Molecular fractal surfaces

In this letter we report that, at the molecular-size range, the surfaces of most materials are fractals, that is, at this range, surface geometric irregularities and defects are characteristically self-similar upon variations of resolution. The whole range of fractal dimension1, 2D<3, is found in the many examples presented. Two representative examples, namely adsorption of polystyrene on alumina and adsorption of krypton on dolomite are discussed in some detail. Our findings suggest a simple solution to the problem of quantifying the degree of surface irregularity2,3 at a resolution which is of relevance to many aspects of surface science. The results provide a general explanation for phenomenological links between various surface parameters, and we derive a set of equations of use in predicting surface variables.