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

Abstract

The authors develop a theoretical formalism to incorporate the effect of intramolecular hydrodynamic interactions (HIs) on the dynamics of flexible branched polymer in the presence of random layered flows. The influence of HIs on the anomalous diffusive behavior of branched polymers is illustrated through the preaveraged Oseen tensor approach. Although the formalism is valid for polymer structures with arbitrary topology, particular attention is paid here to the study of stars and dendrimers. The macromolecular property that is evaluated is the average square displacement (ASD) of drift center of the polymer. Qualitatively, 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 time dependence of the ASD in the presence of HIs within the preaveraging approximation reveals the anomalous long‐time dynamics which is governed by scaling behavior, t2 − α/2. The introduction of HIs in random flows speeds up the dynamics resulting in the shorter crossover time (from subdiffusive to superdiffusive regime) with enhanced magnitude of ASD compared to the free‐draining limit.

Theory for the Dynamics of Polymer Grafted Nanoparticle in Solution

“…These works for the dynamics and conformation of arbitrary branched flexible homopolymeric structures are multidimensional extensions of the perennial Rouse model, viz. influence of external fields, − semiflexible polymers, − hydrodynamic coupling between segments, ,,, and intrachain excluded volume interactions. − The GGS approach accounts for the geometries like stars, dendrimers, − and different fractal polymer networks − where all constitutive beads and harmonic springs are equal. External forces such as electric fields are used to understand the dielectric response; − the oscillating shear force is used for the shear modulus; ,− ,, and random forces , through elastic turbulence may have uncorrelated as well as long-range correlated behavior and dynamic light scattering for the time-dependent correlation function and intrinsic viscosity .…”

“…The theoretical approach for such a class of problems hinges on the diagonalization of the connectivity matrix of GGS with and without hydrodynamic interactions. 48,49 The single scale GGS approach for the polymer dynamics is not applicable for heteropolymers, block copolymer, miktoarm star, and polymer grafted nanoparticles. Thus, the theoretical formalism of multiscale GGS for the polymer dynamics is required to understand problems related to heteropolymers and polymer grafted nanoparticles (see Figure 1).…”