Star polymers in shear flow

Deciphering the Scattering of Mechanically Driven Polymers Using Deep Learning

We present a deep learning approach for analyzing two-dimensional scattering data of semiflexible polymers under external forces. In our framework, scattering functions are compressed into a three-dimensional latent space using a Variational Autoencoder (VAE), and two converter networks establish a bidirectional mapping between the polymer parameters (bending modulus, stretching force, and steady shear) and the scattering functions. The training data are generated using off-lattice Monte Carlo simulations to avoid the orientational bias inherent in lattice models, ensuring robust sampling of polymer conformations. The feasibility of this bidirectional mapping is demonstrated by the organized distribution of polymer parameters in the latent space. By integrating the converter networks with the VAE, we obtain a generator that produces scattering functions from given polymer parameters and an inferrer that directly extracts polymer parameters from scattering data. While the generator can be utilized in a traditional least-squares fitting procedure, the inferrer produces comparable results in a single pass and operates 3 orders of magnitude faster. This approach offers a scalable automated tool for polymer scattering analysis and provides a promising foundation for extending the method to other scattering models, experimental validation, and the study of time-dependent scattering data.

Assembly of polysaccharide-based polymer brush for supramolecular hydrogel dressing

Extracted from Platycodon grandiflorum, platycodon grandiflorum polysaccharides (PGPs) with diverse biological functions have been extensively employed for modification and fabrication of hydrogels for biomedical applications, such as wound dressings. However, since the lack of effective structural design, the reported polysaccharide-based hydrogel dressings are still suffered from structural failures and limited bio-functionality. Herein, we demonstrate a facile and general strategy to fabricate a supramolecular hydrogel composed of PGP-based polymer brush as building blocks combined with a Ca2+-mediated self-assembly process. The specific polymer brush with high branch functionality was achieved with polyacrylamide arms evenly grown on the PGP (grafting efficiency as high as 80 %) with series of chemical modifications. With above structural merits, the resulting hydrogel with densely crosslinked polymer brush featured enhanced mechanical strength as well as self-healing, and shear-thinning behaviors. Further biocompatible investigation indicated the as-prepared hydrogels with admirable performances in self-adhesion (adhesive strength of 16.7-79.5 kPa), a pH-responsive swelling ratio as high as 44 at pH 5.4, and pH-responsive degradation. They also showed antioxidant capacity by scavenging DPPH activity of nearly 80 % in 20 min, hemocompatibility, cell viability and cell migration. Impressively, the PGP-based polymer brush hydrogel served as a wound dressing revealed significant acceleration on wound closure.

Supercoiled ring polymers under shear flow

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.

Effects of Linking Topology on the Shear Response of Connected Ring Polymers: Catenanes and Bonded Rings Flow Differently

We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BRs develop a novel motif, termed gradient tumbling, rotating around the gradient axis. For the PCs the rings are stretched and display another new pattern, termed slip tumbling. The dynamics of BRs is continuous and oscillatory, whereas that of PCs is intermittent between slip-tumbling attempts. Our findings demonstrate the interplay between topology and hydrodynamics in dilute solutions of connected polymers.

Glassy phases of the Gaussian core model

We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we analyse the transition from the low-density hard-sphere-like glassy dynamics to the high-density one. The dynamics at low densities is well described by the caging mechanism, giving rise to intermittent dynamics. At high densities, the particles undergo a more continuous motion in which the concept of cage loses its meaning. We elaborate on the idea that these different supercooled dynamics are in fact the precursors of two different glass states.

