Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations

Abstract

The basic idea of fast Monte Carlo (MC) simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping. This gives much faster system relaxation and better sampling of the configurational space than conventional molecular simulations with "hard" repulsions that prevent particle overlapping. Here we present fast lattice MC (FLMC) simulations for confined homopolymers, where multiple occupancy of lattice sites is allowed with a proper Boltzmann weight and thus the evaluation of nearest-neighbor interactions can also be avoided. When compared with the corresponding lattice field theories based on the same Hamiltonian, FLMC simulations further provide a powerful means for unambiguously and quantitatively revealing the correlation/fluctuation effects. PACS numbers: 05.10.Ln, 61.25.H-, 64.60.DeSignificant advances have been made in the past three decades in applying conventional, "particle-based" molecular simulation techniques (e.g., Monte Carlo (MC) and molecular dynamics simulations) to the study of polymeric systems. Even with coarse-grained models where each segment represents several to tens of repeat units of real polymers, however, conventional molecular simulations of multi-chain systems are still hindered by "hard" excluded-volume interactions and, for off-lattice simulations, expensive pair-potential calculations. The former is implemented in off-lattice simulations commonly by either hard-sphere repulsion or the harsh Lennard-Jones repulsion, and in lattice simulations by the self-and mutual-avoiding walk (SMAW). While such hard-core repulsions are needed to produce realistic dynamics, they greatly reduce the chain relaxation towards equilibrium configurations as well as the efficiency of sampling the configurational space. On the other hand, the pair-potential calculations are expensive for dense polymeric systems, and lattice simulations are in general much faster and thus widely used.The basic idea of fast MC simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping (i.e., by soft particles whose interaction energy u(r) is finite when they overlap). This avoids the hard repulsions (i.e., u(r → 0) → ∞ as in the Lennard-Jones potential) used in conventional molecular simulations, thus allowing much faster chain relaxation and better sampling of the configurational space. Such coarse-grained models are particularly suitable for the study of equilibrium properties of soft matter such as polymers. It turns out that soft potentials are commonly used in polymer field theories (e.g., the widely applied self-consistent field (SCF) theory with great * Electronic address: q.wang@colostate.edu success for many polymeric systems)[1], where individual polymer segments are modeled as volumeless points with the excluded-volume interactions described by either the Helfand compressibility [2] or the incompressibility...

Multiscale approach to equilibrating model polymer melts

“…Since multiple chains pervade an entanglement volume, multiple blobs can occupy the same lattice site. We regard the We utilize the recently published lattice polymer model of Wang [52]. This model has the computational advantage that the Hamiltonian does not include pair-interactions, which makes it computationally very effective.…”

Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations. VI. Phase behavior of incompressible symmetric binary homopolymer blends

“…This is the sixth paper in our series of study, [1][2][3][4][5] where fast lattice Monte Carlo (FLMC) simulations 6 are directly compared with the corresponding polymer lattice field theories based on the same model system (Hamiltonian), thus without any parameter-fitting, to unambiguously and quantitatively reveal the effects of fluctuations/correlations either neglected or treated approximately in the theories. In the preceding paper in this series, 5 we generalized the cooperative motion algorithm (CMA), the only Monte Carlo (MC) method for simulating incompressible and monodisperse polymer melts, originally proposed by Pukula 7 for the self-and mutual-avoiding walk (SMAW) to the case of multiple occupancy of lattice sites (MOLS), 6 and quantified the Gaussian and non-Gaussian fluctuations/correlations in the incompressible homopolymer melts in two dimensions (2D). We found that FLMC results approach the lattice Gaussian-fluctuation predictions with increasing ρ 0 (the total number of polymer segments on each lattice site), and that the leading order of non-Gaussian fluctuation effects on the single-chain properties is inversely proportional to ρ 2 0 .…”

Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

“…In one work this author used basically the same model as described in the previous section. In a second paper [20], he employed the Hamiltonian (62) but, instead of describing the molecular conformations by an off-lattice bead-spring Hamiltonian (2), the author used random walks on a simple cubic lattice. The latter strategy speeds up the calculation of the non-bonded interactions but a finer chain discretization, N , is required to mimic the Gaussian chain architecture.…”

“…The advances are rooted in the development of predictive and computationally efficient soft coarse-grained models for polymer [12][13][14][15][16][17][18][19][20][21] and lipid systems [5,6,8,11,[22][23][24], as well as the development of simulation techniques [15,[25][26][27][28][29][30][31]. In this paper we review some computational aspects of soft coarse-grained models and discuss the relation of these particle-based models to a field-theoretic description.…”