The dimensions and shape of polymethylene coils in solution. Computer simulation

Abstract

The behaviour in solution of isolated polymethylene macromolecules containing N ⩽ 351 units in the chain, has been simulated by the Monte Carlo method. The details of local chain structure taken into account are the hindrance to and interdependence of internal rotation of units in pairs, and interaction between all the units. Temperature (from 0 to 413°K) and the thermodynamic quality of the solvent were used as independent variables. The mean square end-to-end distance of the chain and the average maximal length of the polymer coil along the three principal axes of inertia were calculated. It is shown that if in a thermodynamically good solvent increase in temperature brings about a gradual transition from an extended to a coiled chain conformation, when interaction of the units is sufficiently strong the volume occupied by chain fluctuations decreases sharply and the chain takes up a conformation with lower asymmetry of shape than a random coil. The ratio of 1 : 1·61 : 3·00 found for the coil dimensions of an infinite chain with prohibition of self-crossing, remains virtually unchanged on passing to a γ-solvent. Increase in chain rigidity assists attainment of the γ-point and favours formation of more compact intramolecular structures.