Generalized Rosenfeld-Tarazona scaling and high-density specific heat of simple liquids

Abstract

The original Rosenfeld-Tarazona (RT) scaling of the excess energy in simple dense fluids predicts a $\propto T^{3/5}$ thermal correction to the fluid Madelung energy. This implies that the excess isochoric heat capacity scales as $C_{\mathrm{v}}^{\mathrm{ex}}\propto T^{-2/5}$. Careful examination performed in this paper demonstrates that the exponent $-2/5$ is not always optimal. For instance, in the Lennard-Jones fluid in some vicinity of the triple point, the exponent $-1/3$ turns out to be more appropriate. The analysis of the specific heat data in neon, argon, krypton, xenon, and liquid mercury reveals that no single value of the exponent exists, describing all the data simultaneously. Therefore we propose a generalized RT scaling in the form $C_{\mathrm{v}}^{\mathrm{ex}}\propto T^{-\alpha }$, where $\alpha$ is a density- and material-dependent adjustable parameter. The question concerning which material properties and parameters affect the exponent $\alpha$ and whether it can be predicted from general physical arguments requires further investigation.

References in corpus (33)

• Two liquid states of matter: A new dynamic line on a phase diagram
• The phonon theory of liquid thermodynamics
• "Liquid-gas" transition in the supercritical region: Fundamental changes in the particle dynamics
• Liquid-like behavior of supercritical fluids
• Emergence and evolution of $k$-gap in spectra of liquid and supercritical states
• What constitutes a simple liquid?
• Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: Mixtures and soft particles
• Breakdown of The Excess Entropy Scaling for the Systems with Thermodynamic Anomalies
• Transition in the supercritical state of matter: experimental evidence
• Practical expressions for the internal energy and pressure of Yukawa fluids
• Excess entropy determines the applicability of Stokes-Einstein relation in simple fluids
• Practical thermodynamics of Yukawa systems at strong coupling
• Collective modes in simple melts: Transition from soft spheres to the hard sphere limit
• Freezing and melting line invariants of the Lennard-Jones system
• Explaining the specific heat of liquids based on instantaneous normal modes
• The Rosenfeld-Tarazona expression for liquids' specific heat: A numerical investigation of eighteen systems
• Universal lower bounds on energy and momentum diffusion in liquids
• Elementary vibrational model for transport properties of dense fluids
• Accurate freezing and melting equations for the Lennard-Jones system
• Modelling of liquid internal energy and heat capacity over a wide pressure-temperature range from first principles
• Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms
• Minima of shear viscosity and thermal conductivity coefficients of classical fluids
• Vibrational model of thermal conduction for fluids with soft interactions
• Self-diffusion and shear viscosity for the TIP4P/Ice water model
• Thermal conductivity of strongly coupled Yukawa fluids
• Freezing density scaling of fluid transport properties: Application to liquefied noble gases
• Note: Gas-liquid crossover in the Lennard-Jones system
• Excess entropy of strongly coupled Yukawa fluids
• Note: Stokes-Einstein relation without hydrodynamic diameter in the TIP4P/Ice water model
• Vibrational model of heat transfer in strongly coupled Yukawa fluids (dusty plasma liquids)
• Elementary vibrational model for thermal conductivity of Lennard-Jones fluids: Applicability domain and accuracy level
• Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid
• Comment on "Explaining the specific heat of liquids based on instantaneous normal modes"

Cited by in corpus (5)

• Revisiting the phonon theory of liquid heat capacity: low-frequency shear modes and intramolecular vibrations
• Speed of sound in dense simple liquids
• Heat capacity of dense liquids: A link between two-phase model and melting temperature scaling
• Theory of Generalized Hertzian Hyperspheres
• Variational approach to Yukawa fluids. I. Thermodynamics