Classical Density-Functional Theory Studies of Fluid Adsorption on Nanopatterned Planar Surfaces

This contribution is based on our talk at the BIRS Workshop on "Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications". Our aim here is to summarize and bring together recent advances in wetting of nanostructured surfaces, using classical density-functional theory (DFT). Classical DFT is an ab initio theoretical-computational framework with a firm foundation in statistical physics allowing us to systematically account for the fluid spatial inhomogeneity, as well as for the non-localities of intermolecular fluid-fluid and fluid-substrate interactions. The cornerstone of classical DFT, is to express the grand free energy of the system as a functional of its one-body density, thus generating a hierarchy of N-body correlation functions. Unconstrained minimization of a properly approximated free-energy functional with respect to the one-body density then yields the basic DFT equation. And since most macroscopic quantities of interest can often be cast as averages over a one-body distribution, this equation provides a very useful and accessible computational tool. Indeed, there has been a rapid growth of classical DFT applications across a broad variety of fields, including phase transitions in solutions of macromolecules, interfacial phenomena, and even nucleation. Here we attempt to give a taste of what simple equilibrium DFT models look like, and what they can and cannot capture, as far as wetting on chemically heterogeneous substrates is concerned. We review recent progress in the understanding of planar prewetting and interface unbending on such substrates and compute substrate-fluid interfaces and wetting isotherms.