Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids

A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a virial expansion with accuracy to the terms quadratic in particle concentration. The virial expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentration and magnetic fields in the devices (for example, magnetic fluid seals and acceleration sensors), which use a concentrated magnetic fluid as a working fluid. The Monte-Carlo methods and the analytical approach are employed to study the magnetic fluid stratification generated by the gravitational field in a cylinder of finite height. The coefficient of concentration stratification of the magnetic fluid is calculated in relation to the average concentration of particles and the dipolar coupling constant. It is shown that the effective particle attraction causes a many-fold increase in the concentration inhomogeneity of the fluid if the average volume fraction of particles does not exceed 30%. At high volume concentrations steric interactions play a crucial role.     

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.     

Theoretical Study of the Effects of Templated Materials on Aggregate Formation

Summary: We have conducted Monte Carlo simulations to investigate a greatly simplified model for a blend composed of templated materials (polymers or monomers), smaller reacting particles and solvents on a two‐dimensional lattice. In the simulations, we compute the mean chain conformation of flexible templated polymers, and the distribution of the number of adjacent reacting particles aligned along the same axis to rationalize how templated materials affect the physical aggregation of smaller particles in a blend. We first examine the effects of the effective interactions between templated materials and smaller reacting particles. For repulsive interactions, flexible templated polymers tend to contract to reduce repulsions arising from smaller reacting particles, but for attractive interactions, mean chain dimension increases to maximize attraction. When templated material composition is increased, the conformational deformation of templated polymers becomes more pronounced. Moreover, in the presence of attractive interactions, reacting particles are more dispersed in the blend. In contrast, repulsive interactions increase the probability of aggregation of reacting particles. Also, our findings show that templated monomers (without chain connectivity) interact with reacting particles more effectively than with templated polymers due to the greater interacting area per monomer, which enhances the dispersion and segregation of reacting particles in the blend due to the attractive and repulsive interaction, respectively. In addition, as templated material composition is increased, the probability of forming a larger aggregate decreases. This simple model allows us to elucidate the role of templated materials on the physical aggregation of smaller particles in a blend.

Probability distribution P(m) of finding m adjacent reacting particles along the same axis in the presence of templated polymers (open symbols) and templated monomers (solid symbols) for different monomer‐reacting particle ratio, 1:3 (□/▪), 1:1 (○/•) and 3:1 (▵/▴):.     

Structure and stability of silica particle monolayers at horizontal and vertical octane-water interfaces

Monolayers of silica particles at horizontal and vertical octane-water interfaces have been studied by microscopy. It is found that their structure and stability depend strongly on the particle hydrophobicity. Very hydrophobic silica particles, with a contact angle of 152 degrees measured through the water, give well-ordered monolayers at interparticle distances larger than 5 particle diameters which are stable toward aggregation and sedimentation. In contrast, monolayers of less-hydrophobic particles are disordered and unstable. Two-dimensional particle sedimentation has been observed in the case of vertical monolayers. The results have been analyzed with a simple two-particle model considering the sedimentation equilibrium as a balance between the long-range electrostatic repulsion through the oil, the gravity force, and the capillary attraction due to deformation of the fluid interface around particles. The value of the charge density at the particle-octane interface, 14.1 muC/m(2), found for the most hydrophobic particles is reasonable. It drastically decreases for particles with lower hydrophobicity, which is consistent with the order-disorder transition in monolayer structure reported by us before. The pair interactions between particles at a horizontal octane-water interface have been analyzed including the capillary attraction due to undulated three-phase contact line caused by nonuniform wetting (the contact angle hysteresis). The results are in agreement with the great stability of very hydrophobic silica particle monolayers detected experimentally, even at low pH at the point of zero charge of the particle-water interface, and with the aggregated structure of hydrophilic particle monolayers.     

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.     

