A Monte Carlo study of effects of chain stiffness and chain ends on dilute solution behavior of polymers. I. Gyration-radius expansion factor

Abstract

A Monte Carlo (MC) study is made of the mean-square radius of gyration 〈S2〉 and the gyration-radius expansion factor αS for the freely rotating chain of bond angle 109° and with the Lennard-Jones (LJ) 6-12 intramolecular potentials between beads in a cutoff version for the number n of bonds in the chain ranging from 10 to 1500 at the reduced temperature ranging from 3.6 to 8.0, which is defined as the absolute temperature multiplied by the Boltzmann constant and divided by the depth of the well of the LJ potential. It is shown that the ratio 〈S2〉/n approaches asymptotically a constant independent of n for very large n at the value 3.72±0.05 of the reduced temperature, which value is equal to the reduced Θ temperature Θ* of the MC model system, and that possible effects of chain ends on 〈S2〉 and therefore on αS are negligibly small. Taking the values of 〈S2〉 at Θ* as the unperturbed ones, αS2 is evaluated from those at various reduced temperatures higher than Θ*. It is then found that the behavior of αS2 may be well explained in the quasi-two-parameter scheme or is in good agreement with that of real experimental data. Further, the binary cluster integral for a bead in the chain is found to be much smaller in magnitude than that for a single isolated bead at reduced temperatures higher than Θ*, the result being consistent with a previous finding.