Rotational Dynamics of a Protein under Shear Flow Studied by the Eckart Frame Formalism

Proteins are natural polymers that play an essential role in both living organisms and biotechnological applications. During certain bioprocessing steps, they can be exposed to significant mechanical stress induced by, for example, shear flow or sonication, resulting in reduced therapeutic efficacy, aggregation, or even a loss of activity. For this reason, there is a need to understand and determine the susceptibility of the protein activity to the experienced mechanical stress. To acquire this knowledge, it is necessary to study the rotational dynamics of the protein. Commonly, the rotational dynamics of soft molecules is interpreted based on a theoretical analysis performed in an inertial laboratory frame. However, the obtained angular velocity mixes pure rotations and vibrations with angular momentum, consequently lacking a clear dynamical interpretation. On the other hand, the use of the noninertial internal Eckart frame allows the determination of pure angular velocity as it minimizes the coupling between the rotational and vibrational degrees of freedom. In the present work, by conducting open-boundary molecular dynamics simulations and exploiting the Eckart frame formalism, we study the rotational dynamics of a small protein under the shear flow of various strengths. Our results show that the angular velocity increases nonlinearly with increasing shear rate. Furthermore, the protein gains vibrational angular momentum at higher shear rates, which is reflected in the higher angular velocity computed by employing the Eckart frame formalism and confirmed by analysis of the contributions to the total kinetic energy of the biomolecule.

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.

Dynamical and Structural Properties of Comb Long-Chain Branched Polymer in Shear Flow

Using hybrid multi-particle collision dynamics (MPCD) and a molecular dynamics (MD) method, we investigate the effect of arms and shear flow on dynamical and structural properties of the comb long-chain branched (LCB) polymer with dense arms. Firstly, we analyze dynamical properties of the LCB polymer by tracking the temporal changes on the end-to-end distance of both backbones and arms as well as the orientations of the backbone in the flow-gradient plane. Simultaneously, the rotation and tumbling behaviors with stable frequencies are observed. In other words, the LCB polymer undergoes a process of periodic stretched–folded–stretched state transition and rotation, whose period is obtained by fitting temporal changes on the orientation to a periodic function. In addition, the impact induced by random and fast motions of arms and the backbone will descend as the shear rate increases. By analyzing the period of rotation behavior of LCB polymers, we find that arms have a function in keeping the LCB polymer’s motion stable. Meanwhile, we find that the rotation period of the LCB polymer is mainly determined by the conformational distribution and the non-shrinkable state of the structure along the velocity-gradient direction. Secondly, structural properties are numerically characterized by the average gyration tensor of the LCB polymer. The changes in gyration are in accordance with the LCB polymer rolling when varying the shear rate. By analyzing the alignment of the LCB polymer and comparing with its linear and star counterparts, we find that the LCB polymer with very long arms, like the corresponding linear chain, has a high speed to reach its configuration expansion limit in the flow direction. However, the comb polymer with shorter arms has stronger resistance on configuration expansion against the imposed flow field. Moreover, with increasing arm length, the comb polymer in shear flow follows change from linear-polymer-like to capsule-like behavior.

Electroosmotic Flow Induced Lift Forces on Polymer Chains in Nanochannels

A major objective of research in nanofluidics is to achieve better selectivity in manipulating the fluxes of nano-objects and in particular of biopolymers. Numerical simulations allow one to better understand the physical mechanisms at play in such situations. We performed hybrid mesoscale simulations to investigate the properties of polymers under flows in slit pores at the nanoscale. We use multiparticle collision dynamics, an algorithm that includes hydrodynamics and thermal fluctuations, to investigate the properties of fully flexible and stiff polymers under several types of flow, showing that Poiseuille flows and electroosmotic flows can lead to quantitatively and qualitatively different behaviors of the chain. In particular, a counterintuitive phenomenon occurs in the presence of an electroosmotic flow: When the monomers are attracted by the solid surfaces through van der Waals forces, shear-induced forces lead to a stronger repulsion of the polymers from these surfaces. Such focusing of the chain in the middle of the channel increases its flowing velocity, a phenomenon that may be exploited to separate different types of polymers.

