Nonuniform van der Waals theory

M. K.H. Kiessling, J. K. Percus

Research output: Contribution to journalArticlepeer-review


The liquid-vapor interface of a confined fluid at the condensation phase transition is studied in a combined hydrostatic/mean-field limit of classical statistical mechanics. Rigorous and numerical results are presented. The limit accounts for strongly repulsive short-range forces in terms of local thermodynamics. Weak attractive longer-range ones, like gravitational or van der Waals forces, contribute a self-consistent mean potential. Although the limit is fluctuationfree, the interface is not a sharp Gibbs interface, but its structure is resolved over the range of the attractive potential. For a fluid of hard balls with ∼-r-6 interactions the traditional condensation phase transition with critical point is exhibited in the grand ensemble: A vapor state coexists with a liquid state. Both states are quasiuniform well inside the container, but wall-induced inhomogeneities show up close to the boundary of the container. The condensation phase transition of the grand ensemble bridges a region of negative total compressibility in the canonical ensemble which contains canonically stable proper liquid-vapor interface solutions. Embedded in this region is a new, strictly canonical phase transition between a quasiuniform vapor state and a small droplet with extended vapor atmosphere. This canonical transition, in turn, bridges a region of negative total specific heat in the microanonical ensemble. That region contains subcooled vapor states as well as superheated very small droplets which are microcanonically stable.

Original languageEnglish (US)
Pages (from-to)1337-1376
Number of pages40
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Mar 1995


  • Liquid-vapor interface
  • continuum limit
  • numerical results
  • rigorous results
  • van der Waals theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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