Effective electrical conductivity of carbon nanotube-polymer composites: a simplified model and its validation

A simplified model is presented to predict the effective electrical conductivity of carbon nanotube (CNT)-polymer composite with different material proportions, which is validated by the experiments of multi-walled CNT/polydimethylsiloxane (PDMS) composites. CNTs are well dispersed in a PDMS matrix, and the mixture is then cured and cast into thin films for electrical characterization. The CNTs are assumed to be statistically uniformly distributed in the PDMS matrix with the three-dimensional (3D) waviness. As the proportion of CNTs increases to a certain level, namely the percolation threshold, the discrete CNTs start to connect with each other, forming a 3D network which exhibits a significant increase of effective electrical conductivity. The eight-chain model has been used to predict the effective electrical conductivity of the composite, in which the contact resistance between CNTs has been considered through the Simmons' equation. The eight-chain network features can be significantly changed with the modification to mixing process, CNT length and diameter, and CNT clustering and curling. A Gaussian statistics-based formulation is used to calculate the effective length of a single CNT well dispersed in the matrix. The modeling results of effective electrical conductivity agree with the experiments very well, which are highly dependent on a contact resistance between CNTs and the waviness of the CNTs. The effect of inner-nanotube distance and diameter of CNTs on the effective electrical conductivity of the CNT/PDMS composite is also discussed.