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

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 B\'{e}zier 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 a mean-field approximation (MFA), we derived the total electrical conductance of the 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.