69 7.81 6.57 3.82

a

No induction period.

the reaction with the induction period, t ) 0 corresponds to the time at which there was a sharp rise in the Qr value (ca. 13 min after addition of the initiator solution). It is seen that the reaction rate was higher and the reaction time shorter when there was no induction period. The particle concentration in the final latex was 6.29 × 1016 (dm of water)-3. Because the particle concentration is lower without the induction period [6.29 × 1016 (dm of water)-3 compared to 6.95 × 1016 (dm of water)-3 with the induction period], the increase in rate is attributed to a higher value of n j in the absence of oxygen. For reactions carried out under nitrogen flow and at agitation speeds of 300 and 800 rpm, the particle concentrations in the final latexes were 6.29 × 1016 dm-3 and 6.86 × 1016 (dm of water)-3, respectively. Although there is an increase in the number of particles at the higher agitation speed, this increase is not as much as in the presence of oxygen. Effect of Agitation on Molecular Weight Distribution. Oxygen has a significant solubility in monomers. Cunningham et al. have estimated the solubility of oxygen in styrene to be ca. 35 ppm (ca. 1 mM) at 60 °C.3 As the concentration of oxygen in the aqueous phase increases, the oxygen concentration in the monomerswollen particles will also be higher. Hence, the rate of termination of the growing chains in the polymer particles will be higher, and there will be fewer propagating radicals (lower n j ). Because the monomer availability is the same, the fewer radicals propagate to higher degrees of polymerization, whereas the radicals terminated early by oxygen contribute to the lowmolecular-weight end of the distribution. Thus, in the presence of oxygen, a broad distribution of molecular weights is expected. This is evident from the molecular weights reported in Table 1. These values were obtained by gel permeation chromatography (GPC). Mn and Mw are the number-average and weight-average molecular

Figure 10. Effect of agitation on the molecular weight distribution of the polymers in the final latexes: (a) dw/d log M vs log M and (b) W(M) vs M.

weights, respectively. The molecular weight of the polymer prepared in the absence of the inhibiting and retarding effect of oxygen shows a narrower distribution (PDI ca. 3.8). In Table 1, it is seen that the molecular weights decrease with increasing agitation speed. The sharp transition between 400 and 600 rpm corresponds to similar transitions in the induction period and particle diameter values. The polydispersity indices reported in Table 1 characterize the broad distribution of molecular weights. The molecular weights for the latex prepared using an agitation speed of 300 rpm under continuous nitrogen flow through the reactor (so that there was no induction period) are also shown in Table 1. As expected, the number-average molecular weight of the polymer formed in the absence of oxygen is higher than those from the reactions that showed oxygen inhibition. Figure 10 shows the GPC molecular weight distributions of polymers in the final latexes prepared using different agitation speeds. w(M) denotes the weight fraction of polymer chains in the sample with molecular weights less than M, and W(M) dM is the weight fraction of polymer chains with molecular weights between (M - dM/2) and (M + dM/2). Thus

W(M) )

dw dM

(3)

The distributions shown in Figure 10 have been normalized so that the area under the curve for each distribution is unity. Mathematically

dw d log M ) ∫W(M) dM ) 1 ∫d log M

(4)

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form a primary precursor particle. The value of jcr is given by

Table 2. Critical Micelle Concentrations of SDS in Different Media at Room Temperature medium

cmc (mM)

water water saturated with BMA 9.6 mM NaHCO3 solution in water 9.6 mM NaHCO3 solution in water saturated with BMA water containing 3 mM KPS and 9.6 mM NaHCO3

