## 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 C_{p}-C_{V} 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 _{b}ln( xi /sub //// xi _{b}) provided omega

Original language | English |
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Article number | 030 |

Pages (from-to) | 7207-7238 |

Number of pages | 32 |

Journal | Journal of Physics Condensed Matter |

Volume | 1 |

Issue number | 39 |

DOIs | |

Publication status | Published - 1989 |