Shear induced ordering in systems with competing interactions: A machine learning study
Jakub Pękalski, Wojciech Rządkowski, Athanassios Z. Panagiotopoulos
备注：
The following article has been accepted by the Journal of Chemical Physics AIP. After it is published, it will be found at https://aip.scitation.org/journal/jcp
When short-range attractions are combined with long-range repulsions in colloidal particle systems, complex microphases can emerge. Here, we study a system of isotropic particles which can form lamellar structures or a disordered fluid phase when temperature is varied. We show that at equilibrium the lamellar structure crystallizes, while out of equilibrium the system forms a variety of structures at different shear rates and temperatures above melting. The shear-induced ordering is analyzed by means of principal component analysis and artificial neural networks, which are applied to data of reduced dimensionality. Our results reveal the possibility of inducing ordering by shear, potentially providing a feasible route to the fabrication of ordered lamellar structures from isotropic particles.
Soft Glassy Materials, Non Linear Rheology, Lattice Kinetic models, frustrated phase separation} We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizating the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear-banding and histeresys. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheolo…
Competing time scales generate novelty. Here, we show that a coupling between the time scales imposed by instrument inertia and the formation of inter-particle frictional contacts in shear-thickening suspensions leads to highly asymmetric shear-rate oscillations. Experiments tuning the presence of oscillations by varying the two time-scales validate our model. The observed oscillations give access to a shear-jamming portion of the flow curve that is forbidden in conventional rheometry. Moreover, the oscillation frequency allows us to quantify an intrinsic relaxation time for particle contacts.…
The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as $γt^{5/4}$ (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.
The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi--Edwards--Kuzuu theory is possible, as we obtain a master curve for different concentrations, scali…
Mixed surfactant systems with strongly bound counterions show many interesting phases such as the random mesh phase consisting of a disordered array of defects (water-filled nano-pores in the bilayers). The present study addresses the non-equilibrium phase transition of the random mesh phase under shear to an ordered mesh phase with a high degree of coherence between nano-pores in three-dimension. In-situ small-angle synchrotron X-ray study under different shear stress conditions shows sharp Bragg peaks in the X-ray diffraction, successfully indexed to the rhombohedral lattice with R$\bar{3}$m…
We use lattice Boltzmann simulations to study the effect of shear on the phase ordering of a two-dimensional binary fluid. The shear is imposed by generalising the lattice Boltzmann algorithm to include Lees-Edwards boundary conditions. We show how the interplay between the ordering effects of the spinodal decomposition and the disordering tendencies of the shear, which depends on the shear rate and the fluid viscosity, can lead to a state of dynamic equilibrium where domains are continually broken up and re-formed.
We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
We carry out numerical simulations of soft, U-shaped, frictionless particles in $d=2$ dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction $ϕ$ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction $ϕ_J$ than observed in compression. A growing relaxation time and translational correlation length is f…
We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension, observing modest shear-induced ordering and a nearly linear flow profile. At high concentration ($ϕ= 0.55$) and applied stress just below shear thickening, we report ordering fluctuations with high temporal resolution, and directly measure a decrease in order with distance from the suspension's bottom boundary as well as a direct correlation between order and …
Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over $10^5$ particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for $Pe>1$, the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering …
We study the rheological properties of colloidal microphases in two dimensions simulating a model of colloidal particles with competing interactions. Due to the competition between short-range attraction and long-range repulsion, as a function of the density the model exhibits a variety of microphases such as clusters, stripes or crystals with bubbles. We prepare the system in a confined microphase employing Monte-Carlo simulations and then quench the system at T=0. The resulting configurations are then sheared by applying a drag force profile. We integrate numerically the equation of motion f…
A transition from solid-like to liquid-like behavior occurs when colloidal gels are subjected to a prolonged exposure to a steady shear. This phenomenon, which is characterized by a yielding point, is found to be strongly dependent on the packing fraction. However, it is not yet known how the effective inter-particle potential affects this transition. To this aim, we present a numerical investigation of the rheology of equilibrium gels in which a short-range depletion is complemented by a long-range electrostatic interaction. We observe a single yielding event in the stress-strain curve, occur…
Self-organized monolayers of highly flexible \Frechet dendrons were deposited on graphite surfaces by solution casting. Scanning tunneling microscopy (STM) reveals an unprecedented variety of patterns with up to seven stable hierarchical ordering motifs serving as a versatile model system. The essential molecular properties determined by molecular mechanics simulations are condensed to a coarse grained interaction site model of various chain configurations. In a Monte Carlo approach with random starting configurations the experimental pattern diversity can be reproduced in all facets of the lo…
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(ϕ,F)$: at low $ϕ$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $ϕ$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy w…
We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $α\to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is non-monotonic in the packing fraction $ϕ$, and that as $α\to 0$ $S_{2}$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts p…
Self-assembly of nanoparticles can enable composites with pre-designed properties but remains challenged by reproducing structural diversity of atomic and molecular crystals. We combine anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. Orientations of nanocrystals, as well as crystallographic axes of ensuing triclinic colloidal …
From Landau-Alexander-McTague theory and Monte-Carlo simulation results we show that the modulated liquid obtained by subjecting a colloidal system to a periodic laser modulation has long range bond-orientational order and non-zero shear rigidity. From infinite field simulation results we show that in the modulated liquid phase, the translational order parameter correlation function decays to zero exponentially while the correlation function for the bond-orientational order saturates to a finite value at large distances.
