2012
DOI: 10.1063/1.3691102
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Polymer adsorption on a fractal substrate: Numerical study

Abstract: 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. We find estimates for the surface crossover exponent governing the scaling of the adsorption … Show more

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Cited by 11 publications
(9 citation statements)
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“…To clarify the conception of these two shape descriptors in our results, the value of κ 2 for a doublet and a triplet with particles sat on the corners of an equilateral triangle is 1.0 and 0.25, respectively, and the value of b / R g 2 is 1.0 and 0.29. For a planar conformation, this parameter approaches 0.25. According to Figure , one can see the same plateaus in the shape descriptors of the formed aggregates as what were observed in the plots of their size and gyration radius, depicted in Figure .…”
Section: Resultsmentioning
confidence: 97%
“…To clarify the conception of these two shape descriptors in our results, the value of κ 2 for a doublet and a triplet with particles sat on the corners of an equilateral triangle is 1.0 and 0.25, respectively, and the value of b / R g 2 is 1.0 and 0.29. For a planar conformation, this parameter approaches 0.25. According to Figure , one can see the same plateaus in the shape descriptors of the formed aggregates as what were observed in the plots of their size and gyration radius, depicted in Figure .…”
Section: Resultsmentioning
confidence: 97%
“…For planar symmetric objects, the relative shape anisotropy converges to the value of 1/4. [36][37][38][39][40] The last descriptor, the asphericity parameter b, measures the deviation from the spherical symmetry (recall that λ 1 is the largest eigenvalue):…”
Section: B Observablesmentioning
confidence: 99%
“…Combining the mean-field theory and MC, Chakraborty and co-workers , found that a transition from a weak to a strong adsorption regime may occur when statistical patterns of heteropolymers and the heterogeneous substrate are related in a specific way. Besides, surfaces found in nature might not have necessarily random or pattern distributions of chemical species but instead be fractal. , Several works studied the influence of nontrivial surface geometries on polymer adsorption employing lattice-based models. For instance, Blavatska and Janke investigated the adsorption transition of an end-grafted flexible polymer on a percolation cluster formed by a substrate with the fraction of the attractive sites at the percolation threshold. The authors revealed that the critical quantities characterizing the adsorption transition, that is, the crossover exponent and the critical adsorption temperature, for the fractal surface differ from the ones of the attractive homogeneous surface.…”
Section: Introductionmentioning
confidence: 99%