Fractal dimensions of surfaces. The use of adsorption data for the quantitative evaluaton of geometric irregularity

A basic characterization of powdered materials, is the degree of surface-irregularity of an average particle. This parameter is crucial for the understanding of adsorbate-particle interactions, particle-particle interactions and participate dynamics. The main currently used methods for quantification of this surface property are the roughness factor and the analysis of the "coast-line" of the particle, as appears, e.g., in electron microscope pictures. We briefly review a different approach, which offers the fractal-dimension, D, of the surface as a powerful property of matter, characterizing its geometric irregularity at the molecular domain. The development of this method as a general and useful tool in the study of particulate adsorbents, becomes possible following our discovery that self similarity of surface irregularities is very common in powdered materials. Self similarity can be revealed upon successive magnifications: if m-fold magnification reveals m new characteristic details, then the surface is a fractal of dimension 2 ≤ D < 3. The higher the D value, the more wiggly is the surface. That this notion is indeed powerful, is evident from the wealth of relations between a variety of surface parameters which may now be linked by the use of D. An example is the relation between the surface area, A, of a fixed amount of a powdered material as measured from monolayer coverage, and the particle radius R: A ∝ R^D-3. By the use of this equation, D of a variety of materials has been determined. A special feature of our method is, that even the hidden surface of the porous particle is probed.