Fast Reaction and Micro-Brownian Motion of Flexible Polymer Molecules in Solution

Abstract

The rate of fast reactions in solution between two flexible polymer molecules with active chain ends is studied in relation to the theory of micro-Brownian motion of polymer segments in solution. The comparison of relaxation times for five types of molecular and segmental motions indicates that the translational diffusion of chain end segments is the rate-determining step. The segmental diffusion coefficient depending on the position based on the model of random flights with correlations is related to the rate constant by using the Smoluchowski equation and the potential energy function for intermolecular interaction. The rate constant can be expressed as a product of three components without any arbitrary parameters, ‹k›=A(α)B(n)C(ζ0,T) where A(α) represets the effect of solution properties, B(n) the effect of molecular weight, and C(ζ0, T) the effect of frictional properties of the segment. This equation predicts that the rate constant is inversely proportional to solvent viscosity, decreases with increassing molecular weight to some extent, and is markedly affected by the excluded volume effect and chain flexibility. Close agreement is found between the calculated rate constants and those experimentally obtained.