Flexible polymers in a nematic medium: a Monte Carlo simulation

Monte Carlo simulations of self-avoiding random walks surrounded by aligned rods on a square lattice and a simple cubic lattice were performed to address the topological constraints involved for dilute solutions of flexible polymers in a highly oriented nematic solvent. The nematic constraint exerted by the solvent is modelled by requiring that the distance between nearest neighbour chain segments in the direction of the director of the nematic solvent is such that a discrete number of rods, representing the perfectly ordered nematic solvent, fits exactly in between. Rod lengths of one or two lattice spacings are used. In this case interesting scaling behaviour for the radius of gyration and the end-to-end distance is found. Perpendicular to the director the coil behaves as a two(or onein the case of a square lattice) dimensional self-avoiding walk, whereas parallel to the director it behaves as a random walk. The conformations have a disk-like shape with the radius of gyration perpendicular to the director being considerably larger than the parallel component. These simulations address only one aspect of flexible polymers in nematic solvents. In reality the presence of the coil also reduces the entropy of the solvent which has exactly the opposite effect on the shape of the polymer coil.