Number of polymer particles

The number of polymer particles is the prime determinant of the rate and degree of polymerization since it appears as the first power in both Eqs. 4-5 and 4-7. The formation (and stabilization) of polymer particles by both micellar nucleation and homogeneous nucleation involves the adsorption of surfactant from the micelles, solution, and monomer droplets. The number of polymer particles that can be stabilized is dependent on the total surface area of surfactant present in the system asS, where as is the interfacial surface area occupied by a surfactant molecule and S is the total concentration of surfactant in the system (micelles, solution, monomer droplets). However, N is also directly dependent on the rate of radical generation. The quantitative dependence of N on asS and R,- has been derived as 

The predicted dependence of N on S and R,- for the formation of polymer particles by micellar and homogeneous nucleation followed by coagulative nucleation is given by Eq. 4-11 [Feeney et al., 1984]  

The occurrence of coagulative nucleation does not alter the -power dependence of N on R,. However, the coagulative nucleation mechanism indicates a more complex dependence of N on S. The exponent of S decreases monotonically from 1.2 to 0.4 with increasing S. The concentration of polymer particles is higher and the nucleation time is longer for systems with high surfactant concentrations. Polymer particle formation becomes less efficient at longer 

Under Smith-Ewart Case 1 conditions, for a given solids content and if termination in the aqueous phase is negligible, n 1/Np. Therefore, the polymerization rate is independent of the number of polymer particles. If termination in the aqueous phase is significant, the polymerization rate increases with the number of polymer particles. 

For large particles (dp 200 run), high initiator concentrations or redox initiators, and slow termination rates (gel effect), n 0.5 (Smith-Ewart Case 3) and it can be calculated as follows  

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During Stage I the number of polymer particles range from 10 to 10 per mL. As the particles grow they adsorb more emulsifier and eventually reduce the soap concentration below its critical micelle concentration (CMC). Once below the CMC, the micelles disappear and emulsifier is distributed between the growing polymer particles, monomer droplets, and aqueous phase. 

This, in turn, reduced the number of polymer particles (the loci of reaction) and hence the reaction rate fell. However, this explanation is at variance with the results reported in Figure 12 where the molecular weight (weight-average) clearly increases with increasing Reynolds number. It seems more likely that the turbulent flow results could be explained by a decrease in the effective initiator concentration. This low concentration would also explain why there is no further reaction after a period of about one hour as contrasted with the batch reactions where the reaction is still proceeding after two to three hours. The current absence of corroborating evidence makes this explanation very tentative. 

Under conditions normally employed, the rate p of generation of radicals from the initiator is of the order of 10 per cc. per second, and the number of polymer particles is about 10 per cc. (10 to 10 per cc. would include nearly all cases). Hence if all of the initiator radi-... 

The mechanism of emulsion polymerisation is complex. The basic theory is that originally proposed by Harkins21. Monomer is distributed throughout the emulsion system (a) as stabilised emulsion droplets, (b) dissolved to a small extent in the aqueous phase and (c) solubilised in soap micelles (see page 89). The micellar environment appears to be the most favourable for the initiation of polymerisation. The emulsion droplets of monomer appear to act mainly as reservoirs to supply material to the polymerisation sites by diffusion through the aqueous phase. As the micelles grow, they adsorb free emulsifier from solution, and eventually from the surface of the emulsion droplets. The emulsifier thus serves to stabilise the polymer particles. This theory accounts for the observation that the rate of polymerisation and the number of polymer particles finally produced depend largely on the emulsifier concentration, and that the number of polymer particles may far exceed the number of monomer droplets initially present. 

In continuous emulsion polymerization of styrene in a series of CSTR s, it was clarified that almost all the particles formed in the first reactor (.2/2) Since the rate of polymerization is, under normal reaction conditions, proportional to the number of polymer particles present, the number of succeeding reactors after the first can be decreased if the number of polymer particles produced in the first stage reactor is increased. This can be realized by increasing emulsifier and initiator concentrations in the feed stream and by lowering the temperature of the first reactor where particle formation is taking place (2) The former choice is not desirable because production cost and impurities which may be involved in the polymers will increase. The latter practice could be employed in parallel with the technique given in this paper. 

Our final goal in the present paper is to devise an optimal type of the first stage reactor and its operation method which will maximize the number of polymer particles produced in continuous emulsion polymerization. For this purpose, we need a mathematical reaction model which explains particle formation and other kinetic behavior of continuous emulsion polymerization of styrene. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

Let us consider the steady state characteristics of continuous emulsion polymerization of styrene in the first stage reactor. The steady state value of the number of polymer particles formed in the first stage reactor can be calculated using the following equations. From Eqs. (1) and (2), we have ... 

This is the reason why the steady state value of the number of polymer particles coincide with each other, as shown in Figure 4, regardless of the form of e when the first stage reactor is operated at comparatively longer residence time. On the other hand, if Eq.(23) is used instead of Eq.(16) for calculating Ap value, we have ... 

