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

摘要

A Monte Carlo (MC) study is made of the mean-square radius of gyration and the gyration-radius expansion factor alpha_S for the freely rotating chain of bond angle 109 deg and with the Lennard-Jones (LJ) 6-12 intramolecular potentials between beads in a cutoff version for the number n of bonds in teh chain ranging form 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 BJ potential. It is shown that the ratio appraoches 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 THETA temperature THETA~* of the MC model system, and that possible effects of chain ends on and therefore on alpha_S are negligibly small. Taking the values of AT THETA~* as the unperturbated ones, alpha_S~2 is evaluated from those at various reduced temperatures higher than THETA~*. It is then found that the behavior of alpha_S~2 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 THETA~*, the result being consistent with a previous finding.