Electrical conductivity of crack-template-based transparent conductive films: A computational point of view.

Crack-template-based transparent conductive films (TCFs) are promising kinds of junction-free, metallic network electrodes that can be used, e.g., for transparent electromagnetic interference shielding. Using image processing of published photos of TCFs, we have analyzed the topological and geometrical properties of such crack templates. Additionally, we analyzed the topological and geometrical properties of some computer-generated networks. We computed the electrical conductance of such networks against the number density of their cracks. Comparison of these computations with predictions of the two analytical approaches revealed the proportionality of the electrical conductance to the square root of the number density of the cracks was found, this being consistent with the theoretical predictions.

Electrical conductivity of random metallic nanowire networks: an analytical consideration along with computer simulation.

The current interest in the study of the 2D systems of randomly deposited metallic nanowires is inspired by a combination of their high electrical conductivity with excellent optical transparency. Metallic nanowire networks show great potential for use in numerous technological applications. Although there are models that describe the electrical conductivity of the random nanowire networks through wire resistance, junction resistance, and number density of nanowires, they are either not rigorously justified or contain fitting parameters. We have proposed a model for the electrical conductivity in random metallic nanowire networks. We have mimicked such random nanowire networks as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We studied the electrical conductivity of these RRNs using a mean-field approximation. An analytical dependency of the electrical conductivity on the main physical parameters (the number density and electrical resistances of these wires and of the junctions between them) has been derived. Computer simulations have been performed to validate our theoretical predictions. We computed the electrical conductivity of the RRNs against the number density of the conductive fillers for the junction-resistance-dominated case and for the case where the wire resistance and the junction resistance were equal. The results of the computations were compared with this mean-field approximation. Our computations demonstrated that our analytical expression correctly predicts the electrical conductivity across a wide range of number densities.

Electrical conductivity of nanorod-based transparent electrodes: Comparison of mean-field approaches.

We mimic nanorod-based transparent electrodes as random resistor networks (RRNs) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We suppose that the number density (the number of objects per unit area of the surface) of these sticks exceeds the percolation threshold, i.e., the system under consideration is a conductor. We computed the electrical conductivity of random resistor networks versus the number density of conductive fillers for the wire-resistance-dominated case, for the junction-resistance-dominated case, and for an intermediate case. We also offer a consistent continuous variant of the mean-field approach. The results of the RRN computations were compared with this mean-field approach. Our computations suggest that, for a qualitative description of the behavior of the electrical conductivity in relation to the number density of conductive wires, the mean-field approximation can be successfully applied when the number density of the fillers n>2n_{c}, where n_{c} is the percolation threshold. However, note the mean-field approach slightly overestimates the electrical conductivity. We demonstrate that this overestimate is caused by the junction potential distribution.

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models.

The electrical conductivity of two-dimensional films filled with rodlike particles (rods) was simulated by the Monte Carlo method. The main attention has been paid to the investigation of the effect of the rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, and (v) the films may simultaneously be both highly transparent and electrically anisotropic.

Mathematical modeling of pattern formation caused by drying of colloidal film under a mask.

In our model, we simulate an experiment (D.J. Harris, H. Hu, J.C. Conrad, J.A. Lewis, Patterning colloidal films via evaporative lithography, Phys. Rev. Lett. 98, 148301 (2007)). A thin colloidal sessile droplet is allowed to dry out on a horizontal hydrophilic surface. A mask just above the droplet predominantly allows evaporation from the droplet free surface directly beneath the holes in the mask. We consider one special case, when the holes in the mask are arranged so that the system has rotational symmetry of order m . We use a speculative evaporative flux to mimic the real system. Advection, diffusion, and sedimentation are taken into account. FlexPDE is utilized to solve an advection-diffusion equation using the finite element method. The simulation demonstrates that the colloidal particles accumulate below the holes as the solvent evaporates. Diffusion can reduce this accumulation.