Figure 5 represents a typical example of the variation of the number of polymer particles with mean residence time 0. The solid line shows the theoretical value predicted by the Nomura and Harada model with e= 1.28x 10 . The dotted line is that predicted by the Gershberg model(or the Nomura and Harada model with Case C for ), where Eq. (23) was used instead of Eq.(16) for Ap. The value of Nt produced at longer mean residence time differs, therefore, by a factor of T(5/3) between the solid and dotted lines in Figure 5. From the comparison between the experimental and theoretical results shown in Figure 5, it is confirmed that the steady state particle number can be maximized by operating the first stage reactor at a certain low value of mean residence time max which is considerably lower than that in the succeeding reactors. This is so-called "pre-reactor principle". It is, therefore, desirable to operate the first reactor at such mean residence time as producing something like a maximum number of polymer particles in order to increase the rate of polymerization in the succeeding reactors. This will result in a decrease in the number of necessary reactors and hence, in the capital cost.

Figure 5. Effect of mean residence time of the first reactor on the number of polymer particles formed (SF = 12.5 g/L H20 lF = 1.25 g/L H20 = 0.5...

The maximum number of polymer particles produced in the first stage reactor being operated at max can be obtained by introducing Eq.(30) into Eq. (26). Thus,... 

On the other hand, the number of polymer particles formed in batch operation with the same recipe as in continuous operation is given... 

This means that as long as a CSTR is used as the first stage reactor and all the recipe ingrediants are fed into the first stage reactor, one cannot have more than 57% of the number of particles produced in a batch reactor with the same recipe as in continuous operation. The validity of these expression is clear from the comparison between the experimental and theoretical values shown in Figure 5. From Figure 5, it is found that the optimum mean residence time of the first stage reactor is about 10 minutes under these reaction conditions. Equation(30) predicts 10.0 minutes, while experimental value is 10.4 minutes where the number of polymer particles is about 60% of that produced in a batch reactor. 

Another method to increase the number of polymer particles produced in the first stage reactor with initiator and emulsifier concentrations fixed is to employ a plug flow type reactor such as a tubular reactor for the first stage. The minimum residence time of a plug flow reactor 6 necessary to produce the same number of polymer particles as in E batch reactor is tc. Thus, from Eq.(31) We have ... 

This means that one can increase the number of polymer particles about 75% higher than that formed when a CSTR of 0m is used, by employing a plug flow type reactor which is only 20% bigger in volume than a CSTR of max ... 

Nomura and Harada already reported an experimental and theoretical study on the effect of lowering the amount of monomer initially charged on the number of polymer particles formed in a batch reactor(14). Under usual conditions in batch operation, micelles disappear and the formation of particles terminates before the disappearance of monomer droplets in the water phase. However, if the initial monomer concentration is extremely low, micelles would exist even after the disappearance of monomer droplets and hence, particle formation will continue until all emulsifier molecules are adsorbed on the surfaces of polymer particles. This condition is quantitatively expressed by the following emulsifier balance equation., ... 

Figures 6, 7 and 8 show experimental verification of Eq.(40) in batch emulsion polymerization of styrene ( 14). The number of polymer particles was measured by electron micrscopy, not at finite but at 1 hour after the start of polymerization. Figure 6 represents the effect of lowering the initial monomer concentration, Mq on the number of polymer particles formed at fixed initial initiator and emulsifier concentrations. The number of polymer particles formed is constant even if M is lowered to the critical value Mc. This is because normal°condition that micelles disappear before the disappearance of monomer droplets is satisfied in the range of monomer concentration above Mc. The value of Mc can be calculated by the following equation obtained by equating XMc, the monomer conversion where micelles disappear, to XMc2, the monomer conversion where monomer droplets disappear.

In case of styrene emulsion polymerization, X 2 is 0.43. If Mq is further decreased below Mc, the number of polymer particles formed increases with decreasing MQ, as shown in Figure 6. The solid lines in the figures represent theoretical values predicted by Eq.(40) using the following numerical constants ... 

The reason why the experimental values of particle number are somewhat lower than the theoretical values seems to be that the time where the number of polymer particles was measured is not at infinite but at only 1 hour after the start of polymerization. Figure 9 shows that the number of polymer particles increases with reaction time. The solid lines represent the theoretical values predicted by the Nomura and Harada model. However, since Nt= 0 when Mq= 0, there would be an optimum value of MQ where the number of polymer particles formed becomes maximum. Unfortunately, it is difficult at present to predict the optimum value of MQ theoretically because any reaction model cannot yet explain perfectly the kinetic behavior at high monomer-conversion range. Therefore, one cannot help determining, at present, the optimum value of MQ experimentally. Figures 7 and 8 also show that Eq.(40) roughly satisfies the experimental results. 

The number of polymer particles formed in the first stage reactor can be generally expressed by the following form ... 

However, the concentration of polymer particles will be diluted by f times with the rest of water fed into the second stage. Therefore, the number of polymer particles in the second stage reactor Nt2 is given by ... 

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