Chain length dependence of the polymer-solvent critical point parameters

TL;DR

This study uses Monte Carlo simulations to analyze how polymer chain length affects the critical point parameters in polymer-solvent systems, revealing scaling behaviors that align with experiments but differ from classical theory.

Contribution

It provides detailed simulation data on critical point scaling with chain length, employing advanced Monte Carlo methods and universal distribution matching.

Findings

Critical temperature scales as N^{-0.5}, consistent with Flory theory.

Critical volume fraction scales as N^{-0.37}, matching experimental data.

Chains are not collapsed at the critical point.

Abstract

We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the Bond Fluctuation model. By employing Configurational Bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed-point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e. \Theta-T_c\sim N^{-0.5}. The critical volume fraction, on the other hand, was found to scale like \phi_c\sim N^{-0.37}, in clear disagreement with the Flory theory prediction \phi_c\sim N^{-0.5}, but in good agreement with experiment. Measurements of the chain length dependence of the end-to-end distance indicate that the chains are not collapsed at the critical point.