Structure and dynamics of repulsive magnetorheological colloids in two-dimensional channels

Percolation transitions of confinement-induced layering and intralayer structural orders in three-dimensional Yukawa liquids

The disorder-order transitions of layering and intralayer structural orders of three-dimensional Yukawa liquids, under the enhanced confinement effect with decreasing normal distance z to the confinement boundary, is investigated numerically. The liquid between the two flat boundaries is segmented into many slabs parallel to the boundary, with the same slab width as the layer width. In each slab, particle sites are binarized into sites with layering order (LOSs)/ layering disorder (LDSs) and with intralayer structural order (SOSs)/disorder (SDSs). It is found that with decreasing z, a small fraction of LOSs starts to heterogeneously emerge in the form of small clusters in the slab, followed by the emergence of the large percolating LOS clusters spanning over the system. The smooth rapid rise of the fraction of LOSs from small values followed by their gradual saturations, and the scaling behavior of multiscale LOS clustering, are similar to those of the nonequilibrium systems governed by the percolation theory. The disorder-order transition of intraslab structural ordering also exhibits a similar generic behavior as that of layering with the same transition slab number. The spatial fluctuations of local layering order and local intralayer structural order are uncorrelated in the bulk liquid and the outmost layer next to the boundary. Approaching the percolating transition slab, their correlation gradually increases to the maximum.

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Surface-Induced Layering of Quenched 3D Dusty Plasma Liquids: Micromotion and Structural Rearrangement

We experimentally demonstrate confinement surface induced layering with a fluctuating layering front, and investigate the heterogeneous 3D crystalline ordered structure, cooperative micromotion, and structural rearrangement in the layered region of a quenched dusty plasma liquid. It is found that, after quenching the liquid with 2 to 3 layers adjacent to its flat bottom boundary, the layering front invades upward and exhibits turbulentlike fluctuations with power law decays in spatial and temporal power spectra. The layered region can be viewed as a 2+1D system with vertically coupled horizontal 2D layers, in which particle translayer motions are nearly fully suppressed. Each layer exhibits hexatic structure with a slow decay of long-range triangular lattice order. The nearly parallel but with different horizontal shifts of intralayer lattice lines of adjacent layers allows the heterogeneous fcc, bcc, and hcp structures with specific lattice orientations. In each layer, particles exhibit thermally excited horizontal motions of alternative cage rattling and cooperative hopping, which cause intralayer lattice line wiggling and triangular crystalline domain rupture or healing, respectively. The different intralayer cooperative motion of adjacent layers is the key for interlayer slip causing the structural rearrangement of 3D crystalline ordered domains.

Thermodynamics and dynamics of two-dimensional systems with dipolelike repulsive interactions

Thermodynamics and dynamics of a classical two-dimensional system with dipolelike isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical approximations. This interaction potential, which decays as an inverse cube of the interparticle distance, belongs to the class of very soft long-ranged interactions. As a result, the investigated system exhibits certain universal properties that are also shared by other related soft-interacting particle systems (like, for instance, the one-component plasma and weakly screened Coulomb systems). These universalities are explored in this article to construct a simple and reliable description of the system thermodynamics. In particular, Helmholtz free energies of the fluid and solid phases are derived, from which the location of the fluid-solid coexistence is determined. The quasicrystalline approximation is applied to the description of collective modes in dipole fluids. Its simplification, previously validated on strongly coupled plasma fluids, is used to derive explicit analytic dispersion relations for the longitudinal and transverse wave modes, which compare satisfactory with those obtained from direct MD simulations in the long-wavelength regime. Sound velocities of the dipole fluids and solids are derived and analyzed.

Avalanches, plasticity, and ordering in colloidal crystals under compression

Using numerical simulations we examine colloids with a long-range Coulomb interaction confined in a two-dimensional trough potential undergoing dynamical compression. As the depth of the confining well is increased, the colloids move via elastic distortions interspersed with intermittent bursts or avalanches of plastic motion. In these avalanches, the colloids rearrange to minimize their colloid-colloid repulsive interaction energy by adopting an average lattice constant that is isotropic despite the anisotropic nature of the compression. The avalanches take the form of shear banding events that decrease or increase the structural order of the system. At larger compression, the avalanches are associated with a reduction of the number of rows of colloids that fit within the confining potential, and between avalanches the colloids can exhibit partially crystalline or anisotropic ordering. The colloid velocity distributions during the avalanches have a non-Gaussian form with power-law tails and exponents that are consistent with those found for the velocity distributions of gliding dislocations. We observe similar behavior when we subsequently decompress the system, and find a partially hysteretic response reflecting the irreversibility of the plastic events.

Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

A two-dimensional crystal of repulsive dipolar particles is studied in the vicinity of its melting transition by using Brownian dynamics computer simulation, dynamical density-functional theory, and phase-field-crystal modeling. A vacancy is created by taking out a particle from an equilibrated crystal, and the relaxation dynamics of the vacancy is followed by monitoring the time-dependent one-particle density. We find that the vacancy is quickly filled up by diffusive hopping of neighboring particles towards the vacancy center. We examine the temperature dependence of the diffusion constant and find that it decreases with decreasing temperature in the simulations. This trend is reproduced by the dynamical density-functional theory. Conversely, the phase-field-crystal calculations predict the opposite trend. Therefore, the phase-field model needs a temperature-dependent expression for the mobility to predict trends correctly.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

Freezing of a two-dimensional fluid into a crystalline phase: density functional approach

A free-energy functional for a crystal proposed by Singh and Singh [Europhys. Lett. 88, 16005 (2009)] which contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of a two-dimensional fluid. The results found for fluids interacting via the inverse power potential u(r)=ε(σ/r)(n) for n=3,6, and 12 are in good agreement with experimental and simulation results. The contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is found to increase with the softness of the potential. Our results explain why the Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] free-energy functional gave good account of freezing transitions of hard-core potentials but failed for potentials that have soft core and/or attractive tail.

Stochastic transport of particles across single barriers

Transport phenomena of interacting particles are of high interest for many applications in biology and mesoscopic systems. Here we present measurements on colloidal particles, which are confined in narrow channels on a substrate and interact with a barrier, which impedes the motion along the channel. The substrate of the particle is tilted in order for the particles to be driven towards the barrier and, if the energy gained by the tilt is large enough, surpass the barrier by thermal activation. We therefore study the influence of this barrier as well as the influence of particle interaction on the particle transport through such systems. All experiments are supported with Brownian dynamics simulations in order to complement the experiments with tests of a large range of parameter space which cannot be accessed in experiments.

Motion, relaxation dynamics, and diffusion processes in two-dimensional colloidal crystals confined between walls

The dynamical behavior of single-component two-dimensional colloidal crystals confined in a slit geometry is studied by Langevin dynamics simulation of a simple model. The colloids are modeled as pointlike particles, interacting with the repulsive part of the Lennard-Jones potential, and the fluid molecules in the colloidal suspension are not explicitly considered. Considering a crystalline strip of triangular lattice structure with n=30 rows, the (one-dimensional) walls confining the strip are chosen as two rigidly fixed crystalline rows at each side, commensurate with the lattice structure and, thus, stabilizing long-range order. The case when the spacing between the walls is incommensurate with the ideal triangular lattice is also studied, where (due to a transition in the number of rows, n → n-1) the confined crystal is incommensurate with the confining boundaries, and a soliton staircase forms along the walls. It is shown that mean-square displacements (MSDs) of particles as a function of time show an overshoot and then saturate at a horizontal plateau in the commensurate case, the value of the plateau being largest in the center of the strip. Conversely, when solitons are present, MSDs are largest in the rows containing the solitons, and all MSDs do not settle down at well-defined plateaus in the direction parallel to the boundaries, due to the lack of positional long-range order in ideal two-dimensional crystals. The MSDs of the solitons (which can be treated like quasiparticles at very low temperature) have also been studied and their dynamics are found to be about an order of magnitude slower than that of the colloidal particles themselves. Finally, transport of individual colloidal particles by diffusion processes is studied: both standard vacancy-interstitial pair formation and cooperative ring rotation processes are identified. These processes require thermal activation, with activation energies of the order of 10T(m) (T(m) being the melting temperature of the crystal), while the motions due to long-wavelength phonons decrease only linearly in temperature.

Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with Yukawa interactions

We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.

