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. The slip lengths measured at all concentrations collapse onto a master curve when scaled using a simple two-layer depletion model with non-Newtonian viscosity. A transition from an apparent slip boundary condition to a chain-sized adsorption layer is moreover highlighted by screening the charge with additional salt in the anionic polymer solutions. We anticipate that our study will be a starting point for more complex studies relating the polymer dynamics at interfaces to their chemical and physical composition.
We numerically and theoretically investigate how the softness of particles affects the rheology of sheared dilute granular gases. We find that the kinetic theory predicts the deviation of the flow curve from the Bagnold scaling, and it works well below a certain shear rate when we compare with the simulation results. It is also found that there is no theoretical solution above this shear rate, which is because the energy loss due to inelastic collisions cannot be balanced with the energy injection by the shear.
Of all complex fluids, it is probably the rheology of polymers we understand best. In-depth insight into the entanglement and reptation of individual polymers allows us to predict for instance the shear-thinning rheology and the behaviour in virtually any flow situation of practical importance. The situation is markedly different when we move from passive to active polymers where the coupling of filament activity, hydrodynamic interactions, and conformations open the way to a plethora of novel structural and dynamical features. Here we experimentally study the rheology of long, slender and ent…
Rheology and Programmable Gelation of DNA Origami Polymer Tadpoles
School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院）；School of Chemical, Materials and Biological Engineering, University of Sheffield（谢菲尔德大学化学、材料与生物工程学院）；MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh（爱丁堡大学生物遗传研究所人类遗传学单元）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM 2 ), Hiroshima University（广岛大学可拓手性超物质可持续发展国际研究所）
Vesicles under shear flow exhibit various dynamics: tank-treading ($tt$), tumbling ($tb$) and vacillating-breathing ($vb$). A consistent higher order theory reveals a direct bifurcation from $tt$ to $tb$ if $C_a\equiv τ\dotγ$ is small enough ($τ$= vesicle relaxation time towards equilibrium shape, $\dotγ$=shear rate). At larger $C_a$ the $tb$ is preceded by the $vb$ mode. For $C_a\gg 1$ we recover the leading order original calculation, where the $vb$ mode coexists with $tb$. The consistent calculation reveals several quantitative discrepancies with recent works, and points to new features. We…
We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 micron. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.
Semiflexible polymers form central structures in biological material. Modeling approaches usually neglect influences of polymer-specific molecular features aiming to describe semiflexible polymers universally. Here, we investigate the influence of molecular details on networks assembled from filamentous actin, intermediate filaments, and synthetic DNA nanotubes. In contrast to prevalent theoretical assumptions, we find that bulk properties are affected by various inter-filament interactions. We present evidence that these interactions can be merged into a single parameter in the frame of the g…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and non-equilibrium molecular dynamics simulations we have systematically investigated the structure, dynamics and rheology of perfectly controlled ring/linear polymer blends with chains of such length and flexibility that the number of entanglements is up to about 14 per chain, which is comparable to experimental systems examined in the literature. The smallest conc…
We develop the rheology of a dilute granular gas mixture. Motivated by the interaction of charged granular particles, we assume that the grains interact via a square shoulder and well potential. Employing kinetic theory, we compute the temperature and the shear viscosity as functions of the shear rate. Numerical simulations confirm our results above the critical shear rate. At a shear rate below a critical value, clustering of the particles occurs.
Single polymer dynamics offers a powerful approach to study molecular-level interactions and dynamic microstructure in materials. Direct visualization of single chain dynamics has uncovered new ideas regarding the rheology and non-equilibrium dynamics of macromolecules, including the importance of molecular individualism, dynamic heterogeneity, and molecular sub-populations that govern macroscale behavior. In recent years, the field of single polymer dynamics has been extended to increasingly complex materials, including architecturally complex polymers such as combs, bottlebrushes, and ring p…
We study the rheology of semi-dilute solutions of the sodium salt of calf-thymus DNA in the linear and nonlinear regimes. The frequency response data can be fitted very well to the hybrid model with two dominant relaxation times $τ_{\circ}$ and $τ_{1}$. The ratio $\frac{τ_{\circ}}{τ_{1}} \sim$ 5 is seen to be fairly constant on changing the temperature from 20$^{\circ}$C to 30$^{\circ}$C. The shear rate dependence of viscosity can be fitted to the Carreau model.
