Critical Fluctuations in Polymer Solutions: Crossover from Criticality to Tricriticality

TL;DR

This paper explores how critical fluctuations in polymer solutions transition from Ising-like criticality to tricriticality as the polymer molecular weight increases, highlighting the crossover governed by competing length scales.

Contribution

It provides a detailed analysis of the crossover from critical to tricritical behavior in polymer solutions based on the interplay of correlation length and polymer size.

Findings

Ising-like critical behavior dominates when correlation length exceeds polymer size.

Tricritical behavior emerges when polymer size exceeds correlation length.

The Ising critical region diminishes with increasing polymer molecular weight.

Abstract

Critical fluctuations in fluids and fluid mixtures yield a nonanalytic asymptotic Ising-like critical thermodynamic behavior in terms of power laws with universal exponents. In polymer solutions, the amplitudes of these power laws depend on the degree of polymerization. Nonasymptotic behavior (upon the departure from the critical point) is particularly interesting in the case of polymer solutions, where it is governed by a competition between the correlation length of the critical fluctuations and the radius of gyration of the polymer molecules. If the correlation length is the dominant length scale, Ising-like critical behavior is observed. If, however, the radius of gyration exceeds the correlation length, tricritical behavior with mean-field critical exponents is observed. The Ising-like critical region shrinks with the increase of the polymer molecular weight. In the limit of an infinite degree of polymerization, the Ising-like critical region vanishes, yielding to theta-point tricriticality.