Adsorption isotherms on fractal substrata

By means of Monte Carlo simulations, diffusion-limited recombination reactions, followed by desorption and the desorption of single particles from fractal and multifractal substrata, are studied. From all these results, we conjecture that for both processes (a) the dissociative adsorption and associative desorption of diatomic molecules and (b) the nondissociative adsorption and desorption of single particles, the relationship between the particle coverage {Θ} and the applied pressure p at the steady state (i.e., the adsorption isotherm) may be written, in the limit {Θ}{→}0 as Θ1/2+1/2f(1-{Θ})^-1{∝}p1/2 for (a) and {Θ}(-ln{Θ})^1-1/f(1-{Θ})^-1{∝}p1/2 for (b), where f is the site-visitation random-walk exponent of the substratum. Classical isotherms are recovered for homogeneous surfaces with f=1.