3D Monte Carlo simulations of a magnetic disk-like particle dispersion

We have investigated the aggregate structures of a colloidal dispersion composed of ferromagnetic disk-like particles with a magnetic moment normal to the particle axis at the particle center, by means of 3D Monte Carlo simulations. Such disk-like particles have been modeled as a circular disk-like particle with the side section shape of spherocylinder. We have attempted to clarify the influences of the magnetic field strength, magnetic interactions between particles and volumetric fraction of particles. In order to discuss quantitatively the aggregate structures of clusters, we have focused on the radial distribution and orientational pair correlation functions, etc. For no applied magnetic field cases, long column-like clusters come to be formed with increasing magnetic particle–particle interactions. The internal structures of these clusters clearly show that the particles incline in a certain direction and their magnetic moments alternate in direction between the neighboring particles in the clusters. For applied magnetic field cases, the magnetic moment of each particle inclines in the magnetic field direction and therefore the column-like clusters are not formed straightforwardly. If the magnetic field is much stronger than magnetic particle–particle interactions, the particles do not have a tendency to form the clusters. As the influence of magnetic particle–particle interactions is significantly strong, thick chain-like clusters or column-like clusters or brick-wall-like clusters come to be formed along the magnetic field direction.     

Rheological properties and particle behaviors of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow: analysis by means of mean-field approximation for the two typical external magnetic field directions

We have analyzed the orientational distributions and rheological properties of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow. In order to understand the effects of the magnetic interactions between the particles, we have applied the mean-field theory to a nondilute colloidal dispersion for the two typical external magnetic field directions, that is, the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The main results are summarized as follows. The particle-particle interactions suppress the Brownian motion of the particles and, therefore, make the particles incline toward the same direction. For the magnetic direction parallel to the shear flow, the influence of the particle-particle interactions makes the peak of the orientational distribution sharper and higher. The viscosity generally increases as the interactions between particles become stronger in the case where the effects of the shear flow and magnetic field are relatively small. For the magnetic direction parallel to the angular velocity vector of the shear flow, the influence of the particle-particle interactions on the orientational distribution appears significantly, when the influences of the shear flow and magnetic field are not so strong that the particles can be aligned sufficiently to form stable chainlike clusters in a certain direction.     

Two-dimensional Monte Carlo simulations of a colloidal dispersion composed of rod-like ferromagnetic particles in the absence of an applied magnetic field

Influences of the magnetic interaction between particles and the aspect ratio of particles on aggregate structures in a colloidal dispersion composed of rod-like ferromagnetic particles were investigated by means of the cluster-moving Monte Carlo method. The internal structures of the aggregates obtained in simulations were analyzed in terms of the number density distribution of the clusters and radial distribution functions. The results show that as the magnetic interaction between particles increases, many small clusters such as anti-parallel particle pairs, raft-like clusters, and small loop-like clusters are formed; these gather to form larger aggregates. In the case of a relatively strong magnetic interaction between particles, solid-like rectangular clusters are formed when the aspect ratio is approximately 2, since the suitable distance between magnetic charges enables particles to form a fundamental structure of two normal anti-parallel particle pairs. As the aspect ratio increases beyond 2, many more stable raft-like clusters are formed, since the increase in distance between magnetic charges makes the two normal anti-parallel particle pair structures unstable. For a significantly larger aspect ratio, large network microstructures are produced by the formation of many chain-like and loop-like structures.     

Rheology and orientational distributions of rodlike particles with magnetic moment normal to the particle axis for semi-dense dispersions (analysis by means of mean field approximation)

We have considered a semi-dense dispersion composed of ferromagnetic rodlike particles with a magnetic moment normal to the particle axis to investigate the rheological properties and particle orientational distribution in a simple shear flow as well as an external magnetic field. We have adopted the mean field approximation to take into account magnetic particle-particle interactions. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the magnetic moment of the rodlike particle is strongly restricted in the field direction, so that the particle points to directions normal to the flow direction (and also to the magnetic field direction). This characteristic of the particle orientational distribution is also valid for the case of a strong particle-particle interaction, as in the strong magnetic field case. To the contrary, for a weak interaction among particles, the particle orientational distribution is governed by a shear flow as well as an applied magnetic field. When the magnetic particle-particle interaction is strong under circumstances of an applied magnetic field, the magnetic moment has a tendency to incline to the magnetic field direction more strongly. This leads to the characteristic that the viscosity decreases with decreasing the distance between particles, and this tendency becomes more significant for a stronger particle-particle interaction. These characteristics concerning the viscosity are quite different from those for a semi-dense dispersion composed of rodlike particles with a magnetic moment along the particle direction.     

