Effects of the Carnahan-Starling free energy within theories of fluids with short-range attraction

TL;DR

This paper investigates how the Carnahan-Starling free energy impacts phase predictions in colloid-polymer mixture theories, revealing that its use can lead to unphysical gas-liquid binodals especially with short-range attractions.

Contribution

It demonstrates that replacing the Carnahan-Starling free energy with an alternative significantly alters phase behavior predictions in FVAO theory.

Findings

Replacing CS free energy affects predicted phase diagrams.

CS's influence is critical in regimes with short-range attractions.

The choice of reference free energy impacts fractionation predictions.

Abstract

Within the Free-Volume Asakura-Oosawa-Vrij (FVAO) theory of colloid-polymer mixtures, we show that unphysical gas-liquid binodals predicted in the regime of small attraction range (i.e. polymer size) are caused in part by the use of the Carnahan-Starling (CS) hard sphere (HS) reference free energy. Replacement of the CS expression with an alternative dramatically affects predicted phase behaviour and, for polydisperse colloid, the resultant fractionation predictions. Although short-range attractions render FVAO, as a perturbative HS-based theory, less accurate anyway, we argue that the particular effects of CS in this regime are an important consideration -- usually ignored -- in the evaluation of such theories. We refer to a variety of literature exhibiting similarly inaccurate gas-liquid binodals, and suggest CS's status as the de facto choice of hard sphere reference should be carefully considered where short-range attractions are present.