Characterization and structural investigation of fractal porous-silica over an extremely wide scale range of pore size

Abstract

We have succeeded in creating Menger sponge-like fractal body, i.e., porous-silica samples with Menger sponge-like fractal geometries, by a novel template method utilizing template particles of alkylketene dimer (AKD) and a sol-gel synthesis of tetramethyl orthosilicate (TMOS). We report here the first experimental results on characterization and structural investigations of the fractal porous-silica samples prepared with various conditions such as calcination temperature and packing condition of the template particles. In order to characterize the fractal porous-silica samples, pore volume distribution, porosity and specific surface area were measured over an extremely wide scale from 1 nm to 100 m by means of mercury porosimetry, 1 H NMR cryoporometry, and nitrogen gas adsorption experiments together with direct evaluations of cross-sectional fractal dimension D cs , size limits of D cs . We have found that the pore volume distribution and specific surface area of the fractal porous-silica samples can be discussed in terms of different fractal porous structures at different scale regions.

Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K

“…We derived the Hausdorff dimension $\overline{\mathit{d}}$ of our porous Si material using scanning electron microscopy (SEM) images and the box counting algorithm [31]. The SEM images reflect the fractal microstructure of the material.…”

Correlation between Curie temperature and system dimension

“…If we introduce a decay constant α and use the Curie constant C, T C can be formulated as a function of α, D, J 1 and S. Moreover, the T C /T bulk C obtained from the formula phenomenologically explains the experimental results in low-dimensional ferromagnets, and may be extended to the discussion on T N in antiferromagnets. Recently, we have prepared Menger sponge-like fractal bodies; fractal porous silica with D = 2.5 -2.7 with a pore size within the range of 50 nm -30 μm [35,36,37]. We are now preparing fractal antiferromagnets of transition metal oxides.…”

Preparation of Porous Titania by Sol–Gel Method Using Alkylketene Dimers as a Template

“…To quantitatively characterize the surface structure, we determined the fractal dimensions of cross sections of the prepared titania particles by the box-counting method using the FE-SEM and TEM trace images. The equations for calculation of the surface fractal dimension are as follows (Shibuichi et al, 1996;Ono et al, 2009).…”