Shearing of nanocomposites has shown to produce ordered nanostructures and orientation in the polymeric matrix. Due to the importance of the formation of an ordered structure of nanoparticles in a polymeric matrix to device wearable, flexible and photonic materials, its useful to get an insight of the shear-induced ordering and other properties of the polymeric nanocomposites. In this paper, we use a model Wormlike micellar matrix to study the arrangement and morphology of nanoparticles in the composite when the system is sheared using a hybrid multiparticle dynamics and molecular dynamics sim…
By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically-symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex three-dimensional periodically ordered cluster phases such as lamellae, two-dimensional hexagonally packed cylinders, gyroid structures or spherical micelles. While the bulk phase behavior has been studied extensively in earlier work, in this paper we focus on such structures confined between planar repulsive walls under shear flow. For sufficiently high she…
A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strength of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determines the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures, and when considering the periodic ordering of the system at low te…
Utilizing molecular dynamics simulations, we report a non-monotonic dependence of the shear stress on the strength of an external magnetic field ($H$) in a liquid-crystalline mixture of magnetic and non-magnetic anisotropic particles. This non-monotonic behavior is in sharp contrast with the well-studied monotonic $H$-dependency of the shear stress in conventional ferrofluids, where the shear stress increases with $H$ until it reaches a saturation value. We relate the origin of this non-monotonicity to the competing effects of particle alignment along the shear-induced direction, on the one ha…
Dense assemblies of self propelled particles, also known as active or living glasses are abundantaround us, covering different length and time scales: from the cytoplasm to tissues, from bacterialbio-films to vehicular traffic jams, from Janus colloids to animal herds. Being structurally disorderedas well as strongly out of equilibrium, these systems show fascinating dynamical and mechanicalproperties. Using extensive molecular dynamics simulation and a number of different dynamicaland mechanical order parameters we differentiate three dynamical steady states in a sheared modelactive glassy sy…
Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, $λ$, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered …
Hard sphere colloidal particles are a basic model system for general research into phase behavior, ordering and out-equilibrium glass transitions. Experimentally it has been shown that oscillatory shearing of a monodisperse hard sphere glass, produces two different crystal orientations; a Face Centered Cubic (FCC) crystal with the close packed direction parallel to shear at high strains and an FCC crystal with the close packed direction perpendicular to shear at low strains. Here, using Brownian dynamics simulations of hard sphere particles, we have examined high volume fraction shear-induced …
We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or the ratio of the number of particles to the number of substrate minima we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perp…
Despite the extensive research that has been conducted for decades on the behavior of confined liquids, detailed knowledge of this phenomenon, particularly in the mixed/boundary lubrication regime, remains limited. This can be attributed to several factors including the difficulty of direct experimental observations of the behavior of lubricant molecules under non-equilibrium conditions, the high computational cost of molecular simulations to reach steady state, and the low signal-to-noise ratio at extremely low shear rates corresponding to actual operating conditions. To this end, we studied …
Oscillatory flows are commonly experienced by swimming microorganisms in the environment, industrial applications and rheological investigations. We experimentally characterise the response of the alga {\it Dunaliella salina} to oscillatory shear flows, and report the surprising discovery that algal swimming trajectories orient perpendicular to the flow-shear plane. The ordering has the characteristics of a resonance in the driving parameter space. The behaviour is qualitatively reproduced by a simple model and simulations accounting for helical swimming, providing the mechanism for ordering a…
We study colloidal gels formed by competing electrostatic repulsion and short-range attraction by means of extensive numerical simulations under external shear. We show that, upon varying the repulsion strength, the gel structure and its viscoelastic properties can be largely tuned. In particular, the gel fractal dimension can be either increased or decreased with respect to mechanical equilibrium conditions. Unexpectedly, gels with stronger repulsion, despite being mechanically stiffer, are found to be less viscous with respect to purely attractive ones. We provide a microscopic explanation o…
We use numerical simulations to study the shear-driven steady-state flow of athermal, frictionless, overdamped, two dimensional cross-shaped particles of varying aspect ratios, and make comparison with the behavior of rod-shaped and staple-shaped particles. We find that the extent of non-convexity of the particle shape plays an important role in determining both the value of the jamming packing fraction as well as the rotational motion and orientational ordering of the particles.
