Two-Dimensional vs. Three-Dimensional Clustering and Percolation in Fields of Overlapping Ellipsoids

Abstract

Maximum depth-to-particle-dimension ratios in which systems can be treated as two-dimensional (2D) rather than three-dimensional (3D) systems in determining percolative properties have not been reported. This problem is of great technological significance. 3D solutions for percolation in even low-density systems pose much more intensive computational problems than their 2D analogs and also result in significantly different predictions for percolation onset. Moreover, many materials and sensing applications require analysis of domains of finite thickness. Adequate loading of particles is required, e.g., in electrodes in advanced batteries and fuel cells to ensure good conductivity. Adequate deployment of sensors into fields of finite thickness such as oblate, neuronal cells is required, e.g., to detect specific ions. A systematic determination of the effect of these arrangements on percolation properties is needed for both applications. Here, we provide comparisons of cluster sizes, densities, and percolation points among monodisperse, 2D and 3D systems of overlapping ellipsoids by systematically increasing the depth of the 3D system relative to particle dimensions. We investigate the effect of several boundary condition assumptions on the resulting particle orientations, emphasizing the probability of formation of large clusters. A method of experimental determination of percolation onset is also suggested, using the maximum change in cluster size. © 2004 The Electrochemical Society. All rights reserved.