Two-dimensional Monte Carlo simulations of a colloidal dispersion composed of polydisperse ferromagnetic particles in an applied magnetic field

We have investigated aggregation phenomena in a polydisperse colloidal dispersion of ferromagnetic particles simulated by employing the cluster-moving Monte Carlo method in an applied magnetic field. The influence of both particle-particle and particle-field interactions on the aggregate structures is analyzed in terms of a pair correlation function. The results obtained in this study are summarized as follows: Under a strong magnetic field, chainlike clusters are formed along the magnetic field direction, and they become thickly clustered with an increase in the strength of the external magnetic field. Moreover, the thickly clustered chains are formed for a polydisperse system that has a large standard deviation of particle diameters. In contrast, for a very weak magnetic field, the strong interaction between the larger particles gives rise to the formation of various shapes in the chainlike clusters, including bending, looping, and branching. With an increase in the external magnetic field, these structures reorganize to form straight chainlike clusters. Furthermore, the thickness of the chainlike clusters for the polydisperse system is found to depend on the standard deviation of the particle-size distribution but is found to be independent of the magnetic field strength.     

Influence of magnetic interactions between clusters on particle orientational characteristics and viscosity of a colloidal dispersion composed of ferromagnetic spherocylinder particles: analysis by means of mean field approximation for a simple shear flow

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.     

Two-dimensional Monte Carlo simulations of a polydisperse colloidal dispersion composed of ferromagnetic particles for the case of no external magnetic field

We have investigated the aggregation phenomena in a polydisperse colloidal dispersion composed of ferromagnetic particles by means of the cluster-moving Monte Carlo method. The results have been compared with those for a monodisperse system. The internal structures of aggregates have been analyzed in terms of the radial distribution function in order to clarify the quantitative differences in the internal structures of clusters. In addition, the cluster size distribution and angular distribution function have been investigated. The results obtained in the present study are summarized as follows. In a monodisperse system, open necklacelike clusters are formed and they extend with increasing strength of the magnetic particle-particle interaction. In a polydisperse system with a small standard deviation in the particle size distribution, sigma=0.2, larger necklacelike clusters are formed and some looplike clusters can also be observed. In a polydisperse system with a larger standard deviation, sigma=0.35, clumplike clusters are formed for a weak magnetic particle-particle interaction. For a stronger magnetic interaction, larger size clusters that exhibit a complicated network structure are formed. These complicated cluster formations found in a polydisperse system are mainly due to the effect of the presence of larger particles.     

Influence of perpendicular external magnetic field on microstructures of monolayer composed of ferromagnetic particles: analysis by means of quasi-two-dimensional Monte Carlo simulation

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.     

Periodic structure of spicular magnetic clusters in a magnetic liquid

The behavior of clusters formed by magnetic particles of magnetic liquid placed into a cylindrical capillary tube in magnetic field is described. Spicular clusters are formed from the sediment at the application of a magnetic field. They arrange themselves along the capillary repeating the direction of external magnetic field. Clusters distribute uniformly in the region of a magnetic field maximum. Such a state remains steady with respect to changes of the magnetic field gradient profile in definite limits. The structure of the uniformly ordered clusters is obtained experimentally. The capability of control of the structure period is shown. It is observed that increasing of magnetic field gradient up to the magnitude higher than a certain threshold value results in rearrangement of the clusters row into a multi-row hexagonal structure.     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Structural properties of charge-stabilized ferrofluids under a magnetic field: a Brownian dynamics study

We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field.     

