Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations. I. Compressible homopolymer melts

Abstract

Using fast lattice Monte Carlo (FLMC) simulations both in a canonical ensemble and with Wang-Landau–Transition-Matrix sampling, we have studied a model system of compressible homopolymer melts (or equivalently, homopolymers in an implicit, good solvent). Direct comparisons of the simulation results with those from the corresponding lattice self-consistent field (LSCF) and Gaussian fluctuation (LGF) theories, all of which are based on the same Hamiltonian (thus without any parameter-fitting among them), unambiguously and quantitatively reveal the fluctuations and correlations in the system. At finite chain number density C and N/κ > 0 (where N is the number of segments on a chain and κ the Helfand compressibility), the LSCF theory underestimates the internal energy and free energy but overestimates the entropy per chain, and does not capture the chain swelling due to excluded-volume interactions. At large C, the LSCF predictions of internal energy, free energy and entropy per chain, as well as the mean-square chain end-to-end distance and radius of gyration, are all approached by FLMC results at a rate of 1/C. LGF theory predicts this 1/C behavior at all C, independent of the system dimensionality. For our model system, both theories become exact only in the limit of C → ∞, where the excluded-volume interactions are fully screened (thus no chain correlations) and the system is in the ground state (with no fluctuations).