Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Intermolecular Forces

Background:

• Isomorph theory and Rosenfeld-Tarazona temperature scaling are theoretical frameworks used to understand fluid behavior.
• These approaches are particularly relevant for dense fluids where repulsive interparticle interactions dominate, such as near the freezing line.
• Previous studies have noted deviations in temperature dependence when analyzing isochoric heat capacity and its relation to isomorph theory.

Purpose of the Study:

• To comparatively discuss isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry.
• To investigate the conditions under which these theoretical approaches yield consistent results.
• To utilize thermodynamic geometry to define state regions characterized by dominant repulsive interactions.

Main Methods:

• Analysis based on the Lennard-Jones potential.
• Application of isomorph theory and Rosenfeld-Tarazona temperature scaling.
• Utilizing Riemannian thermodynamic scalar curvature (R) to classify thermodynamic states.
• Examining the isomorphic character of the freezing line.

Main Results:

• Both isomorph theory and Rosenfeld-Tarazona scaling effectively approximate high-density fluid states near the freezing line.
• Deviations in temperature dependence were observed in previous studies concerning isochoric heat capacity and isomorph theory.
• The Riemannian thermodynamic scalar curvature (R>0) was identified as an indicator of predominantly repulsive interactions.
• Consistency between isomorph theory and Rosenfeld-Tarazona scaling was found to be limited to a specific, small state region.

Conclusions:

• A precise definition of the state region where repulsive interactions dominate is crucial for consistent application of isomorph theory and Rosenfeld-Tarazona scaling.
• Thermodynamic geometry, specifically the scalar curvature, provides a means to classify these relevant state regions.
• The isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona scaling are consistent only within a restricted thermodynamic domain.