Unique viscoelastic behaviors of colloidal nanocrystalline cellulose aqueous suspensions

Unique rheological and phase behaviors of rod-like nanocrystalline cellulose (NCC) suspensions in aqueous media are revealed in the present article. Specifically, the NCC aqueous suspension remained isotropic in a wide NCC concentration range in which the suspension underwent transition from dilute solution to gel, and the relative viscosity of the NCC suspension could be well fitted by the Sato-Teramoto theory in the full concentration range tested. Correspondingly, both zero-shear viscosity and complex viscosity increased monotonically with NCC concentration, and no maximum value was observed along the curves of zero-shear viscosity or complex viscosity versus NCC concentration, indicating a deviation from the lyotropic system. However, a shear-induced birefringence phenomenon was observed, indicating the NCC suspension formed a temporary ordered structure in the external force field but was unable to form an anisotropic (liquid crystalline) phase. The Cox-Merz rule was not applicable for the NCC suspension as a result of oriented domains, i.e., rod-like NCC particles. Moreover, time-concentration superposition was successfully applied to both the storage and loss modulus, attributed to the isotropic feature of the NCC suspension in the tested concentration range. The reason why this NCC suspension remained isotropic could be because of the strong electrostatic repulsions between NCC particles and the weak tendency or driving force of anisotropy formation as a result of the small aspect ratio of NCC particles, Na⁺ counterions and large amounts of negative charges along the NCC particles. The results suggested that not all the rod-like particles were able to form an anisotropic phase in aqueous suspension, but dominated by various factors.     

Transport coefficients and orientational distributions of rodlike particles with magnetic moment normal to the particle axis under circumstances of a simple shear flow

We have investigated the influences of the magnetic field strength, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This dispersion is composed of ferromagnetic spheroidal particles with a magnetic moment normal to the particle axis. In the present analysis, these spheroidal particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the rodlike particle is significantly restricted in the field direction, so that the particle points to a direction normal to the flow direction (and also to the magnetic field direction). However, the present particle does not exhibit a strong directional characteristic, which is one of the typical properties for the previous particle with a magnetic moment parallel to the particle axis. That is, the particle can rotate around the axis of the magnetic moment, although the magnetic moment nearly points to the field direction. The viscosity significantly increases with the field strength, as in the previous particle model. The particle of a larger aspect ratio leads to the larger increase in the viscosity, since such elongated particles induce larger resistance in a flow field. The diffusion coefficient under circumstances of an applied magnetic field is in reasonable agreement between theoretical and experimental results.     

Preparation and sedimentation behavior in magnetic fields of magnetite-covered clay particles

This work is devoted to the preparation of magnetite-covered clay particles in aqueous medium. For this purpose, magnetite nanoparticles were synthesized by a coprecipitation method. These magnetic particles are adhered to sodium montmorillonite (NaMt) particles in aqueous suspensions of both materials, by appropriate control of the electrolyte concentrations. The best condition to produce such heteroaggregation corresponds to acid pH and approximately 1 mol/L ionic strength, when the electrokinetic potentials (zeta-potential) of both NaMt and Fe3O4 particles have high enough and opposite sign, as demonstrated from electrophoresis measurements. When a layer of magnetite re-covers the clay particles, the application of an external magnetic field induces a magnetic moment in clay-magnetite particles parallel to the external magnetic flux density. The sedimentation behavior of such magnetic particles is studied in the absence or presence of an external magnetic field in a vertical direction. The whole sedimentation behavior is also strongly affected by the formation of big flocculi in the suspensions under the action of internal colloidal interactions. van der Waals and dipole-dipole magnetic attractions between magnetite-covered clay particles dominate the flocculation processes. The different relative orientation of the clay-magnetite particles (edge-to-edge, face-to-edge, and face-to-face) are discussed in order to predict the most favored flocculi configuration.     

Sedimentation of concentrated monodisperse colloidal suspensions: role of collective particle interaction forces

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle-particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle-particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle-particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.     

Layer-by-layer electrostatic assembly with a control over orientation of molecules: anisotropy of electrical conductivity and dielectric properties

While forming layer-by-layer (LbL) electrostatic assembly of a magnetic organic molecule, namely, nickel phthalocyanine (NiPc), we apply a magnetic field. The field orients the magnetic moment of the molecules on a monolayer along the direction of magnetic field. Such an orientation of the molecules is then electrostatically immobilized with a monolayer of a polycation. By repeating the dipping cycle, we form LbL films with planar NiPc molecules facing a particular direction. With NiPc's moment perpendicular to the molecular plane, two types of LbL films were formed: (a) NiPc's molecular plane parallel to the substrate (moment is perpendicular) and (b) molecules perpendicular to the substrate and facing one particular direction, the direction of magnetic field. Such films, with the molecules lying either (a) parallel or (b) perpendicular to the substrate, provide unique systems to study anisotropy of optical, dielectric, and electrical characteristics in these planar organic molecules. The latter film responds to the polarization of incident beam in electronic absorption spectroscopy. Here we show methods to obtain an orientation of molecules in LbL films and study anisotropy of dielectric constant and conductivity of the molecules in ultrathin films.     