Aggregation Stability of Aqueous Dispersions of Microcrystalline Cellulose: pH Dependence

The aggregation stability of aqueous dispersions of microcrystalline cellulose (MCC) was studied by the flow ultramicroscopy in a wide range of pH (1–11). The calculations of the molecular and ion-electrostatic components of the interparticle interaction energy, which were performed according to the DLVO theory with and without allowance for the particle conductivity, demonstrated that, in most cases, the loss of the aggregation stability can not be explained without taking into account the concept of additional attraction forces between the MCC particles. It was assumed that such forces could be attributed to the dipole–dipole interactions or hydrogen bonding between hydrated particles.     

Forming chainlike filaments of magnetic colloids: the role of the relative strength of isotropic and anisotropic particle interactions

The influence of the interplay between anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of aqueous suspensions of electric double layered magnetic particles was studied. Therefore, the particles were aggregated under the action of an external magnetic field and in the presence of different amounts of an indifferent 1:1 electrolyte. After removing the field, linear aggregates remained in the sample. Static light scattering and electron micrographs confirmed the chainlike cluster morphology. Dynamic light scattering was used for monitoring the average diffusion coefficient of these magnetic filaments. A theoretical model that allows the experimental mean diffusion coefficient to be related to the average chain length was successfully employed. The results show that, at fixed exposure time and field strength, the average filament size is proportional to the amount of electrolyte added. The light scattering data and transmission electron microscopy micrographs prove that permanent chains coexist with a relatively large fraction of individual particles when no or little electrolyte was added to the samples. A plausible explanation for this "selective aggregation" phenomenon could be given in terms of surface charge heterogeneities. The chain growth was found to follow a power law with a similar exponent for all the electrolyte concentrations studied. Scaling theories were employed for estimating the ratio of particles taking part in the aggregation process.     

Aggregation of paramagnetic particles in the presence of a hydrodynamic shear

We present an experimental study of the aggregation of paramagnetic particles, in the presence of controlled laminar shear flow, conducted in microchannels subjected to an external magnetic field. The microfluidic channels are made of either glass/silicon or polydimethylsiloxane. In ranges of time up to hundreds of seconds, the growth mechanism of the linear chain consists of the accumulation of isolated particles or small clusters onto existing chains, which are all moving at different speeds. In this time regime the chain length increases linearly and has a growth rate that increases as a power law with the shear. At longer times the chain lengths saturate. The Smoluchovski model, which assumes single particle-chain interactions only, closely reproduces the observations both qualitatively and quantitatively. In particular, the evolution of the growth rate of the mean chain length with respect to the shear rate S, predicted as S1/4, is found to be consistent with the experiments.     

Effect of temperature on the reentrant condensation in polyelectrolyte-liposome complexation

Interactions of oppositely charged macroions in aqueous solution give rise to intriguing aggregation phenomena, resulting in finite-size, long-lived clusters, characterized by a quite narrow size distribution. Particularly, the adsorption of highly charged linear polyelectrolytes on oppositely charged colloidal particles is strongly correlated and some short-range order arises from competing electrostatic interactions between like-charged polymer chains (repulsion) and between polymer chains and particle surface (attraction). In these systems, in an interval of concentrations around the isoelectric point, relatively large clusters of polyelectrolyte-decorated particles form. However, the mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well-defined size of the aggregates are not completely understood. Nor is clear the role that the correlated polyion adsorption plays in the aggregation, although the importance of "patchy interactions" has been stressed as the possible source of attractive interaction term between colloidal particles. Different models have been proposed to explain the formation of the observed cluster phase. However, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregates. To elucidate this point, in this work, we have investigated the effect of the temperature on the cluster formation. We employed liposomes built up by DOTAP lipids interacting with a simple anionic polyion, polyacrylate sodium salt, over an extended concentration range below and above the isoelectric condition. Our results show that the aggregation process can be described by a thermally activated mechanism.     

Selective recovery of micrometer particles from mixtures using a combination of selective aggregation and dissolved-air flotation

Particle–particle separation in biotechnology has gained interest over the years due to the large number of processes that yield particle mixtures. Direct isolation of the product-containing particles is a logical and efficient downstream processing route in these processes. Dissolved-air flotation is applicable for these separations when the particles that require separation have different interactions with the air bubbles and/or differ in aggregation behaviour.