Electric-field-induced ordering and pattern formation in colloidal suspensions

The long-time dynamics and pattern formation in semidilute suspensions of colloidal spheres in a viscous electrolyte under a uniform electric field are investigated using numerical simulations. The rapid chain formation that occurs in the field direction as a result of dipolar interactions is found to be followed by a slow coarsening process by which chains coalesce into hexagonal sheets and eventually rearrange to form mesoscale cellular structures, in qualitative agreement with recent experiments. The morphology and characteristic wavelength of the patterns that emerge at steady state are shown to depend on the suspension's volume fraction, electrode spacing, and field strength, suggesting additional ways of controlling effective suspension properties in practical applications.

Packing and melting of mesoscopically confined two-dimensional Coulomb crystals in straight narrow channels

The microstructure and melting dynamics of the two-dimensional mesoscopic Coulomb crystal with 1/r-type mutual interaction force and parabolic transverse confining potential, under different degrees of incommensurability, are investigated through molecular-dynamics simulation. To tune the degree of incommensurability, N(a) extra particles are added into the commensurate uniform triangular lattice which has seven-layer structure and 40 particles in each layer with the periodic longitudinal boundary condition, until the system reaches another commensurate packing with eight-layer structure at N(a)=40. It is found that the increasing incommensurability with the increasing N(a) or 40-N(a) gradually deteriorates the structural order with the presence of intrinsic defects and the anisotropic bond-length distribution, except for the defect-free configurations at a few magic N(a)'s. The system prefers the seven- and the eight-layer single structures through the entire crystal for the low- and the high-N(a) regimes, respectively, and the configurations with seven- and eight-layer domain mixtures for 18≤N(a)≤24. The increasing strain or the worse local particle interlocking around the intrinsic defects with the increasing incommensurability also causes the easier structural rearrangement associated with the easier particle hopping and the earlier onset of melting transition. The transverse confinement suppresses the transverse motion, induces nonuniform melting, and sustains the layered structure after melting.

Colloidal systems in three-dimensional microchannels: lattice control via channel width and external force

The structural behavior of hard spheres interacting with repulsive (screened Coulomb) interaction in narrow constrictions is investigated using Brownian dynamics simulations. The system of particles adapts to the confining potential and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of planes throughout the three-dimensional channel. The presence of hard walls leads to structural deviations from the unbounded (infinite) crystal. The arrangement of the particles is perturbed by diffusion and an external driving force leading to a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of planes if it is energetically favorable. This reduction in the number of planes is analogous to the reduction in the number of layers in two-dimensional systems. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior.

A two-component mixture of charged particles confined in a channel: melting

The melting of a binary system of charged particles confined in a quasi-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different kinds of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four-chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two kinds of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct kinds of charges is observed.

Density reduction and diffusion in driven two-dimensional colloidal systems through microchannels

The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of layers throughout the channel and of a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of layers one by one when it is energetically favorable. The position of the layer reduction zone fluctuates with time while the particles continuously pass this zone. The flow behavior of the particles is studied in detail. The velocities of the particles and their diffusion behavior reflect the influence of the self-organized order of the system.

Derivation of the phase-field-crystal model for colloidal solidification

The phase-field-crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field-crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density-functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field-crystal model is proposed which involves less approximations than the standard phase-field-crystal model. We finally test the validity of these phase-field-crystal models against dynamical density-functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field-crystal model in order to match the bulk freezing transition point.

Structure of quasi-one-dimensional ribbon colloid suspensions

We report the results of an experimental study of a colloid fluid confined to a quasi-one-dimensional (q1D) ribbon channel as a function of channel width and colloid density. Our findings confirm the principal predictions of previous theoretical studies of such systems. These are (1) that the density distribution of the liquid transverse to the ribbon channel exhibits stratification; (2) that even at the highest density the order along the strata, as measured by the longitudinal pair correlation function, is characteristic of a liquid; and (3) the q1D pair correlation functions in different strata exhibit anisotropic behavior resembling that found in a Monte Carlo simulation for the in-plane pair correlation function of a hard sphere fluid in a planar slit.

Colloidal crystal growth at externally imposed nucleation clusters

We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk crystal.

Effect of disorder on DNA electrophoresis in a microfluidic array of obstacles

The size-based separation of electrophoresing DNA chains of varying lengths has been experimentally achieved in microfluidic obstacle arrays. The separation is actuated by the occurrence of size-dependent chain-obstacle collisions and the subsequent formation of hooked chain configurations in the array. We investigate the role played by disorder in array geometry in determining chain dynamics in the array. As a prototypical example of a disordered post array, we select a self-assembled array of magnetic colloids, wherein the degree of disorder may be varied by varying the magnetic field strength under which the array is generated. We employ Brownian dynamics simulations of chain electrophoresis in the array to compute the mobility, dispersivity, chain-obstacle collision probability, and mean chain stretch in the device, and demonstrate the link between the orientational order of the array and the resulting chain dynamics.

