EMULSION POLYMERIZATIONS .3. THEORY OF EMULSION COPOLYMERIZATION KINETICS

On the basis of an extended Smith-Ewart theory, explicit analytic solutions are derived describing the locus population distribution of emulsion copolymerizing systems. By means of a two-variable transform, the infinite set of partial differential difference equations reduces to a single, highly symmetrical, linear partial differential equation whose solution gives the generating function for the Nr,i-r number fraction of loci containing r growing radicals of type A and i - r radicals of type B. Solutions to this equation, in both the stationary and nonstationary state, are given for the pseudohomopolymerization approach and for systems where termination by mutual annihilation is of negligible occurrence. On these grounds, it is concluded that, apart from very special cases, the pseudohomopolymerization approach represents a suitable approximation for systems of practical interest.