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

F Vargas-Lara and AM Hassan and EJ Garboczi and JF Douglas, JOURNAL OF CHEMICAL PHYSICS, 143, 204902 (2015).

DOI: 10.1063/1.4935970

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 (alpha(E), alpha(M)) of the CNT and GS
nanoparticles. These properties determine the conductivity virial
coefficient **sigma** in the conductive and insulating particle limits,
which are required to estimate **sigma** in the general case in which the
conductivity contrast Delta between the nanoparticle and the polymer
matrix is arbitrary. Finally, we propose approximate relationships for
alpha(E) and alpha(M) that should be useful in materials design and
characterization applications.

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