Dynamics of generalized Gaussian polymeric structures in random layered flows

Abstract

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.

Dynamics of Branched Polymers in Random Layered Flows with Intramolecular Hydrodynamic Coupling: Star and Dendrimer

“…Similar result was observed for the linear chain in refs . and also branched polymer for the Rouse (without HI) case …”

“…The main goal of this work is to elucidate the impact of the hydrodynamic interactions on the dynamics of dilute solution of flexible branched polymer with arbitrary topology in random layered flow. This work is an extension of our previous work where the same system was investigated without considering the intramolecular hydrodynamic effects . So now introducing these hydrodynamic interactions reveals the distance dependent aspect into the dynamics that strongly influence the dynamics of macromolecules in dilute solution.…”

“…So in the present study we will try to address answers to these two questions. Moreover, to better understand the HI induced transition in the dynamics, we have presented and compared our results with and without HI …”

“…This work is an extension of our previous work where the same system was investigated without considering the intramolecular hydrodynamic effects. [40] So now introducing these hydrodynamic interactions reveals the distance dependent aspect into the dynamics that strongly influence the dynamics of macromolecules in dilute solution. We work in the framework of the bead-spring model taking into account the hydrodynamic interactions based on the preaveraged Oseen tensor.…”

Dynamics of Dual Scale-Free Polymer Networks

“…In this model, the average displacement depends only on the eigenvalues λ n of the connectivity matrix A, but not on its eigenvectors. In the case of more complex force configurations, such as used for layered flows [38], the eigenvectors are indispensable. From Eq.…”