The Geometry Factor in Photoprocesses on Irregular (Fractal) Surfaces. 1. Static Considerations

Surface geometry effects on photoprocesses of adsorbates are discussed, with special emphasis on problems which originate from surface irregularities of silica. It is shown that the common practice of idealizing irregular surfaces as flat ones leads to inaccuracies in the evaluations of a variety of adsorption parameters, such as effective surface area, the area occupied by one molecule, intermolecular distances, etc. Data from a number of recent reports in surface photochemistry is reanalyzed to demonstrate the possible errors and to show that the interpretation of results may be altered if the calculations are carried out without the flat surface assumption. These literature examples are the photodimerization of cyanophenanthrene, the chemiluminescent oxidation of fatty acids, the benzophenone triplet quenching, and the excimerization process in pyrenyl-derivatized silica. Calculation procedures for the above mentioned parameters on irregular surfaces are suggested based both on classical surface-science considerations and on recent fractal considerations. Computational simulations demonstrate the effect of surface irregularities on these parameters. The replacement of the flat picture with the real irregular one reveals a number of new interesting concepts: the effective surface area for reaction (the reaction area) is smaller than the effective surface area available to the reactants; the effective surface area toward an excited state adsorbed molecule is different than the ground-state case; the distance between a large and small molecule depends on which molecule diffuses toward the other; in bimolecular reactions, not all of the smaller molecules are available at any time to the larger ones. Surface heterogeneity and environmental relaxation around an excited state are discussed in terms of geometry.