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.     

Two-dimensional crystallization of microspheres by a coplanar AC electric field

The particle-field and particle-particle interactions induced by alternating electric fields can be conveniently used for on-chip assembly of colloidal crystals. Two coplanar electrodes with a millimeter-sized gap between them are used here to assemble two-dimensional crystals from suspensions of either latex or silica microspheres. When an AC voltage is applied, the particles accumulate and crystallize on the surface between the electrodes. Light diffraction and microscopic observations demonstrate that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is turned off, and the process can be repeated many times. The diffraction patterns from all consecutively formed crystals are identical. This assembly is driven by forces that depend on the electric field gradient, and a model is proposed involving a combination of dielectrophoresis and induced dipole chaining. The organization of large two-dimensional crystals allows characterization of the electrostatic interactions in the particle ensembles. The process can be controlled via the field strength, the frequency, and the viscosity of the liquid media. It could be used to make rudimentary optical switches or to separate mixtures of particles of different sizes.     

Application of time-resolved fluorescence in the study of lipid aggregates II. Motions and order of pyrene probes in an aligned lyotropic nematic phase

Time-resolved polarized fluorescence spectroscopy has for the first time, been applied to the study of chromophores in a macroscopically aligned lyotropic nematic phase. The phase is composed of potassium dodecanoate, potassium chloride and water and contains long rod-like aggregates, that are aligned with their long axes parallel to an applied magnetic field. Pyrene, 1-pyrene dodecanoic acid, 1-dodecylpyrene and l-palmitoyl-2-(6-pyrenylhexanoyl)-sn-glycero-3-phosphoryl-choline are solubilized in these aggregates. The photophysics of these probes is a single exponential and typically between 130 and 200 ns in non-degassed samples. For all the probes the plane of the pyrene molecule tends to be oriented perpendicular to the symmetry axis (C_∞ axis) of the aggregate. The order parameters describing the orientation of the electronic transition dipole moment relative to this axis are typically c. -0.05. It is concluded that the translational and the local rotational motions of the probes are fast compared to the fluorescence lifetimes. The correlation times characterizing these motions are shorter than 20 ns. Finally, no slow motions such as fluctuations of the normal to the surface of the rod-like aggregate or a slow wobbling of the C_∞ -axis can be detected during c. 1 μmls.     

Strong magnetic field effects on solid-liquid and particle-particle interactions during the processing of a conducting liquid containing non-conducting particles

The behavior of micrometer-sized weak magnetic insulating particles migrating in a conductive liquid metal is of broad interest during strong magnetic field processing of materials. In the present paper, we develop a numerical method to investigate the solid-liquid and particle-particle interactions by using a computational fluid dynamics (CFDs) modeling. By applying a strong magnetic field, for example, 10 Tesla, the drag forces of a single spherical particle can be increased up to around 15% at a creeping flow limit. However, magnetic field effects are reduced when the Reynolds number becomes higher. For two identical particles migrating along their centerline in a conductive liquid, both the drag forces and the magnetic interaction will be influenced. Factors such as interparticle distance, Reynolds number and magnetic flux density are investigated. Shielding effects are found from the leading particle, which will subsequently induce a hydrodynamic interaction between two particles. Strong magnetic fields however do not appear to have a significant influence on the shielding effects. In addition, the magnetic interaction forces of magnetic dipole-dipole interaction and induced magneto-hydrodynamic interaction are considered. It can be found that the induced magneto-hydrodynamic interaction force highly depends on the flow field and magnetic flux density. Therefore, the interaction between insulating particles can be controlled by applying a strong magnetic field and modifying the flow field. The present research provides a better understanding of the magnetic field induced interaction during liquid metal processing, and a method of non-metallic particles manipulation for metal/ceramic based materials preparation may be proposed.