Elena N. Brodskaya

The Irving–Kirkwood stress tensor has been calculated in spherical and infinite cylindrical cavities inside of an amorphous solid, with the cavities simulating pores of an adsorbent. The expressions obtained for the components of the stress tensor satisfy the conditions of mechanical equilibrium. The limiting behavior of the stress tensor under the conditions of a small curvature of the bounding surfaces coincides with the results of the asymptotic approach to the considered contribution from the solid surfaces.

The Irving–Kirkwood stress tensor has been calculated in a cylindrical slit inside an amorphous solid in terms of dispersion forces. The contribution of curvature to the disjoining pressure has been estimated and compared with the case of a spherical slit. It has been shown that, under the conditions of small curvature, the results for two slits coincide with each other when using the average curvature radius.

The Irving–Kirkwood stress tensor has been calculated in a spherical slit inside an amorphous solid, with the slit simulating an adsorbate-containing spherical pore in an adsorbent. Both normal and tangential components of the stress tensor have been calculated. Although their local variations are similar, the normal component is about two times higher than the tangential one. At a preset slit width, the stress tensor components take different values on the surfaces bounding the slit, and the absolute values of the components on a nanoparticle surface are higher than those on a macrophase surface. The contribution of an empty cavity to the stresses of a spherical film has been estimated to be insignificant. The disjoining pressure of the spherical slit has been calculated and compared with that in a plane-parallel slit. The average difference between the two functions is approximately 20%. It is seen that the slit curvature leads to an increase in the absolute value of the disjoining pressure along the entire slit.

In addition to our previous work [1], a detailed analysis has been carried out for the angular dependences of all components of the pressure tensor in a wedge-shaped cavity of a solid with dispersion forces. It has been shown that the pressure tensor components satisfy the conditions of mechanical equilibrium as a function of the distance from the walls of the wedge-shaped cavity and the angular variable. Additional contributions to the pressure tensor relative to the tensor in a planar slit have been obtained in the case of small angles.

The 21st century was marked by a new outbreak of interest in dispersion forces in nanoscale systems. However, now the consideration is conducted at a different level. Whereas earlier the main object of study was infinite plane-parallel films, now it is a question of calculations for systems of a more complex configuration with non-parallel and finite surfaces of various shapes. On the other hand, it is not the average interaction force that is estimated, but the detailed mechanical state of the interacting bodies, for which statistical mechanics and the Irving – Kirkwood stress tensor are involved. This review summarizes the theoretical studies of plane-parallel, but finite-area films, wedge-shaped films, systems with spherical, cylindrical, and conical surfaces. Particular consideration is given to interactions involving nanoparticles. Spheroidal particles, rod-like and disc-shaped particles are analyzed. The shape factor of the interaction of particles with a flat surface is estimated. The calculation of the contribution of dispersion forces to surface, line and point tension is explained. Among the latest news is the calculation (brought to numbers) of the contribution of dispersion forces to the graphene point energy. The bibliography includes 109 references.

Hamaker’s classical approach has been used to derive relations for the energy and force of the interaction between nanoparticles with different shapes and a planar solid surface. The shapes...

— The Irving–Kirkwood pressure tensor and the pair potential of dispersion forces without retardation have been employed to calculate the local normal pressure on the end surface of a...

Lennard-Jones fluid adsorption in bounded slits has been calculated by the Monte Carlo method. Isotherms of methane adsorption in circular finite carbon slits with different widths have been calculate