Dynamics of a semiflexible polymer or polymer ring in shear flow

Excluded volume effects on tangentially driven active ring polymers

The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.

Single-polymer dynamics of starch-like branched ring polymers in steady shear flow

The stretching dynamics and dynamical behaviors of individual branched ring polymer (BRP), a coarse-grained model for some types of the starch, in steady shear flow are studied by using a hybrid mesoscale simulation approach that combines multiparticle collision dynamics with standard molecular dynamics. By analyzing the stretched configuration of BRPs, we find the polymer size increases nonmonotonically with increasing branch length. Meanwhile, the decrease of the alignment angle of the stretched configuration of BRPs follows a universal power law during the first downward phase as the shear rate increases. Constructing the three-dimensional surface of the polymer's ring backbone and tracing the temporal fluctuations of the surface's normal vector along the simulation trajectory, the tumbling and tank-treading motion are clearly reflected by periodic and non-periodic changes of the normal vector. Interestingly, these temporal changes are much more regular than that of the gyration tensor. Thus, a novel cross-correlation function, which is the correlation between fluctuations of the normal vector along the flow direction and the velocity-gradient direction, is proposed to analyze the tumbling motion that usually coexists with the tank-treading motion. This function can naturally address the fails of traditional method that analyzing the tumbling motion by determining the correlation of temporal fluctuations of the gyration tensor G_αα. By analyzing the dynamical behaviors of BRPs, diverse dependences of the tumbling frequency ω_TB and tank-treading frequency ω_TT on the shear rate γ̇ are observed at a wide range of shear rates and polymer sizes. Furthermore, our simulations also reveal that the tank-treading motion is more stable than the tumbling motion for small-branch-size BRPs but the tumbling motion is more stable than the tank-treading motion for large-branch-size BRPs.

Dynamics of flexible filaments in oscillatory shear flows

The fluid-structure interactions between flexible fibers and viscous flows play an essential role in various biological phenomena, medical problems, and industrial processes. Of particular interest is the case of particles freely transported in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations, and theoretical modeling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler-Bernoulli rods whose hydrodynamics are described by local slender-body theory.

Self-Attractive Semiflexible Polymers under an External Force Field

The dynamical response of a tethered semiflexible polymer with self-attractive interactions and subjected to an external force field is numerically investigated by varying stiffness and self-interaction strength. The chain is confined in two spatial dimensions and placed in contact with a heat bath described by the Brownian multi-particle collision method. For strong self-attraction the equilibrium conformations range from compact structures to double-stranded chains, and to rods when increasing the stiffness. Under the external field at small rigidities, the initial close-packed chain is continuously unwound by the force before being completely elongated. For double-stranded conformations the transition from the folded state to the open one is sharp being steeper for larger stiffnesses. The discontinuity in the transition appears in the force-extension relation, as well as in the probability distribution function of the gyration radius. The relative deformation with respect to the equilibrium case along the direction normal to the force is found to decay as the inverse of the applied force.

Wall-anchored semiflexible polymer under large amplitude oscillatory shear flow

The properties of semiflexible polymers tethered by one end to an impenetrable wall and exposed to oscillatory shear flow are investigated by mesoscale simulations. A polymer, confined in two dimensions, is described by a linear bead-spring chain, and fluid interactions are incorporated by the Brownian multiparticle collision dynamics approach. At small strain, the polymers follow the applied flow field. However, at high strain, we find a strongly nonlinear response with major conformational changes. Polymers are stretched along the flow direction and exhibit U-shaped conformations while following the flow. As a consequence of confinement in the half-space, frequency doubling in the time-dependent polymer properties appears along the direction normal to the wall.

Crowded solutions of single-chain nanoparticles under shear flow

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows

The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.

The shape of pinned forced polymer loops

Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.

Individual circular polyelectrolytes under shear flow

Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics.

