Adhesion of carbon nanotubes on elastic substrates with finite thickness

Abstract

How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three stable adhesive states (initial non-adhesive, partially adhesive, and fully wrapping states) can be achieved, dependent on the substrate thickness, the number of CNT walls, and the interfacial adhesion work. The stability of adhesive configurations is explored by analyzing the energy variations corresponding to the adhesive deformation. We show that there exist several modes of energy variations, depending on the adhesion work and the substrate-CNT bending stiffness ratio, which exhibit linear and nonlinear influences, respectively. Our results could serve as guidelines to design CNT-on-substrate systems.