Mean dimension of a polymer chain in athermal solutions and in bulk phase

Athermal polymer solutions are approximated by an assembly of nonintersecting self-avoiding walks on the simple cubic lattice. The mean-square end-to-end distance 〈rn2〉 of walks involving n lattice sites is evaluated for n = 6, 10, 20, and 30 by means of a Monte Carlo method allowing for handling of highly concentrated systems; the fractional occupancy φ of the lattice approaches 0.95 in some cases. It is observed that 〈rn2〉 diminishes steadily as φ increases. The relative decrease of 〈rn2〉 with respect to the mean-square distance 〈rn2〉0 of the infinitely diluted system grows with n. Extrapolating the data to φ = 1(bulk polymer), we find that 〈rn2〉1 varies approximately like n1.08 in the asymptotic limit (to be compared with 〈rn2〉0 ∼ n1.20). This result is compared with existing theories and presently available experimental data.SCOPUS: ar.j