EFFECTS OF VARIABLE EXCLUDED-VOLUME ON THE DIMENSIONS OF OFF-LATTICE POLYMER-CHAINS

The expansion of bead-stick models of polymer chains by excluded volume has been obtained by Monte Carlo methods for chains with ratios d of hard-sphere bead diameter to stick length between zero (no excluded volume) and unity (connected beads touching) for chains of from 9 to 99 beads. We report values of mean-sauare end-to-end length [l2] and apparent power-law exponents 2nu = partial derivative ln[l2]/partial derivative ln(N-1) for chains of N beads, for eight values of d from 0.30 to 0.93. For the range of chain lengths reported here, the apparent power-law exponent 2nu is not independent of d but rather shows a smooth, gradual transition from the well-known result for d = 0 to the previously-reported value for d = 1. The variation of 2nu with bead size is remarkably similar to its variation with short-range attractive energy in other models. The results reported here are compared with those obtained by other workers on and off lattices, for hard-sphere and Lennard-Jones potentials, and with predictions of two-parameter and scaling theories.