Phase behavior near and beyond the thermodynamic stability threshold

TL;DR

This study investigates the phase behavior of stabilized macromolecular dispersions near the stability threshold, revealing how increased attraction leads to instability and phase separation, with implications for colloidal stability and destabilization processes.

Contribution

It introduces a double-Gaussian model to analyze the effects of attraction strength on phase stability and demonstrates how adding a hard core stabilizes the system, linking to colloidal destabilization mechanisms.

Findings

System becomes Ruelle-unstable above a critical attraction strength.

Approaching the threshold causes anomalous widening of the liquid-vapor region.

Adding a hard core restores stability and creates a fluid-fluid transition.

Abstract

The phase behavior of stabilized dispersions of macromolecules is most easily described in terms of the effective interaction between the centers of mass of solute particles. For molecules like polymer chains, dendrimers, etc., the effective pair potential is {\em finite} at the origin, allowing "particles" to freely interpenetrate each other. Using a double-Gaussian model (DGM) for demonstration, we studied the behavior of the system as a function of the attraction strength $\eta$. Above a critical strength $\eta_{\rm c}$, the infinite-size system is Ruelle-unstable, in that it collapses to a cluster of finite volume. As $\eta_{\rm c}$ is approached from below, the liquid-vapor region exhibits an anomalous widening at low temperature, and the liquid density apparently diverges at the stability threshold. Above $\eta_{\rm c}$, the thermodynamic plane is divided in two regions, differing in the value of the {\em average} waiting time for collapse, being finite and small on one side of the boundary line, while large or even infinite in the other region. Upon adding a small hard core to the DGM potential, stability is fully recovered and the boundary line is converted to the spinodal line of a transition between fluid phases. We argue that the destabilization of a colloidal dispersion, as induced by the addition of salt or other flocculant, finds a suggestive analogy in the process by which a strengthening of the attraction pushes a stabilized-DGM system inside the fluid-fluid spinodal region.