Effective radius of a contact diffusion-controlled reaction between small solutes and a polymer chain

The aim of this study was to develop a formula for estimating the effective radius of a diffusion-controlled irreversible contact reaction between diffusing solutes and a nonlinear immobile polymer molecule. Analytical expressions for the reaction radius were obtained that took into account averaging over conformations for chains with arbitrary segment-to-segment angles and distributions of dihedral angles. A comparison of the analytical results with the results of computer stochastic modeling of the reaction showed good agreement over a wide range of parameters. Based on an analysis of these expressions, parameter ranges were established in which it was possible to use either the linear chain or Gaussian coil approximation to describe the reaction kinetics. A comparison of several distributions over chain lengths showed that, as a first approximation, the radius of reaction can be estimated as that for a chain corresponding to the number-averaged molecular weight. Results of earlier experimental studies on charge scavenging by polymer molecules have been explained.