Pair distribution function and pair potential of lattice model chains under theta conditions, 1. Numerical evaluation

Abstract

Abstract Ensembles of unbranched non‐selfintersecting 4‐way cubic lattice chains consisting of 100 chains each occupying 50 lattice points have been developed for Θ‐conditions by a Metropolis‐Rosenbluth ‐Monte‐Carlo technique using a kind of square well potential to describe the segment‐segment interaction. For these equilibrated ensembles the pair distribution function G(R) and the average pair potential U(R) have been estimated by calculating the intermolecular energy for all isolated pairs, which can be depicted from the ensemble, as a function of the distance of the centers of gravity R of the two chains. The resulting G(R) being less than one for small R and exceeding one for large R does not correspond to that of an ideal gas. This means that for thermodynamic reasons alone there can be no free interpenetration of chains at the Θ‐point. U(R) can be split into a repulsive and an attractive part both being approximately Gaussian in type. Thus, U(R) at the Θ‐point can be represented by the general expression. with A>A′ and a>a′ .