9.1 7.6 6.2 6.2 5.1

It is evident from Figure 10b that the weight fraction of the lower-molecular-weight polymer chains is higher at the higher agitation speeds. This can be attributed to the increased rate of formation of dead chains by oxygen termination. The growing free radicals in the polymer particles are terminated by oxygen present in the particle and also by a free radical that enters the particle from the aqueous phase. The probability of entry of an aqueousphase free radical is lower in the presence of oxygen. If this reduction in the entry rate has a greater effect than the termination by oxygen in the polymer particles, an increase in the molecular weight is expected. However, this effect does not seem to be significant from the experimental data. Mathematical Model for the Effect of Oxygen Mass Transfer on the Induction Period. This section presents a mathematical model for the effect of agitation speed, and hence the rate of mass transfer of oxygen from the gas phase to the aqueous phase, on the duration of the induction period. De Bruyn et al. have discussed different reactions that occur between the aqueous-phase radicals and dissolved oxygen and obtained the probability of an aqueous-phase monomeric radical growing to a z-mer.5 The probability that a radical adds an additional monomer is given by the ratio of the rate of propagation to the sum of the rate of propagation and the rates of all radical termination reactions. De Bruyn et al. investigated seed emulsion polymerization reactions and hence were interested in the probability that an initiator-derived free radical enters the polymer particles (the entry efficiency), fentry. We determined the critical micelle concentration of the surfactant using the technique of continuous surfactant titration and the Sensadyne (model 6000) bubble tensiometer.10 The values at room temperature are given in Table 2. The critical micelle concentrations were also determined at 70 °C. The cmc in water at 70 °C was 11.5 mM. An aqueous solution saturated with BMA and containing 3 mM KPS, 9.5 mM NaHCO3, and 3 mM hydroquinone (added as a polymerization inhibitor) resulted in a cmc of ca. 8 mM at 70 °C. The increase in the cmc with temperature and its decrease in the presence of electrolytes are consistent with the observations of other researchers.11 Thus, the cmc at the reaction temperature of 50 °C employed in this work is expected to be between 5 and 8 mM. The surfactant concentration of 4 mM used in our recipe, being lower than the critical micelle concentration, is expected to result in particle nucleation by the homogeneous nucleation mechanism. In the case of ab initio emulsion polymerization with the surfactant concentration below the critical micelle concentration, particle nucleation occurs by propagation of an initiator-derived free radical (-OSO3*) to a certain critical degree of polymerization, jcr, at which point the oligomer loses solubility in water and precipitates to

jcr ≈ 1 -

55 kJ/mol RT ln [M]sat aq

(5)

sat where [M]aq (mol‚dm-3) is the saturation concentration of monomer in water, R (J‚mol‚K-1) is the universal gas constant and T (K) is the temperature. The saturation concentration of BMA in water at 50 °C is ca. 3 × 10-3 mol‚dm-3.6 Thus, the value of jcr can be estimated to be ca. 5. The fraction of the initiator-derived free radicals that propagate jcr times and precipitate to result in the nucleation of a precursor particle will be denoted by fnuc. It can be shown that fnuc is the ratio of the rate of formation of oligomers with degree of polymerization jcr, -SO M *(aq), to the rate of formation of the initiator4 jcr derived free radicals, SO4-*. Again, the probability that the radical -SO4M*(aq) grows to a jcr-mer is determined by the relative rates of propagation (jcr - 1 times) and the sum of the rates of the termination reactions. Once the precursor particle forms, the rate of polymerization increases significantly, because of the higher monomer concentration in the freshly formed polymer particle. As an example, for propagation in the aqueous phase, the concentration of BMA in the aqueous phase is ca. 3 × 10-3 mol‚dm-3, whereas for propagation in a polymer particle, the monomer concentration is ca. 3.8 mol‚dm-3 (or even higher during the initial stages of the polymerization where the particle size is small7). According to the reaction mechanism proposed by De Bruyn et al.,5 an equation for fnuc can be obtained as

fnuc ≈

{

kp[M]aq + kt,O2[O2]aq +

x(k

2 t,O2[O2]aq)

}

jcr-1

kp[M]aq + 4kt,aqkd[I]

(6)

where kp is the propagation rate constant of the monomer at the polymerization temperature; kt,O2 is the rate constant of termination of a propagating free radical, -SO M *(aq), with oxygen; k 3 -1 -1 4 i t,aq (dm ‚mol ‚s ) is the bimolecular termination rate constant for the aqueousphase radicals; kd (s-1) is the dissociation rate constant of the initiator; and [I] (mol‚dm-3) is the molar concentration of the initiator. Equation 6 neglects further reaction of the peroxy radical, -SO4MiOO*(aq), formed by addition of oxygen to -SO4Mi*(aq), with the monomer. Termination reactions between the peroxy radicals are also neglected. The reader is referred to the Appendix for the derivation. Figure 11 shows the efficiency of nucleation at different concentrations of oxygen in the aqueous phase for the polymerization of BMA at 50 °C. A value of 1 × 109 dm3‚mol-1‚s-1 has been assumed for both kt,O2 and kt,aq. As expected from eq 6, the maximum value of fnuc (when [O2]aq ) 0) is quite sensitive to the value of kt,aq. However, irrespective of the value of kt,aq, it is observed that the efficiency of nucleation is almost zero when the oxygen concentration is above 10-5 mM. Hence, particle nucleation will begin only when the concentration of oxygen in the aqueous phase drops below ca. 10-5 mM. Inhibition due to oxygen can be modeled as a reaction in the aqueous phase with mass transfer of oxygen from the gas phase to the aqueous phase. Transfer of oxygen


be close to the bulk concentration, cg, and c/l will be equal to the saturation concentration of oxygen in water when the gas-phase concentration is cg. Thus

c/l )

cg H

(8)

where H is related to the Henry’s constant for oxygen solubility in water. For simplicity of notation, cl will be used instead of [O2]aq. The mass balance for oxygen in the liquid phase is given by Figure 11. Effect of the aqueous-phase oxygen concentration on the fraction of the initiator-derived free radicals that form polymer particles by the homogeneous nucleation mechanism at 50 °C (jcr ) 5, kp ) 796 dm3‚mol-1‚s-1, 8 [M]aq ) 3.1 × 10-3 mol‚dm-3,6 kt,O2) 1 × 109 dm3‚mol-1‚s-1, kt,aq) 1 × 109 dm3‚mol-1‚s-1, kd ) 1.2 × 10-6 s-1,9 [I] ) 3 × 10-3 mol‚dm-3).

