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The absorption of molecules on a one -dimensional lattice is considered for repulsive interactions between adsorbate molecules are presented. Spatial confinement and strong attraction to active sites can cause compression of an adsorbed phase and that repulsive interactions between adsorbed molecules result in steps in the adsorption isotherms.

Low temperature, Grand Canonical Monte Carlo simulations were used to study the adsorption of fluid layers on cubic, hexagonal, and atomically smooth substrates to determine the effects of registry and surface compression on the system. The size of the fluid molecules was fixed to be 20% larger than the substrate molecules in order to observe the transition from an expanded to commensurate and finally to an incommensurate monolayer. For relatively weak fluid-substrate interactions, the cubic system underwent a first-order phase transition. As the strength of the fluid-substrate interactions increased, the molecules became fixed at commensurate locations and the transition from low density to commensurate packing became continuous. The strong fluid-substrate interactions lead to the development of a kink in the adsorption isotherm that showed the increased stability of the commensurate phase. This kink became more pronounced as the system temperature was decreased. The hexagonal system showed less dramatic results due to a decrease in the substrate well depth of the relative to the cubic system. The system did experience a first-order phase transition for a weak fluid-substrate interactions and the transition became much more gradual as the fluid-substrate interaction increased. The molecules became fixed to commensurate substrate locations, but the surface was not corrugated sufficiently to have a stable commensurate phase. The atomically smooth substrate showed the first-order phase transition expected of a low temperature system with no effects of registry.

Liquid-vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.

The Kelvin equation for a compressible liquid in nanoconfinement is written in a form that takes into account not only Laplace's pressure, but also the oscillatory compression pressure. This leads to a simple analytical equation for pressure in nanocapillaries. The corrected equation is used to analyze properties of aqueous systems, including the oscillatory structural forces between attractive surfaces and inert surfaces, repulsive "hydration" forces between hydrophilic surfaces, and attractive "hydrophobic" forces between hydrophobic surfaces. Relative vapor pressure in a nanocapillary also is discussed.

Influence of adsorption compression on nanocapillarity is discussed. Kelvin's equation for a compressible liquid is written in a form that takes into account not only Laplace's pressure, but also adsorption compression. This leads to a simple analytical equation for pressure in nanocapillaries. It is shown that the ratio of Laplace's pressure to the adsorption compression pressure determines different types of nanocapillary behavior. When the Laplace pressure dominates, it results in classical capillarity that is well studied and understood. There is an intermediate range where Laplace's pressure is partially or fully compensated by adsorption compression, and the resulting pressure in a capillary is an interplay between attraction to walls and repulsions from neighboring molecules in compressed adsorbed fluid. If the adsorption compression pressure dominates, it results in inversion of capillary pressure and the fluid adsorbed in the nanocapillary presses on walls from inside. This phenomenon has been observed experimentally for fluids in nanoporous solids; in particular, high-precision measurements have shown significant expansion of nanoporous adsorbents loaded with various fluids. It is also shown that oscillatory adhesion forces and internal forces in nanoporous adsorbents have a common thermodynamic origin and can be discussed in the framework of adsorption compression mechanisms.