Morphological transitions of elastic filaments in shear flow

The morphological dynamics, instabilities, and transitions of elastic filaments in viscous flows underlie a wealth of biophysical processes from flagellar propulsion to intracellular streaming and are also key to deciphering the rheological behavior of many complex fluids and soft materials. Here, we combine experiments and computational modeling to elucidate the dynamical regimes and morphological transitions of elastic Brownian filaments in a simple shear flow. Actin filaments are used as an experimental model system and their conformations are investigated through fluorescence microscopy in microfluidic channels. Simulations matching the experimental conditions are also performed using inextensible Euler-Bernoulli beam theory and nonlocal slender-body hydrodynamics in the presence of thermal fluctuations and agree quantitatively with observations. We demonstrate that filament dynamics in this system are primarily governed by a dimensionless elasto-viscous number comparing viscous drag forces to elastic bending forces, with thermal fluctuations playing only a secondary role. While short and rigid filaments perform quasi-periodic tumbling motions, a buckling instability arises above a critical flow strength. A second transition to strongly deformed shapes occurs at a yet larger value of the elasto-viscous number and is characterized by the appearance of localized high-curvature bends that propagate along the filaments in apparent "snaking" motions. A theoretical model for the as yet unexplored onset of snaking accurately predicts the transition and explains the observed dynamics. We present a complete characterization of filament morphologies and transitions as a function of elasto-viscous number and scaled persistence length and demonstrate excellent agreement between theory, experiments, and simulations.

Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers

The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.

Topology-Sensitive Microfluidic Filter for Polymers of Varying Stiffness

The separation of polymers based on their size, rigidity, and topology is an essential but also highly challenging task for nanoscience and engineering. Using hybrid molecular dynamics simulations that correctly take into account hydrodynamics, we have designed microfluidic channels for separating linear from ring polymers in dilute solutions. We establish that the transport velocity of the polymers is independent of their topology and rigidity when the channel walls are smooth and repulsive. However, when the walls are decorated with attractive spots arranged on lines parallel to the flow, ring polymers exhibit an order of magnitude higher transport velocity compared to linear chains. The spots induce a homeotropic-like reorientation of ring polymers close to walls leading to a tank treading motion along them, whereas linear chains are immobilized upon adsorption. This mechanism becomes more enhanced with increasing polymer rigidity. The presented technique holds thus promise for reliably separating nanoparticles based on their topology.

Lateral migration of electrospun hydrogel nanofilaments in an oscillatory flow

The recent progress in bioengineering has created great interest in the dynamics and manipulation of long, deformable macromolecules interacting with fluid flow. We report experimental data on the cross-flow migration, bending, and buckling of extremely deformable hydrogel nanofilaments conveyed by an oscillatory flow into a microchannel. The changes in migration velocity and filament orientation are related to the flow velocity and the filament's initial position, deformation, and length. The observed migration dynamics of hydrogel filaments qualitatively confirms the validity of the previously developed worm-like bead-chain hydrodynamic model. The experimental data collected may help to verify the role of hydrodynamic interactions in molecular simulations of long molecular chains dynamics.

Efficient simulation of semiflexible polymers with stiff bonds

We investigate the simulation of stiff (extensible) and rigid (inextensible) semiflexible polymers in solution. In particular, we focus on polymers represented as chains of beads, interconnected by bonds with a low to zero extensibility, and significant persistence in the bond orientations along the chain, whose dynamical behavior is described by the Langevin equation. We review the derivation of the pseudopotential needed for rigid bonds. The efficiency of a number of routines for such simulations is determined. We propose a routine for handling rigid bonds which is, for longer chains, substantially more efficient than the existing ones. We also show that for extensible polymers, the Rouse modes can be exploited to achieve highly efficient simulations. At realistic values for the extensibility, e.g., that of double-stranded DNA, the simulations are orders of magnitude faster than those for rigid bonds. With increasing stiffness, however, the allowable time step and hence the efficiency decreases, until a crossover point is reached below which the routines with rigid bonds are more efficient; we present a numerical estimate of this crossover point.