Fluctuations at a constrained liquid-solid interface

We study the interface between a solid trapped within a bath of liquid by a suitably shaped nonuniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields, or a surface template. We study a two-dimensional case where a thin strip of solid, created in this way, is surrounded on either side by a bath of liquid with which it can easily exchange particles. Since height fluctuations of the interface cost energy, this interface is constrained to remain flat at all length scales. However, when such a solid is stressed by altering the depth of the potential beyond a certain limit, it responds by relieving stress by novel interfacial fluctuations, which involve addition or deletion of entire lattice layers of the crystal. This "layering" transition is a generic feature of the system regardless of the details of the interaction potential. We show how such interfacial fluctuations influence mass, momentum, and energy transport across the interface. Tiny momentum impulses produce weak shock waves, which travel through the interface and cause the spallation of crystal layers into the liquid. Kinetic and energetic constraints prevent spallation of partial layers from the crystal, a fact which may be of some practical use. We also study heat transport through the liquid-solid interface and obtain the resistances in liquid, solid, and interfacial regions (Kapitza resistance) as the solid undergoes such layering transitions. Heat conduction, which shows strong signatures of the structural transformations, can be understood using a free volume calculation.

Transition from two-dimensional to three-dimensional behavior in the self-assembly of magnetorheological fluids confined in thin slits

We study the effects of extreme confinement on the self assembly of the colloids found in magnetorheological (MR) fluids using Brownian dynamics simulations. The MR fluid is confined in a thin slit with a uniform external magnetic field directed normal to the slit. We find a crossover in the behavior of the system from two dimensions to three dimensions as the slit thickness is increased. A simple model is presented to describe this crossover as a function of the slit thickness and volume fraction of the MR fluid. The model is able to predict the salient features of the structure formation that has been observed in these systems. Furthermore, the model predicts the approximate time scales for structure formation under a variety of conditions. We present a quantitative analysis of the effect of volume fraction on the behavior of the system. Additionally, we show quantitatively how energy barriers to structure formation play a crucial role in determining the steady state structure of these systems. Our analysis explains the discrepancies between previous experimental and theoretical work on the self-assembly of MR fluids confined in thin slits.

Ordering of two-dimensional crystals confined in strips of finite width

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential proportional, variantr;{-12} in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two "walls" providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.

Layer reduction in driven 2D-colloidal systems through microchannels

The transport behavior of a system of gravitationally driven superparamagnetic colloidal particles is investigated. The motion of the particles through a narrow channel is governed by magnetic dipole interactions, and a layered structure forms parallel to the walls. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity leading to a density gradient along the channel. Our main result is the reduction of the number of layers. Experiments and Brownian dynamics simulations show that this occurs due to the density gradient along the channel.

Lack of long-range order in confined two-dimensional model colloidal crystals

We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance D in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced ("layering"), but destroyed parallel to the wall.

Computer simulations of two-dimensional melting with dipole-dipole interactions

We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length xi 6 and susceptibility chi 6 are measured, and the data are fitted to the theoretical ansatz. An algebraic decay is detected for both spatial and temporal bond orientational correlation functions in an intermediate temperature regime, and it provides an explicit evidence for the existence of the hexatic phase. From the finite-size scaling analysis of the global bond orientational order parameter, the disclination unbinding temperature Ti is estimated. In addition, from dynamic Monte Carlo simulations of the positional order parameter, we extract the critical exponents at the dislocation unbinding temperature Tm. All the results are in agreement with those from experiments and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.

Experimental study of structure and dynamics in a monolayer of paramagnetic colloids confined by parallel hard walls

We study the structural and dynamical properties of paramagnetic colloidal spheres interacting as repulsive dipoles in two dimensions and confined between parallel hard walls. We observed that the structure and dynamics of the self-assembled colloids are strongly dependent upon the width of the confining channel. The system exhibits re-entrant behavior as a function of the channel width, transitioning from solid-like to liquid-like repeatedly in excellent agreement with simulation results. For large channels, an ordered layered structure self-assembles near the walls, but this local structure is not commensurate with the bulk structure, leading to localized stable defects.