dcl ) -kd[I] + kLag(c/l - cl) dt

(9)

where kd (1/s) is the dissociation rate constant for KPS and [I] (mol/m3) is the KPS concentration (in the aqueous phase). Implicit in eq 9 is the fact that the rate of depletion of oxygen in the aqueous phase is limited by the rate of generation of free radicals by dissociation of the initiator

d[SO4-*] ) -2kd[I] dt Figure 12. Mass transfer of oxygen from the gas phase to the liquid phase [cg and cl are the oxygen concentrations in the bulk gas phase and the bulk liquid phase, respectively; cint is the g concentration of oxygen on the gas side of the interface (cint g ≈ cg); the interfacial oxygen concentration on the liquid side of the interface, cint l , is assumed to be the equilibrium concentration int / corresponding to cint g (or cg because cg ≈ cg) and is denoted by cl ].

also takes place between the monomer-droplet phase and the aqueous phase. However, if the volume of the monomer phase is small compared to that of water, as in a recipe with a low volume fraction of monomer, this transfer can be neglected in the mathematical model. The reactor is considered to be a closed system with respect to mass transfer. In other words, there is no entry of atmospheric oxygen into the reactor during the reaction. The only oxygen in the reactor is that remaining after nitrogen gas has been passed through the headspace for 30 min before the addition of the initiator solution. Both the gas phase and the liquid phase are assumed to be well-mixed. Equation 7 gives the mass balance for oxygen in the gas (denoted by subscript g)

()

dcg Vl ) -kLag(c/l - cl) dt Vg

(7)

where kL (m/s) is the liquid-side mass-transfer coefficient, ag (1/m) is the gas-liquid interfacial area per unit volume of aqueous phase, Vl (m3) is the volume of aqueous phase in the reactor, and Vg (m3) is the volume of the gas phase. c/l (mol/m3) is the concentration of oxygen on the liquid side of the gas-liquid interface (cf. Figure 12). When the gas-side resistance to the mass transfer of oxygen across the interface is negligible, the concentration of oxygen on the gas side of the interface, cint g , will

(10)

where the factor 2 arises because each initiator molecule generates two free radicals. However, each oxygen molecule consumes two initiator-derived free radicals.5 Hence, the factor 2 is omitted in eq 9. The initiator concentration is assumed to decay exponentially with time according to

[I] ) [I]0 exp(-kdt)

(11)

Thus, the differential equations for simultaneous mass transfer and chemical reaction are

( )( )

cg Vl dcg ) -kLag - cl dt H Vg

(12)

and

(

cg dcl ) -kd[I]0 exp(-kdt) + kLag - cl dt H

)

(13)

with the initial conditions cg ) cg0 and cl ) cl0 at t ) 0. Equation 13 is multiplied by (Vl/Vg) and added to eq 12, and the resulting expression is integrated to yield

cl ) cl0 - [I]0{1 - exp(-kdt)} +

Vg (c - cg) Vl g0

(14)

Upon substitution into eq 12 and simplification, we obtain

dcg + Acg ) B + C exp(-kdt) dt

(15)

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where

(

A ) kLag 1 +

1 Vl H Vg

)

(

Vl Vl B ) kLag cg0 + cl0 - [I]0 Vg Vg

)

(16)

and

Vl C ) kLag[I]0 Vg The solution of eq 15 using exp(At) as the integrating factor results in

cg )

C B + exp(-kdt) + A A - kd C B cg0 - exp(-At) (17) A A - kd

(

)

The liquid-phase oxygen concentration, cl, is then obtained from eq 14, upon substitution for cg as

cl ) D - E exp(-kdt) - F exp{-At}

(18)

( (

)( )

E ) kd[I]0 -

kLag Vl [I] (A - kd)-1 H Vg 0

parameter

-1

[

(

H* ) exp 40.622 1 -

)

135 kJ mol-1 RT

(19)

)

(

)