Rheology of a Nanopolymer Synthesized through Directional Assembly of DNA Nanochambers, for Magnetic Applications

We present a numerical study of the effects of monomer shape and magnetic nature of colloids on the behavior of a single magnetic filament subjected to the simultaneous action of shear flow and a stationary external magnetic field perpendicular to the flow. We find that based on the magnetic nature of monomers, magnetic filaments exhibit a completely different phenomenology. Applying an external magnetic field strongly inhibits tumbling only for filaments with ferromagnetic monomers. Filament orientation with respect to the flow direction is in this case independent of monomer shape. In contrast, reorientational dynamics in filaments with superparamagnetic monomers are not inhibited by applied magnetic fields, but enhanced. We find that the filaments with spherical, superparamagnetic monomers, depending on the flow and external magnetic field strength, assume semipersistent, collapsed, coiled conformations, and their characteristic time of tumbling is a function of field strength. However, external magnetic fields do not affect the characteristic time of tumbling for filaments with cubic, superparamagnetic monomers, but increase how often tumbling occurs.

Polymer Translocation Time

The force- and flow-induced translocation processes of linear and ring polymers are studied using a combination of multiparticle collision dynamics and molecular dynamics, focusing on the behavior of the polymer translocation time. We compare the force- and flow-induced translocations of linear and ring polymers. It is found that when the translocation time (τ*) is characterized by scaling exponents, δ, δ', and α, via the relations τ* ∼ f^δN^α and τ* ∼ J^δ'N^α, the scaling exponents are not constants. For long chains tested, α = 1.0 for both force- and flow-induced translocations. The difference between the force- and flow-induced translocations stems from different monomer crowding effects due to distinct flow patterns outside the channel. Furthermore, general relations for polymer translocation time are derived for these two translocation processes, which are in good agreement with the simulation results. Our results provide clear molecular pictures for the force- and flow-induced translocations, which shed light on the understanding of translocation dynamics and provide guidance for practical applications such as molecular sequencing and ultrafiltration.

Small-Angle Neutron Scattering Study of the Structural Relaxation of Elongationally Oriented, Moderately Stretched Three-Arm Star Polymers

We present structural relaxation studies of a polystyrene star polymer after cessation of high-rate extensional flow. During the steady-state flow, the scattering pattern shows two sets of independent correlations peaks, reflecting the structure of a polymer confined in a fully oriented three-armed tube. Upon cessation of flow, the relaxation constitutes three distinct regimes. In a first regime, the perpendicular correlation peaks disappear, signifying disruption of the virtual tube. In a second regime, broad scattering arcs emerge, reflecting relaxation from highly aligned chains to more relaxed, still anisotropic form. New entanglements dominate the last relaxation regime where the scattering pattern evolves to a successively elliptical and circular pattern, reflecting relaxation via reptation.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

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.

Dynamical Properties of Concentrated Suspensions of Block Copolymer Stars in Shear Flow

Block copolymer stars (BCSs) have been demonstrated to constitute versatile, self-assembling building blocks with tunable softness, functionalization, and shape. We investigate the dynamical properties of suspensions of short-arm BCSs under linear shear flow by means of extensive particle-based multiscale simulations. We determine the properties of the system for representative values of monomer packing fraction ranging from semidilute to concentrate regimes. We systematically analyze the formed network structures as a function of both shear rate and packing fraction, the reorganization of solvophobic patches, and the corresponding radial correlation functions. Connecting our findings with rheology, we calculate the viscosity as a function of shear rate and discuss the implications of the found shear thinning behavior.

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations

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 that interact by local momentum-conserving stochastic MPCs. 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 polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t^-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L^-1/2. Good agreement is found between the analytical and simulation results.

Nanoparticle transport phenomena in confined flows

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Multi-particle collision dynamics for a coarse-grained model of soft colloids

