# A corresponding-state framework for the structural transition of supercritical fluids across the Widom delta

## TL;DR

This paper introduces a novel classification algorithm using radical Voronoi tessellation and percolation theory to define the Widom delta in supercritical fluids, revealing structural transitions and a corresponding state theorem.

## Contribution

It presents a new classification method for supercritical fluid phases and establishes a three-parameter corresponding state theorem based on structural analysis.

## Key findings

- The method detects the influence of attractive interactions on structural transitions.
- The Widom delta overlaps with response function maxima ridges.
- A three-parameter corresponding state theorem is derived.

## Abstract

This work proposes a classification algorithm based on the radical Voronoi tessellation to define the Widom delta, supercritical gas-liquid coexistence region, of polyatomic molecules. In specific, we use a weighted mean-field classification method to classify a molecule into either gas-like or liquid-like. Classical percolation theory methods are adopted to understand the generality of the structural transition and to locate the Widom delta. A structural analysis on various supercritical fluids shows that the proposed method detects the influence of the attractive interaction on the structural transition of supercritical fluids. Moreover, we demonstrate that the supercritical gas-liquid coexistence region of water overlap with the ridges of the response function maxima. From the pressure-temperature relation, a three-parameter corresponding state theorem is derived, which states that the fraction of gas-like molecules of a substance is equal to that of another if their reduced pressure, reduced temperature and the critical compressibility factor are the same.