}(

)

cg0 1 Vl - cl0 (A - kd) - kd[I]0 1 + H H Vg

-1

(A - kd)-1

The time t required for the aqueous-phase oxygen concentration to fall to cl (from the initial value of cl0) can be obtained by solving eq 18. Figure 13 shows the evolution of the oxygen concentration in the gas and liquid phases with time, calculated using eqs 17 and 18 for two different values of kLag and an initial gas-phase oxygen concentration of 2 × 10-2 mM (which corresponds to a partial pressure of ca. 53.7 N/m2, ca. 0.25% of the oxygen partial pressure in atmospheric air). The kLag values of 0.009 and 0.3 s-1 were estimated using Calderbank’s equations for the mass-transfer coefficient, kL, and the bubble diameter, at two different agitation speeds (300 and 600 rpm).10,12 The interfacial area, ag, was obtained from the estimated bubble diameter and the experimentally observed gas holdup in the liquid phase of the reactor. The initial oxygen concentration in the aqueous phase was assumed to be the equilibrium concentration corresponding to a partial pressure in the gas phase of 53.7 N/m2. The Benson and Krause equation was used to obtain the Henry’s constant, H*, that relates the equi-

2

) ] 59502 atm 0.02 mM

librium mole fraction of oxygen in the aqueous phase, xO2, to its partial pressure, pO2 (atm) in the gas phase13

xO2 )

{(

1.2 × 10-6 s-1

168.85 168.85 - 36.855 1 T T

cg0

and

F)

value 600 cm3 400 cm3 3 mM 323.15 K

Vl Vg [I]0 T kd (s-1) ) 8 × 1015 exp -

)

Vl Vl 1 1 Vl c + cl0 - [I]0 1+ H g0 Vg Vg H Vg

Table 3. Values of Parameters Used To Determine the Time Evolution of the Oxygen Concentrations in the Gas and Aqueous Phases

(

where

D)

Figure 13. Evolution of the oxygen concentration in the gas phase (+ and - - -) and in the liquid phase (× and O) with time (calculated using eqs 17 and 18) for an initial concentration of oxygen in the gas phase equal to 0.02 mM [kLag ) (+ and ×) 0.009 and (- - - and O) 0.3 s-1].

pO2 H*

(20)

The molar concentration of oxygen in the liquid phase is then given by

cw )

( )

xO2 Fw Mw 1 - xO2

(21)

where Fw is the density of water and Mw is its molecular weight. The ideal gas law was used to relate the partial pressure, pO2, and concentration, cg, of oxygen in the gas phase

cg )

pO2 RT

(22)

Thus

H≈

( )

Mw H* FwRT

(23)

The values of different parameters used to obtain the results presented in Figure 13 are listed in Table 3. It can be seen that the oxygen concentration in the aqueous phase decreases at a lower rate at the higher value of kLag of 0.3 s-1 than at 0.009 s-1. Because the


Figure 14. Volume of gas-liquid dispersion in the reactor vs agitation speed.

Figure 15. Primary precursor particle -OSO3M5* (molecular model obtained using CS Chem3D Pro, LP ) lone pair on carboxyl oxygen).

induction period corresponds to the time required for the reduction of the oxygen concentration in the aqueous phase to ca. 10-5 mM, the induction period is longer (61 vs 14.5 min) when kLag is higher (0.3 vs 0.009 s-1). These values of the induction period are in reasonable agreement with the experimentally observed values. Even at the end of the induction period, the oxygen concentration in the gas phase is seen to be fairly high. Thus, a continuous retardation of the polymerization is expected, wherein oxygen is transferred from the reactor headspace into the aqueous phase (at a rate dependent on kLag and, hence, on the agitation), affecting the reaction kinetics. The mass-transfer coefficient, kL, and the gas-liquid interfacial area per unit volume, ag, are both agitationdependent. The mass-transfer coefficient depends on the energy input per unit volume. The interfacial area depends on the gas holdup and the bubble diameters, both of which are affected by agitation. The volumes of the gas-liquid dispersion at different agitation speeds were experimentally obtained by noting the heights of the dispersions on the calibrated wall of the reactor. It was observed that, whereas the mixing at 300 and 400 rpm was gentle and the surface of the liquid in the reactor was quiescent with small ripples, intense agitation with gas bubbles dispersed in the emulsion resulted at the higher agitation speeds, especially at 600 and 800 rpm. The gas-liquid dispersion was formed by the phenomenon of aspiration wherein the gas in the headspace is sucked into the liquid phase promoted by agitation. The gas-liquid dispersion has a higher volume than the liquid phase alone, with the difference arising from the gas holdup of the liquid. Thus, for the reactor geometry described in the Materials and Methods section, the critical agitation speed at which there is significant suction of gas from the reactor headspace into the liquid is between 400 and 500 rpm, as seen in Figure 14. Marked changes in the heat-transfer coefficient, the duration of the induction period, the particle concentrations, the reaction kinetics, and the molecular weights also occur between 400 and 500 rpm. The cause of these changes seems, therefore, to be related to the phenomenon of gas aspiration from the reactor headspace, which is consistent with our proposed explanations based on trace levels of residual oxygen in the reactor headspace at the start of the reaction. In their study of the influence of oxygen on the kinetics of seeded emulsion polymerization, Lo´pez de Arbina et al. found that the induction period increased

