A Monte Carlo study: dynamic scaling properties of single, self-avoiding polymer chains as a function of temperature or solvent quality

Dynamic Monte Carlo simulations of self-avoiding, single polymer chains were performed on body-centered (BCC), face-centered (FCC), and simple cubic (SC) lattices for a variety of chain lengths. A potential energy interaction between the non-bonded nearest-neighbor beads for each lattice was included to simulate the effects of temperature or solvent quality. Scaling exponents relating the relaxation times for the normal modes to the chain length and mode number were determined from the data according to the relations

t(L,k) ~ L^a(k)

and

t(L,k) ~ k^b(L)

where t is the relaxation time, k is mode number, and L is chain length. Even in poor solvent conditions the cross-correlations of the normal modes were found to be statistically equal to zero. The data for the mean square end-to-end distance was fit to the scaling relation below in order to determine 2v

< R²> ~ L^2v

For extended chains, the scaling exponents of the lattices were approximately equal for a given value of q*E_r, where q is the coordination number minus one and -E_r is the minimum of the square-well potential divided by k_BT. Within this regime the scaling exponent, a(1), behaved in reasonable agreement with scaling theory predictions for Bead-Spring models, i.e. a(1)=2v+1. The theta point was found to occur of the temperature corresponding to approximately T=1.75(q*E_rk_B)^-1.

In the poor solvent regime the dynamic scaling exponents for the BCC and FCC lattices were approximately equal for the same value of q*E_r. However, the values for the SC lattice were quite different for a given value of q*E_r, presumably because the two-bead crankshaft motions required for obtaining reasonable dynamics in the SC lattice are less likely to be performed due to the high bead density within a collapsed chain.

For all three lattices,in all regimes studied, a(k) values increased with increasing k. This dependence became great in poor solvent conditions. In these conditions b(L) decreased with increasing L. The relaxation times in poor solvent conditions were in general consistent with the predictions of Brochard and deGennes for the creation of gel modes. Also, in the collapsed regime b(L) values were found to be highly correlated with coil density.