Ground state of electrorheological fluids from Monte Carlo simulations

Ground state of dipolar hard spheres confined in channels

We investigate the ground state of a classical two-dimensional system of hard-sphere dipoles confined between two hard walls. Using lattice sum minimization techniques we reveal that at fixed wall separations, a first-order transition from a vacuum to a straight one-dimensional chain of dipoles occurs upon increasing the density. Further increase in the density yields the stability of an undulated chain as well as nontrivial buckling structures. We explore the close-packed configurations of dipoles in detail, and we find that, in general, the densest packings of dipoles possess complex magnetizations along the principal axis of the slit. Our predictions serve as a guideline for experiments with granular dipolar and magnetic colloidal suspensions confined in slitlike channel geometry.

Dipolar Crystals: The Crucial Role of the Clinohexagonal Prism Phase

We report a new phase called clinohexagonal prism (CHP) that accounts for all the ground states of dipolar hard spheres prepared at any density. This phase merely consists of an oblique prismatic lattice with a hexagonal base. Our calculations show that at intermediate densities, a special close packed body-centered orthorhombic phase coincides with the CHP phase in the ground state for a wide density window. In the high packing regime, i.e., in the vicinity of the density of the hexagonal close packed phase, it is a limiting case of the CHP phase with vanishing obliquity that emerges. These findings provide a unified and clarified view of the solid-solid transitions occurring at zero temperature in dipolar systems and should be relevant in other related molecular or soft matter systems governed by anisotropic (and possibly isotropic) soft potentials.

Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system

In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes.

Simulation of a two-dimensional model for colloids in a uniaxial electric field

We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial ac electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in turn form chains. We therefore approximate the system as composed of well-formed chains of dipolar hard spheres of a uniform length. The dipolar interaction between colloidal spheres gives rise to an effective interaction between the chains, which we treat as disks in a plane, that includes a short-range attraction and long-range repulsion. Hence, the system favors finite clustering over bulk phase separation, and indeed we observe at low temperature and density that the system does form a cluster phase. As the density increases, percolation is accompanied by a pressure anomaly. The percolated phase, despite being composed of connected, locally crystalline domains, does not bear the typical signatures of a hexatic phase. At very low densities, we find no indication of a "void phase" with a cellular structure seen recently in experiments.

Structure of ferrofluid nanofilms in homogeneous magnetic fields

We report molecular dynamics simulations results for model ferrofluid films subject to an external, homogeneous magnetic field directed parallel or perpendicular to the film surfaces. The interactions between the magnetic nanoparticles are modeled via the Stockmayer potential. In a previous study [J. Jordanovic and S. H. L. Klapp, Phys. Rev. Lett. 101, 038302 (2008)] we have shown that an external field can control the number and internal structure of the layers characterizing the fluid films, in qualitative agreement with experiments. Here we explore the dependence of the layering effects on thermodynamic conditions, and we analyze the results from an energetic (microscopic and macroscopic) perspective. As a special case we investigate a monolayer to bilayer transition induced via a perpendicular field.

Static shear modulus of electrorheological fluids

We report measurements of the static shear modulus of electrorheological (ER) fluids consisting of water-wetted silica microspheres in silicone oil. A shear-annealing method, using creep-recovery (CR) cycles under an external electric field, is used to enhance ER properties of the fluid. The shear-annealing method enables the silica spheres in the ER fluid to form better aligned and denser column microstructures. A stable state with elastic shear deformation is obtained after a sufficient number of CR cycles, with an optimal combination of stress duration and shear strength. Static shear modulus is obtained by measuring the elastic deformations at different shear stresses for an electric field frequency from 10 to 1000 Hz. A water-bridge model is proposed to explain the enhanced shear modulus.

Phase behavior of dipolar hard and soft spheres

We study the phase behavior of hard and soft spheres with a fixed dipole moment using Monte Carlo simulations. The spheres interact via a pair potential that is a sum of a hard-core Yukawa (or screened-Coulomb) repulsion and a dipole-dipole interaction. The system can be used to model colloids in an external electric or magnetic field. Two cases are considered: (i) colloids without charge (or dipolar hard spheres) and (ii) colloids with charge (or dipolar soft spheres). The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres shows, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and is in agreement with the experimental phase diagram [Nature (London) 421, 513 (2003)]. In both cases, the fluid phase is inhomogeneous but we find no evidence of a gas-liquid phase separation. The validity of the dipole approximation is verified by a multipole moment expansion.

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.

Method to calculate electrical forces acting on a sphere in an electrorheological fluid

We describe a method to calculate the electrical force acting on a sphere in a suspension of dielectric spheres in a host with a different dielectric constant, under the assumption that a spatially uniform electric field is applied. The method uses a spectral representation for the total electrostatic energy of the composite. The force is expressed as a certain gradient of this energy, which can be expressed in a closed analytic form rather than evaluated as a numerical derivative. The method is applicable even when both the spheres and the host have frequency-dependent dielectric functions and nonzero conductivities, provided the system is in the quasistatic regime. In principle, it includes all multipolar contributions to the force, and it can be used to calculate multibody as well as pairwise forces. We also present several numerical examples, including host fluids with finite conductivities. The force between spheres approaches the dipole-dipole limit, as expected, at large separations, but departs drastically from that limit when the spheres are nearly in contact. The force may also change sign as a function of frequency when the host is a slightly conducting fluid.