with decreasing initiator concentration and increasing ratio of the headspace and liquid-phase volumes.14 These results are also in accord with our mathematical model. The induction period in the case of a seeded polymerization would be the time required for the oxygen concentration in the aqueous phase to decrease to such a value that the entry efficiency, fentry, becomes significantly high.5 A longer induction period is expected for a lower value of [I]0 or a higher value of Vg/Vl. Effect of Agitation on Particle Nucleation. The experimental results indicate that an increase in the degree of agitation leads to an increase in the number of polymer particles through the inhibition effect of oxygen. The rate of oxygen transport into the reaction mixture is accelerated by agitation, and the concentration of oxygen in the aqueous phase is higher at a higher agitation speed. In the case of micellar nucleation, the Smith-Ewart analysis shows that the total number of polymer particles at the end of the nucleation stage is inversely proportional to the rate of growth of polymer particles during the nucleation stage.7 Oxygen lowers the particle growth rate by terminating the propagating polymer radicals and, hence, is expected to produce more particles, as proposed by Nomura et al.1 The nucleation mechanism in our system, however, where the surfactant concentration is below the cmc, is likely to be homogeneous or coagulative.7 The particle nucleation begins with the formation of the primary precursor particles when the initiator-derived free radical precipitates after propagating to a chain length of jcrit (cf. Figure 15). The primary precursor particles undergo propagational or coagulative growth to form the precursor particles. Colloidal stability is derived from the initiator-derived charged end groups and from the adsorbed surfactant. The aggregation between the precursor particles continues with a reduction in the total surface area, until the surface charge density (charge per unit area of particle surface) increases above a critical value necessary for colloidal stability. The rate of nucleation of the polymer particles is equal to the difference between the rate of formation of the precursor particles and their rate of coagulation. The rate of formation of the primary precursor particles is higher when the oxygen concentration in the aqueous phase is lower. Clearly, a greater number of initiator-derived free radicals will be able reach the critical length of jcrit by propagation when there are fewer oxygen molecules in the aqueous phase to terminate the radicals. The rate of coagulation of the primary precursor particles is

6340


expected to show a second-order dependence on their number concentration.15 Thus, at a lower concentration of oxygen, a rapid increase in the number of the primary precursor particles could actually result in a lower overall rate of nucleation because of a higher coagulation rate and, eventually, a lower final number of colloidally stable mature particles. In contrast, when the oxygen concentration in the aqueous phase is higher, the primary precursor particles form more gradually. The rate of coagulation is thus lower, and the overall rate of nucleation is higher. The kinetic data in Figures 4-6 support this hypothesis. From Figure 6, it can be concluded that, during the nucleation stage, the overall rate of polymerization is higher at 300 rpm than at 800 rpm. This can be attributed to a combined effects of (1) a higher rate of polymerization in the aqueous phase due to a reduced oxygen concentration and (2) a higher rate of polymerization in the particle phase due to a greater number of polymer particles. However, the particle concentration does not remain higher throughout, in comparison to the reaction using the 800 rpm stirrer speed. The slight dip in Qr at 300 rpm seen in Figure 5a is indicative of aggregation between the rapidly formed precursor particles. In contrast, the rate of heat evolution at 800 rpm shows a monotonic increase and eventually exceeds that at 300 rpm because of a greater number of mature particles. There is another factor that might be important in determining the final numbers of particles at different agitation speeds. The higher oxygen concentration obtained with a stirrer speed of 800 rpm will produce a greater number of oligomeric chains that are terminated by oxygen before attaining a degree of polymerization equal to jcrit. These oligomeric chains with charged sulfato end groups can act as surfactant molecules and stabilize the precursor particles. This generation of in situ surfactant can result in a higher particle number. Using the results obtained in this work, it is difficult to estimate the relative importance of the two mechanisms. Nevertheless, the two the mechanisms predict effects in the same direction. Finally, the peroxides formed by termination of the growing free radicals with oxygen can act as additional initiator molecules, but for reasons discussed by De Bruyn et al., their effect will not be significant.5 Expected Influence of Temperature, Initiator Concentration, and Monomer Type on the Duration of the Induction Period. When the polymerization was carried out using the same recipe and procedure (with a limited nitrogen purge of the reactor headspace for 30 min) at a temperature of 70 °C, no significant induction period was observed.10 Upon calculation of the nucleation efficiencies using eq 6, at the three different temperatures 50, 60, and 70 °C, it is observed that particle nucleation can begin at higher values of [O2]aq, thus resulting in shorter induction periods. The propagation rate constants at these temperatures are 796, 1015, and 1277 dm3‚mol-1‚s-1, respectively,8 and the decomposition rate constants of KPS are 1.2 × 10-6, 5.4 × 10-6, and 2.3 × 10-5 s-1, respectively. Moreover, the kinetics of oxygen consumption in the aqueous phase is faster at higher temperature, because of the higher rate of generation of free radicals by initiator decomposition. This is seen in Figure 16 where the concentrations of oxygen in the gas and aqueous phases are plotted as a function of time