Microstructure of Sheared Entangled Solutions of Semiflexible Polymers

We study the influence of finite shear deformations on the microstructure and rheology of solutions of entangled semiflexible polymers theoretically and by numerical simulations and experiments with filamentous actin. Based on the tube model of semiflexible polymers, we predict that large finite shear deformations strongly affect the average tube width and curvature, thereby exciting considerable restoring stresses. In contrast, the associated shear alignment is moderate, with little impact on the average tube parameters, and thus expected to be long-lived and detectable after cessation of shear. Similarly, topologically preserved hairpin configurations are predicted to leave a long-lived fingerprint in the shape of the distributions of tube widths and curvatures. Our numerical and experimental data support the theory.

Dynamics of a double-stranded DNA segment in a shear flow

We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi_{c}, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.

Efficient simulation of semiflexible polymers

Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modeled with one bead-spring element per base pair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymer's fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of 5% of several key observables, the model allows for single Langevin time steps of ≈1.6, 8, 16, and 16 ps for a dsDNA model chain consisting of 64, 128, 256, and 512 base pairs (i.e., chains of 0.55, 1.11, 2.24, and 4.48 persistence lengths), respectively. Correspondingly, in 1 h, a standard desktop computer can simulate 0.23, 0.56, 0.56, and 0.26 ms of these dsDNA chains, respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretized) wormlike chain (WLC) model. Importantly, we demonstrate that at the same level of discretization, i.e., when each discretization element is one base pair long, our algorithm gains about five to six orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one on one to a discretized version of the extensible WLC model, implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behavior of a dsDNA segment in a shear flow.

Effects of excluded volume and hydrodynamic interaction on the deformation, orientation and motion of ring polymers in shear flow

A ring polymer is a classical model to explore the behaviors of biomacromolecules. Compared with its linear counterpart in shear flow, the ring polymer should be more sensitive to excluded volume and hydrodynamic interaction attributed to the absence of chain ends. We carried out multiparticle collision dynamics combined with molecular dynamics simulation to study the effects of excluded volume and hydrodynamic interaction on the behaviors of ring polymers in shear flow. The results show that in the absence of the strong excluded volume interaction, the ring polymer prefers a two-strand linear conformation with high deformation and orientation in the flow-gradient plane, and the tank-treading motion is nearly negligible. Ring polymers without excluded volume show no significant difference from linear polymers in the scaling exponents for the deformation, orientation and tumbling motion. We also observed that the hydrodynamic interaction could efficiently slow down the relaxation of ring polymers while the scaling exponents against the Weissenberg number have rarely been affected.

Mechanochemistry of Topological Complex Polymer Systems

Although existing since the concept of macromolecules, polymer mechanochemistry is a burgeoning field which attracts great scientific interest in its ability to bias conventional reaction pathways and its potential to fabricate mechanoresponsive materials. We review here the effect of topology on the mechanical degradation of polymer chains and the activation of mechanophores in polymer backbones. The chapter focuses on both experimental and theoretical work carried out in the past 70 years. After a general introduction (Sect. 1), where the concept, the history, and the application of polymer mechanochemistry are briefly described, flow fields to study polymer mechanochemistry are discussed (Sect. 2), results of mechanochemistry study are presented for linear polymers (Sect. 3), cyclic polymers (Sect. 4), graft polymers (Sect. 5), star-shaped polymers (Sect. 6), hyperbranched polymers and dendrimers (Sect. 7), and systems with dynamic topology (Sect. 8). Here we focus on (1) experimental results involving the topological effect on the coil-to-stretch transition and the fracture of the polymer chains, (2) the underlying mechanisms and the key factor that determines the mechanical stability of the macromolecules, (3) theoretical models that relate to the experimental observations, and (4) rational design of mechanophores in complex topology to achieve multiple activations according to the existing results observed in chain degradation.