Equation of State for Macromolecules of Variable Flexibility in Good Solvents: A Comparison of Techniques for Monte Carlo Simulations of Lattice Models

TL;DR

This study compares three Monte Carlo simulation techniques for determining the equation of state of lattice models of macromolecules with variable stiffness, highlighting their efficiency and accuracy in different regimes.

Contribution

It provides a critical comparison of the repulsive wall, thermodynamic integration, and sedimentation equilibrium methods for lattice models of macromolecules.

Findings

Sedimentation equilibrium method is more efficient than the repulsive wall method.

Thermodynamic integration and sedimentation equilibrium methods have similar efficiency.

Nematic order affects the accuracy of the sedimentation equilibrium method in stiff chains.

Abstract

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the repulsive wall method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.