Employing appropriate finite element formulations, the governing

Employing appropriate finite element formulations, the governing equation of an electrical resistor can be written as (3) where I ij is the

electrical current passing between the ith and jth node; k ij is the conductance of the resistor between nodes i and j; and V i is the voltage of the ith node measured with respect to a node connected to ground. The system of the nonlinear equations governing the electrical behavior of the nanocomposite was obtained by assembling the governing equations for the individual elements. The resulting nonlinear system of equations was solved employing an iterative method. Results and discussion Modeling results The developed model was employed to investigate the electrical behavior of a polymer with λ = 0.5 ev made conductive through the uniform VS-4718 molecular weight dispersion of conductive circular nanoplatelets with a diameter

of 100 nm. In the AUY-922 simulations, the Tideglusib mw size of the RVE was chosen to be nine times the diameter of the nanodisks, which was ascertained to be large enough to minimize finite size effects. In an earlier study [15], the authors showed that the Monte Carlo simulation results are no longer appreciably RVE-size dependent when the RVE size is about eight times the sum of 2R + d t , where R and d t are the radius of the nanoplatelets and tunneling distance, respectively.The graph in Figure 5 depicts the effect of filler loading on nanocomposite conductivity. As expected, a critical volume fraction

indicated by a sharp increase in nanocomposite conductivity, i.e., the percolation threshold, can be inferred from the graph.In the following, electric current PIK3C2G densities passing through the nanocomposite RVE were computed for different electric field levels and filler volume fractions. As illustrated by Figure 6, the current density versus voltage curves were found to be nonlinear. The depicted electrical behavior of the conductive nanocomposite is thus clearly governed by the applied voltage in a nonohmic manner, which, as mentioned above, matches the expectation for a conductive nanocomposite at higher electric field levels. Figure 5 Conductivity of nanocomposite with respect to filler loading of conductive nanodisks with diameter of 100 nm. Figure 6 Electric current density of nanocomposites with 100-nm-diameter nanoplatelets versus the applied electrical field. Figure 7 shows the variation of resistivity as a function of the applied electric field E in order to compare the nonohmic behavior for nanocomposites with different filler loadings. Note that resistivity values were normalized with respect to a reference resistivity measured at E = 0.8 V/cm. The results as displayed in Figure 7 indicate that the magnitude of the applied electric field plays an important role in the conductivity of nanoplatelet-based nanocomposites.

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