Relaxation dynamics of Sierpinski hexagon fractal polymer

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, relaxation dynamics of polymer networks, and energy transfer.
We extends the theoretical works on relaxation dynamics of polymers with complex architectures by considering a new class of fractal structures, namely the Sierpinski hexagon gaskets. Our work is motivated both, by the outstanding results of G.R. Newkome et al. who succeeded to synthesize the first nondendritic fractal polymer based on Sierpinski hexagonal gaskets and also by the search of scaling in the intermediate time/frequency region of the quantities which describe the relaxation dynamics.
We perform our calculations in the framework of the generalized Gaussian structures (GGS) 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. The main advantage of GGS model is that, in the Rouse-type approach the quantities which describe the relaxation dynamics can be calculated only by making use of the eigenvalues of the connectivity matrix of the structure.
In the Rouse-type approach, based on real-space renormalization transformations, we develop an analytical method for determining of the complete eigenvalue spectrum of the connectivity matrix. Thus, the investigation of the relaxation dynamics of huge fractal structures (N=6^10 monomers) can be easily performed. The general picture that emerges in the Rouse type-approach is that Sierpinski hexagon fractal polymers do obey scaling and the sole fractal parameter of importance for their relaxation dynamics is the spectral dimension.
The introduction of hydrodynamic interactions, on the other hand, completely changes the picture. Our use of the Zimm formalism, based on the preaveraged Oseen tensor, does not lead anymore to scaling forms in the intermediate domain of the relaxation quantities.
Our theoretical findings with respect to scaling in the Rouse model are well supported by experimental results obtained for physical polymer gels, F-actin solutions, hexagonal liquid crystals, and hexagonal micelles.