Dynamics of a polyelectrolyte in simple shear flow

The configurational dynamics of a polyelectrolyte (PE), subjected to a simple shear flow, is studied using Brownian dynamics (BD) and Dissipative Particle Dynamics (DPD) simulations of a bead-spring model with explicit counterions. We explore the effect of counterion condensation on the tumbling and extension of PEs by varying the shear rates for a range of values of the electrostatic coupling parameter A (which is defined as the ratio of the Bjerrum length to the size of the monomer). In all cases, the power spectrum of Rs(t) (which characterizes the projected length of the PE in the flow direction as a function of time) exhibits a power law decay at high frequencies, similar to that for a dumbbell in shear flow. For lower values of A (A ~ 2), the tumbling of the PE is periodic and is always associated with folding and stretching, which is in contrast to the oscillatory transition between the extended and globular states seen at higher values of A (A ~ 15). We observe that for A ~ 2 the tumbling frequency decreases and the average tumbling time increases with hydrodynamic interaction (HI). For A > 15, we observe a critical shear rate γ[combining dot]c below which there is considerable counterion condensation and the PE remains in the globular state with a structure akin to that of a neutral polymer in poor solvent. The γ[combining dot]c and the behavior of the PE above the critical shear rate are dependent on the HI. For a given shear rate, when there is considerable condensed counterion fluctuation, the PE extends as a whole and then collapses by the formation of folds with no observable periodicity in tumbling. When the condensed counterion fluctuations are suppressed, the polymer exhibits periodic tumbling. Simulation artifacts resulting from the implicit nature of the solvent and that due to boundary conditions are discussed by comparing the BD results with that obtained from the DPD simulations incorporating Ewald summation for electrostatics.