A continual approach to Van der Waals interactions in carbon nanotube based systems

Abstract

Ordered arrays of carbon nanotubes (CNT) are promising elements of nanoelectromechanical systems based on transformation of electromagnetic fields into mechanical motion. Simulation of these phenomena accounting various nonlinear interactions can be realized on the basis of macroelectrodynamics of moving media, theory of elasticity and van der Waals interactions’ phenomenological theory. The balance equations of mass, momentum, angular momentum and energy as well as entropy inequality describing interacting continua of the mass, electric charge and internal spin are presented. To include van der Waals forces the additional terms are introduced into these equations which transform the system into indegro- differencial one. It is shown that integral terms can be neglected if the gap between tubes is greater than CNT outer diameter. The occurrence of multiple resonant vibrations of ordered CNT arrays is characteristic of them. Solving the system numerically the essential influence of van der Waals forces on CNT array resonant frequencies was proved.