Dynamics of end-linked star-polymer structures

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 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.

Dynamics of generalized Gaussian polymeric structures in random layered flows

We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.

Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices

The family of Vicsek fractals is one of the most important and frequently studied regular fractal classes, and it is of considerable interest to understand the dynamical processes on this treelike fractal family. In this paper, we investigate discrete random walks on the Vicsek fractals, with the aim to obtain the exact solutions to the global mean-first-passage time (GMFPT), defined as the average of first-passage time (FPT) between two nodes over the whole family of fractals. Based on the known connections between FPTs, effective resistance, and the eigenvalues of graph Laplacian, we determine implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical results. The obtained closed-form solution shows that the GMFPT approximately grows as a power-law function with system size (number of all nodes), with the exponent lies between 1 and 2. We then provide both the upper bound and lower bound for GMFPT of general trees, and show that the leading behavior of the upper bound is the square of system size and the dominating scaling of the lower bound varies linearly with system size. We also show that the upper bound can be achieved in linear chains and the lower bound can be reached in star graphs. This study provides a comprehensive understanding of random walks on the Vicsek fractals and general treelike networks.

Spacers’ role in the dynamics of hyperbranched polymers

We investigate hyperbranched polymers (HBPs) and highlight the relation between their architecture and their viscoelastic behavior, while paying special attention to the role of the chainlike spacer segments between branching points. For this we study the dynamics of HBP in solution, based on the generalized Gaussian structure formalism, an extension of the Rouse model, which disregards hydrodynamical and excluded volume effects. For HBP the dynamical effects display, beside the obvious contributions of localized modes on the spacers, also remarkable features, as we highlight based on the exact renormalization procedure recently developed by us in J. Chem. Phys. 123, 034907 (2005). We exemplify these features by analyzing the dynamics of randomly linked star polymers and study the impact both of the length and of the spacers' mobility on the normal modes' spectra. We compute these modes both by numerical diagonalization and also by employing our renormalization procedure; the excellent agreement between these methods allows us to extend the range of investigations to very large HBP.