Abstract
Size effects are inherent in all nanostructures and continue to attract the attention of not only physicists, but
also biologists, physicians, and other specialties. In addition to fundamental problems, optical phenomena (including luminescence) in nanostructures are of great practical interest. In the present work, an empirical multilevel model of the surface layer of solids is proposed, which explains all the observed size effects in nanostructures, including luminescence. To obtain the equations, we used the method of nonequilibrium statistical thermodynamics. The surface layer of a solid body consists of three layers – a de Broglie layer d0 ~ ((0.01-0.1) nm for metals) and layers d(I) and d(II). Size effects in a layer d(I) are determined by the entire collective of atoms in the system (collective processes). Such “semiclassical” size effects are observed only in nanoparticles and nanostructures.
The layer d(II) should have many dimensional effects associated with a certain critical characteristic parameter: the mean free path of carriers in transport phenomena, the dimensions of domains/domain walls, the diameter of the Frank-Read loop for gliding dislocations, etc. When h=d in the surface layer, a phase transition occurs. It is shown that the thickness of the surface layer d(I) is determined by one fundamental parameter – the molecular (atomic) volume of a solid, which is different for metals, amorphous solids, glasses, and polymers. The proposed multilevel model of nanostructured states in solids, which explains all the observed size effects in nanostructures, including luminescence.

Keywords: nanostructure, multilevel model, size effects, luminescence, small particle, surface.