Transverse mechanical properties of carbon nanotube crystals. Part II: sensitivity to lattice distortions

Perfect crystals of carbon nanotubes tend to form aligned bundles that assume a hexagonal packing configuration in a minimum energy state. The theoretical constitutive relation for these defect-free crystals is highly anisotropic with a large axial stiffness due to a network of strong delocalized carbon–carbon bonds and transverse properties that are orders of magnitude lower due to a sole dependence on non-bonding van der Waals forces. The assemblage of a large number of collimated nanotubes may be expected to exhibit a distribution of lattice sites containing imperfections caused by packing faults or inclusions that will function as ‘weak-links’ and adversely affect local stiffness and strength. The present study is therefore directed towards quantifying the effects of distorted bundle configurations on mechanical properties. To illustrate distortion sensitivity, the transverse shear and bulk moduli are calculated by considering various magnitudes of random perturbations in nanotube packing. Monte Carlo simulations are performed to obtain a statistical distribution of predicted moduli. The present analysis demonstrates that even small perturbations to the lattice geometry give rise to large variations in transverse moduli, and suggests that chemical functionalization to improve nanotube bundle cohesion may be required for successful structural applications.