The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity, and the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer/site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HI) are taken into account by the Rotne-Prager-Yamakawa tensor, or by an implementation of the active polymer in the multiparticle collision dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HI via polymer relaxation times. With increasing activity, HI lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in presence of HI or free-draining polymers. The polymer mean square displacement is enhanced by HI. Over a wide range of time scales, hydrodynamics leads to a subdiffusive regime of the site mean square displacement for flexible active polymers, with an exponent of (5/7), larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.
The configurations taken by polymers embedded in out-of-equilibrium baths may have broad effects in a variety of biological systems. As such, they have attracted considerable interest, particularly in simulation studies. Here we analyze the distribution of configurations taken by a passive flexible chain in a bath of hard, self-propelled, vibrated disks and systematically compare it to that of the same flexible chain in a bath of hard, thermal-like, vibrated disks. We demonstrate experimentally that the mean length and mean radius of gyration of both chains obey Flory's Law. However, the Kuhn …
In this topical review, we give an overview of the structure and dynamics of a single polymer chain in active baths, Gaussian or non-Gaussian. The review begins with the discussion of single flexible or semiflexible linear polymer chains subjected to two noises, thermal and active. The active noise has either Gaussian or non-Gaussian distribution but has a memory, accounting for the persistent motion of the active bath particles. This finite persistence makes the reconfiguration dynamics of the chain slow as compared to the purely thermal case and the chain swells. The active noise also result…
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin equation for all the monomers subject to white noise. However, stochastic motion for only a tagged monomer is observed to occur in the presence of colored noise. The qualitative change in the observations arises from the boundary shift decided by the observer. The Langevin dynamics analyses interpret the colored noise as the emergence of the polymeric elasti…
The equilibrium structure and dynamics of a single polymer chain in a thermal solvent is by now well-understood in terms of scaling laws. Here we consider a polymer in a bacterial bath, i.e. in a solvent consisting of active particles which bring in nonequilibrium fluctuations. Using computer simulations of a self-avoiding polymer chain in two dimensions which is exposed to a dilute bath of active particles, we show that the Flory-scaling exponent is unaffected by the bath activity provided the chain is very long. Conversely, for shorter chains, there is a nontrivial coupling between the bacte…
Hydrodynamic forces may significantly affect the motion of polymers. In sheet-like cavities, such as the cell's cytoplasm and microfluidic channels, the hydrodynamic forces are long-range. It is therefore expected that that hydrodynamic interactions will dominate the motion of polymers in sheets and will be manifested by Zimm-like scaling. Quite the opposite, we note here that although the hydrodynamic forces are long-range their overall effect on the motion of polymers vanishes due to the symmetry of the two-dimensional flow. As a result, the predicted scaling of experimental observables such…
We investigate configuration dynamics of a flexible polymer chain in a bath of active particles with dynamic chirality, i.e., particles rotate with a deterministic angular velocity $ω$ besides self-propulsion,by Langevin dynamics simulations in two dimensional space. Particular attentions are paid to how the gyration radius $R_{g}$ changes with the propulsion velocity $v_{0}$,angular velocity $ω$ and chain length. We find that in a chiral bath with a typical nonzero $ω$, the chain first collapses into a small compact cluster and swells again with increasing $v_{0}$, in quite contrast to the ca…
We investigate numerically the dynamical behaviour of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions both accelerate polymer collapse and alter the folding pathway.
We study the propulsion of a one-dimensional (1D) polymer chain under sinusoidal external forces in the overdamped (low Reynolds number) regime. We show that, when hydrodynamical interactions are included, the polymer presents directional motion which depends on the phase differences of the external force applied along the chain. Moreover, the velocity shows a maximum as a function of the frequency. We discuss the relevance of all these results in light of recent nanotechnology experiments.
The viscoelastic effect on the hydrodynamic relaxation in semidilute polymer solutions is investigated. From the linearized two-fluid model equations, we predict that the dynamical asymmetry coupling between the velocity fluctuations and the viscoelastic stress influences on the hydrodynamic relaxation process, resulting in a wave-number-dependent shear viscosity.
