A Model for Conductive Percolation in Ordered Nanowire Arrays
The combined processes of anodization and electrodeposition lead to highly ordered arrays of cylindrical nanowires. This template-based self-assembly fabrication method yields nanowires embedded in alumina. Commonly, chemical etching is used to remove the alumina and free the nanowires. However, it has been experimentally observed during the etching process that the nanowires tend to form clumps. In this work, the nanowires are modeled as elastic rods subject to surface interaction forces. The dynamics of the model give rise to the aforementioned clumping behavior which is studied via percolation theory. This work finds that percolation takes place with probability $P \sim (t-t_c)^x$, where the exponent $x = 2.8$ and $t_c$ is the time at which percolation takes place. The critical exponents which entirely determine the system are found to be for (dimension) $d = 2$, $\beta = 2.1, \gamma = 0.57, \Delta = 2.7, \alpha = -2.8, \nu = 2.4,$ and $\delta = 1.3$.