Distribution Function of the End-to-End Distances of Linear Polymers With Excluded Volume Effects

The distribution function of the absolute values of chain lengths of a polymer molecule which displays the excluded volume effect cannot assume a Gaussian form. This fact follows directly from theoretical considerations based on the application of the Central Limit Theorem to the theory of Markov chains. In order to determine the exact shape of the polymer chain-end distribution function we calculated its various moments taken about the origin, and their dependence on the number of polymer segments, using a Monte Carlo technique for generating polymer chains on a lattice. The results obtained from the extrapolation of various combinations of these moments of the general form are used to determine the shape of the polymer distribution function. It is found that the chain-end distribution function can be approximated by the following form: with t=3.2 and α being a parameter, determinable from the average mean square chain-end distances.