Aalto University School of Science and Technology（阿尔托大学理工学院）；The University of Western Ontario（韦仕敦大学）；University of Waterloo（滑铁卢大学）；Brown University（布朗大学）
The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete linear chain composed of active Brownian particles is considered, analytically, a continuous linear semiflexible polymer with active velocities changing diffusively. The force-free nature of active monomers is accounted for - no Stokeslet fluid flow induced by active forces - and higher order hydrodynamic multipole moments are neglected. The nonequilibrium chara…
For various polymers with different topological structures we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We call polymers with nontrivial topology topological polymers. We evaluate the two quantities both for ideal and real chain models and show that the ratios of the quantities among different topological types do not depend on the existence of excluded volume if the topological polymers have only up to trivalent vertices, as far as the polymers investigated. We also evaluate the ratio of the gyration radius to the hy…
The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of f…
We analyze the conformational dynamics and statistical properties of an active polymer model. The polymer is described as a freely-jointed bead-rod chain subject to stochastic active force dipoles that act on the suspending solvent where they drive long-ranged fluid flows. Using Langevin simulations of isolated chains in unconfined domains, we show how the coupling of active flows with polymer conformations leads to emergent dynamics. Systems with contractile dipoles behave similarly to passive Brownian chains with enhanced fluctuations due to dipolar flows. In systems with extensile dipoles, …
We investigate the driven polymer translocation through a nanometer-scale pore in the presence and absence of hydrodynamics both in good and bad solvent. We present our results on tension propagating along the polymer segment on the cis-side that is measured for the first time using our method that works also in the presence of hydrodynamics. For simulations we use stochastic rotation dynamics, also called multi-particle collision dynamics. We find that in the good solvent the tension propagates very similarly whether hydrodynamics is included or not. Only the tensed segment is by a constant f…
The characterization of the interactions between two fully flexible self-avoiding polymers is one of the classic and most important problems in polymer physics. In this paper we measure these interactions in the presence of active fluctuations. We introduce activity into the problem using two of the most popular models in this field. One where activity is effectively embedded into the monomers' dynamics, and the other where passive polymers fluctuate in an explicit bath of active particles. We establish the conditions under which the interaction between active polymers can be mapped into the c…
Hydrodynamic interactions as modeled by Multi-Particle Collision Dynamics can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways not known for any other polymer architecture or topology. We show that steady shear leads to an inflation scenario exclusive to ring polymers, which depends not only on Weissenberg number but also on contour length of the ring. By analyzing velocity fields of the solvent around the polymer, we show the existence of a hydrodynamic pocket which allows the polymer to self-stabilize at a certain alignment angle to the flow axis. This self…
We study the elastic properties of a rigid filament in a bath of self-propelled particles. We find that while fully flexible filaments swell monotonically upon increasing the strength of the propelling force, rigid filaments soften for moderate activities, collapse into metastable hairpins for intermediate strengths, and eventually re-expand when the strength of the activity of the surrounding fluid is large. This collapse and re-expansion of the filament with the bath activity is reminiscent of the behavior observed in polyelectrolytes in the presence of different concentrations of multivalen…
Extensional rheometry and Brownian Dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil--stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration $c^\ast$ before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer soluti…
We consider a simple model for steady-state luminescence of single polymer chains in a dilute solution in the case when excitation quenching is due to energy transfer between a donor and an acceptor attached to the ends of the chain. We present numerical results for Rouse chains without or with hydrodynamic interactions, which are taken into account in a perturbative manner. We consider the situations of a quiescent solvent as well as the chain in a shear flow and discuss the dependence of the steady-state luminescence intensity on the strength of hydrodynamic interaction and on the shear rate…
We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core--shell structures (with the short polymers forming the shel…
The hydrodynamic lift force that polymers experience near boundaries is known to be a crucial element when considering rheological flows of dilute polymer solutions. Here we develop theory to describe the hydrodynamic lift force on extended polymers flowing near flat surfaces. The lift force is shown to display a non-monotonic character increasing linearly with the distance to the wall $Z$ in the near-surface regime defined as $Z<L$, with $L$ being the contour length of the polymer. At heights $Z \sim L$ the lift force displays a maximum, and for $Z>L$ we recover the well known far-field resul…
The hydrodynamic forces between Brownian spheres are determined from a measurement of the correlated thermal fluctuations in particle position using a new method, two-particle cross-correlation spectroscopy (TCS). A pair of 1.3 um diameter polymer-coated poly(methyl methacrylate) were held at separations of between 2 um and 20 um using optical traps. The mobility tensor is determined directly from the statistically-averaged Brownian fluctuations of the two spheres. The observed distance dependence of the mobility tensor is in quantitative agreement with low-Reynolds number calculations.
We analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. Our analyses reveal that equilibrium polymer dynamics in dilute solution, under a typical DPD simulation conditions, obey the Zimm model very well. With a further reduction in the Schmidt number, a deviation…
We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, …
We study single-chain motion in semidilute solutions of polymers of length N = 1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.
The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer solutions, is discussed. In particular, recent advances in the treatment of hydrodynamic interaction are reviewed, and the successive refinements which have ultimately led to the prediction of universal viscometric functions in theta solvents are highlighted.
We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comp…
This article presents a comprehensive review of the Hydrodynamic Scaling Model for the dynamics of polymers in dilute and nondilute solutions. The Hydrodynamic Scaling Model differs from some other treatments of non-dilute polymer solutions in that it takes polymer dynamics up to high concentrations to be dominated by solvent-mediated hydrodynamic interactions, with chain crossing constraints presumed to create at most secondary corrections. Many other models take the contrary stand, namely that chain crossing constraints dominate the dynamics of nondilute polymer solutions, while hydrodynamic…
The theory of the dynamics of polymers in solution is developed coming from the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ) model. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the previous RZ models based on the Einstein theory of BM. The MSD of the polymer coil is at short times proportional to t^2 (instead of t). At long times it contains additional (to the Einstein term) contributions, the leading of which is ~ t^{1/2}. The relaxation of the internal normal modes of the polymer differs from the tra…
We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one end of the polymer using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two r…
Nonequilibrium molecular dynamics simulations are used to investigate the influence of hydrodynamic interactions on vertical segregation (stratification) in drying mixtures of long and short polymer chains. In agreement with previous computer simulations and theoretical modeling, the short polymers stratify on top of the long polymers at the top of the drying film when hydrodynamic interactions between polymers are neglected. However, no stratification occurs at the same drying conditions when hydrodynamic interactions are incorporated through an explicit solvent model. Our analysis demonstrat…
The present research is dedicated to provide deeper understanding of the impact of complex architecture of branched polymers on their behaviour in solvents. The folding dynamics of macromolecules and hydrodynamics of polymer fluids are strongly dependent on size and shape measures of single macromolecules, which in turn are determined by their topology. For this aim, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing $f^c$ linear branches and $f^r$ closed loops graf…
The screening of hydrodynamic interactions (HI) essentially affects macroscopic properties of polymeric solutions. This screening depends not only on the polymer concentration but has a dynamic nature. In the present work, a bead-spring theory is developed, in which this phenomenon is described for solutions of nonentangled polymer coils. The equation of motion for the beads of a test polymer is solved together with the Brinkman's equation for the solvent velocity that takes into account the presence of other coils in solution. The time correlation functions for the polymer normal modes are fo…
We introduce a mesoscale method for simulating hydrodynamic transport and self assembly of inhomogeneous polymer melts in pressure driven and drag induced flows. This method extends dynamic self consistent field theory (DSCFT) into the hydrodynamic regime where bulk material transport and viscoelastic effects play a significant role. The method combines four distinct components as a single coupled system, including (1) non-equilibrium self consistent field theory describing block copolymer self-assembly, (2) multi-fluid Navier-Stokes type hydrodynamics for tracking material transport, (3) cons…
