4.7 Article

Trapping in dendrimers and regular hyperbranched polymers

Journal

JOURNAL OF CHEMICAL PHYSICS
Volume 137, Issue 4, Pages -

Publisher

AMER INST PHYSICS
DOI: 10.1063/1.4737635

Keywords

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Funding

  1. National Natural Science Foundation of China (NNSFC) [61074119]
  2. Hong Kong Research Grants Council under the General Research Funds [CityU 1114/11E]

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Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees and Vicsek fractals, respectively. In this paper, we study the trapping problem in Cayley trees and Vicsek fractals with different underlying geometries, focusing on a particular case with a perfect trap located at the central node. For both networks, we derive the exact analytic formulas in terms of the network size for the average trapping time (ATT)-the average of node-to-trap mean first-passage time over the whole networks. The obtained closed-form solutions show that for both Cayley trees and Vicsek fractals, the ATT display quite different scalings with various system sizes, which implies that the underlying structure plays a key role on the efficiency of trapping in polymer networks. Moreover, the dissimilar scalings of ATT may allow to differentiate readily between dendrimers and hyperbranched polymers. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4737635]

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