Smith and Ewart Theory for State II of Emulsion Polymerization

3 SMITH AND EWART THEORY FOR STATE II OF EMULSION POLYMERIZATION [1,2] 

The total number of polymer partieles per unit volume of emulsion in the seeond stage of the emulsion polymerization is assumed to be A,. Out of these, Nq partieles are assumed to have no polymer ladieals, Aj to have one polymer radieal each, N2 to have two polymer radicals, and so forth. Therefore, 

If is the total number of polymer radicals per unit volume in the reaction mass, then 

The upper limit on these summations would theoretically be infinity. It is assumed that p primary radicals are generated in the aqueous phase per unit time per unit volume. These primary radicals enter the polymer particles and generate polymer radicals therein. These polymer radicals can also difiuse out of the particle or undergo a mutual termination with other polymer radicals in the particle. Because primary radicals are generated in the aqueous phase at a rate of p radicals per unit volume per unit time and there are polymer particles per unit volume, p/Nf primary radicals per unit time (on average) enter a given particle. Polymer radicals can diffuse out of a particle at a rate rj, given by 

This form of the equation appears because the polymer radical cannot react with itself. The term n(n — l)/v is proportional to the total niunber of collisions between the radicals per unit volume. 

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