Understanding confined flows of complex fluids requires simultaneous access to the mechanical behaviour of the liquid and the boundary condition at the interfaces. Here, we use evanescent wave microscopy to investigate near-surface flows of semi-dilute, unentangled polyacrylamide solutions. By using both neutral and anionic polymers, we show that monomer charge plays a key role in confined polymer dynamics. For solutions in contact with glass, the neutral polymers display chain-sized adsorbed layers, while a shear-rate-dependent apparent slip length is observed for anionic polymer solutions. T…
The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polym…
We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two dimensional system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that larger activities of SPPs yield a higher effective temperature of the bath and thus facilita…
The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers, which interact by local momentum-conserving stochastic MPC collisions. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various p…
How hydrodynamic interactions alter polymer stretching in turbulence
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度孟买理工学院-蒙纳士大学联合研究院）；Indian Institute of Technology Bombay（印度孟买理工学院）；Monash University（蒙纳士大学）；Université Côte d’Azur（蔚蓝海岸大学）
We discuss the hydrodynamic radius $R_H$ of polymer chains in good solvent, and show that the leading order correction to the asymptotic law $R_H \propto N^ν$ ($N$ degree of polymerization, $ν\approx 0.59$) is an ``analytic'' term of order $N^{-(1 - ν)}$, which is directly related to the discretization of the chain into a finite number of beads. This result is further corroborated by exact calculations for Gaussian chains, and extensive numerical simulations of different models of good--solvent chains, where we find a value of $1.591 \pm 0.007$ for the asymptotic universal ratio $R_G / R_H$, $…
We present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. A molecular dynamics algorithm for the polymer is coupled to a direct simulation Monte Carlo algorithm for the solvent. We give an explicit expression for the velocity autocorrelation function of the centre of mass of the polymer which agrees well with numerical results if Brownian dynamics, hydrodynamic correlations and sound wave scattering are included.
We follow the dynamics of an ensemble of interacting self-propelled semi-flexible polymers in contact with a thermal bath. We characterize structure and dynamics of the passive system and as a function of the motor activity. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained by using a tracer particle as a thermometer. The effective temperature takes a higher value than the temperature of the bath when the effect of the motors is not correlated with the structural rearrangements they induce. Our d…
Within Kirkwood theory, we study the translational diffusion coefficient of a single polymer chain in dilute solution, and focus on the small difference between the short--time Kirkwood value $D^{(K)}$ and the asymptotic long--time value $D$. We calculate this correction term by highly accurate large--scale Brownian Dynamics simulations, and show that it is in perfect agreement with the rigorous variational result $D < D^{(K)}$, and with Fixman's Green--Kubo formula, which is re--derived. This resolves the puzzle posed by earlier numerical results (Rey {\em et al.}, Macromolecules 24, 4666 (19…
The hydrodynamic radius of a polymer chain, obtained using Brownian dynamics simulations of the continuum Edwards model, is found to obey a crossover in the excluded volume parameter z, which is significantly different from that observed for the radius of gyration. It is shown that this difference arises from contributions due to dynamic correlations to the diffusivity, which are ignored in the commonly used definition of hydrodynamic radius based on the Kirkwood expression. The swelling of the hydrodynamic radius from the theta-state, obtained from simulations, shows remarkable agreement with…
The analysis of the dynamics of tracer particles in a complex bath can provide valuable information about the microscopic behaviour of the bath. In this work, we study the dynamics of a forced tracer in a colloidal bath by means of Langevin dynamics simulations and a theory model within continuum mechanics. In the simulations, the bath is comprised by quasi-hard spheres with a volume fraction of 50% immersed in a featureless quiescent solvent, and the tracer is pulled with a constant small force (within the linear regime). The theoretical analysis is based on the Navier Stokes equation, where …
