Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations. V. incompressible homopolymer melts

Using fast lattice Monte Carlo (FLMC) simulations (Wang, Q. Soft Matter 2009, 5, 4564) and the corresponding polymer lattice field theories, including the lattice self-consistent field and Gaussian-fluctuation (LGF) theories, we studied a model system of incompressible homopolymer melts on a hexagonal lattice, where each lattice site is occupied by a total of ρ(0) ≥ 1 polymer segments. We generalized the cooperative motion algorithm (Pakula, T. Macromolecules 1987, 20, 679), as well as the related vacancy diffusion algorithm (Reiter, J.; Edling, T.; Pakula, T. J. Chem. Phys. 1990, 93, 837), originally proposed for the self- and mutual-avoiding walk (where ρ(0) = 1) to the case of ρ(0) > 1, where our generalized algorithm is highly efficient (i.e., nearly rejection-free). On the other hand, we extended the method of Wang (Wang, Z.-G. Macromolecules 1995, 28, 570) to calculate various single-chain properties in LGF theory. Direct comparisons between FLMC and LGF results, both of which are based on the same Hamiltonian (thus without any parameter-fitting between them), unambiguously and quantitatively reveal the effects of non-Gaussian fluctuations neglected by the latter. We found that FLMC results approach LGF predictions with increasing ρ(0), and that the leading order of non-Gaussian fluctuation effects on the single-chain properties is inversely proportional to ρ(0)(2). Our work suggests that theories capturing the first-order non-Gaussian fluctuation effects may give quantitative agreement with FLMC simulations of incompressible homopolymer melts at ρ(0) ≥ 2 in two and three dimensions.