Surface Quasi-Elastic Light Scattering (SQELS) is an application of dynamic light scattering to measure the dynamics of the thermal roughness of liquid surfaces. An analysis of the spectrum of thermal fluctuations provides information on surface properties like tension and elasticity. In this work we will focus particularly on its use to study polymer or polymer-like Langmuir monolayers. We review work in this area and give an up-to-date overview of the method. Important advances have very recently taken place in the theoretical understanding of this problem, and this has allowed improvements …
We propose a single chain slip-spring model, which is based on the slip-spring model by Likhtman [A. E. Likhtman, Macromolecules, 38, 6128 (2005)], for fast rheology simulations of entangled polymers on a GPU. We modify the original slip-spring model slightly for efficient calculations on a GPU. Our model is designed to satisfy the detailed balance condition, which enables us to analyze its static or linear response properties easily. We theoretically analyze several statistical properties of the model, such as the linear response, which will be useful to analyze simulation data. We show that …
The classical rheological theories of entangled polymeric liquids are built upon two pillars: Gaussian statistics of entanglement strands and the assumption that the stress arises exclusively from the change of intramolecular configuration entropy. We show that these two hypotheses are not supported by molecular dynamics simulations of polymer melts. Specifically, the segment distribution functions at the entanglement length scale and below deviate considerably from the theoretical predictions, in both the equilibrium and deformed states. Further conformational analysis reveals that the intrac…
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…
The behavior of a supercooled polymer melt composed of short chains with ten beads near an oscillating plate are simulated by using a hybrid simulation of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, the macroscopic dynamics are solved by using CFD, but, instead of using any constitutive equations, a local stress is calculated by using a non-equilibrium MD simulation associated at each lattice node in the CFD calculation. It is seen that the local rheology of the melt varies considerably in a thin viscous diffusion layer that arises near an oscillating plate. …
We present rheology experiments on dilute solutions of vesicles and red blood cells (RBC). Varying the viscosity ratio $λ$ between internal and external fluids, the microscopic dynamics of suspended objects can be qualitatively changed from tank-treading ($tt$) to tumbling ($tb$). We find that in the tt regime the viscosity $η$, decreases when $λ$ increases, in contrast with droplet emulsions and elastic capsule theories which are sometimes invoked to model RBC dynamics. At a critical $λ$ (close to the tt-tb transition) $η$ exhibits a minimum before it increases in the tb regime. This is consi…
Rheology of a dilute cohesive granular gas is theoretically and numerically studied. The flow curve between the shear viscosity and the shear rate is derived from the inelastic Boltzmann equation for particles having square-well potentials in a simple shear flow. It is found that (i) the stable uniformly sheared state only exists above a critical shear rate and (ii) the viscosity in the uniformly sheared flow is almost identical to that for uniformly sheared flow of hard core granular particles. Below the critical shear rate, clusters grow with time, in which the viscosity can be approximated …
The swelling of the viscosity radius, $α_η$, and the universal viscosity ratio, $U_{ηR}$, have been determined experimentally for linear DNA molecules in dilute solutions with excess salt, and numerically by Brownian dynamics simulations, as a function of the solvent quality. In the latter instance, asymptotic parameter free predictions have been obtained by extrapolating simulation data for finite chains to the long chain limit. Experiments and simulations show a universal crossover for $α_η$ and $U_{ηR}$ from $θ$ to good solvents in line with earlier observations on synthetic polymer-solvent…
We study the structure and dynamics of a transient network composed of droplets of microemulsion connected by telechelic polymers. The polymer induces a bridging attraction between droplets without changing their shape. A viscoelastic behaviour is induced in the initially liquid solution, characterised in the linear regime by a stretched exponential stress relaxation. We analyse this relaxation in the light of classical theories of transient networks. The role of the elastic reorganisations in the deformed network is emphasized. In the non linear regime, a fast relaxation dynamics is followed …
As a stiff polymer tumbles in shear flow, it experiences compressive viscous forces that can cause it to buckle and undergo a sequence of morphological transitions with increasing flow strength. We use numerical simulations to uncover the effects of these transitions on the steady shear rheology of a dilute suspension of stiff polymers. Our results agree with classic scalings for Brownian rods in relatively weak flows but depart from them above the buckling threshold. Signatures of elastoviscous buckling include enhanced shear thinning and an increase in the magnitude of normal stress differen…
