Density fluctuations and correlations of confined fluids

The density fluctuations about the equilibrium structure of fluids confined by parallel planar walls are analyzed for the cases of identical and symme trically opposed fields at the walls. We determine the stability matrix (of the second derivatives of the free energy functional with respect to the d ensity) for conditions both above and below the wetting transition temperat ure T-w of the semi-infinite system and corroborate in all cases that the e quilibrium configurations are stable. We identify the fluctuations close to the walls and in the middle of the slab and discuss their effect when the wall separation L diverges. For competing walls above T-w the localized flu ctuation with lowest eigenvalue describes the displacements of the incipien t wetting films that become unimpeded interfacial translations for L --> in finity. Below T-w the fluctuations with lowest eigenvalue correspond to sti ffer deformations extended across the slab. For identical walls above T-w c oexisting states display incipient prewetting films and the lowest eigenval ue describes the nature of their growth as L increases. We also calculate t he pair correlation function for the inhomogeneous states and, for symmetri cally opposed walls, we obtain standard Ornstein-Zernike (OZ) behavior at t he walls, but find significant deviations from this law at the interface-li ke region in the middle of the slab. To model fluids with short-ranged forc es we use a ferromagnetic Ising-type Hamiltonian in mean-field approximatio n. (C) 1999 Elsevier Science B.V. All rights reserved.