Concentration and energy fluctuations in a critical polymer mixture

TL;DR

This study uses advanced Monte Carlo simulations and finite-size-scaling analysis to investigate the critical behavior of an asymmetric binary polymer mixture, confirming its Ising universality class and estimating critical parameters.

Contribution

It introduces a mixed-field finite-size-scaling approach to analyze the critical properties of asymmetric polymer mixtures, providing new estimates of critical parameters and confirming universality class.

Findings

Critical point identified using cumulant intersection method.

Critical behavior consistent with 3D Ising universality class.

Estimated field mixing parameters compared with previous methods.

Abstract

A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed using a mixed-field finite-size-scaling theory that takes due account of the lack of symmetry between the coexisting phases. The essential Ising character of the binary polymer critical point is confirmed by mapping the critical scaling operator distributions onto independently known forms appropriate to the 3D Ising universality class. In the process, estimates are obtained for the field mixing parameters of the model which are compared both with those yielded by a previous method, and with the predictions of a mean field calculation.