The application of SAXS to determine the fractal properties of porous carbon-based materials

Comparison of Techniques for Determining the Fractal Dimensions of Clay Minerals

“…The large DsAxs value observed for hectorite can also be explained by realizing that while the narrow pores are inaccessible to adsorbed molecules the surface heterogeneity of this impure hectorite could be accessible in the scattering experiment (Farin and Avnit 1989). The SAXS technique probes the "overall" interface of the solid material by detecting the heterogeneity in electron density on the surface while adsorption has the advantage of probing the accessible or open surface, which is of more interest or relevance in the characterization of surface morphology of these clays (Reich et al 1990). The fractal exponent obtained by this approach however, does not depend only upon the material's geometry and size of adsorbate used.…”

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

“…The fractal nature of colloids can be experimentally quantified using scattering techniques, and based on a combination of theoretical and experimental evidence [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] two distinct scaling laws have been used to describe experimental observations: mass fractals and surface fractals. Mass fractal scaling can be associated with the packing efficiency of an aggregate, which in turn depends on the type of aggregation, e.g., diffusion or reaction limited mechanism.…”

“…[13][14][15][16][17][18][19][20][21] On the other hand, surface fractal scaling only relates to the perimeter of a particle or aggregate of particles and correlates with its specific surface area. [1][2][3][4][5] The core idea behind mass fractals stems from our need to statistically describe aggregation processes involving primary particles. To exemplify this, we will assume for simplicity that a system only has spherical and monodisperse particles with radii r 0 .…”

“…Consequently, the yardsticks and fractal properties are two-dimensional, and thus a yardstick can be linked to the surface area α described in Eq. (2). Although the surface fractal formalism does not exclude the existence of primary particles (i.e., larger than a single atom) making up the surface of the aggregate, it is typically assumed that surface fractal scaling extends to the infinitely small "atomic" level and hence r → 0 (in analogy to Fig.…”

The Pore Structure in Processed Victorian Brown Coal

“…The length scales over which these techniques may be used to study coal are typically from the meso to micro porous regimes. These length scales are of great interest to workers studying coal processes as this porosity is clearly important in determining coal products when dried, combusted, liquefied, or coked (9)(10)(11). Further this coal porosity has been linked to coal's wetting behavior, adsorption characteristics, and even bulk mechanical properties (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20).…”