Pseudo Bulk System Smith-Ewart Case

2 Pseudo Bulk System (Smith-Ewart Case 3) 

For Smith-Ewart Case 3, the number of radicals per particle is large and the kinetics approaches bulk polymerization. In this case, the concentration of radicals in the polymer particles is given by Eq. (19) and the molecular weight is mainly controlled by chain transfer and bimolecular termination. The rate of generation of polymer of length m in particles with i radicals is given by Eq. (46). 

From Eq. (46) the moments of the inactive chains can be calculated according to Eqs. (47), and the moments of the active chains can be calculated by applying the pseudo steady state in the material balance of the active radicals [Eqs. (48) and (49)]. 

The instantaneous number and weight-average molecular weights are then given by Eqs. (50). 

If bimolecular termination is predominant, then the instantaneous average molecular weights reduce to Eqs. (51). 

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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. 

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. )... 

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