We investigated the viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples ranged from fluids to gels. Already in the liquid phase the viscoelastic properties significantly changed when approaching the gelation boundary, indicating the formation of clusters and transient networks. This is supported by an increasing correlation length of the density fluctuations, observed by static light scattering and microscopy. A…
We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts…
Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient $μ$ scales with the squ…
The hydrodynamics and rheology of a sheared dilute gas-solid suspension, consisting of inelastic hard-spheres suspended in a gas, are analysed using anisotropic Maxwellian as the single particle distribution function. The closed-form solutions for granular temperature and three invariants of the second-moment tensor are obtained as functions of the Stokes number ($St$), the mean density ($ν$) and the restitution coefficient ($e$). Multiple states of high and low temperatures are found when the Stokes number is small, thus recovering the "ignited" and "quenched" states, respectively, of Tsao \&…
We show that simulations of polymer rheology at a fluctuating mesoscopic scale and at the macroscopic scale where flow instabilities occur can be achieved at the same time with dissipative particle dynamics (DPD) technique.} We model the visco-elasticity of polymer liquids by introducing a finite fraction of dumbbells in the standard DPD fluid. The stretching and tumbling statistics of these dumbbells is in agreement with what is known for isolated polymers in shear flows. At the same time, the model exhibits behaviour reminiscent of drag reduction in the turbulent state: as the polymer fracti…
Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…
The breakdown of dynamical scaling for a dilute polymer solution in 2D has been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)]. However, we show here both numerically and analytically that dynamical scaling holds when the finite-size dependence of the relevant dynamical quantities is properly taken into account. We carry out large-scale simulations in 2D for a polymer chain in a good solvent with full hydrodynamic interactions to verify dynamical scaling. This is achieved by novel mesoscopic simulation techniques.
Rheo-optical measurements on Polyemethyl methacrylate (PMMA) and 4-Butoxycarbonylmethylurethane (4-BCMU) show that these synthetic random coil polymer chains compress in Couette flow at semi-dilute concentrations. All previous models of polymer flow behaviour have assumed that the chains extend. A new model of polymers in flow in semi-dilute solution is presented where the chains compress in accord with the experimental findings. The chains are modeled as simple blobs exposed to a linear shear gradient which results in a compressive hydrodynamic force on the chain. Equating the hydrodynamic an…
Concentrated fabric softeners are water-based formulations containing around 10 - 15 wt. % of double tailed esterquat surfactants primarily synthesized from palm oil. In recent patents, it was shown that a significant part of the surfactant contained in today formulations can be reduced by circa 50 % and replaced by natural guar polymers without detrimental effects on the deposition and softening performances. We presently study the structure and rheology of these softener formulations and identify the mechanisms at the origin of these effects. The polymer additives used are guar gum polysacch…
The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semi-dilute solutions are characterized by large fluctuations in concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can self-entangle in semi-dilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress, we still lack a complete molecular-level …
We construct colloidal ``sticky'' rods from the semi-flexible filamentous fd virus and temperature-sensitive polymers poly(N-isopropylacrylamide) (PNIPAM). The phase diagram of fd-PNIPAM system becomes independent of ionic strength at high salt concentration and low temperature, i.e. the rods are sterically stabilized by the polymer. However, the network of sticky rods undergoes a sol-gel transition as the temperature is raised. The viscoelastic moduli of fd and fd-PNIPAM suspensions are compared as a function of temperature, and the effect of ionic strength on the gelling behavior of fd-PNIPA…
We investigate the steady-state extensional rheology of a dilute suspension of spherical particles in a dilute polymer solution. For a particle-free polymeric fluid, in addition to the solvent viscosity, the extensional viscosity due to the polymers, $μ^\text{poly}$, contributes to the total non-dimensionalized extensional viscosity $1+μ^\text{poly}$. When a small volume fraction, $ϕ$, of spheres is added to a polymeric fluid, the stress is altered by the Einstein viscosity of 2.5$ϕ$ and two additional stress contributions: the interaction stresslet and the particle-induced polymer stress (PIP…
In this work, we consider a semi-dilute solution of identical star-polymers, made of attached flexible long polymer chains of the same polymerization degree N. We first compute the effective pair-potential between star-polymers. Such a potential results from the excluded volume forces between monomers. We show that this potential is logarithmic, below some known characteristic distance, σ, depending on the number of attached chains per star-polymer, f, and volume fraction of polymers, φ0 . Beyond σ, the potential fails exponentially. Second, we investigate the structure and ther…