Figure 16. Effect of temperature on the evolution of the oxygen concentration for an initial gas-phase concentration of 0.02 mM. The top curves are the gas-phase concentrations, and the bottom curves are the concentrations in the aqueous phase. (- ‚ ‚ -) 50, (- - -) 60, and (s) 70 °C. kLag ) 0.3 s-1.

Figure 17. Effect of the aqueous-phase oxygen concentration on the nucleation efficiency for the emulsion polymerizations of methyl methacrylate (-‚‚-, kp ) 650 dm3‚mol-1‚s-1, [M]aq ) 0.15 mol‚dm-3, jcrit ) 12)5 and vinyl acetate (s, kp ) 6700 dm3‚mol-1‚s-1, [M]aq ) 0.3 mol‚dm-3, jcrit ) 18)5 at 50 °C. kt,O2 ) 1 × 109 dm3‚mol-1‚s-1, kt,aq ) 1 × 109 dm3‚mol-1‚s-1, kd ) 1.2 × 10-6 s-1, [I] ) 3 × 10-3 mol‚dm-3.

for the three temperatures. The induction period is much shorter at 70 °C than at 50 °C. An increase in the initiator concentration will have a similar effect on the duration of inhibition period as an increase in the temperature. At 50 °C and kLag ) 0.3 s-1, the time required for [O2]aq to fall below 1 × 10-5 mM can be calculated to be ca. 188 min when the concentration of KPS is 1 mM and ca. 17 min when the KPS concentration is 10 mM. It is instructive to calculate the nucleation efficiencies, fnuc, versus the aqueous-phase oxygen concentration for monomers with significantly higher water-solubility values than BMA. Figure 17 shows the results for methyl methacrylate (MMA) and vinyl acetate (VAc). Comparison with the data in Figure 11 indicates that these monomers show a higher probability of forming primary precursor particles than BMA. Although the aqueous-phase oligomeric radicals have to propagate to longer chain lengths before they can precipitate to form the precursor particles (because of higher water solubility), fnuc is higher because of the higher concentration of monomer available in the aqueous phase for the propagation reaction. Under identical conditions, the induction period is expected to be shorter in the case of VAc polymerization as the formation of precursor par-


ticles will begin even when the oxygen concentration is ca. 1 × 10-4 mM. However, there will be a greater retardation of the polymerization rate due to the relatively higher oxygen concentration in the system when particle nucleation begins. Role of Agitation in Large-Scale Reactors. Agitation plays an important role in emulsion polymerization. It is necessary for emulsification of the monomer, for maintenance of fluid composition homogeneity in different parts of the reactor, and for heat transfer during the exothermic polymerization reaction. According to Kolmogoroff’s theory of isotropic turbulence, the agitation power input per unit volume of the reaction fluid is an important criterion for scale-up from laboratoryscale reactors to industrial reactors. Using the equation P ) NpFN 3D5, where P is the power input, Np is the power number for the agitator, F is the fluid density, N is the agitation speed, and D is the agitator diameter, the agitation power input was calculated to be ca. 0.3 kW/m3 at 300 rpm and ca. 6.1 kW/m3 at 800 rpm. The power number for the Rushton turbine agitator is ca. 5 during turbulent flow. The mass-transfer coefficient, kL, usually scales with the agitation power input per unit volume. For example, the Calderbank equation16 gives

kL ) 0.592DO20.5

(µVP )

0.25

(24)

where DO2 is the diffusion coefficient of oxygen in the liquid, µ is the viscosity of the liquid, and V is the liquid volume. The interfacial area between the gas and the liquid depends on the reactor dimensions and agitation. At low stirring speeds, the area is equal to the crosssectional area of the reactor. As the agitation speed is progressively increased, the liquid initially forms a vortex. Later, ripples begin to appear at the surface. The interfacial area therefore increases with the agitation speed. Kittilsen et al. have discussed the influence of agitation and reactor dimensions on the interfacial area.17 At a certain agitation speed, N*, bubble aspiration from the gas atmosphere above the liquid occurs, and a gas-liquid dispersion is formed. The agitator speed at which this occurs is given by18

N* ) 2

( ) ( )( σg F

0.25

)

