Percolation and electrical conduction in random systems of curved linear objects on a plane: Computer simulations along with a mean-field approach

Abstract

Using computer simulations, we have studied the percolation and the electrical conductance of two-dimensional, random percolating networks of curved, zero-width metallic nanowires. We mimicked the curved nanowires using circular arcs. The percolation threshold decreased as the aspect ratio of the arcs increased. Comparison with published data on the percolation threshold of symmetric quadratic Bézier curves suggests that when the percolation of slightly curved wires is simulated, the particular choice of curve to mimic the shape of real-world wires is of little importance. Considering the electrical properties, we took into account both the nanowire resistance per unit length and the junction (nanowire/nanowire contact) resistance. Using mean-field approximation (MFA), we derived the total electrical conductance of nanowire-based networks as a function of their geometrical and physical parameters. The MFA predictions have been confirmed by our Monte Carlo numerical simulations. For our random homogeneous and isotropic systems of conductive curved wires, the electric conductance decreased as the wire shape changed from a stick to a ring when the wire length remained fixed.

Percolation threshold and electrical conductivity of conductive polymer composites filled with curved fibers in two-dimensional space

“…Our final purpose is to quantify the relationship between the electrical conductivity of CPC and its composition and microstructure. Various approaches, including theoretical composites models, [57][58][59] mean-field approach, 60 and numerical techniques, [61][62][63] have even been used to predict the effective electrical conductivity s eff of composite materials. For instance, McLachlan 57 and Xu et al 58,59 proposed a general effective medium theory (GEMT) and continuum percolation-based generalized effective medium theory (CP-GEMT) to link the s eff of CPC to the f c of conductive fiber.…”

“…For instance, McLachlan 57 and Xu et al 58,59 proposed a general effective medium theory (GEMT) and continuum percolation-based generalized effective medium theory (CP-GEMT) to link the σ eff of CPC to the ϕ c of conductive fiber. Tarasevich et al 60 developed a mean-field approach (MFA) to predict the σ eff of the curved nanowires, Balberg et al , 61 Ni et al 62 and Tarasevich et al 63 studied a random resistor network model (RRNM) to establish the relationship between the effective electrical conductivity of composites and the area fraction of the conductive phase. It is noted that theoretical models only consider the influence of the area fraction of the conductive phase but lack information on particle shape.…”