Wetting transitions in fluids with short-ranged forces: Correlation functions and criticality

Robert Evans*, A. O. Parry

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)

Abstract

The nature of the pairwise correlation function G for a fluid undergoing critical and complete wetting transitions at an adsorbing substrate (wall) is examined using various and statistical-mechanical treatments. Sum-rule and scaling arguments predict that, in critical wetting at bulk coexistence, capillary-wave fluctuations manifest themselves throughout the wetting film, up to the wall, so that the (divergent) transverse correlation length xi /sub /// is the same for all pairs of particles. By contrast, in the case of complete wetting from off-bulk coexistence, a divergent correlation length is appropriate only for particles located in the liquid-gas edge of the wetting film. These predictions are confirmed by explicit formulae for the transverse moments of G derived from a mean-field, density-functional theory of a Yukawa fluid in the presence of a short-ranged (exponential) wall-fluid potential. The sumrule analysis also provides a surface analogue of the Cp-CV thermodynamic relation, which is used to determine a rigorous relationship between the exponents that characterise critical wetting. The same thermodynamic relation predicts corrections to scaling in bulk dimension d=3 that are similar to those found in renormalisation-group (RG) studies of effective interfacial Hamiltonians. By unfreezing capillary-wave fluctuations on a mean-field density profile and making use of a sum rule that relates a derivative of the surface tension to the profile near the wall, relationships between xi /sub /// and the thickness t of the wetting film derived for critical wetting with finite-ranged forces. For dBT/4 pi sigma lg xi b 2, where sigma lg is the liquid-gas surface tension, xi b is a bulk correlation length and t=(2+ omega -1/ nu /sub ///) xi bln( xi /sub //// xi b) provided omega

Original languageEnglish
Article number030
Pages (from-to)7207-7238
Number of pages32
JournalJournal of Physics Condensed Matter
Volume1
Issue number39
DOIs
Publication statusPublished - 1989

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