Asymmetry of the vapor-liquid coexistence curve: the asymptotic behavior of the "diameter"

TL;DR

This paper investigates the asymptotic behavior of the vapor-liquid coexistence curve's diameter near the critical point using a novel, model-independent equation of state that aligns well with experimental data.

Contribution

It introduces a simple, non-parametric equation of state that accurately captures the asymptotic behavior of the coexistence curve without model field-mixing, and explicitly determines the amplitude of the leading temperature-dependent term.

Findings

The equation reproduces experimental data with high accuracy.

The leading temperature-dependent term is proportional to |T - T_c|^{2β}.

Explicit expressions for the amplitude D_{2β} are provided.

Abstract

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the "diameter" of the coexistence curve asymptotically close to the vapor-liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D_{2 \beta} | \tau |^{2 \beta}, where | \tau | = | T - T_{c} | / T_{c}, and \beta is the critical exponent for the order parameter. The amplitude D_{2 \beta} is determined explicitly for the volume-temperature and entropy-temperature planes.