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Isomorphs, hidden scale invariance, and quasiuniversality.

Jeppe C Dyre1

  • 1DNRF Center "Glass and Time,"IMFUFA, Dept. of Sciences, Roskilde University, P. O. Box 260, DK-4000 Roskilde, Denmark.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Classical liquids with good isomorphs exhibit a hidden scale invariance, a property termed "pseudohomogeneous." This paper formulates this quasiuniversality using a reduced-coordinate potential-energy function for Roskilde-simple liquids.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Condensed Matter Physics

Background:

  • Classical liquids with good isomorphs, termed Roskilde-simple liquids, exhibit unique properties.
  • Recent work rationalized their quasiuniversality via a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces.

Purpose of the Study:

  • Establish an approximate scaling property of the potential-energy function for classical liquids with good isomorphs.
  • Provide a potential-energy formulation for the quasiuniversality of monatomic Roskilde-simple liquids.
  • Introduce a quasiuniversal reduced-coordinate potential-energy function.

Main Methods:

  • Analysis of the potential-energy function's scaling properties.
  • Development of a potential-energy formulation for liquid quasiuniversality.
  • Derivation of a quasiuniversal reduced-coordinate potential-energy function.

Main Results:

  • Demonstration of a "pseudohomogeneous" property in the potential-energy function, revealing hidden scale invariance.
  • A novel potential-energy formulation of quasiuniversality for Roskilde-simple liquids.
  • Introduction of a quasiuniversal reduced-coordinate potential-energy function.

Conclusions:

  • The pseudohomogeneous property elucidates the hidden scale invariance in Roskilde-simple liquids.
  • The potential-energy formulation offers new insights into liquid quasiuniversality.
  • The derived function has implications for understanding the behavior of classical liquids.