Contributions of short-range and excluded-volume interactions to unperturbed polymer chain dimensions

A Monte Carlo study is made of the mean-square radius of gyration for the freely rotating chain with such fictitious excluded-volume interactions that the Lennard-Jones 6-12 potentials at the Theta temperature act only between the fourth-through (3+Delta)th-neighbor beads (Delta > or = 1) along the chain. The behavior of the asymptotic value ( /n)infinity of the ratio /n as a function of the number n of bonds in the chain in the limit of n --> infinity is examined as a function of Delta. It is shown that the approach of ( /n)infinity to its value for the real unperturbed chain with Delta = infinity is so slow that the interactions between even up to about 100th-neighbor beads should be taken into account in order to reproduce nearly its dimension. The result implies that the unperturbed polymer chain dimension as experimentally observed at the Theta temperature depends not only on short-range interactions but also to a considerable extent on the long-range excluded-volume interactions, and that the asymptotic value Cinfinity of the characteristic ratio Cn for the rotational isomeric state model in the limit of n --> infinity, which is determined only by the very local conformational energy, cannot be directly compared with the corresponding experimental value.