The fractal nature of molecule-surface chemical activities and physical interactions in porous materials

We report that fractal scaling laws relate the details of the complex reactive and non-reactive geometries of porous materials with a wide variety of chemical and physical molecule-surface interactions. These scaling laws relate the following property/scale pairs: physisorption monolayer value/particle size of the adsorbent; chemisorption capacity/particle size; catalytic activity of supported metal catalysts/dispersion or catalyst particle size; adsorbate surface reaction rate/particle size; monolayer value/physiorbed adsorbate size; monolayer of adsorbed polymer/the molecular weight of the polymer; the amount of derivatizing agent necessary for full surface grafting/size of the reverse-phasing reagent; In all these cases the property/scale relation has the form of a power-law in which the exponent is a simple function of the effective fractal dimension of the process. Well over one hundred case analyses show the generality and applicability of fractal scaling laws in heterogeneous chemistry.