Coordination number model to quantify packing morphology of aligned nanowire arrays

Abstract

The average inter-wire spacing in aligned nanowire systems strongly influences both the physical and transport properties of the bulk material. Because most studies assume that the nanowire coordination is constant, a model that provides an analytical relationship between the average inter-wire spacings and measurable physical properties, such as nanowire volume fraction, is necessary. Here we report a continuous coordination number model with an analytical relationship between the average nanowire coordination, diameter, and volume fraction. The model is applied to vertically aligned carbon nanotube (VACNT) and nanofiber (VACNF) arrays, and the effective nanowire coordination number is established from easily accessible measures, such as the nanowire spacing and diameter. VACNT analysis shows that the coordination number increases with increasing nanowire volume fraction, leading the measured inter-CNT spacing values to deviate by as much as 13% from the spacing values predicted by the typically assumed hexagonal packing. VACNF analysis suggests that, by predicting an inter-fiber spacing that is within 6% of the reported value, the continuous coordination model outperforms both square and hexagonal packing in real nanowire arrays. Using this model, the average inter-wire spacing of nanowire arrays can be predicted, thus allowing more precise morphology descriptions, and thereby supporting the development of more accurate structure-property models of bulk materials comprised of aligned nanowires.

Aligned carbon nanotube–epoxy composites: the effect of nanotube organization on strength, stiffness, and toughness

“…It is obvious that liquid densification causes merging of CNT bundles, enhancing their packing efficiency in the fibre and resulting in local curvature which is less distinct than in the uncondensed CNT mats. The less local curvature (so-called ''waviness'') was also observed for the vertically aligned CNT arrays upon their mechanical densification [18].…”

Morphology and processing of aligned carbon nanotube carbon matrix nanocomposites

“…The forests were grown on 1 cm × 1 cm Si substrates to form CNT arrays that are ∼ 1 mm tall, have an average inter-CNT spacing of ∼ 80 nm 40 , and volume fractions of ∼ 1% CNTs 41 . A post-growth H 2 anneal 45 is used to weaken the attachment of the CNTs to the catalyst layer, which enables the easy delamination of the CNT forest from the Si substrate using a standard lab razor blade, thereby allowing further CNT processing to be performed in their free-standing state.…”

“…3 if necessary for nanofiber arrays with lower φ o values (volume fractions > 1%), such as densified CNT arrays 15,16,18,24,40 . Because Eq.…”

“…To characterize the surface morphology of CNT ACMNCs, SEM analysis was performed using a JEOL 6700 cold field-emission gun scanning electron microscope using secondary electron imaging at an accelerating voltage ranging from 1.0 (for CNT forests) 40 to 3.0 kV (for CNT A-CMNCs) 23,24 and a working distance of either 3.0 mm (Fig. 2a and Fig.…”

“…Previous studies on the morphology of the CNT arrays, known as forests, indicate that the average inter-CNT spacing in the as-grown (∼ 1 vol. %) CNT forests is ∼ 80 nm 18,40 , meaning that the fabrication of low porosity A-PNCs is possible. However, once the polymer precursors are heat treated, additional porosity forms, and modeling indicates that its reduction to a value similar to that of carbon fiber reinforced carbon matrix composites ( 20%) 28 may not be possible using wet infusion in A-CMNCs.…”