Fractals are of particular relevance in many fields of science. In physics and chemistry the concept of fractals is widely used for describing the disordered systems, growth phenomena, chemical reactions controlled by... [ view full abstract ]
Fractals are of particular relevance in many fields of science. In physics and chemistry the concept of fractals is widely used for describing the disordered systems, growth phenomena, chemical reactions controlled by diffusion, and relaxation dynamics of polymer networks.
Because of their shape and topology dendrimers are very interesting macromolecules both to pure science and everyday life. Most of the properties of dendrimers are related to the nature of their numerous terminal groups that may be varied at will to fulfil the desired properties. Dendrimers have potential applications in different fields, such as in biosensors, catalysis, nanomedicine for drug delivery and gene therapy.
The present work extends the theoretical studies on relaxation dynamics of polymers with complex architectures by considering a new multihierarchical polymer network which is built through the replication of the dual Sierpinski gasket in the form of a regular dendrimer.
The relaxation dynamics of the multihierarchical structure is investigated in the framework of generalized Gaussian structure model which represents the extensions of the Rouse and Zimm models, developed for linear polymer chains, to polymer systems with arbitrary topologies and which highlight both the connectivity of the molecules under investigation, as well as the influence of hydrodynamic interactions.
In the Rouse model, taking the advantage that the main relaxation patterns depend only on the eigenvalues, we have developed a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multihierarchical structure can be determined iteratively. Based on the eigenvalues obtained in the interative manner we are able to investigate the dynamics of the multihierarchical structure at very large generations, impossible to attain through numerical diagonalizations.
Remarkably, the general picture that emerges from both approaches, even though we have a mixed growth algorithm and the monomers interactions are taken into account specifically to the adopted approach, is that the multihierarchical structure preserves the individual relaxation behaviors of its constituent components. Our theoretical findings with respect to the splitting of the intermediate domain of the relaxation quantities are well supported by mechanical experiments performed on associative polymer networks, micelles networks, physical polymer gels, and supramolecular dendritic polymer network.
