Pseudo-bulk system

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. 

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. 

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

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. )... 

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). 

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. 

AT=Tci-T = 8 °C where T is the temperature of the measurements and Tci is the doud point. DOP is a neutral solvent for PS and PB and weakens repulsive segmental interactions between PS and PB. ° The system can be approximately treated as a pseudo-binciry system where a phase separation between PS and PB occurs in the medium of DOP and the phase separation between the polymers and the solvent is insignificant. The pseudo-binary system is regarded to be equivalent to bulk systems when the segments of polymers in bulk are replaced by the blobs, as already pointed out at the beginning of Section 2.30.2.1. 

Poly(acrylic acid) is not soluble in its monomer and in the course of the bulk polymerization of acrylic acid the polymer separates as a fine powder. The conversion curves exhibit an initial auto-acceleration followed by a long pseudo-stationary process ( 3). This behaviour is very similar to that observed earlier in the bulk polymerization of acrylonitrile. The non-ideal kinetic relationships determined experimentally in the polymerization of these two monomers are summarized in Table I. It clearly appears that the kinetic features observed in both systems are strikingly similar. In addition, the poly(acrylic acid) formed in bulk over a fairly broad range of temperatures (20 to 76°C) exhibits a high degree of syndiotacticity and can be crystallized readily (3). 

In MOMs dimensionality is a major issue. As discussed back in Chapter 1, although all materials are structurally 3D, some of them exhibit physical properties with lower dimensionality, ID or 2D, mainly due to the pseudo-planar conformation of the molecules. In fact for bulk materials one cannot strictly use the terms ID or 2D because intermolecular interactions build anisotropic but indeed 3D networks. Hence, one is led to using the prehxes pseudo or quasi when referring to ID or 2D systems. However, ideal ID and 2D systems can be artihcially prepared exhibiting real ID and 2D properties, respectively, and we will hnd some examples of this in the next sections. 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

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