Dynamics of Dual Scale-Free Polymer Networks

Abstract

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.

Shape analysis of random polymer networks

“…For example, the polymer networks with a power law distribution of functionalities of junction points (corresponding to the so-called scale-free networks) have been constructed and analyzed recently in Refs. [39,40].…”

“…Starting from the set of polymer units with given distribution of chemical functionalities, the formation of polymer network with known properties results. For example, the polymer networks with a power law distribution of functionalities of junction points (corresponding to the so-called scale-free networks) have been constructed and analyzed recently in references [40,41].…”

Dynamics of a Polymer Network Modeled by a Fractal Cactus

“…The problem of relating the dynamical features of macromolecules with their structure has a long standing history, starting from the landmark works of Rouse [1] and Zimm [2] who focused on the investigation of dilute solutions of linear polymers. With the continuous advancement in polymer synthesis and analysis, the attention turned to macromolecules with more and more complex architectures like star polymers [3,4,5], dendrimers [5,6,7,8,9,10,11,12,13], hyperbranched polymers [5,14,15,16,17,18,19,20,21,22], and polymer networks [23,24,25,26,27,28,29,30]. Nowadays, available experimental techniques in supramolecular chemistry allow for synthesizing a large variety of polymers with precisely controlled molecular structures such as the spherical and cylindrical supramolecular dendrimers [31], the gel-like supramolecular networks [32], and the honeycomb lattices [33], culminating with molecular fractals [34,35,36,37,38].…”