Surface adsorption of a self-avoiding polymer chain on a family of finitely ramified fractals

Abstract

We study the surface adsorption of a flexible self-avoiding polymer chain on a family of Sierpinski gasket-type fractals using the real space renormalization group technique. The members of this family are characterized by an integer scale factor b which runs from 2 to infinity . The Hausdorff dimension of these fractals tends to 2 from below as b to infinity . We calculate the crossover exponent phi for the desorption transition exactly for b=2 to 6. For b to infinity , we use finite size scaling arguments to show that phi to 1/4 .