In this work, model particles consisting of micrometer-sized protein-coated polystyrene particles were used to investigate the requirements for the application of dissolved-air flotation for particle–particle separation in biotechnology. These model particles have heterogeneous surfaces with surface groups (brushes) that extend out into the solution. Therefore, steric (or brush) repulsion and so-called hydrophobic interactions between the particles need to be taken into account. The flotation behaviour of the protein-coated particles was related to the size of the aggregates and the foaming behaviour of the proteins. Prediction of their aggregation behaviour was performed on the basis of calculations of the Van der Waals, electrostatic, hydrophobic and brush interactions. The brush interaction force proves to be essential for the prediction of the aggregation behaviour of the particles.     

Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Aggregation phenomena in the suspension polymerization of VCM

In the suspension polymerization of VCM, insoluble polymer particles are formed inside the monomer droplets. The growth and aggregation of these particles are responsible for important polymer properties, such as porosity. It is well established that the most characteristic polymer particles, the primary particles, are of a narrow distribution with a size (diameter) ranging from 0.10–0.20 m. This work studied the formation of primary particles based on the aggregation phenomena that take place inside a monomer droplet. This was done by formulating a population balance equation, which was based on the following considerations: a) polymerization occurs in both the monomer and the polymer phases; b) there is continuous formation of the basic particles in the monomer phase; c) the growth of the polymer particles occurs as a result of both polymerization in the polymer phase and aggregation of the particles; d) the colloidal properties of the particles that are responsible for the aggregation phenomena were considered to be the net result of attraction and repulsion energies.It was shown that for particles carrying a constant charge it was not possible to predict the formation of primary particles of size 0.10–0.20 m. The particle size distribution had a mode diameter equal to the diameter of the basic particles. Consequently, the particle charge was allowed to vary in a way proportional to the particle radius raised to a power coefficient. For values of the coefficient greater than zero, i. e., when the particle charge increased during polymerization, the aggregation of the basic particles was efficient enough to result in the formation of large primary particles.     

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.     

Study of the magnetorheological response of aqueous magnetite suspensions stabilized by acrylic acid polymers

In this paper we describe the magnetorheological (MR) behavior of aqueous suspensions consisting of magnetite particles stabilized by poly(acrylic acid) polymers (PAA). A previous work on the colloidal stability of the same systems for different pH values and polymer concentrations demonstrated that the addition of PAA polymers has a very significant effect on the stability. In the present contribution, we study the MR effect of the suspensions stabilized by two different commercial polymers, as a function of pH, magnetic field strength and magnetite volume fraction. All the results are discussed in terms of the interfacial properties of the systems. It is demonstrated that for a given concentration of micrometer particles, the rheological response strongly depends on pH, on the volume fraction of magnetite particles, on the type of polymer added for increasing the stability and on the magnetic field strength. Changing the polymer used provokes clear rheological differences for the same sample conditions (field strength, volume fraction and pH). This is suggested to be due to the hydrophobic/hydrophilic balance of the polymer affecting the magnetic field ability to form magnetic structures by aggregation of the magnetized particles. The results are compared to the predictions of the so-called standard chain model, based on the assumption that the MR effect is the result of the balance between the magnetic interactions (tending to establish some degree of order in the suspension by formation of particle chains in the direction of the field) and hydrodynamic ones (tending to destroy the formed structures by viscous stress on the chains). It is found that the behavior of the yield stress does not agree well with the predictions of the model when the relative proportion of both particle and polymer confers optimum stability to the dispersions. This is likely due to the fact that the presence of the stabilizing polyelectrolyte provokes that the magnetic field is not as effective in structuring the suspension as deduced from the chain model.     

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.     

