Energetics of imperfectly bonded carbon nanotube arrays in flexure

Van der Waals interactions in carbon nanotube (CNT) arrays with hexagonal symmetry and consisting of identical diameter single-walled CNT are modeled by examining elasto-static properties of collimated arrays subjected to flexural deformations and by imposing the condition of imperfect bonding in the array. Array compliance is shown to provide a direct measure of the shearing traction between the CNT and thereby an indirect measure of van der Waals interactions. The array compliance, state of stress and strain energy are calculated for CNT arrays consisting of 7, 19, 37, 61, 91, 127, …, CNT, where the condition of bonding imperfection is characterized by the shear transfer efficiency (0 < k < 1.0). In addition, the strain energy of the array is decomposed into components due to flexure, extensional and shearing stresses. Finally the relative contribution of each component to the array total strain energy is examined for the 7, 61 and 127 CNT arrays.