Coordination number model to quantify packing morphology of aligned nanowire arrays

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.