We numerically and analytically analyze the startup continuous shear rheology of heavily entangled rigid rod polymer fluids based on our self-consistent, force-level theory of anharmonic tube confinement. The approach is simplified by neglecting stress-assisted transverse barrier hopping, and irreversible relaxation proceeds solely via deformation-perturbed reptation. This process is self-consistently coupled to tube dilation and macroscopic rheological response. We predict that with increasing strain the tube strongly dilates, entanglements are lost, and reptation speeds up. As a consequence,…
Orientational origin of nonlinear shear rheology in unentangled polymer melts
Department of Chemical Science and Engineering, Kyoto University（京都大学化学工程系）；Advanced Manufacturing Technology Institute, Kanazawa University（金泽大学先进制造技术研究所）
We use non-equilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star polymers ($\mathrm{C_{25}H_{52}}$) to study the steady-state viscoelastic response under confinement within nanoscale hematite $\left ( \mathrm{α-Fe_2O_3} \right )$ channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low shear rates. We link these effects to bond alignment such that chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the…
We study the conformational behavior of polarizable polymer chain under an external homogeneous electric field within the Flory type self-consistent field theory. We consider the influence of electric field on the polymer coil as well as on the polymer globule. We show that when the polymer chain conformation is a coil, application of external electric field leads to its additional swelling. However, when the polymer conformation is a globule, a sufficiently strong field can induce a globule-coil transition. We show that such $"$field-induced$"$ globule-coil transition at the sufficiently smal…
We use Brownian dynamics (BD) simulations and single molecule experiments to investigate the influence of topological constraints and hydrodynamic interactions on the dynamics and rheology of solutions of ring-linear polymer blends at the overlap concentration. We find agreement between simulation and experiment in that rings in solution blends exhibit large conformational fluctuations, including extension overshoots in the startup of flow and tumbling and tank-treading at steady state. Ring polymer fluctuations increase with blend fraction of linear polymers and are peaked at a ring Weissenbe…
A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as finitely elongated nonlinear elastic dumbbells, where effective charges (interacting through a simple Coulomb force) are added to the beads in order to model the repulsion between the charged sections of polyelectrolyte chains. It is shown that the relative strength of this repulsion is regulated by the electric-to-elastic energy ratio, $E$, which is one of the key parameters of the model. In particular, $E$ accounts for the intrinsic rigidit…
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, …
We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is solved together with Brinkman's equation for the solvent velocity that takes into account the presence of other polymer coils in the solution. The equation for the polymer normal modes is obtained and the relevant time correlation functions are found. A tendency to the time-dependent hydrodynamic screening is demonstrated on the diffusion of the polymers as we…
The shear viscosity eta_s(w) of dilute polymer solutions (of flexible coils) has been classically measured and interpreted in terms of the Zimm modes. We point out that the longitudinal viscosity eta_l(w) is the sum of two components eta_l=4*eta_s/3+eta_p, where eta_p is due to an effect of pressure on the coil size. We discuss eta_p for a crude model involving a dependence of both the Kuhn length a and the Flory parameter chi on pressure. We find that eta_p is comparable to eta_s for good solvent conditions, but that eta_p should dominate over eta_s near the theta point.
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $ϕ_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $ϕ_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a fun…
In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model for randomly crosslinked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erd\H os-Rényi random graphs or three-dimensional bond percolation. Within this model the critical behaviour of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size $n$ with $n$. We investigate these Mark--Houwink like scaling relations nume…
The coil-stretch transition in extensional flows of viscoelastic dilute polymer solutions is known to be associated with a strong hysteresis in molecular conformations and rheo-optical properties. At infinite dilution, hysteresis is caused by the large difference in frictional drag coefficient between undeformed isotropic polymer coils and highly stretched conformations. At the low extension rates in the hysteresis regime, stretched molecules pervade larger volumes than equilibrium coils since the flow is too weak to suppress transverse fluctuations. The onset of intermolecular overlap occurs …
We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle dista…
Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g., nucleated cells, hydrogels, microcapsules etc. In this work, we analyze the flow in and around a concentric compound particle and investigate the deformation and reorientation dynamics of the confining drop and its stability against breakup in imposed linear flows. We obtain analytical expressions for the flow fields upto O(Ca) (capillary number) and the deformed shape of the conf…
