Dynamics of generalized Gaussian polymeric structures in random layered flows

Static Structure Factor and Viscoelastic Properties of Dendrimer Grafted Nanoparticles in Solution

The theory for the dynamics of multiscale branched polymeric structures is applied to understand the dendrimer-grafted nanoparticles in a dilute solution. The multiscale nature of dendrimer-grafted nanoparticles arises due to larger beads for the nanoparticles and the smaller beads for the polymeric structure connected through the harmonic springs. The multiscale generalized Gaussian structure approach allows us to study several viscoelastic properties: (i) storage and loss moduli and (ii) intrinsic viscosity. The influence of nanoparticles in the dendrimer structure is reflected in low and intermediate frequency regimes of the viscoelastic relaxation moduli. The increase in the size and the number fraction of nanoparticle shows an anomalous enhancement in the relaxation moduli. The increase in number fraction of nanoparticle in dendrimer-grafted nanoparticles decreases the transition frequency between solid- and liquid-like viscoelastic region. The intrinsic viscosity of dendrimer-grafted nanoparticles increases with increasing the size of nanoparticle. The inclusion of hydrodynamic interactions facilitates the dynamics of dendrimer-grafted nanoparticles. The Kratky plot of the static structure factor of all conformation of dendrimer-grafted nanoparticles is also analyzed as a function of number fraction and the size of the nanoparticles. At low wavenumbers, all conformations of dendrimer-grafted nanoparticles show a universal behavior. The compactness of dendrimer-grafted nanoparticles increases with the increase in number fraction and the size of the nanoparticles.

Dynamics of Dual Scale-Free Polymer Networks

We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding a link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameters' set ( γ , p ) , we encounter for these dynamical properties regions of constant in-between slope.

Dynamics of comb-of-comb-network polymers in random layered flows

We analyze the dynamics of comb-of-comb-network polymers in the presence of external random flows. The dynamics of such structures is evaluated through relevant physical quantities, viz., average square displacement (ASD) and the velocity autocorrelation function (VACF). We focus on comparing the dynamics of the comb-of-comb network with the linear polymer. The present work displays an anomalous diffusive behavior of this flexible network in the random layered flows. The effect of the polymer topology on the dynamics is analyzed by varying the number of generations and branch lengths in these networks. In addition, we investigate the influence of external flow on the dynamics by varying flow parameters, like the flow exponent α and flow strength W_{α}. Our analysis highlights two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The anomalous long-time dynamics is governed by the temporal exponent ν of ASD, viz., ν=2-α/2. Compared to a linear polymer, the comb-of-comb network shows a shorter crossover time (from the subdiffusive to superdiffusive regime) but a reduced magnitude of ASD. Our theory displays an anomalous VACF in the random layered flows that scales as t^{-α/2}. We show that the network with greater total mass moves faster.

Extended Vicsek fractals: Laplacian spectra and their applications

Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the large-scale properties, such as the gyration radius of the polymeric structures, or the global mean-first passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.