DIFFUSION-LIMITED POLYMERIZATION OF RIGID RODLIKE MOLECULES - SEMIDILUTE SOLUTIONS

The rotational diffusivity and the translational diffusivity perpendic ular to the rod axis of rigid rodlike (RRL) molecules decreases rapidl y with increasing molecular length, during polymerization in semidilut e solutions. This can result in slowing of step-growth polymerizations of RRL molecules with reactive groups at the rod ends and a near-coll inearity requirement for reaction. Here a theoretical analysis of the rate of RRL polymerization in semidilute solutions, based on Smoluchow ski's approach, and incorporating the rotational and anisotropic trans lational diffusion of the molecules is presented. The work is an exten sion of our analysis of polymerization in dilute solutions in which th e translational diffusion was assumed to be isotropic V. Chem. Phys. % , 7125 (1992)]. The effective second order rate constant for the syste m 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 fou nd to decrease to a limiting value determined by only the translationa l flux of the correctly oriented molecules. Similarly, for a given rot ational diffusivity, with reduction in translational diffusivity perpe ndicular to the rod axis, the reaction rate constant is found to decre ase to a limiting value determined by the flux only due to translation al 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 rat e constant, even for reactions with relatively slow intrinsic kinetics . A qualitative comparison of the theoretical predictions with experim ental results is presented.