Aggregation of nanosized colloidal silica in the presence of various alkali cations investigated by the electrospray technique

The slow aggregation process of a concentrated silica dispersion (Bindzil 40/220) in the presence of alkali chlorides (LiCl, NaCl, KCl, RbCl, and CsCl) was investigated by means of mobility measurements. At intervals during the aggregation, particles and aggregates were transferred from the liquid phase to the gas phase via electrospray (ES) and subsequently size selected and counted using a scanning mobility particle sizer (SMPS). This method enables the acquisition of particle and aggregate size distributions with a time resolution of minutes. To our knowledge, this is the first time that the method has been applied to study the process of colloidal aggregation. The obtained results indicate that, independent of the type of counterion, a sufficient dilution of the formed gel will cause the particles to redisperse. Hence, the silica particles are, at least initially, reversibly aggregated. The reversibility of the aggregation indicates additional non-DLVO repulsive steric interactions that are likely due to the presence of a gel layer at the surface. The size of the disintegrating aggregates was monitored as a function of the time after dilution. It was found that the most stable aggregates were formed by the ions that adsorb most strongly on the particle surface. This attractive effect was ascribed to an ion-ion correlation interaction.     

Microstructure and depletion forces in polymer-colloid mixtures from an interfacial statistical associating fluid theory

By using a classical density functional theory (interfacial statistical associating fluid theory), we investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. The theory is tested under a wide range of conditions and performs very well in comparison to simulation data. A comprehensive study is conducted characterizing the role of polymer concentration, particle/polymer-segment size ratio, and polymer chain length on the structure, polymer induced depletion forces, and the colloid-colloid osmotic second virial coefficient. The theory correctly captures a depletion layer on two different length scales, one on the order of the segment diameter (semidilute regime) and the other on the order of the polymer radius of gyration (dilute regime). The particle/polymer-segment size ratio is demonstrated to play a significant role on the polymer structure near the particle surface at low polymer concentrations, but this effect diminishes at higher polymer concentrations. Results for the polymer-mediated mean force between colloidal particles show that increasing the concentration of the polymer solution encourages particle-particle attraction, while decreasing the range of depletion attraction. At intermediate to high concentrations, depletion attraction can be coupled to a midrange repulsion, especially for colloids in solutions of short chains. Colloid-colloid second virial coefficient calculations indicate that the net repulsion between colloids at low polymer densities gives way to net attraction at higher densities, in agreement with available simulation data. Furthermore, the results indicate a higher tendency toward colloidal aggregation for larger colloids in solutions of longer chains.     

Adsorption in Mixtures with Competing Interactions

A binary mixture of oppositely charged particles with additional short-range attraction between like particles and short-range repulsion between different ones in the neighborhood of a substrate preferentially adsorbing the first component is studied by molecular dynamics simulations. The studied thermodynamic states correspond to an approach to the gas–crystal coexistence. Dependence of the near-surface structure, adsorption and selective adsorption on the strength of the wall–particle interactions and the gas density is determined. We find that alternating layers or bilayers of particles of the two components are formed, but the number of the adsorbed layers, their orientation and the ordered patterns formed inside these layers could be quite different for different substrates and gas density. Different structures are associated with different numbers of adsorbed layers, and for strong attraction the thickness of the adsorbed film can be as large as seven particle diameters. In all cases, similar amount of particles of the two components is adsorbed, because of the long-range attraction between different particles.     

Effect of electric-field-induced capillary attraction on the motion of particles at an oil-water interface

Here, we investigate experimentally and theoretically the motion of spherical glass particles of radii 240-310 microm attached to a tetradecane-water interface. Pairs of particles, which are moving toward each other under the action of lateral capillary force, are observed by optical microscopy. The purpose is to check whether the particle electric charges influence the particle motion, and whether an electric-field-induced capillary attraction could be detected. The particles have been hydrophobized by using two different procedures, which allow one to prepare charged and uncharged particles. To quantify the hydrodynamic viscous effects, we developed a semiempirical quantitative approach, whose validity was verified by control experiments with uncharged particles. An appropriate trajectory function was defined, which should increase linearly with time if the particle motion is driven solely by the gravity-induced capillary force. The analysis of the experimental results evidences for the existence of an additional attraction between two like-charged particles at the oil-water interface. This attraction exceeds the direct electrostatic repulsion between the two particles and leads to a noticeable acceleration of their motion.     

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.