Polymer adsorption on a fractal substrate: Numerical study

We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p(c) of attractive sites. The percolation cluster is characterized by a fractal dimension d(s)(pc) = 91/49. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method. We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of transition point, phi(pc)(s) = 0.425 +/- 0.009, and for adsorption transition temperature, T-A(pc) = 2.64 +/- 0.02. As expected, the adsorption is diminished when the fractal dimension of the substrate is smaller than that of a plain Euclidean surface. The universal size and shape characteristics of a typical spatial conformation which attains a polymer chain in the adsorbed state are analyzed as well. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3691102]