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

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 d<3 this analysis predicts the correlation-length exponent nu /sub ///=2/(3d-5). For d=3 critical exponents depend on the dimensionless parameter omega =k B T/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 <2. The procedure accounts for the other fluctuation regimes found in the RG studies and provides new insight into the origin of the omega -dependence of the exponents. The singularities that occur in critical wetting can be described in terms of a simple ansatz for G, similar but not identical to that proposed by Henderson.