Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures

TL;DR

This paper presents evidence for an entropy-driven quintuple phase point in colloid-polymer mixtures, challenging traditional phase rules by incorporating additional length scales as variables.

Contribution

It introduces a minimal algebraic thermodynamic model that predicts a quintuple phase equilibrium involving multiple liquid crystal and solid phases.

Findings

Evidence for a quintuple phase point in colloid-polymer mixtures

Model aligns with computer simulation data

Reconciles with a generalized Gibbs phase rule

Abstract

Using a minimal algebraic model for the thermodynamics of binary rod--polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our model is based on equations of state for the relevant liquid crystal phases that are in quantitative agreement with computer simulations. We argue that the appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic and smectic liquid crystal, and two solid phases can be reconciled with a generalized Gibbs phase rule in which the two intrinsic length scales of the athermal colloid--polymer mixture act as additional field variables.