SURFACE-ADSORPTION OF A SELF-AVOIDING POLYMER-CHAIN ON A FAMILY OF FINITELY RAMIFIED FRACTALS

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 --> infinity. We calculate the crossover exponent phi for the desorption transition exactly for b = 2 to 6. For b --> infinity, we use finite size scaling arguments to show that phi --> 1/4.