Phase boundaries and the Widom line from the Ruppeiner geometry of fluids

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Geometric Methods in Physics

Background:

• Ruppeiner geometry offers novel methods for phase boundary and Widom line construction in fluids.
• Existing methods using Ruppeiner geometry face limitations with general fluid equations of state.

Purpose of the Study:

• To investigate the applicability of Ruppeiner geometric constructions to more general fluids.
• To develop a general equation-of-state expansion for fluids near a critical point.
• To refine the construction of phase boundaries and the Widom line using thermodynamic geometry.

Main Methods:

• Developed a general equation-of-state expansion for fluids near critical points, assuming analyticity with respect to number density.
• Proved the equivalence of Ruppeiner and Maxwell constructions for phase boundaries near critical points.
• Introduced and utilized the Ruppeiner-N surface and its induced metric for Widom line and phase space classification.

Main Results:

• Established the equivalence between Ruppeiner and Maxwell constructions for phase boundaries near critical points.
• Demonstrated that the standard Ruppeiner geometry prescription fails to accurately predict the Widom line for general fluids.
• Showed that the Ruppeiner-N surface precisely generates the Widom line for the van der Waals fluid, even away from the critical point.
• Improved the Diósi et al. phase classification scheme using the Ruppeiner-N metric, making boundaries sensitive to the Widom line.

Conclusions:

• The Ruppeiner-N surface and its induced metric are more appropriate for studying phase diagrams with thermodynamic geometry.
• The Ruppeiner-N surface provides an exact construction of the Widom line and an improved phase classification scheme.
• This work extends the application of thermodynamic geometry to a broader range of fluid systems.