Quantum theory of adhesion in the approximation of one-electron bound surface states

The paper presents a quantum model of adhesion based on the consideration of single-electron bound surface states. The limitations of classical adhesion theories, such as mechanical, diffusion and electrostatic, were analyzed, and the need to take into account quantum effects for describing adhesion at the interface of solids, especially for nanomaterials and at low temperatures, was substantiated. A one-dimensional model of two potential wells with a barrier simulating the contact of two different surfaces was considered. The problem of finding the energy spectrum and wave functions of bound electron states was solved using the Schrödinger equation for a piecewise constant potential. The conditions for the existence of bound states, their spectral properties and features of wave functions for symmetric and asymmetric wells were analyzed. Particular attention was paid to calculating the average interaction force between particles and surfaces, as well as collective effects when levels were filled with electrons at zero temperature. It is shown that the quantum mechanical model allows to explain both attraction and repulsion between surfaces depending on the system parameters and the level filling scheme. The results of the work expand the fundamental understanding of adhesion mechanisms and can be used to model bonding in nanostructured materials.