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.
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