Statistical-mechanical theory of the overall magnetic properties of mesocrystals

The mesocrystal showing both electrorheological and magnetorheological effects is called electro-magnetorheological (EMR) solids. Prediction of the overall magnetic properties of the EMR solids is a challenging task due to the coexistence of the uniaxially anisotropic behavior and structural transition as well as long-range interaction between the suspended particles. To consider the uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fröhlich equation for calculating the effective permeabilities by adopting an explicit characteristic spheroid rather than a characteristic sphere used in the derivation of the usual Kirkwood-Fröhlich equation. Further, by applying an Ewald-Kornfeld formulation we are able to investigate the effective permeability by including the structural transition and long-range interaction explicitly. Our theory can reduce to the usual Kirkwood-Fröhlich equation and Onsager equation naturally. To this end, the numerical simulation shows the validity of monitoring the structure of EMR solids by detecting their effective permeabilities.

Shear-enhanced yield stress in electrorheological fluids

We report the enhancement of yield stress in electrorheological (ER) fluids by a shear-annealing method, using creep-recovery (CR) cycles under an external electric field. The enhancement depends on the duration and the strength of the applied shear stress, as well as on the number of the CR cycles. The shear-annealing method enables the particles in the ER fluid to form microstructures with an increased yield stress, manifest as better aligned and denser columns. For a sufficiently large number of CR cycles, with an optimal combination of stress duration and shear strength, a stable state can be obtained whereby shear deformation becomes elastic.

Ground state of a polydisperse electrorheological solid: beyond the dipole approximation

The ground state of an electrorheological (ER) fluid has been studied based on our recently proposed dipole-induced dipole (DID) model. We obtained an analytical expression of the interaction between chains of particles which are of the same or different dielectric constants. The effects of dielectric constants on the structure formation in monodisperse and polydisperse electrorheological fluids are studied in a wide range of dielectric contrasts between the particles and the base fluid. Our results showed that the established body-centered tetragonal ground state in monodisperse ER fluids may become unstable due to a polydispersity in the particle dielectric constants. While our results agree with that of the fully multipole theory, the DID model is much simpler, which offers a basis for computer simulations in polydisperse ER fluids.

Electrorheological Toners for Electrophotography

The electrorheological (ER) behavior of pigment suspensions dispersed in a nonaqueous solvent was examined for their application as liquid toners for electrophotography. In electric fields, particles can align into chains along the field vector by dielectric polarization forces and the suspensions undergo a rapid transition from Newtonian fluids to Bingham bodies. However, the migration and deposition of particles can take place by the electrophoretic effect, because charge control agents are added to liquid toners for fast development. The combined effects of dielectric polarization forces, electrophoretic forces, and hydrodynamic forces make rheological behavior very complicated. To simulate the ER behavior of liquid toners in reprographic processes, viscosity measurements were carried out in electrodes with a honeycomb pattern. Nonuniform electric fields enhance the dipole-dipole interactions between particles and give rise to a striking ER effect. Based on measurements in honeycomb pattern electrodes, new ER toners were developed which can reproduce images with high quality.

Ground state of a dipolar crystal

We provide some of the strongest evidence to date that the ground state structure of an infinite collection of point dipoles with hardcore sphere interactions is body-centered tetragonal. The structure with the next highest binding energy is not face-centered cubic; a particular honeycomb structure has lower energy.

Phase behavior of aligned dipolar hard spheres: integral equations and density functional results

Using reference hypernetted chain integral equations, we investigate the phase behavior of a system of dipolar hard spheres with perfect orientational order. At low densities, the correlation functions show a strong tendency to the formation of head-to-tail chains. The occurrence of a condensation of the chains, as suggested by a recent simulation, is critically discussed. At higher densities the structure of the liquid phase already reflects well defined positions of the chains relative to each other, similar to a body-centered-tetragonal structure. Minimizing a density functional of the grand canonical free energy which is based on the liquid correlation functions, we calculate the coexistence lines at freezing. Interestingly, the system freezes at much lower temperatures than the corresponding isotropic fluid.

Effect of Electrode Pattern on the Column Structure and Yield Stress of Electrorheological Fluids

For electrorheological (ER) suspensions, the aggregate structures of particles were observed in electric fields by the use of transparent cells with different electrode patterns. Although the suspension is dispersed to noninteracting particles without electric fields, many aggregates are formed on the electrode surface in electric fields. Since the dipole-dipole interactions cause chain structures of particles and equilibrium conformations of chains are always aligned with electric field, the aggregates indicate the presence of columns spanning the electrode gap. The particle concentration in columns which are developed between parallel-plate electrodes is about 22 vol %. In striped electrodes, the particles construct striped aggregates along the electrodes and no particles remain in the insulating region. The particle concentration in striped aggregates is about 35 vol %. The nonuniformity of electric field is responsible for the high particle concentration. The increase in particle concentration of column lead to the high yield stress of electrified suspension. Therefore, the ER performance of suspension as an overall response can be improved by the electrode design.

Electrorheological Fluids

Suspensions of polarizable particles in nonpolarizable solvents form fibrillated structures in strong electric fields. The resulting increase in viscosity of these "electrorheological" fluids can couple electrical to hydraulic components in a servomechanism. The physical properties of these fluids are unusual owing to the long-range, anisotropic nature of the interparticle forces. Immediately after the electric field is applied, elongated chains or columns of particles form parallel to the field. This structure then coarsens as a result of thermal forces between the columns. In shear flows, fluids show yielding behavior at low stresses followed by shear-thinning behavior at higher stresses.