We focus on Vicsek fractals (VF), which are regular hyperbranched macromolecules. As such, they belong to the same family as the dendrimers, without suffering from the growth problems of the latter. We compute the mechanical and dielectric properties of VF in dilute solutions. The evaluation of the static and dynamical properties of VF in the framework of generalized Gaussian structures (GGS) reveals that they, distinct from the dendrimers, obey scaling. Theoretically speaking, VF are probably the most natural extension of GGS from linear chains to nontrivial loopless fractal objects. We encourage the synthesis and experimental characterization of the properties of this class of hyperbranched macromolecules.

We consider the dynamics of Vicsek fractals of arbitrary connectivity, models for hyperbranched polymers. Their basic dynamical properties depend on their eigenvalue spectra, which can be determined iteratively. This paves the way for theoretical studies to very high precision for regular, finite, arbitrarily large hyperbranched structures.

We numerically analyze the scaling behavior of experimentally accessible dynamical relaxation forms for networks modeled through finite Sierpinski-type lattices. Previous work has established unequivocally for such lattices that in the Rouse picture both the mechanical and the dielectric relaxation forms scale in frequency and in time. As we show here, in the Zimm model, based on the preaveraged Oseen tensor, the picture changes drastically; the introduction of the hydrodynamic interactions leads to relaxation patterns which do not scale. Our results show that the relaxation forms are very sensitive to the number of monomers in the network and to the strength of the hydrodynamic interaction parameter.

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The reaction of alkali-metal (Na, Cs) clusters with water clusters embedded in helium nanodroplets is studied using femtosecond photoionization as well as electron-impact ionization. Unlike Na clusters, Cs clusters are found to completely react with water in spite of the ultracold helium droplet environment. Mass spectra of the Csn+(H2O)m reaction products are interpreted in terms of stability with respect to fragmentation using high-level molecular structure calculations.