Monte Carlo studies of the configurational properties of freely rotating polymer chains subject to excluded volume conditions

The dependence of the mean square end-to-end distance < R n 2 > on the number of links n of a polymer chain subject to excluded volume conditions has been studied, using Monte Carlo techniques on a digital computer. The individual molecules of the chain are considered as spheres, and the chain is not constrained by a lattice framework. The results, up to n = 90, have been fitted to the usual formula < R n 2 > = an γ using the method of least squares, for different values of the excluded volume ratio, i.e. the ratio of the minimum permitted centre separation of any two non-consecutively added spheres to the corresponding distance when the addition is consecutive. For excluded volume ratios of 0.1 and 0.2, γ has been evaluated as 1.050 ± 0.021 and 1.065 ± 0.017 respectively while, from two independent investigations of 20-link chains, with excluded volume ratios of 0.5, γ has been determined as 1.161 ± 0.017. These results suggest that the formula < R n 2 > = an γ , where a only is dependent on the magnitude of the excluded volume, may apply only for excluded volume ratios in excess of a certain minimum value. Assuming that the γ value of 6/5 arrived at by Edwards in 1965 is correct, this minimum value has been tentatively assessed as approximately 0.5.