Determination of pore fractal dimensions and porosity of silica glasses from the dielectric response at percolation

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Abstract
The analysis of the dielectric relaxation spectrum at percolation was used for the determination of the dimensions of pore fractals and porosity of silica glasses. The percolation phenomenon in the porous glasses is related to the transfer of the electric excitation within the developed network of open pores due to migration of protons and ions along the pore surface of connected pores. The dielectric spectroscopy technique allows us to identify the relaxation process related to percolation, and to extract the fractal dimensions of the paths of excitation transfer associated with migration of charge carriers within the porous medium. The random fractal model describes the geometrical disorder of the porous matrix. In the framework of this model, the relationship between the porous space fractal dimension and the porosity of the medium has been obtained. The juxtaposition of the structural and the relaxation models enables us to derive the relationship between the value of porosity and the fractal dimensions of the paths of excitation transfer within the porous medium. The experimental porosity values for several porous silica glasses obtained by means of the developed theoretical approach and dielectric spectroscopy measurements are presented. The porosity values obtained from the dielectric spectroscopy method are found to be in good agreement with the data obtained from the measurements of the relative mass decrements.