Tumbling and Deformation of Isolated Polymer Chains in Shearing Flow

Abstract

Using Brownian dynamics simulations of polymer chains over a wide range of resolution, we find universal scaling laws for polymer coil dimensions and tumbling time. At high shear rates γ, the coil thickness in the gradient direction becomes independent of chain length, scaling as N K 0 γ̇− 1/4 , where N K denotes the numbers of Kuhn steps, and the tumbling time scales as N K γ̇− 3/4 , correcting scaling laws presented in prior studies. We find this to be a consequence of the formation of loops whose length is limited by the time required to stretch them and derive scaling laws from a balance of convection and diffusion of monomers. We find that, in the absence of hydrodynamic interaction (HI) and excluded volume (EV), for wormlike chains, the shrinkage in chain stretch observed at ultrahigh shear rates is pushed out to arbitrarily high shear rates if the chain is resolved increasingly finely below the persistence length. Finally, scaling laws in the presence of excluded volume and hydrodynamic interactions are derived that are expected to be valid for long chains at high shear rates. ■ INTRODUCTIONThe dynamics of isolated flexible and semiflexible polymer chains in shear flow has attracted considerable attention and is thought to be well understood as a result of single-molecule imaging of DNA molecules 1−3 and Brownian dynamics simulations. 4,5 These studies have shown that the average molecular extension of a polymer chain in the flow direction (x) increases with shear rate (γ) and reaches a plateau at high shear rates. The failure to reach full extension at high shear rates is a consequence of repeated end-over-end tumbling of the polymer molecule, due to the equal strength of the extensional and rotational components in a shear flow. The plateau of polymer extension at high shear rate was assumed to be the asymptotic response at high shear rates, until some recent simulations, 6,9,12 performed over a wide range of shear rates, revealed a highly nonmonotonic response in chain stretch. Quite surprisingly, without excluded volume (EV) and hydrodynamic interactions (HI), the average chain stretch was shown to reach a maximum and then decrease at the highest shear rates. (This effect almost vanished in the presence of EV but became more pronounced again when both HI and EV were included. 6 ) We show in what follows that this nonmonotonic behavior disappears in the absence of EV and HI when a bending potential is included in the chain model to represent more accurately the behavior of a semiflexible wormlike chain, such as double-stranded DNA or other biopolymers.In addition, coarse-grained simulations 7,8 have indicated that the tumbling time decreases with shear rate as γ̇2 /3 at high shear rates, which was further confirmed by a theoretical analysis. 11 For a DNA chain, the measured tumbling time approximately followed this power law for shear flows with Wi > 10, 7,8 where Wi is the Weissenberg number, which is the product of shear rate γ̇and the relaxation time of the polymer chain. It seems doubtful, however, ...

Influence of shear on globule formation in dilute solutions of flexible polymers

“…63 It also indicates that decrease in polymer size observed in this article is not related to ultra-high shear rate (Wi > N 2 K ) compaction of the polymer chain studied by Sendner and Netz, 67 and later elucidated by Dalal et al 66 Further evidence pointing to attachment of colloids in stretched polymers leading to globule formation by the mechanism described above is that the MFPT is inversely proportional to colloid concentration as shown in the supplementary material. 63 The breakup of globules in shear flow has received much attention recently due to its importance in biology and in determining properties of gels.…”

Multiscale dynamics of semiflexible polymers from a universal coarse-graining procedure

“…Such simulations become computationally expensive for chains much longer than a persistence length, as long length and time scales require correspondingly larger numbers of beads and time steps. While other studies have combined different fine and coarse-grained models to expand the accessible range [15], we present here a single consistent model that can systematically and efficiently reconcile all time scales associated with the dynamics of long chains.…”

“…We note that for the chain length used here, limiting the discretization to < 0.1 as would be required if employing the bead-rod model would require increasing the number of time steps by a factor of about 10 4 to reach the terminal relaxation time. While other studies have targeted a wide range of time scales by joining together different models to represent fine and coarse-grained behavior [15,26], our model presents an alternative unified approach that can be used to span over the full range of scales while assuring the correct statistics and dynamics at long lengths.…”

Conformational and Dynamical Evolution of Block Copolymers in Shear Flow

“…[48] Further supported by fluorescence microscopy, semiflexible polymers exhibit U-turn like motion and there is a scaling law for the critical end-to-end orientation angle ϕ C against the shear rate: ϕ C~. [47,49] Such scaling law for ensemble averaged parameters has been gradually recognized, [50] whereas it is still elusive for local motions and the onset of motions for semiflexible polymer chains.…”