A model calculation of multilayer adsorption on a fractal surface

We calculate the film coverage N on a model fractal substrate embedded in a two-dimensional space. We define a nominal thickness d as that which would be present on a flat surface exposed to the same vapor. The result of our analysis is N ∝ d^2-D over the range of film thickness corresponding to the fractal scaling behavior of the substrate; a plausible deviation is observed outside this range. The result is consistent with general arguments yielding N ∝ d^3-D in our three-dimensional world.