Scaling relations quantify the hierarchical self-assembly of capillary-densified nanofiber arrays into shape-tunable architectures

Capillary-mediated densification is a facile and versatile method to create high-density, hierarchical structures from nanofiber (NF) arrays, such as aligned carbon nanotubes, whose exceptional intrinsic properties motivate their use as shape-tunable materials. Here, scaling relations are presented that accurately predict the morphology of capillary-densified NF arrays exhibiting multiple spatial scales, including long-range cellular networks formed from bulk-scale arrays, and solid, micron-scale pins formed via the densification of patterned arrays within the critical pattern size separating cell vs. pin formation. Both experiments and models show that the effective elastic modulus of the densifying NF arrays governs the resulting geometries, including the cell width and area, cell and pin wall thickness, and the NF volume fraction within the densified walls, which increase monotonically with array height. Further structural tunability, including the densification of mm- to cm-tall NF arrays, is possible by altering the NF-substrate adhesion strength. Collectively, these results could enable the broad use of capillary densification to predictably pattern hierarchical NF arrays for applications in optoelectronics, composite reinforcement, and advanced thermomechanical devices.