Aarão Reis F D A, di Caprio Dung
Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil.
Institut de Recherche de Chimie Paris, CNRS, Chimie ParisTech, 11, rue P. et M. Curie, 75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062126. doi: 10.1103/PhysRevE.89.062126. Epub 2014 Jun 19.
Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long-time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.
研究了由弹道式生长模型产生的多孔沉积物内壁吸附粒子的随机游走（RW）。粒子从沉积物的外表面开始，进入其孔隙，以模拟一种物质向多孔固体的外部通量。在短时间内，游走者浓度随深度z呈拉伸指数衰减，但在大多数样品中观察到向长时间正常扩散的转变。如果游走者的步长限制在最近邻，则在非常多孔的固体中，长时间内异常浓度分布仍然存在，并伴有亚扩散特征。这些发现与探索区域随z的衰减相关。对留在固体内部的示踪粒子的随机游走研究排除了用位置依赖系数的扩散方程进行解释的可能性。一个横截面减小的管中的随机游走模型通过展示从有效亚扩散区域到渐近正常扩散的长转变来解释这些结果。对于面积随z指数减小的管，解析计算了转变位置和密度，与数值数据显示出良好的一致性。浓度分布的异常衰减被解释为管形状对每个深度处扩散粒子总数的模板效应，而实际探索的多孔区域中的体积浓度可能没有显著衰减。这些结果可能解释了近期工作中观察到的金属原子在多孔沉积物中的异常扩散。它们还证实了在解释近期工作中报道的关于异常输运的实验或计算数据时的困难，特别是如果只测量浓度分布的话。