The growing interest in the dynamical properties of colloidal suspensions, both in equilibrium and under an external drive such as shear or pressure flow, requires the development of accurate methods to correctly include hydrodynamic effects due to the suspension in a solvent. In the present work, we generalize Multiparticle Collision Dynamics (MPCD) to be able to deal with soft, polymeric colloids. Our methods build on the knowledge of the monomer density profile that can be obtained from monomer-resolved simulations without hydrodynamics or from theoretical arguments. We hereby propose two different approaches. The first one simply extends the MPCD method by including in the simulations effective monomers with a given density profile, thus neglecting monomer-monomer interactions. The second one considers the macromolecule as a single penetrable soft colloid (PSC), which is permeated by an inhomogeneous distribution of solvent particles. By defining an appropriate set of rules to control the collision events between the solvent and the soft colloid, both linear and angular momenta are exchanged. We apply these methods to the case of linear chains and star polymers for varying monomer lengths and arm number, respectively, and compare the results for the dynamical properties with those obtained within monomer-resolved simulations. We find that the effective monomer method works well for linear chains, while the PSC method provides very good results for stars. These methods pave the way to extend MPCD treatments to complex macromolecular objects such as microgels or dendrimers and to work with soft colloids at finite concentrations.

Determining Gyration Tensor of Orienting Macromolecules through Their Scattering Signature

A method is presented for quantitatively evaluating the shape and size of deformed particles in dispersion from their two-dimensional anisotropic spectra by small-angle scattering. By means of real spherical harmonic expansion, we derive analytical expressions of the gyration tensor R in terms of experimentally measured anisotropic scattering functions, yielding a tensorial extension of the Guinier law. We demonstrate the usefulness of this approach by a model study of an affinely deformed Gaussian chain. We further show that radius of gyration R_g is the source term of intraparticle structure factor at the mean-field limit, and from this perspective, we address the connection between R and conformation asphericity. The developed method not only facilitates quantitative scattering studies of deforming materials, but also provides insightful information regarding their deformation behavior at the molecular level based on the symmetric properties of real spherical harmonics.

Controlled self-aggregation of polymer-based nanoparticles employing shear flow and magnetic fields

Star polymers with magnetically functionalized end groups are presented as a novel polymeric system whose morphology, self-aggregation, and orientation can easily be tuned by exposing these macromolecules simultaneously to an external magnetic field and to shear forces. Our investigations are based on a specialized simulation technique which faithfully takes into account the hydrodynamic interactions of the surrounding, Newtonian solvent. We find that the combination of magnetic field (including both strength and direction) and shear rate controls the mean number of magnetic clusters, which in turn is largely responsible for the static and dynamic behavior. While some properties are similar to comparable non-magnetic star polymers, others exhibit novel phenomena; examples of the latter include the breakup and reorganization of the clusters beyond a critical shear rate, and a strong dependence of the efficiency with which shear rate is translated into whole-body rotations on the direction of the magnetic field.

Self-organization of gel networks formed by block copolymer stars

The equilibrium properties of block copolymer star networks (BCS) are studied via computer simulations. We employ both molecular dynamics and multiparticle collisional dynamics simulations to investigate the self-organization of BCS with f = 9 functionalized arms close to their overlap concentrations under conditions of different fractions of functionalization and varying attraction strength. We find three distinct macroscopic self-organized states depending on fraction of attractive end-monomers and the strength of the attraction. At weak attractions, ergodic, diffusive liquids result, with short-lived bonds between the stars. As the attraction strength grows, the whole system forms a percolating cluster, while at the same time the individual molecules are diffusive. Finally, arrested gels emerge when the attractions become strong. The conformation of the BCS in these solutions is found to be strongly affected by the concentration, with the stars assuming typically spherical, open configurations in seeking to maximize inter-star associations as opposed to the inter-star collapse that results at infinite dilution, giving rise to strongly aspherical shapes and reduced sizes.

Tethered Semiflexible Polymer under Large Amplitude Oscillatory Shear

The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. For small shear rates, the tethering of the ends leads to a more-or-less linear oscillatory response. However, at high shear rates, we found a strongly nonlinear reaction, with a polymer (partially) wrapped around the fixation points. This leads to an overall shrinkage of the polymer. Dynamically, the location probability of the polymer center-of-mass position is largest on a spatial curve resembling a limaçon, although with an inhomogeneous distribution. We found shear-induced modifications of the normal-mode correlation functions, with a frequency doubling at high shear rates. Interestingly, an even-odd asymmetry for the Cartesian components of the correlation functions appears, with rather similar spectra for odd x- and even y-modes and vice versa. Overall, our simulations yielded an intriguing nonlinear behavior of tethered semiflexible polymers under oscillatory shear flow.

Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow

The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer deformability. Brownian motion caused the droplet position to fluctuate with a distribution that primarily depended on the balance between inertial lift forces pushing the droplet outward and elastic forces from the polymers driving it inward. The droplet shape was controlled by the local shear rate, and so its average shape depended on the droplet distribution.

Kinetics of polymer tumbling in shear flow: A coarse-grained description

We study the classic problem of dynamical evolution of a polymer in a shear flow. Interestingly, the polymer goes through several distinctly identifiable conformations during its passage from coiled to stretched states back and forth. We identify these conformations assumed by the polymer while tumbling and study the kinetics of the process in terms of the residence and recurrence times of individual conformations. The distribution of residence times exhibits exponentially decaying tails which helps us build an effective Markovian picture of the truly non-Markovian problem. We present the explicit W matrix for the coarse-grained evolution via a master equation and study its elements as a function of the Weissenberg number. We show that the timescales of decay of the autocorrelation function for the full Langevin dynamics compare quite well with the approximate results from the master equation approach.

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.

Rotation Dynamics of Star Block Copolymers under Shear Flow

Star block-copolymers (SBCs) are macromolecules formed by a number of diblock copolymers anchored to a common central core, being the internal monomers solvophilic and the end monomers solvophobic. Recent studies have demonstrated that SBCs constitute self-assembling building blocks with specific softness, functionalization, shape and flexibility. Depending on different physical and chemical parameters, the SBCs can behave as flexible patchy particles. In this paper, we study the rotational dynamics of isolated SBCs using a hybrid mesoscale simulation technique. We compare three different approaches to analyze the dynamics: the laboratory frame, the non-inertial Eckart's frame and a geometrical approximation relating the conformation of the SBC to the velocity profile of the solvent. We find that the geometrical approach is adequate when dealing with very soft systems, while in the opposite extreme, the dynamics is best explained using the laboratory frame. On the other hand, the Eckart frame is found to be very general and to reproduced well both extreme cases. We also compare the rotational frequency and the kinetic energy with the definitions of the angular momentum and inertia tensor from recent publications.

Flow Behavior of Chain and Star Polymers and Their Mixtures

Star-shaped polymers show a continuous change of properties from flexible linear chains to soft colloids, as the number of arms is increased. To investigate the effect of macromolecular architecture on the flow properties, we employ computer simulations of single chain and star polymers as well as of their mixtures under Poiseuille flow. Hydrodynamic interactions are incorporated through the multi-particle collision dynamics (MPCD) technique, while a bead-spring model is used to describe the polymers. For the ultradilute systems at rest, the polymers are distributed uniformly in the slit channel, with a weak dependence on their number of arms. Once flow is applied, however, we find that the stars migrate much more strongly towards the channel center as the number of arms is increased. In the star-chain mixtures, we find a flow-induced separation between stars and chains, with the stars located in the channel center and the chains closer to the walls. In order to identify the origin of this flow-induced partitioning, we conduct additional simulations without hydrodynamic interactions, and find that the observed cross-stream migration originates from a combination of wall-induced hydrodynamic lift forces and viscoelastic effects. The results from our study give valuable insights for designing microfluidic devices for separating polymers based on their architecture.

Structural Studies of Three-Arm Star Block Copolymers Exposed to Extreme Stretch Suggests a Persistent Polymer Tube

We present structural small-angle neutron scattering studies of a three-armed polystyrene star polymer with short deuterated segments at the end of each arm. We show that the form factor of the three-armed star molecules in the relaxed state agrees with that of the random phase approximation of Gaussian chains. Upon exposure to large extensional flow conditions, the star polymers change conformation resulting in a highly stretched structure that mimics a fully extended three-armed tube model. All three arms are parallel to the flow, one arm being either in positive or negative stretching direction, while the two other arms are oriented parallel, right next to each other in the direction opposite to the first arm.