T Hl - Ha T D2

0.5

(25)

where σ is the surface tension of the liquid, F is its density, g is the gravitational acceleration, T is the diameter of the reactor, Hl is the height of the liquid in the reactor, and Ha is the height of the agitator (so that Hl - Ha is the height of the liquid above the agitator). The interfacial area of gas bubbles per unit volume of liquid in the gas-liquid dispersion can now be calculated using

ag )

(π/4)T2 + (6Hu/dB) V

(26)

where Hu is the total volume of gas in the gas-liquid dispersion and dB is the volume-surface average diameter of the gas bubbles, both of which depend on agitation. In the case of pure liquids, Calderbank found that

P -0.4 -0.2 0.5 F g dB ) 0.0009 + 4.15σ0.6 V

()

(27)

where g is the volume fraction of the dispersion that is gas and all of the variables are expressed in the SI units.19 To minimize the effects of oxygen inhibition, the agitator diameter and speed should be chosen such that the heat-transfer coefficient is high enough for good heat removal and there is good emulsification of monomer to prevent phase separation of the monomer to form a monomer pool but there is no aspiration of bubbles into the liquid. Conclusions The emulsion polymerization of n-butyl methacrylate was carried out at different agitation speeds using a recipe in which the surfactant concentration was below its critical micelle concentration. The reaction mixture was thoroughly deoxygenated before the reaction was started (by the bubbling of nitrogen through the water and monomer). Nitrogen was passed through the reactor headspace for 30 min before addition of the initiator. However, 30 min of nitrogen purging was insufficient to completely replace the initial oxygen by nitrogen. All of the reactions carried out using different agitation speeds showed an induction period, the duration of which depended on the agitation speed. The kinetics of the polymerization that ensued, the particle concentration in the final latex, and the molecular weight distribution showed a strong dependence on the agitation speed. The leveling of the values between agitation speeds of 600 and 800 rpm could be because of the fact that, at these agitation speeds, the rate of mass transfer of oxygen far exceeds the rates of reaction events in the liquid phase and is no longer the controlling factor. This can be verified using the simple mathematical model we have proposed to explain the influence of the masstransfer rate on the duration of the induction period. Using the parameters given in Table 3, it was found that, above a kLag value of ca. 0.1 s-1, the effect of kLag on the induction period was not significant. The effect of agitation on particle nucleation in the presence of the retarding effect of oxygen is especially interesting. The rate data in Figure 6 show that the rate of reaction is lower during the nucleation stage when the agitation speed is higher. This is expected because the higher agitation speed results in a higher concentration of oxygen in the aqueous phase. However, the reaction rates at 600 and 800 rpm soon exceeded those at the lower agitation speeds. It is proposed that the rates of nucleation at the higher agitation speeds were lower, but more polymer particles resulted by the end of the nucleation stage because of the gradual increase in the surface area during the nucleation stage and the greater availability of surfactant to stabilize more particles. In this work, we were interested in studying how agitation affects the kinetics of emulsion polymerization below the critical micelle concentration of the surfactant. Hence, we employed a low surfactant concentration and a low monomer concentration (to avoid coagulation). We have also studied the effects of agitation using a recipe in which the solids content was higher (ca. 20%) and the surfactant concentration was above the critical micelle concentration,10 and these results will be discussed separately. Acknowledgment Financial support from the Emulsion Polymers Industrial Liaison Program is greatly appreciated.

6342


Appendix

The nucleation efficiency, fnuc, is given by

Derivation of an Expression for the Nucleation Efficiency. The reactions involving the aqueous-phase radicals and oxygen are as follows:5 kp,I

-

SO4 * + M(aq) 98 SO4M*(aq) 9

-

SO4Mi*(aq) + M(aq) 98 SO4Mi+1*(aq) kp,aq ) 10 dm3/(mol s)

-

kt,O

SO4Mi*(aq) + O2(aq) 98 -SO4MiOO*(aq) 2

kt,O2 ≈ 109 dm3/(mol s) kt,aq

2[-SO4Mi*(aq)] 98 (-SO4Mi)2(aq) kt,aq ≈ 109 dm3/(mol s) -

SO4Mi*(aq) + SO4MjOO*(aq) 98 SO4MiOOMjSO4k6

-

k5 ≈ 109 dm3/(mol s)

-

2[ SO4MjOO*(aq)] 98 ( SO4MjOO)2(aq) k6 ≈ 107 dm3/(mol s) -

k7

SO4MjOO*(aq) + M(aq) 98 -SO4MjOOM*(aq) k7 ≈ 1 dm3/(mol s)

