I. ABSTRACTThermal and electrical transport through a low-conductivity matrix containing high-conductivity fibers is important to several applications including flexible thin-film transistors, PEM fuel cells, and direct energy-conversion devices. Nanofibers can limit thermal transport through phonon confinement and boundary scattering while maintaining high electrical conductivity. The substrate will not contribute to electrical performance but may participate in thermal transport. The net result is a material whose Lorenz number can be tuned by loading the matrix with fibers. The purpose of the present work is to investigate the effectiveness of several transport models in the context of two-dimensional fiber composites and to compare the thermal and electrical transport through a given material as a function of the conductivity ratio and the fiber density. Three models will be considered and compared: 1)discretized solutions, 2) equivalent resistance, and 3)effective medium approximation. In the case of electrical transport, where the conductivity of the fiber is presumably many orders of magnitude larger than the matrix, the second model provides a fast and reliable way to predict conductance of the combined system. However, if the two materials are similar in conductivity, the second model fails to accurately capture the conductivity. Thermal transport is predicted using the discretized model because the conductivity ratio is nonnegligible. The third model is an analytic approximation based on Maxwell's equation and is used to predict both types of transport through a compound with inclusions of ellipsoidal geometry. This model works well for low fiber densities but predicts lower conductivity for high fiber-densities because the analytic solution fails to account for fiber overlap.
II. INTRODUCTIONThermal and electrical transport through a low-conductivity matrix containing high-conductivity fibers is important to several applications including flexible thin-film transistors (TFT) [4], proton exchange membranes (PEM) [11], and directenergy conversion devices [1].For flexible TFTs, low-temperature processes are required to prevent destruction of the substrate, but most semiconductors with good electrical performance require hightemperature processing [12]. Most research has been directed toward finding compatible high-temperature substrates [6]or high-performance electronic materials with low processing temperatures [5] [8]. Another approach is to combine the good electrical performance of nanofibers into flexible substrates. In fact, Biercuk et al. [2] have shown that nanotube/epoxy composites percolate at 0.1-0.2 wt% loading. This feature suggests that composite materials may retain the flexibility while providing good electrical performance with low processing temperatures. In direct energy conversion devices, particularly Peltier devices, high electrical conductivity and low thermal conductivity are preferred for superior performance [3]. However, most materials do not exhibit both of these properties si...