Three-dimensional Monte Carlo simulations of internal aggregate structures in a colloidal dispersion composed of rod-like particles with magnetic moment normal to the particle axis

We have treated a suspension composed of ferromagnetic rod-like particles with a magnetic moment normal to the particle axis in order to investigate aggregation phenomena of such a suspension by means of cluster-moving Monte Carlo simulations. In the present study, we have considered a three-dimensional mono-dispersed model system composed of such rod-like particles. Internal structures of self-assembled clusters have been discussed quantitatively in terms of radial distribution, pair correlation, orientational pair correlation functions, number distributions of clusters, and order functions. The main results obtained here are summarized as follows. Rod-like particles tend to aggregate to form raft-like clusters along the magnetic moment direction more significantly with magnetic particle-particle interactions. In such raft-like clusters, the direction of each particle axis has a tendency to incline in parallel formation, but is not so parallel as in a two-dimensional dispersion. As the volumetric fraction increases, longer raft-like clusters are formed, but such raft-like clusters do not aggregate further to form thicker clusters, which is in significantly contrast with a dispersion of spherical particles, where thicker chain-like clusters are observed under certain conditions. For the case of strong magnetic particle-particle interactions, sufficiently long raft-like clusters are formed along the magnetic field direction, even if the influence of an external magnetic field is of the same order of that of the thermal energy. However, rod-like particles in such clusters do not necessarily incline in significantly parallel formation along a certain direction. Self-assembled tube-like clusters are formed when magnetic particle-particle interactions are much more dominant than the rotational Brownian motion under circumstances of rod-like particles inclining in a certain 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.     

Visual microscopic studies on hetero-aggregation and selective aggregation

 An optical video microscopic technique was used to study hetero-aggregation and selective aggregation phenomena among n-hexadecane oil drops (40–110 μm in diameter) and two types of polystyrene latex particles (6.76 and 30.2 μm, in diameter), suspended inside an aqueous medium with pH varying between 1.1 and 12.9. A single drop was produced in situ using a micropipette inside the aqueous phase-filled glass microcapillary (100–160 μm i.d.) containing the particles. Interactions between the drop and the solid particles and among the solid particles was achieved by movement of the aqueous medium in and out of a second micropipette. Drop–particle interactions were distinctly different from particle–particle interactions. It was observed that the latex particles aggregated irreversibly with the oil drop in all cases except two, viz. for 6.76 μm particles at around neutral pH whereas the irreversibility of aggregation in particle–particle interactions was only seen at the ends of the pH spectrum. At around neutral pH, the flocs or clusters of small particles were very weak. Visual observations at each pH are explained on the basis of the classical DLVO (Derjaguin–Landau–Verwey–Overbeek) theory. Partial wetting of particles surfaces by oil appears to be a key factor in the irreversibility of drop– particle hetero-aggregation. Results indicate that the display of reversible, irreversible or weak aggregation depends on the location and depth of the secondary minimum and that the long-range, attractive, London–van der Waals force is responsible for the initial formation of an aggregate. Received: 4 July 1996 Accepted: 5 December 1996     

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 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.     

Preparation of disk-like cellulose particles

Disk-like cellulose particles were facilely prepared by stirring a dispersion of spongy cellulose particles that were prepared with a solvent-releasing method (SRM) with a magnetic stir bar. The obtained particles were thick and disk-like and retained their spongy structure in the wet state. The thick, disk-like particles became thinner in a specific direction upon drying because of capillary force. In contrast, when the same procedure was conducted using cellulose particles with dense structures, the particle shapes were not deformed, and disk-like shapes did not appear. Moreover, when the stirring was carried out using a shaking bath or a touch mixer, the shape transformation was not observed. These results suggest that the spongy structure of the cellulose particles would be a pseudo-plasticization state, which can cause the cellulose particles to deform. The disk-like particles formed as a result of the grinding of spongy cellulose particles between the stir bar and the vial. The number of disk-like particles and the degree of deformation increased with increasing of the stirring time, the speed and the contact area.     

Rheological properties and particle behaviors of a non-dilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow (analysis by means of mean-field approximation)

We have investigated the rheological properties and the orientational distributions of particles of a non-dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The mean-field approximation is applied to take into account the interactions between spherocylinder particles. The basic equation of the orientational distribution function has been derived from the balance of the torques (including the term due to the mean field approximation) acting on the particle in an applied magnetic field; this is an integrodifferential equation. Then, the governing equation has been solved by means of the method of successive approximation and Galerkin's method. The results obtained here are summarized as follows. For the case of strong magnetic interactions between particles, the particle exhibits a sharp peak of the orientational distribution even for a weak applied magnetic field. In this case, the mean magnetic moment of the particle becomes large, which leads to strong interactions between the applied magnetic field and the particle. Thus, the particle tends to point to the magnetic filed direction under these situations. Also, in this case, a large increase in viscosity is obtained due to such a restriction concerning the particle orientation.     

