Optimally conductive networks in randomly dispersed CNT:graphene hybrids.

A predictive model is proposed that quantitatively describes the synergistic behavior of the electrical conductivities of CNTs and graphene in CNT:graphene hybrids. The number of CNT-to-CNT, graphene-to-graphene, and graphene-to-CNT contacts is calculated assuming a random distribution of CNTs and graphene particles in the hybrids and using an orientation density function. Calculations reveal that the total number of contacts reaches a maximum at a specific composition and depends on the particle sizes of the graphene and CNTs. The hybrids, prepared using inkjet printing, are distinguished by higher electrical conductivities than that of 100% CNT or graphene at certain composition ratios. These experimental results provide strong evidence that this approach involving constituent element contacts is suitable for investigating the properties of particulate hybrid materials.