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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. [ABSTRACT FROM AUTHOR]

We have studied the resistance of two-dimensional random percolating networks of zero-width metallic nanowires (rings or sticks). We took into account the nanowire resistance per unit length, the junction (nanowire/nanowire contact) resistance, and the busbar/nanowire contact resistance. Using a mean-field approximation (MFA), we derived the total resistance of the nanoring-based networks as a function of their geometrical and physical parameters. We have proposed a way of accounting for the contribution of the busbar/nanowire contact resistance toward the network resistance. The MFA predictions have been confirmed by our Monte Carlo numerical simulations. Our study evidenced that the busbar/nanowire contact resistance has a significant effect on the electrical conductivity when the junction resistance dominates over the wire resistance. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a log-normal distribution. They were allowed to be aligned along a given direction. The impacts of the length dispersity and the extent of the rod alignment on the insulator-to-conductor phase transition were studied. Two alternative computational approaches were compared. Within Model I, the films were transformed into resistor networks with regular structures and randomly distributed conductances. Within Model II, the films were transformed into resistor networks with irregular structures but with equal conductivities of the conductors. A comparison of the models evidenced similar behavior in both models when the concentration of fillers exceeded the percolation threshold. However, a fairly fine mesh should be used in Model I to obtain a reasonable estimation of the electrical conductance. The electrical conductance is slightly overestimated in Model I. In anisotropic systems, the length dispersity of fillers has a more pronounced effect on the electrical conductance along the direction of the rod alignment. Some analytical results were obtained: (i) the relationship between the number of fillers per unit area and the transmittance of the films within Model I and (ii) the electrical conductance of the films for dense networks within Model II. [ABSTRACT FROM AUTHOR]