Adsorption in models of ideal polymer chains on fractal spaces.

Abstract

We study critical adsorption in models of ideal polymer chains situated on fractal spaces in the vicinity of an impenetrable surface. The obtained exact results on fractal lattices, with a coordination number that can vary from site to site of the lattice, reveal a critical behavior that might be quite different from that established for lattices with the same coordination. Specifically, in the cases where localization of the chain takes place, i.e., when the mean end-to-end distance of the chain grows more slowly than any power of its length N, we found that various generating functions of interest usually display multiplicative singular corrections to the leading power law singularities (confluent logarithmic singularities, for example). We have demonstrated with specific examples that the average fraction of steps of the chain on adsorbing surface, at critical adsorption point, vanishes according to the asymptotic law \ensuremath{\sim}${\mathrm{ln}}_{1}^{\mathrm{\ensuremath{\psi}}}$N (where ${\mathrm{\ensuremath{\psi}}}_{1}$0 is a given constant) or \ensuremath{\sim}exp(-c ${\mathrm{ln}}_{2}^{\mathrm{\ensuremath{\psi}}}$N) (where c and ${\mathrm{\ensuremath{\psi}}}_{2}$ are certain positive constants). \textcopyright{} 1996 The American Physical Society.