Diffusion‐limited polymerization of rigid rodlike molecules: Semidilute solutions

The rotational diffusivity and the translational diffusivity perpendicular to the rod axis of rigid rodlike (RRL) molecules decreases rapidly with increasing molecular length, during polymerization in semidilute solutions. This can result in slowing of step‐growth polymerizations of RRL molecules with reactive groups at the rod ends and a near‐collinearity requirement for reaction. Here a theoretical analysis of the rate of RRL polymerization in semidilute solutions, based on Smoluchowski’s approach, and incorporating the rotational and anisotropic translational diffusion of the molecules is presented. The work is an extension of our analysis of polymerization in dilute solutions in which the translational diffusion was assumed to be isotropic [J. Chem. Phys. 96, 7125 (1992)]. The effective second order rate constant for the system is obtained for different parameter values using a numerical finite element method. With reduction in rotational diffusivity, for a fixed translational diffusivity, the effective reaction rate constant is found to decrease to a limiting value determined by only the translational flux of the correctly oriented molecules. Similarly, for a given rotational diffusivity, with reduction in translational diffusivity perpendicular to the rod axis, the reaction rate constant is found to decrease to a limiting value determined by the flux only due to translational diffusion parallel to the rod axis, aided by rotational diffusion. An asymptotic analysis for this case is presented. For low rotational diffusivities, reduction in the translational diffusion perpendicular to the rod axis results in a significant decrease in the effective rate constant, even for reactions with relatively slow intrinsic kinetics. A qualitative comparison of the theoretical predictions with experimental results is presented.