A basic challenge in polymer physics is to understand how the underlying geometries of polymeric materials affect their dynamic behavior. Polymers, being intricate systems, demonstrate a wide range of dynamic features that... [ view full abstract ]
A basic challenge in polymer physics is to understand how the underlying geometries of polymeric materials affect their dynamic behavior. Polymers, being intricate systems, demonstrate a wide range of dynamic features that cannot be fully understood without elucidating the connections between the topology of the structure and its reflection in the dynamics.
The present work enhances the scientific understanding of the relaxation dynamics of polymer networks by considering a new multihierarchical network which links in a regular way the Vicsek fractal with the regular dendrimer. Similar structures have been experimentally synthesized through the crosslinking of regular dendrimers.
The relaxation dynamics of our multihierarchical structure is investigated in the framework of the generalized Gaussian structure model employing both, Rouse and Zimm approaches. In the Rouse type-approach we develop an analytical method for the determining of the whole eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained in the iterative manner we are able to investigate the dynamics of the multihierarchical structure at very large generations, impossible to attain through numerical diagonalizations. In the Rouse type-approach, where the interactions are considered only between nearest neighbors monomers, the general picture that emerges is that the multihierarchical structure preserves the individual behaviors of its constituents. The intermediate time/frequency domain of the dynamical quantities divides into two regions, each region showing the typical behavior of a component of the multihierarchical structure.
Remarkably, the multihierarchical structure still holds the original individual relaxation behaviors of its components even with the hydrodynamic interactions taken into account. Although the Vicsek fractal was replicated in shape of a dendrimer and in the Zimm type-approach one allows to each monomer to interact with any other, not only with nearest neighbors, the intermediate domain of
the dynamical quantities still splits into two independent regions, each highlighting the individual dynamics of a constituent component of the multihierarchical structure.
We address the multihierarchical structure as possible theoretical models for the relaxation dynamics of different polymer systems such as physical polymer gels, associative polymer networks, supramolecular dendritic polymer networks, micelles networks, and dendronized polymers.