We investigate the effects of crowding on the conformations and assembly of confined, highly charged, and thick polyelectrolyte brushes in the osmotic regime. Particle tracking experiments on increasingly dense suspensions of colloids coated with ultra-long double stranded DNA (dsDNA) fragments reveal non-monotonic particle shrinking, aggregation and re-entrant ordering. Theory and simulations show that shrinking is induced by the osmotic pressure exerted by the counterions absorbed in neighbor brushes, while aggregation and re-entrant ordering are the effect of a short-range attraction compet…
For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallization and spatially varying shear flow. For thermodynamic state points within the liquid part of the phase diagram, but close to the crystallization phase boundary, we observe that imposing a Poiseuille flow can induce nonequilibrium crystalline ordering in regions of low shear gradient. The physical mechanism responsible for this phenomenon is shear induced particle migration, which causes particles to drift preferentially towards the center of the flow …
Using Monte Carlo (MC) computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nano-spheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod-matrices we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the ove…
Microswimmers typically operate in complex environments. In biological systems, often diverse species are simultaneously present and interact with each other. Here, we derive a (time-dependent) particle-scale statistical description, namely a dynamical density functional theory, for such multi-species systems, extending existing works on one-component microswimmer suspensions. In particular, our theory incorporates the effect of external potentials, but also steric and hydrodynamic interactions between swimmers. For the latter, a previously introduced force-dipole-based minimal (pusher or pull…
The alignment, ordering and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations. The particles develop an orientational order. In the steady state the time and ensemble averaged direction of the main axis of the particles encloses a small angle with the streamlines. This shear alignment angle is independent of the applied shear rate,…
Recent experiments on particle diffusion in bacterial baths indicate the formation of correlated structures in the form of bacterial swirls. Here we predict that such a structural ordering would give rise to the new effect of propagating shear waves in a bacterial bath at length scales of the order of a swirl, which corresponds to time scales of the order of the lifetime of a swirl. Our prediction can be tested against future experiments in bacterial baths.
Faraday waves (FWs), or surface waves oscillating at half of the natural frequency when a liquid is vertically vibrated, are archetypes of ordering transitions on liquid surfaces. The existence of unbounded FW-patterns sustained upon bulk frictional stresses has been evidenced in highly viscous fluids. However, the role of surface rigidity has not been investigated so far. Here, we demonstrate that dynamically frozen FWs that we call 2D-hydrodynamic crystals do appear as ordered patterns of nonlinear surface modes in water surfaces functionalized with soluble (bio)surfactants endowing in-plane…
This work is dedicated to the study of the discrete version of the Maier-Saupe model in the presence of competing interactions. The competition between interactions favoring different orientational ordering produces a rich phase diagram including modulated phases. Using a mean-field approach and Monte Carlo simulations, we show that the proposed model exhibits isotropic and nematic phases and also a series of modulated phases that meet at a multicritical point, a Lifshitz point. Though the Monte Carlo and mean-field phase diagrams show some quantitative disagreements, the Monte Carlo simulatio…
Hydrodynamic flow can have complex and far-reaching consequences on the rate of homogenous nucleation. We present a general formalism for calculating the nucleation rates of simply sheared systems. We have derived an extension to the conventional Classical Nucleation Theory, explicitly embodying the shear rate. Seeded Molecular Dynamics simulations form the backbone of our approach. The framework can be used for moderate supercoolings, at which temperatures brute-force methods are practically infeasible. The competing energetic and kinetic effects of shear arise naturally from the equations. W…
We study the kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase. At low viscosities, in two dimensions, when hydrodynamic modes become important, dynamical scaling is verified in the form $C(\vec k, t) \sim L^α f[(k-k_M)L]$ where $C$ is the structure factor with maximum at $k_M$ and $L$ is a typical length changing from power law to logarithmic growth at late times. The presence of extended defects can explain the behavior of $L$. Three-dimensional simulations confirm that diffuse grain boundaries inhibit complete ordering of lamellae. Applied shear flow…
The design and development of a parallel plate shear cell for the study of large scale shear flows in granular materials is presented. The parallel plate geometry allows for shear studies without the effects of curvature found in the more common Couette experiments. A system of independently movable slats creates a well with side walls that deform in response to the motions of grains within the pack. This allows for true parallel plate shear with minimal interference from the containing geometry. The motions of the side walls also allow for a direct measurement of the velocity profile across t…
