Fracton dynamics of percolating elastic networks: Energy spectrum and localized nature

Phonon transport properties of particulate physical gels

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, ξ s and ξ G: ξ s measures the length of heterogeneities in the network structure and ξ G is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, [Formula: see text] and ω G, which are associated with ξ s and ξ G, respectively: (i) phonon-like vibrations in the homogeneous medium at [Formula: see text], (ii) phonon-like vibrations in the heterogeneous medium at [Formula: see text], and (iii) disordered vibrations in the glassy clusters at ω > ω G. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at frequencies ω* and ω G (or at wavenumbers of [Formula: see text] and [Formula: see text]). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at [Formula: see text] and diffusive damping at [Formula: see text]. Remarkably, the Ioffe–Regel limit is located at the very low frequency of ω*. Thus, phonon transport is localized above ω*, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.

Local orientational mobility in regular hyperbranched polymers

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.