Chain-Length-Dependent Termination Rate Processes in Free-Radical Polymerizations. 3. Styrene Polymerizations with and without Added Inert Diluent as an Experimental Test of Model

Abstract

Experiments were performed to test a model for the kinetics of free-radical polymerization systems, including the dependence of the termination rate coefficients on the lengths of both chains involved. The model has few adjustable parameters, the values of which are moreover confined within fairly narrow limits. The data comprised the rate of polymerization in a seeded emulsion polymerization of styrene, with and without benzene as diluent, with initiation by persulfate and by gamma-radiolysis. The latter can be switched off instantly, providing relaxation data which are sensitive to termination kinetics. Data from a single relaxation at a fixed weight-fraction polymer (omega(p)) were fitted to fur the unknown parameters, of which the only significant one is the probability p of reaction between two radicals upon encounter, incorporating the effect of spin multiplicity; this must lie between 0.25 and 1. Modeling using the value so obtained then successfully fitted (a) relaxation data at the same omega(p) but with 15 mol % benzene diluent, (b) relaxation data with and without diluent over the range 0.5 less than or equal to omega(p) less than or equal to 0.8, and (c) chemically initiated data over the same omega(p) range. This provides convincing evidence for the correctness of the termination model, which calculates the termination rate coefficients between two chains from the Smoluchowski equation, incorporating p, with diffusion coefficients (as a function of chain length and of omega(p)) obtained from a ''universal'' scaling law inferred from NMR data, and where the interaction distance for termination is the van der Waals radius of a monomeric unit; contributions from ''reaction diffusion'' (whereby a chain end moves by propagating) are also important at high conversion. The data also support a model for initiator efficiency in emulsion polymerization, this model being based on competition between aqueous-phase propagation (to a sufficient degree of polymerization for surface activity) and termination.