| This thesis introduces a comprehensive numerical model for the determination of the electrical properties of carbon nanotube reinforced polymer composites. Procedures of this model are based on a new spanning network identification algorithm and the resistor network method. First, realistic nanotube geometry is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in the representative volume element. Next, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's Current Law is used in conjunction with finite element analysis to solve for the voltages and currents in the system and calculate the effective electrical conductivity of the nanocomposite. The Monte Carlo method is used to eliminate statistical variation by simulating five hundred random geometries. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone, and determines effective conductivity. The accuracy of the model is validated by comparison to both models and experiments reported in the literature. |
