CONTINUOUSLY VARYING CROSSOVER EXPONENT FOR ADSORPTION OF LINEAR-POLYMERS ON FRACTALS

In this work we study the problem of physical (reversible) adsorption of a linear polymer in a good solvent in the case when the container of the polymer-solvent system is taken to be the Mandelbrot-Given (MG) model of a percolation cluster and the plane-filling (PF) fractal lattice. We accept the self-avoiding random walk as a model of the linear polymer, and, in addition, we assume that the adsorption energy pertaining to the bonds that lie in the layer next to the adsorbing boundary depends on their directions and is different from the adsorption energy for the bonds that belong to the boundary. Under these conditions we have found, in the case of both fractals (MG and PF), that the crossover exponent phi (associated with the number of adsorbed monomers) continuously varies with the parameter that measures the monomer-surface interaction along the bonds that are perpendicular to the adsorbing boundary. We discuss this result and its relevance to the understanding of the validity (violation) of the universality hypothesis in the case of critical phenomena on fractals.