SIMULATION OF PERCOLATION BEHAVIOR OF ANISOTROPIC SHORT-FIBER COMPOSITES WITH A CONTINUUM MODEL AND NONCUBIC CONTROL GEOMETRY

A simulation study based on a concentric cylindrical model is presented for the prediction of the percolation threshold in anisotropic composites containing electrically conducting fibers in an insulating matrix. The present study uses both cubic and non-cubic control volumes to model the composite material rather than only cubic ones that have been employed in most earlier investigations. The use of non-cubic boxes has been shown to balance the disparity in the ratios of fiber to control volume (sample) dimensions in the three orthogonal directions for anisotropic fiber orientations. The finite size scaling (FSS) approach was found to be applicable for these non-random fiber orientations with the correlation length exponent being 0.89. The extrapolated threshold volume fractions for percolation in the three principal directions were found to be essentially the same for infinitely large systems. However, the slopes of the FSS curves were significantly different. These slopes, together with effective shape constants for the control volume, were used to predict the trend in threshold values for finite anisotropic systems such as those encountered experimentally. These theoretical arguments are among the first to explain several experimental results that have been reported in the literature for the electrical conductivity of short-fiber composites.