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.

Star Block-Copolymers in Shear Flow

Star block-copolymers (SBCs) have been demonstrated to constitute self-assembling building blocks with specific softness, functionalization, shape, and flexibility. In this work, we study the behavior of an isolated SBC under a shear flow by means of particle-based multiscale simulations. We systematically analyze the conformational properties of low-functionality stars, as well as the formation of attractive patches on their corona as a function of the shear rate. We cover a wide range of system parameters, including functionality, amphiphilicity, and solvent quality. It is shown that SBCs display a richer structural and dynamical behavior than athermal star polymers in a shear flow [ Ripoll Phys. Rev. Lett. , 2006 , 96 , 188302 ], and, therefore, they are also interesting candidates to tune the viscoelastic properties of complex fluids. We identify three factors of patch reorganization under shear that lead to patch numbers and orientations depending on the shear rate, namely, free arms joining existing patches, fusion of medium-sized patches into bigger ones, and fission of large patches into two smaller ones under high shear rates. Because the conformation of single SBC is expected to be preserved in low-density bulk phases, the presented results are a first step in understanding and predicting the rheological properties of semidilute suspensions of this kind of polymers.

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.

Guidance and Self-Sorting of Active Swimmers: 3D Periodic Arrays Increase Persistence Length of Human Sperm Selecting for the Fittest

Male infertility is a reproductive disease, and existing clinical solutions for this condition often involve long and cumbersome sperm sorting methods, including preprocessing and centrifugation-based steps. These methods also fall short when sorting for sperm free of reactive oxygen species, DNA damage, and epigenetic aberrations. Although several microfluidic platforms exist, they suffer from structural complexities, i.e., pumps or chemoattractants, setting insurmountable barriers to clinical adoption. Inspired by the natural filter-like capabilities of the female reproductive tract for sperm selection, a model-driven design, featuring pillar arrays that efficiently and noninvasively isolate highly motile and morphologically normal sperm, with lower epigenetic global methylation, from raw semen, is presented. The Simple Periodic ARray for Trapping And isolatioN (SPARTAN) created here modulates the directional persistence of sperm, increasing the spatial separation between progressive and nonprogressive motile sperm populations within an unprecedentedly short 10 min assay time. With over 99% motility of sorted sperm, a 5-fold improvement in morphology, 3-fold increase in nuclear maturity, and 2-4-fold enhancement in DNA integrity, SPARTAN offers to standardize sperm selection while eliminating operator-to-operator variations, centrifugation, and flow. SPARTAN can also be applied in other areas, including conservation ecology, breeding of farm animals, and design of flagellar microrobots for diagnostics.

Mesoscopic modelling and simulation of soft matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Clustering and dynamics of particles in dispersions with competing interactions: theory and simulation

Dispersions of particles with short-range attractive and long-range repulsive interactions exhibit rich equilibrium microstructures and a complex phase behavior. We present theoretical and simulation results for structural and, in particular, short-time diffusion properties of a colloidal model system with such interactions, both in the dispersed-fluid and equilibrium-cluster phase regions. The particle interactions are described by a generalized Lennard-Jones-Yukawa pair potential. For the theoretical-analytical description, we apply the hybrid Beenakker-Mazur pairwise additivity (BM-PA) scheme. The static structure factor input to this scheme is calculated self-consistently using the Zerah-Hansen integral equation theory approach. In the simulations, a hybrid simulation method is adopted, combing molecular dynamics simulations of colloids with the multiparticle collision dynamics approach for the fluid, which fully captures hydrodynamic interactions. The comparison of our theoretical and simulation results confirms the high accuracy of the BM-PA scheme for dispersed-fluid phase systems. For particle attraction strengths exceeding a critical value, our simulations yield an equilibrium cluster phase. Calculations of the mean lifetime of the appearing clusters and the comparison with the analytical prediction of the dissociation time of an isolated particle pair reveal quantitative differences pointing to the importance of many-particle hydrodynamic interactions for the cluster dynamics. The cluster lifetime in the equilibrium-cluster phase increases far stronger with increasing attraction strength than that in the dispersed-fluid phase. Moreover, significant changes in the cluster shapes are observed in the course of time. Hence, an equilibrium-cluster dispersion cannot be treated dynamically as a system of permanent rigid bodies.

