Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry

Abstract

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path–integral, and finite–element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi–conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self–avoiding worm–like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex–shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient [σ] in the conductive and insulating particle limits, which are required to estimate [σ] in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications.

Nanofibrous poly(ethylene oxide)‐based structures incorporated with multi‐walled carbon nanotube and graphene oxide as all‐solid‐state electrolytes for lithium ion batteries

“…In addition, CN3 and GON2 had a good capacitance of about 1000 and 170 mAs g −1 cm −2 , respectively. The addition of MWCNT and GO to the polymeric matrix caused an increase in the electrical conductivity . The electronic structures of GO and CNTs are different.…”

“…The addition of MWCNT and GO to the polymeric matrix caused an increase in the electrical conductivity. 47 The electronic structures of GO and CNTs are different. Graphene with perfect honeycomb lattice is a zero-band-gap semiconductor but CNTs show either metallic or semiconducting properties.…”

Universal interrelation between measures of particle and polymer size

“…For instance, ν eff is a function of the aspect ratio r for oblate and prolate ellipsoids, where r is the ratio between the largest to the smallest ellipsoid axis. 24 The same situation arises for dendrimers, 25,26 duplex DNA, 27 carbon nanotube domains, 8 nanoparticle with grafted layers of DNA chains, 28,29 etc. In each case, the molecular parameters describing the object must be prescribed over which the mass scaling relation is exhibited.…”

“…(a) Flexible polymers with repulsive excluded volume interactions (swollen random coils) generated via Monte Carlo simulations, 26 (b) flexible capped cylinders generated via MD. 8,33,34 (c) Worm-like chains obtained from the fit functions given in Ref. 10.…”

“…The self-capacitance C of particles is also important in relation to understanding the potential energy of conducting objects and the rate of diffusion-limited reaction because the Smoluchowski rate constant is proportional to C. 2 The self-capacitance also arises in connection to the scattering length in acoustics, 3 quantum mechanics, 4 and other diverse applications. 5 Finally, we mention that α E emerges in continuum property calculations of changes in many material properties such as electric conductivity, thermal conductivity, dielectric constant, and magnetic permeability, among others, when a small concentration of particles is added to another medium [6][7][8] so that α E , as in the case of [η], has a significant potential for particle shape characterization.…”