(Invited) Thermal and Electrical Conductivity of Carbon Nanotube Network Materials: Theoretical Analysis and Mesoscopic Simulations

Abstract

A general framework for theoretical analysis and numerical calculations of the effective thermal and electrical conductivity of homogeneous and isotropic disordered materials composed of carbon nanotubes (CNTs) is developed. The model utilizes similarity in the mathematical description of thermal and electrical transport in nanotube materials. The analysis accounts for both the inter-tube contact conductance and intrinsic conductivity of CNTs, and is performed in a wide space of governing parameters that includes the fiber aspect ratio, Biot number calculated for a single contact between nanotubes, and density ranging from values corresponding to the percolation threshold up to those characteristic of dense fiber networks. For dense networks, exact theoretical equations for the effective conductivity of materials composed of nanotubes with arbitrary aspect ratio and Biot number are derived. The effect of the intrinsic conductivity of nanotubes on the thermal and electrical transport is found to depend on the density of inter-tube contacts and, thus, is usually significant in the dense materials. The theoretical finding are confirmed in large-scale simulations of quasi-two-dimensional CNT films and three-dimensional CNT aerogels, where nanotubes form continuous networks of intertwined bundles. The simulations are performed based on a mesoscopic model of CNT materials, where every nanotube is represented by a curved chain of stretchable cylindrical segments. The dependences of the conductivity on the CNT length, Biot number, and material density predicted in these simulations agree well with the scaling laws derived theoretically. The comprehensive theoretical description developed in this work can facilitate tailoring thermal and electrical conductivity of CNT materials to the needs of practical applications by varying the material density, CNT length, and aspect ratio. Financial support for this work is provided by the National Aeronautics and Space Administration (NASA) through an Early Stage Innovations grant from NASA's Space Technology Research Grants Program (grant NNX16AD99G). A.N.V. also acknowledges support from the National Science Foundation through the CAREER award CMMI-1554589.