Viktoria Blavatska, Wolfhard Janke
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^{p_c}=91/49. The conformational properties of
polymer chains grafted to such a fractal substrate are studied by means of the
pruned-enriched Rosenbluth method (PERM). We find estimates for the surface
crossover exponent governing the scaling of the adsorption energy in the
vicinity of the transition point, \phi_s^{p_c}=0.425\pm0.009, and for the
adsorption transition temperature, T_A^{p_c}=2.64\pm0.02. 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.
View original:
http://arxiv.org/abs/1202.3086
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