  The paper aims at the development of a digital twin modelling the electrical
conductivity of multi-wall carbon nanotube (MWCNT)/polymer nanocomposite. A
comparative analysis is conducted for various formulations of boundary
conditions in the representative volume element (RVE) with uniform and
isotropic distribution of CNTs. Three types of boundary conditions studied:
uniform boundary potentials for an RVE, uniform boundary potentials for a chain
of two RVEs, and periodic boundary potentials. It is demonstrated that to
calculate the electrical conductivity of the material correctly, the
implementation of periodic boundary conditions for the RVE is required; on the
contrary, the use of uniform boundary potentials leads to significant
overestimation in conductance. The sensitivity of average conductivity to the
RVE size is determined for different volume fractions (Vf) of CNTs. For
example, the 5 micrometer size of the RVE is found to be optimal for 1% Vf of
CNTs with 50 nm diameter and 5 micrometer average length. Beside the RVE size,
we verify how model output changes in response to tuning parameters of the CNT
geometry, such as curvature and torsion (twist). We find the presence of the
second parameter, torsion, to be imperative for correct conductivity modelling
since usage of the curvature alone leads to unavoidable dependence on segment
size during CNT discretization. In literature, the influence of intrinsic MWCNT
resistivity is often discarded as negligible due to ballistic transport of
electrons. To verify this assumption, we check the sensitivity of results to
finite resistivity of CNTs. Percolation threshold and the critical index are
calculated for different sets of model parameters. The model finite-size effect
on the percolation threshold is investigated.
