Revealing Density Thresholds of Carbon Nanotube Cross-Links for Load Transfer: A Graph Theory Strategy.

Abstract

We report that the load transfer in carbon nanotube (CNT) networks is determined by the cross-link density <i>via</i> three critical thresholds, namely, percolation, connection, and saturation, which divide the transfer into four different modes. Reminiscent of the connectivity problem in the graph theory, an individual path for the successive load transfer through the network is formed at the first threshold, then all CNTs are connected together by cross-links at the second one, and finally, the connections are gradually converted into tetrahedrons toward a rigidized connectivity until the third saturation threshold. The power-law distribution of the number of cross-links per CNT shows a preferential linking mechanism, <i>i.e.</i>, that the CNTs with high cross-links are more attractive to form new cross-links than the CNTs with low cross-links, while repetitive cross-links could hardly improve the strength of CNT networks.