The steady-state approximation for the free radicals gives

2kd[I] ) kt,O2[-SO4Mi*][O2] + 2kt,aq[-SO4Mi*]2 + k5[ -SO4Mi*][-SO4MjOO*] - k7[-SO4MjOO*][M] (i) and

kt,O2[-SO4Mi*][O2] ) k5[-SO4Mi*][-SO4MjOO*] + 2k6[-SO4MjOO*]2 + k7[-SO4MjOO*][M] (ii) The species -SO4MjOO* occurs in low concentrations. Hence, 2k6[-SO4MjOO*]2 is not significant. Because of the low rate of copolymerization between the peroxy radicals and the monomer, k7[ -SO4MjOO*][M] is also negligible. Thus, eq ii simplifies to

kt,O2[-SO4Mi*][O2] ≈ k5[-SO4Mi*][-SO4MjOO*] (iii) and eq i, therefore, becomes

2kd[I] ≈ 2kt,O2[-SO4Mi*][O2] + 2kt,aq[-SO4Mi*]2 or

kt,aq[-SO4Mi*]2 + kt,O2[-SO4Mi*][O2] - kd[I] ) 0 (iv) Solution of eq iv for [-SO4Mi*] results in -

[ SO4Mi*] )

(vi)

Upon substitution for [ -SO4Mi*] from eq v and simplification, we obtain

fnuc )

{

x(k [O ] + x(k

kp[M] + kt,O2[O2] +

{

) 1+

kt,O2

2

2 t,O2[O2])

t,O2[O2])

kp[M]

}

jcr-1

kp[M]

2

+ 4kt,aqkd[I]

}

+ 4kt,aqkd[I]

1-jcr

(vii)

k5

-

-

)

3

kp,I ≈ 10 dm /(mol s) -

(

jcr-1

kp[M]

kp[M] + kt,O2[O2] + 2kt,aq[-SO4Mi*] + k5[-SO4MiOO*]

-

kp,aq

fnuc )

-kt,O2[O2] +

x(k

t,O2[O2])

2kt,aq

2

+ 4kt,aqkd[I] (v)

Literature Cited (1) Nomura, M.; Harada, M.; Eguchi, W.; Nagata, S. J. Appl. Polym. Sci. 1972, 16 (4), 835-847. (2) Harada, M.; Nomura, M.; Kojima, H.; Eguchi, W.; Nagata, S. J. Appl. Polym. Sci. 1972, 16 (4), 811-833 (3) Cunningham, M. F.; Geramita, K.; Ma, J. W. Polymer 2000, 41 (14), 5385-5392. (4) Kiparissides, C.; Achilias, D. S.; Frantzikinakis, C. E. Ind. Eng. Chem. Res. 2002, 41 (13), 3097-3109. (5) De Bruyn, H.; Gilbert, R. G.; Hawkett, B. S. Polymer 2000, 41, 8633-8639. (6) Geurts, J. M.; Jacobs, P. E.; Muijs, J. G.; Steven van Es, J. J. G.; German, A. L. J. Appl. Polym. Sci. 1996, 61 (1), 9-19. (7) Krishnan, S.; Klein, A.; El-Aasser, M. S.; Sudol, E. D. Macromolecules 2003, 36 (9), 3152-3159. (8) Hutchinson, R. A.; Beuermann, S.; Paquet, D. A., Jr.; McMinn, J. H. Macromolecules 1997, 30, (12), 3490-3493. (9) Gilbert, R. G. Emulsion Polymerization: A Mechanistic Approach; Academic Press: London, 1995. (10) Krishnan, S. Effects of Agitation in Emulsion Polymerization of n-Butyl Methacrylate and its Copolymerization with N-Methylol Acrylamide. Ph.D. Dissertation, Lehigh University, Bethlehem, PA, Jan 2003. (11) Paula, S.; Sus, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 9, 11742-11751. (12) Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; John Wiley & Sons: Chichester, U.K., 1990; p 640. (13) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1999; p 600. (14) Lo´pez de Arbina, L.; Gugliotta, L. M.; Barandiaran, M. J.; Asua, J. M. Polymer 1998, 39 (17), 4047-4055. (15) The rate of coagulation between the precursor particles is usually represented by the Smoluchowski coagulation equation with the coagulation rate coefficient modified to account for the electrostatic repulsion between the charged particles; see ref 4 or 9. (16) Calderbank, P. H. Trans. Inst. Chem. Eng. 1959, 37, 173185. (17) Kittilsen, P.; Tøgersen, R.; Rytter, R.; Svendsen, H. Ind. Eng. Chem. Res. 2001, 40, 1090-1096. (18) Van Dierendonck, L.; De Jong, P.; Van den Hoff, J.; Voncken, H.; Vermijs, R. Adv. Chem. Ser. 1974, 133, 432-448. (19) Calderbank, P. H. Chem. Eng. (London) 1967, 212, CE209CE233.

Received for review March 16, 2004 Revised manuscript received May 16, 2004 Accepted July 1, 2004 IE049796R

Effects of Agitation on Oxygen Inhibition, Particle ... - ACS Publications

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