Vapor-liquid equilibrium (VLE) properties versus critical exponent theory - on new approximate mathematical approach to determine the critical exponent value of the vapor-liquid coexistence curve

TL;DR

This paper introduces a new mathematical method to accurately determine the critical exponent of vapor-liquid coexistence curves near the critical point, applicable to common equations of state like Van der Waals and Dieterici.

Contribution

The paper presents a rigorous mathematical approach for calculating vapor-liquid critical exponents, offering an alternative to traditional thermodynamic limit methods.

Findings

Method successfully applied to Van der Waals and Dieterici equations

Critical exponent values align with classical mean field theory

Provides a new analytical tool for studying phase transitions

Abstract

A novel mathematical rigorous method to obtain the vapor-liquid equilibrium curves near the critical point has been proposed covering the cases of well-known and commonly used equations of state for real gases - Van der Waals and Dieterici, which are prototypes to determine the critical exponent value of the coexistence curves system. We explain that the critical exponent value of the vapor-liquid equilibrium curves can be regarded as the analogy to the results based on classical assumptions - mean field theory. The novelty of our method has been exposed in comparison to the standard thermodynamic limit discussed thoroughly and extensively in the literature.