Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

Abstract

Abstract:In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.

Quasi-Periodic and Fractal Polymers: Energy Structure and Carrier Transfer

“…In the present work, we take B-DNA as a prototype system, because, apart from its biological and nanoscientific importance, it has a rather long persistence length of around 50 nm or 150 base pairs 20 . However, there are several studies concerning charge and energy transfer in other aperiodic polymer systems [21][22][23] . We study the coherent regime, cf.…”

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].…”

“…Fractals, structures with self-repeating patterns at any length scale and a non-integer dimension, are pervasive in nature and emerge in a wide variety of research areas. In physics and chemistry, the fractals are used for describing the dynamics of different polymer networks [39], porous systems [40], stretchable electronics [41], energy storage [42], disordered systems [43], growth phenomena [44], chemical reactions controlled by diffusion [45], and energy transfer [28]. The recourse to the principles of fractal geometry has enabled revealing that most biological elements, either at cellular, tissue or organic level, have self-similar structures within a defined scaling domain which can be characterized by means of the fractal dimension.…”

“…The interdisciplinary character of the connectivity matrix is worth commenting on. Examples are provided from many research areas; in graph theory applied to biological systems [61], reaction–diffusion systems [62], in the study of fluorescence depolarization under dipolar quasiresonant energy transfer [28], in the analysis of dynamic processes occurring on networks or inferring many properties related to the networks themself [63,64], for determining the energy levels in Pariser–Parr–Pople (molecular orbital) quantum calculations [65], the dielectric relaxation functions [17], and the NMR relaxation functions [29,66]. Therefore, knowledge of the eigenvalue spectrum is of great importance and leads to interdisciplinary scientific advances.…”