有序纳米线阵列中的导电渗流模型
A Model for Conductive Percolation in Ordered Nanowire Arrays
摘要：
阳极氧化和电沉积的组合过程导致高度有序的圆柱形纳米线阵列。这种基于模板的自组装制造方法产生嵌入氧化铝中的纳米线。通常，化学蚀刻用于去除氧化铝并释放纳米线。然而，在蚀刻过程中，实验观察到纳米线倾向于形成团块。在这项工作中，纳米线被建模为弹性杆受到表面相互作用力。该模型的动力学引起了上述聚团行为，通过逾渗理论进行了研究。这项工作发现，渗流发生的概率$P \sim (t-t_c)^x$，其中指数$x = 2.8$和$t_c$是渗流发生的时间。发现决定系统的临界指数为（维数）$d = 2$、$β= 2.1, γ= 0.57, Δ= 2.7, α= -2.8, ν= 2.4,$和$δ= 1.3$。
英文摘要：
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) $d = 2$, $β= 2.1, γ= 0.57, Δ= 2.7, α= -2.8, ν= 2.4,$ and $δ= 1.3$.
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