Analysis of the phase behaviour of a nano-confined Lennard-Jones fluid using a pseudo-spectral approach to classical density-functional models

Abstract

Wetting phenomena provide a vivid manifestation of attractive intermolecular forces, putting to a test our microscopic picture of matter. Classical Density Functional (DF) theory is based on first principles of statistical mechanics and provides a way to account for various microscopic effects determining the behaviour of confined fluids. In broad terms, the thesis consists of two parts, each expanding the existing body of knowledge in the respective field. In the first part a novel numerical methodology is developed, which allows one to solve any type of non-local integral or integral-differential equations typical of equilibrium and dynamic DF theories in oneand two-dimensional problems. The approach is based on pseudo-spectral collocation method and is demonstrated to be superior in speed and accuracy to existing commonly used approaches. Novel features include an integrating matrix operator, which is calculated outside of the non-linear solver loops and then used for fast evaluation of the non-local convolution-like terms with the highly accurate ClenshawCurtis quadrature, and a battery of techniques based on arc-length continuation providing a systematic and efficient way to compute density profiles, find surface phase transitions and obtain full phase diagrams. The second part presents a DF study of an atomic fluid at given chemical potential and temperature spatially confined to a semi-infinite rectangular pore. Fluid-fluid and fluidsubstrate interactions are with long-ranged Lennard-Jones forces. Far from the capping wall this prototypical two-dimensional system reduces to a one-dimensional slit pore. However, the broken translational symmetry dramatically changes the phenomenology of wetting from that of a slit pore. Detailed investigation reveals new phenomena related to the geometry. In particular, the existence of capillary wetting temperature, continuous capillary condensation transition, continuous planar prewetting transition, and more. Existence beyond mean-field is discussed briefly. Dynamic extension of the DF theory is used to study the relaxation of the system.