ADSORPTION IN MODELS OF IDEAL POLYMER-CHAINS ON FRACTAL SPACES

We study critical adsorption in models of ideal polymer chains situate d on fractal spaces in the vicinity of an impenetrable surface. The ob tained exact results on fractal lattices, with a coordination number t hat can vary from site to site of the lattice, reveal a critical behav ior that might be quite different from that established for lattices w ith the same coordination. Specifically, in the cases where localizati on of the chain takes place, i.e., when the mean end-to-end distance o f the chain grows more slowly than any power of its length N, we found that various generating functions of interest usually display multipl icative singular corrections to the leading power law singularities (c onfluent logarithmic singularities, for example). We have demonstrated with specific examples that the average fraction of steps of the chai n on adsorbing surface, at critical adsorption point, vanishes accordi ng to the asymptotic law similar to 1n N-psi 1 (where psi(1) < 0 is a given constant) or similar to exp(- c 1n N-psi 2) (where c and psi(2) are certain positive constants).