UC San Diego

A method is proposed for determining electrical percolation thresholds in carbon nanotube (CNT) networks when CNT lengths vary randomly. The random distribution in CNT lengths, commonly observed in practical processing and dispersion, was confirmed to be of the Weibull type. Nanocomposites consisting of both single- and multi-walled CNTs dispersed in reactive ethylene terpolymer were synthesized and the projected theoretical CNT volume concentrations required for electrical percolation were shown to closely correspond to the experimentally determined values. A metric for quantifying the degree of dispersion of nanostructures in polymers, based on information theory, is also suggested. The uniform dispersion of nanoparticles in polymer-based composites enhances material properties such as structural reinforcement, electromagnetic interference shielding, etc. The proposed measure of dispersion uses a quadrat- based sampling algorithm and the average Kullback-Leibler divergence is used to correlate randomness to the dispersion. This allows a quantitative comparison of cross -sectional images of nanostructure networks with different degrees of dispersion in a polymer. Finally, the complex electrical impedances of the nanocomposites were evaluated at different CNT aspect ratios and volume fractions in the 80 MHz - 500 MHz frequency range. The electrical impedances were fit to an equivalent-series resistance (ESR) circuit model, and compared with distributed electrical models such as an RC network and constant phase element representations. Dielectric permittivity measurements demonstrate that the constant phase element model, which corresponds to a distribution/dispersion of relaxation times, best fits the electrical response of the composites