Evaluation of Fractal Dimension by Gas Adsorption
The concepts of fractal geometry elaborated by Mandelbrot  can be applied successfully to the study of solid surfaces. Fractal objects are self-similar, i.e., they look similar at all levels of magnification. The geometric topography (roughness) of the surface structure of many solids can be characterized by the fractal dimension, D. In the case of a Euclidean surface D is 2, however for an irregular (real) surface D may vary between 2 and 3. The magnitude of D may depend on the degree of roughness of the surface and/or the porosity. There exist several experimental methods to determine the fractal dimension, e.g., small-angle X-ray (SAXS) and small-angle neutron scattering measurements (SANS), adsorption techniques and mercury porosimetry. All these techniques search for a simple scaling power law of the type: Amount of surface property ∝ resolution of analysis D , where D is the fractal dimension of the surface for which the property is relevant. Amount of surface property can for instance be related to the intensity of scattered radiation, pore volume or monolayer capacity. The change in resolution is here achieved by changing the scattering angle, pore radius or the size of the adsorbate.
KeywordsFractal Dimension Small Angle Neutron Scattering Mercury Porosimetry Porous Solid Thermodynamic Method
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