Henry's law of adsorption on a fractal surface

The problem of adsorption at low coverage $N$ on a fractal surface is addressed. General, but approximate, arguments are presented to show how the fractal dimension $D$ is related to the Henry's-law coefficient of proportionality between $N$ and the pressure. A semiclassical analysis validates this relation at high temperature. An evaluation for a regular fractal surface demonstrates this behavior explicitly. Relation is made to a fractal Brunauer-Emmett-Teller theory of multilayer adsorption.