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Polymers (Basel). 2017 Nov 4;9(11). pii: E577. doi: 10.3390/polym9110577.

Dynamics of Dual Scale-Free Polymer Networks.

Author information

1
Departamento de Fisica, Universidade Federal do Amazonas, Manaus 69077-000, Brazil. mircea@ufam.edu.br.
2
Departamento de Fisica, Universidade Federal do Amazonas, Manaus 69077-000, Brazil. luantota74@gmail.com.
3
Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany. muelken@physik.uni-freiburg.de.
4
Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany. dolgushev@physik.uni-freiburg.de.

Abstract

We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding a link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameters' set ( γ , p ) , we encounter for these dynamical properties regions of constant in-between slope.

KEYWORDS:

eigenvalue problem; mechanical relaxation; polymer networks; scale-free networks

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