On the Fractal Model of the Porous Layer Formation

Abstract

In the present paper, a fractal model of a porous layer formation is proposed. The consideration of the time-dependent pore growth process has allowed us to calculate such important parameters of porous matrix as the formed surface area, and surface and volume porosity values. We have theoretically shown that the formed surface area strongly depends on the difference between the pore size growth velocities parallel and perpendicular to the surface, i.e. the crystallographic orientation of the material surface. The volume and surface porosity values as well as the formed porous surface area are linear functions on the anodization current density. These results are in rather good agreement with other theoretical and experimental data.

Structural properties of porous media

“…However, the irregular geometrical structure of this material, which, no doubt, plays an important role for its characteristic properties, still remains investigated very insufficiently. We have proposed earlier in [2][3][4] fractal models describing the disordered structure of PS, which support the "graded band gap model" for this material [5]. The "graded band gap model" allows one to present PS as a material where the band gap value E g is smoothly decreasing with the depth into the material.…”

Highly Ordered Anodic Porous Alumina Formation by Self‐Organized Anodizing

“…One very promising approach to the anodic porous alumina description seems to be a fractal model of the porous layer formation [400], and the appearance of hexagonally ordered patterns as a result of Turing systems modeling [401,402].…”

Electrical conductivity mechanisms in porous silicon

“…Taking into account the fact that the concept of percolation threshold is smeared out in PS due to the anisotropy of porosity, it would be expected, that in real cases as p c approaches the value of 0.57, the conductivity through "solid-state" channels will not vanish as drastically as it follows from Eq. (5).…”

“…Fractal models, describing the disordered structure of PS, were suggested in our early studies [3][4][5]. A porous material can be presented as a variable gap material with an energy band gap smoothly decreasing with the depth [6,7].…”