Lattice Monte Carlo Simulations of Polymer Melts

TL;DR

This study uses Monte Carlo simulations to analyze polymer melts with flexible and stiff chains, demonstrating efficient configuration preparation, validating theoretical models, and examining chain statistics and structure factors.

Contribution

It introduces a pre-packing process for initial configuration setup and confirms the validity of the freely rotating chain model for stiff chains in melts.

Findings

Pre-packing accelerates the reduction of overlaps in simulations.

The freely rotating chain model accurately describes end-to-end distances.

Deviations from Gaussian statistics in structure factors are not visible for the chain lengths studied.

Abstract

We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor $S_c(q)$ [minimum in the Kratky-plot] found by Wittmer et al.~\{EPL {\bf 77} 56003 (2007).\} for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.