Pressure-energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams

TL;DR

This paper introduces the concept of isomorphs in the phase diagram of strongly correlating liquids, identifying invariants and validating predictions through simulations, with implications for understanding liquid dynamics and thermodynamics.

Contribution

It presents the novel concept of isomorphs in liquid state diagrams and identifies their invariants, advancing the understanding of strongly correlating liquids.

Findings

Isomorphs are curves along which many thermodynamic and dynamic properties are invariant.

Simulations of Lennard-Jones mixtures validate isomorph predictions.

Isomorph theory explains phenomena like isochronal superposition and non-Arrhenius relaxation.

Abstract

This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the state diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and coworkers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, as well as explains isochronal superposition for strongly correlating viscous liquids.