Monte Carlo Simulations of Lattice Models for Single Polymer Systems

TL;DR

This study uses Monte Carlo simulations to analyze the conformations of single polymer chains on lattice models, comparing flexibility, scaling laws, and the effects of stiffness, providing insights into coarse-graining approaches for polymers.

Contribution

It offers a detailed comparison of lattice models for polymers, extending to semiflexible chains, and verifies theoretical scaling laws with large chain lengths.

Findings

BFM chains are more flexible than SCLM chains at fixed bending energy

Scaling laws are verified across different models and chain stiffnesses

Different coarse-graining ratios are needed for accurate polymer modeling

Abstract

Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length $N \sim {\cal O}(10^4)$. Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between $2$ and $\sqrt{10}$, we investigate the conformations of polymer chains described by self-avoiding walks (SAWs) on the simple cubic lattice, and by random walks (RWs) and non-reversible random walks (NRRWs) in the absence of excluded volume (EV) interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.