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.     

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.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

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 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.     

Alkoxy-derived multiscale porous TiO<Subscript>2</Subscript> gels probed by ultra-small-angle X-ray scattering and small-angle X-ray scattering

Titania (TiO₂) monoliths with well-defined bicontinuous macropores and gel skeletons were prepared through the alkoxy-derived sol–gel process accompanied by spinodal decomposition, and the structural evolution during evaporation drying and heat treatment was probed by a combination of ultra-small-angle X-ray scattering and small-angle X-ray scattering. X-ray scattering profiles of wet and dried gels revealed that microporous structures related to the existence of primary particles are present in the gel skeletons at the wet stage and are preserved during drying. Additionally, it is found that the primary particles swollen in the wet condition are dried to compact aggregates to produce the smooth surface of gel skeletons. Upon heating at 400 °C, the particle–particle correlation associated with regularity of mesostructures is enhanced. From nitrogen adsorption–desorption measurements, the average pore size is less than 1 nm in the dried gel and increases to 3.1 nm by the heat treatment. Homogeneous growth of primary particles due to interparticle-polycondensation reaction is responsible for the increased size and uniform distribution of mesopores in the heat-treated gel.     

A bidimensional simulation of particle-cluster aggregation with variable active sites particles

 In this work a simple program has been developed which simulates the process of particle– cluster aggregation limited by diffusion. All the simulation have been carried out using 2d square lattices with square “particles” having a variable number of active inter-action sites (from 3 to 8) for each particle in order to analyze the effect of such limitation on the fractal dimension of the aggregates. The fractal dimension of such aggregates was calculated by the so-called “box counting” method. It has been shown that there is no change in the value of the fractal dimension (1.70) as the active site number is increased. Instead it appears that there is an average number of active sites of about 2.3 for all the structures no matter how many active interaction sites the particles have. This appears as an interesting result in connection with the aggregation of particles such as renneted casein micelles, which could present differences in the surface density of active sites. Received: 11 February 1997 Accepted: 8 January 1998     

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.     

Enhancement of corrosion resistance of electrocodeposited Ni–SiC composites by magnetic field

The corrosion behavior and surface morphology of Ni–SiC composite coatings produced by electrodeposition with the aid of magnetic field were studied. The results of the electrochemical analysis including polarization resistance and potentiodynamic polarization curves showed that a magnetic field of 0.1 T could significantly improve the corrosion resistance of the composite. The electrochemical impedance spectra revealed that a passive layer was formed on the surface of the Ni–SiC coating with the magnetic field. The microstructures of electrodeposited Ni–SiC composite coatings were also examined. More SiC particles were found to be incorporated into the coating with the presence of magnetic field, which was considered to be one of the reasons for the enhancement of corrosion resistance as SiC particles were reported to be corrosion inhibitors. Contribution to special issue “Magnetic field effects in Electrochemistry”     

Validation of a hybrid MD-SCF coarse-grained model for DPPC in non-lamellar phases

In the framework of a recently developed scheme for a hybrid particle-field simulation technique where self-consistent field theory and molecular dynamics simulation method are combined, specific coarse-grained models for aqueous solutions of phospholipids have been validated. In particular, the transferability of the model in the correct reproduction of non-lamellar phases has been validated against reference particle–particle simulations. By varying the water content, the proposed model is able to correctly describe the different morphologies that are experimentally observed such as micelles and reverse micelles. The lower computational costs of the hybrid techniques allow us to perform simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.     

On forced oscillations of microdroplet aggregates in magnetic fluids

Changes in the shape of microdroplet aggregates exposed to an alternating magnetic field with frequency f from 0.01 to 400 Hz are experimentally studied. Microdroplet aggregates are spherical droplets of a highly concentrated magnetic fluid with a radius from one to several tens of microns dispersed in a liquid with a low concentration of magnetic particles. At f < 20 Hz, large-and small-amplitude forced oscillations of aggregates are observed. Small-amplitude oscillations are practically sinusoidal. Large-amplitude oscillations are of a periodical nonsinusoidal type with higher harmonics and subharmonics in the spectrum. A change in the character of forced oscillations with increasing strength of an external magnetic field is of the threshold type and occurs at the moment when the external field strength reaches a critical value, at which a microdroplet aggregate is elongated in a jumpwise manner and acquires a needle-like shape. The recovery of the spherical shape of a microdroplet aggregate after a sharp switching-off of the external magnetic field follows an aperiodic dependence. Original Russian Text ? V.I. Drozdova, V.V. Kushnarev, G.V. Shagrova, 2006, published in Kolloidnyi Zhurnal, 2006, Vol. 68, No. 2, pp. 166–171.     

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.