Statistical mechanics of Roskilde liquids: Configurational adiabats, specific heat contours and density dependence of the scaling exponent

Abstract

We derive exact results for the rate of change of thermodynamic quantities, in particular the configurational specific heat at constant volume, $C_V$, along configurational adiabats (curves of constant excess entropy $S_{\text{ex}}$). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. Their slope in a double logarithmic representation of the density-temperature phase diagram, $\gamma$ can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where $\gamma$ increases (decreases) with density, the contours of $C_V$ have smaller (larger) slope than configurational adiabats. We clarify also the connection between $\gamma$ and the pair potential. A fluctuation formula for the slope of the $C_V$-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid and the Girifalco fluid. The sign of $d\gamma /d\rho$ is thus a third key parameter in characterizing Roskilde liquids, after $\gamma$ and the virial-potential energy correlation coefficient $R$. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient along adiabats and $C_V$-contours, finding it more invariant along adiabats.

References in corpus (4)

• Pressure-energy correlations in liquids. I. Results from computer simulations
• Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
• Pressure-energy correlations in liquids. II. Analysis and consequences
• Strong pressure-energy correlations in van der Waals liquids

Cited by in corpus (17)

• Simplicity of condensed matter at its core: Generic definition of a Roskilde-simple system
• Invariants in the Yukawa system's thermodynamic phase diagram
• Determination of the Thermodynamic Scaling Exponent from Static, Ambient-Pressure Quantities
• Estimating the density-scaling exponent of a monatomic liquid from its pair potential
• Scaling of the dynamics of flexible Lennard-Jones chains. II. Effects of harmonic bonds
• Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion
• Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. I. Intermediate and long range
• Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. II. Short range
• Freezing density scaling of fluid transport properties: Application to liquefied noble gases
• Isomorph invariance and thermodynamics of repulsive dense bi-Yukawa one-component plasmas
• Thermodynamics and dynamics of the inherent states at the glass transition
• The variation of the dynamic susceptibility along an isochrone
• Hidden scale invariance in the Gay-Berne model
• Estimating melting curves for Cu and Al from simulations at a single state point
• Scaling properties of liquid dynamics predicted from a single configuration: Small rigid molecules
• A pair potential that reproduces the shape of isochrones in molecular liquids
• Variation along liquid isomorphs of the driving force for crystallization