Aligned carbon nanotube array stiffness from stochastic three-dimensional morphology

Abstract

The landmark theoretical properties of low dimensional materials have driven more than a decade of research on carbon nanotubes (CNTs) and related nanostructures. While studies on isolated CNTs report behavior that aligns closely with theoretical predictions, studies on cm-scale aligned CNT arrays (>10¹⁰ CNTs) oftentimes report properties that are orders of magnitude below those predicted by theory. Using simulated arrays comprised of up to 10⁵ CNTs with realistic stochastic morphologies, we show that the CNT waviness, quantified via the waviness ratio (w), is responsible for more than three orders of magnitude reduction in the effective CNT stiffness. Also, by including information on the volume fraction scaling of the CNT waviness, the simulation shows that the observed non-linear enhancement of the array stiffness as a function of the CNT close packing originates from the shear and torsion deformation mechanisms that are governed by the low shear modulus (∼1 GPa) of the CNTs.