Application of the Eckart frame to soft matter: rotation of star polymers under shear flow

The Eckart co-rotating frame is used to analyze the dynamics of star polymers under shear flow, either in melt or solution and with different types of bonds. This formalism is compared with the standard approach used in many previous studies on polymer dynamics, where an apparent angular velocity ω is obtained from the relation between the tensor of inertia and angular momentum. A common mistake is to interpret ω as the molecular rotation frequency, which is only valid for rigid-body rotation. The Eckart frame, originally formulated to analyze the infrared spectra of small molecules, dissects different kinds of displacements: vibrations without angular momentum, pure rotation, and vibrational angular momentum (leading to a Coriolis cross-term). The Eckart frame co-rotates with the molecule with an angular frequency Ω obtained from the Eckart condition for minimal coupling between rotation and vibration. The standard and Eckart approaches are compared with a straight description of the star's dynamics taken from the time autocorrelation of the monomer positions moving around the molecule's center of mass. This is an underdamped oscillatory signal, which can be described by a rotation frequency ω_R and a decorrelation rate Γ. We consistently find that Ω coincides with ω_R, which determines the characteristic tank-treading rotation of the star. By contrast, the apparent angular velocity ω < Ω does not discern between pure rotation and molecular vibrations. We believe that the Eckart frame will be useful to unveil the dynamics of semiflexible molecules where rotation and deformations are entangled, including tumbling, tank-treading motions and breathing modes.

Deciphering the dynamics of star molecules in shear flow

This work analyses the rotation of star polymers under shear flow, in melts, and in good solvent dilute solution. The latter is modeled by single molecule Brownian hydrodynamics, while melts are modeled using non-equilibrium molecular dynamics in closed (periodic) boxes and in open boundaries. A Dissipative Particle Dynamics (DPD) thermostat introduces pairwise monomer friction in melts at will, in directions normal and tangent to the monomer-monomer vectors. Although tangential friction is seldom modeled, we show that it is essential to control hydrodynamic effects in melts. We analyze the different sources of molecular angular momentum in solution and melts and distinguish three dynamic regimes as the shear rate [small gamma, Greek, dot above] is increased. These dynamic regimes are related with the disruption of the different relaxation mechanisms of the star in equilibrium. Although strong differences are found between harmonic springs and finitely extensible bonds, above a critical shear rate the star molecule has a "breathing" mode with successive elongations and contractions in the flow direction with frequency Ω. The force balance in the flow direction unveils a relation between Ω and the orientation angle. Using literature results for the tumbling of rings and linear chains, either in melt or in solution, we show that the relation is general. A different "tank-treading" dynamics determines the rotation of monomers around the center of mass of the molecule. We show that the tank-treading frequency does not saturate but keeps increasing with [small gamma, Greek, dot above]. This is at odds with previous studies which erroneously calculated the molecular angular frequency, used as a proxy for tank-treading.

Solvent Induced Inversion of Core-Shell Microgels

The morphology of core-shell microgels under different swelling conditions and as a function of the core-shell thickness ratio is systematically characterized by mesoscale hydrodynamic simulations. With increasing hydrophobic interaction of the shell polymers, we observe drastic morphological changes from a core-shell structure to an inverted microgel, where the core is turned to the outside, or a microgel with a patchy surface of core polymers directly exposed to the environment. We establish a phase diagram of the various morphologies. Moreover, we characterize the polymer and microgel conformations. For sufficiently thick shells, the changes of the shell size upon increasing hydrophobic interactions are well described by the Flory-Rehner theory. Additionally, this theory provides a critical line in the phase diagram separating core-shell structures from the distinct two other phases. The appearing new phases provide a novel route to nano- and microscale functionalized materials.