Configuration and Free Energy of a Polymer Molecule with Solvent Interaction

Abstract

The lattice model of a polymer molecule with excluded volume and nearest-neighbor forces arising from polymer-solvent interaction is investigated by exact numerical calculation for short chains of up to about ten links. Extrapolation to large values of n, the number of links, is shown to be justified and enables the mean configuration, free energy, entropy, and internal energy to be evaluated as functions of the number of links and of temperature for both poor and ``super-perfect'' solvents. The mean square end-to-end distance is found to vary according to 〈rn2〉≈Anγ, in agreement with Wall et al., but γ=γ(η) is a decreasing function of the nearest-neighbor interaction parameter η=exp[—V0/kT]. For the three-dimensional simple cubic lattice γ(0)≃1.37, γ(1)≃1.20 and Flory's theta point, defined by γ=1, occurs at η≃1.48. For the two-dimensional square lattice γ(0)≃1.57, γ(1)≃1.47, and ηΘ≃2.0. The fractional variance of the distribution of rn2 is found to be appreciably smaller than the corresponding Gaussian value. Numerical data and graphs are presented for the free energy, entropy, and internal energy as functions of η.