Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

Abstract

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b≥2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b=2,3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.