We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration pc of attractive sites. The percolation cluster is characterized by a fractal dimension

$d_s^{p_c}=91/49$
dspc=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,
$\phi _s^{p_c}=0.425\pm 0.009$
φspc=0.425±0.009⁠, and for adsorption transition temperature,
$T_A^{p_c}=2.64\pm 0.02$
TApc=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.

Topics
Magnetic materials, Phase transitions, Thermodynamic properties, Gyration radius, Differential geometry, Geometrical optics, Adsorption, Macromolecules, Regression analysis, Statistical thermodynamics
© 2012 American Institute of Physics.
2012
American Institute of Physics
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