Pseudo bulk

The rate of dispersion (co)polymerization of PEO macromonomers passes through a maximum at a certain conversion. No constant rate interval was observed and it was attributed to the decreasing monomer concentration. At the beginning of polymerization, the abrupt increase in the rate was attributed to a certain compartmentalization of reaction loci, the diffusion controlled termination, gel effect, and pseudo-bulk kinetics. A dispersion copolymerization of PEO macromonomers in polar media is used to prepare monodisperse polymer particles in micron and submicron range as a result of the very short nucleation period, the high nucleation activity of macromonomer or its graft copolymer formed, and the location of surface active group of stabilizer at the particle surface (chemically bound at the particle surface). Under such conditions a small amount of stabilizer promotes the formation of stable and monodisperse polymer particles. 

In this case, the kinetic behavior is quite similar to that of suspension polymerization, except that the polymer particles are supphed with free radicals from the external water phase. When the polymerization proceeds according to Eq. 48, the system is sometimes referred to as obeying pseudo-bulk kinetics. 

The values predicted by Eq. 51 agree well with those predicted by Eq. 49 within less than 4%. This type of plot is called a Ugelstad plot and has been applied as a criterion to determine whether a system under consideration obeys either zero-one kinetics (n<0.5) or pseudo-bulk kinetics (n>0.5). 

Two types of systems are identified in emulsion polymerization the pseudo-bulk system and the zero-one system... 

In this system the number of radicals in a particle is relatively so high that the polymerization resembles bulk polymerization. The average number of radicals per particle, h, is, almost, always greater than 0.5. Compartmentalization has no effect on the kinetics of a pseudo-bulk system, and termination, which is rate determining, is always diffusion controlled. 

The dependence of the maximal Rp on [KPS] is quite similar for both the MMA mini-emulsion polymerization with HD (x=0.4) and the conventional emulsion polymerization (x=0.39) but different on [SDS] (y=0.16,ME) and (y= 0.24, CE) [ 108]. The reaction orders x and y are a complex function of the radical entry (particle nucleation) and the extent of compartmentalization of radicals. The radical entry or particle nucleation increases Rp. Np increases with increasing [KPS] and the degree of increase is more pronounced for the MMA emulsion polymerization (Np°c[KPS]x, x =0.28) as compared with that for the MMA mini-emulsion polymerization (x =0.11) (Table 1). The radical entry events are restricted due to the close-packed droplet surface layer, but the pseudo-bulk ki-... 

Treatments (Smith-Ewart, pseudo-bulk ) have been devised which allow for the possibility of greater than one radical per particle and for the effects of chain length dependent termination. Further discussion on these is provided in the references mentioned above. ... 

A pseudo-bulk system is one in which the compartmentalized nature of the locus of polymerization has no effect on any kinetic property (rate, molar mass or particle size distributions). A system in which n is appreciably greater than 0.5 will always be pseudo-bulk there are so many radicals in a particle that the polymerization will be indistinguishable from the equivalent bulk one. However, a system with a low value of n can also be pseudo-bulk, if (for example) radical desorption results in the desorbed radical suffering no other fate except to re-enter another particle [1,3]. It is then apparent that the polymerization process will not see the walls between particles. Because pseudo-bulk kinetics can occur in systems where n 0.5, a pseudo-bulk system is different from the Smith-Ewart Case 3. 

The quantification of termination kinetics is relatively straightforward in a pseudo-bulk system, as follows [51-55]. Define / ,- as the population of growing... 

In a pseudo-bulk system, the MMD is more complicated. Assuming that the distribution of radical lengths from Equations (5.42) and (5.43) is known, the number MMD is obtained from the total rate of chain-stopping events ... 

Figure 5.13 Instantaneous MMD (arbitraiy units) obtained by successive subtraction of the cumulative MMD for a styrene pseudo-bulk system at 50 C (unswollen seed radius 77 nm, initiator 10 mol dm persulfate) recalculated from data in [57]. The range of tVp (as a percentage) for each sample is shown. The uncertainty is high at low and high...

Some results for a zero-one system are shown in Figure 5.12, and for a pseudo-bulk system in Figure 5.13. It is essential to be aware of the problem of... 

Next, we turn to the straight-line region in data for pseudo-bulk systems. Figure 5.14 shows the predicted and observed value of this slope for a pseudobulk system (a 130 nm latex, where n ranges up to 10). The parameters in the fit were those discussed in Section 5.3.4 for styrene y-relaxation data [49], except that the value of l tr.M was that found using the lnP(A/) data for the 44 nm seed. It can be seen that the accord is adequate, although imperfect. It would seem that the mechanisms and parameter values jHOvide an adequate description of the long-chain MMD. 

Polymer stabilized liquid crystals are formed when a small amount of monomer is dissolved in the liquid crystal solvent and photopolymerized in the liquid crystal phase. The resultant polymer network exhibits order, bearing an imprint of the LC template. After photopolymerization, these networks in turn can be used to align the liquid crystals. This aligning effect is a pseudo-bulk effect which is sometimes more effective than conventional surface alignment. Several characterization techniques... 

Pseudo Bulk System (Smith-Ewart Case 3)... 

Styrene It might be expected that the foregoing concepts developed for methyl methacrylate would be directly applicable to other monomers. This expectation was not, however, realized for styrene (15). Attempts to fit the relaxation curves in this case using the pseudo-bulk equation led to unphysical results. A more convincing interpretation of the relaxation data was obtained by incorporating a chain length dependence of the termination rate coefficient. This was accomplished by elaborating the proposal of Cardenas... 

A system obeying pseudo-bulk behaviour is one wherein the kinetics are such that the rate equations are the same as those for polymerisation in bulk. In these systems, n can take any value in a pseudo-bulk system. Common cases are (a) when the value of n is so high that each particle effectively behaves as a microreactor, and (b) when the value of n is low, exit is very rapid and the exited radical rapidly re-enters another particle and may grow to a significant degree of polymerisation before any termination event. (This case is not the same as Smith and Ewart s Case 3 kinetics, because these were applicable only to systems with n significantly above. )... 

Under any of these circumstances, a pseudo-bulk emulsion polymerisation follows the same kinetics as the equivalent bulk system ... 

Systems whose kinetics do not fall imambiguously into the zero-one or pseudo-bulk categories pose a problem for routine interpretation and prediction, let alone for obtaining useful mechanistic information such as that discussed in the preceding section. One can always use Monte Carlo modelling (Tobita, 1995), but the enormous amount of computer time this requires, and the plethora of imknown parameters, precludes its use for obtaining mechanistic information from experiment. 

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