Relaxation of polymers modeled by generalized Husimi cacti

We focus on the generalized Husimi cacti, which are dual structures to the dendrimers but, distinct from the latter, contain loops. We determine their complete spectra by making use of the normal mode analysis. These spectra have been used in computing some physical quantities, such as the averaged monomer displacement and the mechanical relaxation moduli with its two components: the storage and the loss modulus. We also study the dynamics of Husimi cacti in solutions, introducing the hydrodynamic interactions in a preaveraged Oseen fashion, the so-called Zimm model. We observe that the relaxation quantities mentioned above do not scale, in the presence or in the absence of the hydrodynamic interactions. Our results show that all the relaxation forms depend on the number of monomers in the networks in the absence of the hydrodynamic interactions (Rouse model), while by taking into account the hydrodynamic interactions the results do not vary too much.