ADSORPTION OF HYDROGEN ON FRACTAL SURFACES
Abstract
Solid-state fractal structures, or aggregates have fractional metric dimension values and have the property of self-similarity over multiple spatial scales. Such structures are formed in nonequilibrium conditions. Porous silicon, for instance, has a distinct fractal structure. Such structures are always observed in the analysis of experimental data.
Our study is focused on the dispersive interaction between a neutral atom and a substance with a fractal structure. We present a general analytical formula for the interaction potential that is defined as fractional power function of the distance. The paper demonstrates that the exponent of the potential depends on the volume fractal dimension.
The scattering cross-section and the collision frequency of hydrogen atoms with the fractal manifold were calculated in the quantum (quasiclassical) approximation with arbitrary value of the fractal dimension.
Considering three conditions - that the adsorption rate is equal to the desorption rate, the adsorption rate is determined by the frequency of collisions and effective surface area, and the desorption rate is proportional to the occupied surface area - we propose an isotherm equation for hydrogen adsorption on fractal surfaces. This equation is similar to the Freundlich equation. When the surface is smooth, the proposed equation yields the Langmuir adsorption isotherm. When the pressure is low, the equation yields the Freundlich adsorption isotherm, with the exponent depending on the fractal dimension of the surface. When the pressure is low and the surface is smooth, the equation yields Henry's adsorption isotherm.
Thus, the paper demonstrates that the exponent in the Freundlich empirical equation is determined by the fractal dimension of the surface. According to the experimental data, the exponent in Freundlich adsorption isotherm is also a temperature-dependent value. This means that possible alterations in the surface fractal dimension, caused by temperature changes, can be identified as the second order phase transition on the surface of the material. Such transitions always come before structural transformations in volume and can occur even when there are no phase transformations in the bulk.
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References
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