Scaling of correlation functions near capillary condensation

Abstract

We study the influence of wetting films on (density–density) correlations for a fluid in a slit-like geometry near capillary condensation. We show that, for systems with short-ranged forces, the interaction between the wetting films strongly enhances the amplitude of the exponential decay of correlations and, unlike the interfacial roughness, is independent of a high-momentum cut-off. The correlation function shows scaling behaviour near condensation arising from the equality of two characteristic length scales: the parallel correlation length (associated with the complete wetting films) and a length scale related to the non-local interaction between the wetting films on either side of the slit. We introduce a dimensionless amplitude ratio associated with the decay of correlations which allows us to distinguish between local and non-local effective Hamiltonian theories. Only the latter is fully consistent with microscopic density functional descriptions of correlation functions. The influence of long-ranged intermolecular forces and fluctuation effects in two dimensions is also discussed.

Keywords:

• capillary condensation
• wetting
• correlation function
• effective Hamiltonian
• scaling

Acknowledgements

It is our pleasure to dedicate this paper to Bob Evans on the occasion of his (unexpected) 65th birthday. Throughout his academic life, he has been nothing other than an inspiration. A.O.P. is particularly grateful for the wonderful memories of his time in Bristol. NRB acknowledges support from the Portuguese Foundation for Science and Technology (SFRH/BPD/63183/2009). CR acknowledges support from grants MOSAICO (Ministerio de Educación y Ciencia) and MODELICO (Comunidad de Madrid).