Simulation of diffusion-limited step-growth polymerization in 2D: effect of shear flow and chain rigidity

Abstract

Multimolecule Brownian dynamics simulation results for diffusion controlled polymerization of bead-rod chain molecules in 2D solution are presented. Reaction between any two molecules undergoing Brownian diffusion takes place if the reactive chain ends approach each other to within a certain reaction radius, and if the chain end carrying segments are collinear within certain specified limits. The second order reaction rate constant is found to decrease with time as the molecular lengths increase and the diffusivities decrease. Application of a shear flow is seen to result in alignment of the molecules along the flow direction, thereby enhancing the concentration of molecular pairs with parallel orientation of reactive-end carrying chain segments, and hence the overall reaction rate. This effect is found to be more pronounced in the case of long rigid molecules as compared to flexible molecules because of the slow rotation and high level of orientation under flow of the former. Even the molecular weight distribution (MWD) obtained during polymerization may be affected. For example, longer molecules have lower diffusivities and hence lower reactivities, resulting in a narrower MWD in the absence of flow, as compared to the results with the usual assumption of molecular reactivity being independent of chain length. Furthermore, in the presence of an external flow, the longer molecules orient to a higher degree and hence display a higher enhancement in reactivity. This results in a wider MWD of the polymer. The simulation results are in qualitative agreement with previous experimental data for solution polymerization of rod-like molecules.