BROWNIAN DYNAMICS SIMULATION OF DIFFUSION-LIMITED POLYMERIZATION OF RODLIKE MOLECULES - ANISOTROPIC TRANSLATION DIFFUSION

Step-growth polymerization of rodlike molecules is qualitatively diffe rent from flexible molecules, because rotational and translational dif fusion limitations result in a rate of reaction which is dependent on the molecular weights of the reacting oligomers. an understanding of t he kinetics of polymerization is important for the manufacture of such polymers which have many applications. The theoretical basis and comp utation details of the pairwise Brownian dynamics method [Northrup er al., J. Chem. Phys. 80, 1517 (1984)] to determine the effective rate c onstant for reaction between rodlike molecules are presented. In this method the effective rate constant is obtained in terms of the first v isit flux (for which an analytical expression is derived) and the reac tion probability (which is obtained using Brownian dynamics simulation s). A simple derivation for finite domain correction far the simulatio ns is presented, which explicitly accounts for the spatial and orienta tional variations of the reaction probability. Computations are presen ted to validate assumptions of the technique. The computed rate consta nts decrease with decreasing rotational diffusivity to approach an asy mptotic value, and decrease with decreasing values of the translationa l diffusivity perpendicular the rod axis. The computations show that t he effective rate constants obtained for the case of dilute solutions when ratio of the translational diffusivities perpendicular and parall el to the rod axis is equal to 1/2, is close to the case of isotropic translational diffusion. (C) 1998 American Institute of Physics. [S002 1-9606(98)51312-8].