DETERMINATION OF THE ABSOLUTE PROPAGATION RATE CONSTANTS IN POLYMERIZATION WITH REVERSIBLE AGGREGATION OF ACTIVE-CENTERS

When the propagating active species (P-n*) aggregate reversibly into the nonreactive (dormant) species, [GRAPHICS] both the absolute rate constant of propagation (k(p)) and the equilibrium constant of aggregation (K-a) can be determined simultaneously by using an equation derived recently, assuming polymerization to be living: r(p)(1-m) = -mK(a)/k(p)(m-1) + k(p)[I]0r(p)(-m) (where r(p) = -d ln[M]/dt, m is the aggregation degree, [M] denotes the instantaneous concentration of monomer, and [I](0) is the starting concentration of initiator ([I](0) = [P-n*] + m[(P-n*)(m)])). This equation has been applied in the present work to analyze several polymerizations studied by other authors who previously used numerical methods in determining the involved rate and equilibrium constants. A few systems have been chosen, namely, the anionic polymerization with the Li+ counterion of o-methoxystyrene, methyl methacrylate, and hexamethylcyclotrisiloxane, as well as the anionic polymerization of oxirane with the Cs+ counterion. The k(p) and K-a found analytically are in good agreement with those determined previously numerically.