Effect of nanorope waviness on the effective moduli of nanotube sheets

Abstract

Using a micromechanics approach, we recently investigated the theoretical limits on achievable moduli in nanotube mats by stiffening of bonds. However, the waviness intrinsic to many manufacturing processes also clearly plays an important role in stiffness of these materials. To study the effect of waviness on mechanical properties, we modeled fiber segments as sinusoids, generated networks comprised of these fibers, and performed simulations of deformations of the networks. In contradiction of classical work by Kallmes and Corte [Tappi J. 43, 737 (1960)], we found the number of fiber crossings in these networks to be independent of fiber waviness, leading to identification of the number of fiber crossings as a necessary and sufficient parameter to specify network geometry, for either wavy or straight fibers. Our mechanical modeling results suggest that reducing the waviness of nanotube ropes would significantly improve Young’s moduli in these materials. However, reduction of waviness would not produce the improvements achievable with higher bond density; for random sheets, assuring connections among all intersecting ropes appears to be the most direct route toward improving the overall sheet properties. There remains a persistent discrepancy between statistically predicted bond densities and physical bond densities, based on moduli of these materials.