Relaxation dynamics of multilayer networks modeled with Husimi cacti

Monodendrons and dendrimers have been shown to represent some of the most powerful synthetic building blocks that can be employed in the construction of supramolecular and macromolecular systems with well defined shapes and... [ view full abstract ]

Monodendrons and dendrimers have been shown to represent some of the most powerful synthetic building blocks that can be employed in the construction of supramolecular and macromolecular systems with well defined shapes and sizes. Among these systems, the cylindrical supramolecular dendrimers have well defined multilayer structure. Recently, multilayered assemblies that are constructed through the layer-by-layer (LbL) deposition of dendrimers have attracted much attention because of their facile preparation and versatility in terms of structure and functionality.

We focus on the relaxation dynamics of multilayer polymer structures having as underlying topology the Husimi cactus. The work provides theoretical support to the newly synthesized multilayer polymers. We study the relaxation dynamics of the multilayer network in the framework of Generalized Gaussian Structures model, using both Rouse and Zimm approaches. Such model, in the Rouse-type approach, allows to determine the full dynamical behavior of the polymer system through the diagonalization of its connectivity matrix. Remarkably, for the multilayer structure we develop an analytical method for the determining of the whole eigenvalues spectrum of its connectivity matrix. This fact allows us to study in detail the crossover from a pure Husimi cactus behavior to a predominantly linear chain behavior.

For networks with small number of layers the intermediate times/frequencies domain of the dynamical quantities shows a bulk-like behavior, a mixture between the Husimi cactus behavior and linear chain behavior. For the networks with large number of layers intermediate times/frequencies domain decomposes into two regions. The first, located at middle to lower times/frequencies shows a bulk-like behavior and, the second situated at lower times/frequencies displays a linear chain behavior.

In the Zimm-type approach, which includes the hydrodynamic interactions, the quantities that describe the mechanical relaxation dynamics do not show scaling, except the limiting case, namely, a very large number of layers and low size of the layer.

The theoretical findings are well supported by mechanical relaxation experiments, both with respect to scaling, as well as to the splitting of the intermediate domain.The mechanical experiments were performed on pillared-layered polymers, LbL assembly of dendrimers, supramolecular cylindrical dendrimers, and supramolecular cylindrical micelles.