Effect of mesoscopic fluctuations on equation of state in cluster-forming systems

TL;DR

This paper develops a mesoscopic theory to analyze how fluctuations influence the equation of state in systems with self-assembling particles, revealing increased pressure and altered stability compared to mean-field predictions.

Contribution

It introduces a combined density functional and field-theoretic approach to account for mesoscopic fluctuations in cluster-forming systems, highlighting their impact on phase stability.

Findings

Mesoscopic fluctuations increase pressure in most cases.

Large clusters cause system instability at higher temperatures.

Small clusters do not exhibit phase separation instability.

Abstract

Equation of state for systems with particles self-assembling into aggregates is derived within a mesoscopic theory combining density functional and field-theoretic approaches. We focus on the effect of mesoscopic fluctuations in the disordered phase. The pressure -- volume fraction isotherms are calculated explicitly for two forms of the short-range attraction long-range repulsion potential. Mesoscopic fluctuations lead to an increased pressure in each case, except for very small volume fractions. When large clusters are formed, the mechanical instability of the system is present at much higher temperature than found in mean-field approximation. In this case phase separation competes with the formation of periodic phases (colloidal crystals). In the case of small clusters, no mechanical instability associated with separation into dilute and dense phases appears.