Scaling of demixing curves and crossover from critical to tricritical behavior in polymer solutions

TL;DR

This paper develops a scaling framework for polymer solution phase separation, incorporating critical and tricritical behaviors, and provides methods to estimate Theta-temperatures from experimental and simulation data.

Contribution

It introduces a virial expansion-based scaling description that captures critical, tricritical, and solvent limits, enabling estimation of Theta-temperatures without explicit chain-length dependence assumptions.

Findings

Scaling description matches experimental and simulation data.

Method estimates Theta-temperatures accurately.

Incorporates critical and tricritical fluctuation effects.

Abstract

In this paper we show that the virial expansion up to third order for the osmotic pressure of a dilute polymer solution, including first-order perturbative corrections to the virial coefficients, allows for a scaling description of phase-separation data for polymer solutions in reduced variables. This scaling description provides a method to estimate the Theta-temperature, where demixing occurs in the limit of vanishing polymer volume fraction $\phi$ and infinite chain-length $N$, without explicit assumptions concerning the chain-length dependence of the critical parameters $T_c$ and $\phi_c$. The scaling incorporates three limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the pure solvent limit and, the tricritical limit for the polymer-rich phase asymptotically close to the Theta point. We incorporate the effects of critical and tricritical fluctuations on the coexistence curve scaling by using renormalization-group methods. We present a detailed comparison with experimental and simulation data for coexistence curves and compare our estimates for the Theta-temperatures of several systems with those obtained from different extrapolation schemes.