On the Theory of the Dynamic Properties of Dense Magnetic Fluids: Polydisperse Media

The theoretical model was proposed for determining functions of the dynamic response of moderately concentrated ferrofluids on the external magnetic field and their rheological properties. Ferrofluids are considered to be polydisperse colloidal systems with the interacting (albeit individual) particles. The model is based on the regular approximation of virial expansion in powers of the particle concentration and on the well-known effective field method. The effect of system polydispersity and the magnetodipole and hydrodynamic interactions between particles on the macroscopic and dynamic properties of ferrofluids was estimated. Calculations demonstrated that the interparticle interaction results in an increase in the dynamic functions of uniform ferrocolloids up to several tens of percents.     

Low-temperature susceptibility of concentrated magnetic fluids

The initial susceptibility of concentrated magnetic fluids (ferrocolloids) has been experimentally investigated at low temperatures. The results obtained indicate that the interparticle dipole-dipole interactions can increase the susceptibility by several times as compared to the Langevin value. It is shown that good agreement between recent theoretical models and experimental observations can be achieved by introducing a correction for coefficients in the series expansion of susceptibility in powers of density and aggregation parameter. A modified equation for equilibrium susceptibility is offered to sum over corrections made by Kalikmanov (Statistical Physics of Fluids, Springer-Verlag, Berlin, 2001) and by B. Huke and M. Lucke (Phys. Rev. E 67, 051403, 2003). The equation gives good quantitative agreement with the experimental data in the wide range of temperature and magnetic particles concentration. It has been found that in some cases the magnetic fluid solidification occurs at temperature several tens of kelvins higher than the crystallization temperature of the carrier liquid. The solidification temperature of magnetic fluids is independent of particle concentration (i.e., magneto-dipole interparticle interactions) and dependent on the surfactant type and carrier liquid. This finding allows us to suggest that molecular interactions and generation of some large-scale structure from colloidal particles in magnetic fluids are responsible for magnetic fluid solidification. If the magnetic fluid contains the particles with the Brownian relaxation mechanism of the magnetic moment, the solidification manifests itself as the peak on the "susceptibility-temperature" curve. This fact proves the dynamic nature of the observed peak: it arises from blocking the Brownian mechanism of the magnetization relaxation.     

Dynamics of self-assembled chaining in magnetorheological fluids

The aggregation dynamics of paramagnetic spherical particles embedded in a viscous fluid is investigated via numerical simulations using a fully coupled three-dimensional model. Particles experience simultaneously Brownian motion, dipolar magnetic attraction, and multibody hydrodynamic interactions. When the dipole strength characterizing the ratio of magnetic attraction to random diffusion exceeds a critical value, particles join together forming supraparticle structures. As time evolves, particle/chain and chain/ chain interactions lead to a continuous increase of the cluster size. The mean length of particle chains has a power-law dependence with respect to time, as predicted by the theory of diffusion-limited aggregation. Both the exponent and the characteristic time scale agree very well with the experimental results of Promislow et al.     

Free volumes and the anomalous self-diffusivity of attractive colloids

Free volume theories for the dynamics of dense fluids commonly assume (i) that diffusivity increases with average free volume per particle and (ii) that the size distribution of free volumes can be approximated by that of an equivalent hard-sphere reference system. We use molecular simulations to demonstrate that these assumptions break down when one considers concentrated suspensions of particles with short-range attractions. In these systems, self-diffusivity shows nonmonotonic dependencies on both average free volume and the strength of the interparticle attraction. Moreover, when interparticle attractions are strong, the shape of the free volume distribution is qualitatively different than that of the corresponding hard-sphere reference fluid. We propose a conceptual revision to the traditional free volume perspective that takes into account both the size distribution and the persistence time of the free volumes, and we demonstrate that it can qualitatively capture the disparate behaviors of a model fluid with short-range attractions and its hard-sphere reference fluid.     

Magnetic susceptibility of concentrated ferrocolloids

The initial susceptibility of ferrocolloids (magnetic fluids) is studied within wide ranges of temperature and concentration. Experimental results are compared with the predictions of current theoretical models. A modified formula is proposed for an equilibrium ferrocolloid susceptibility, which allowed us to obtain quantitative agreement with the experimental data. It is shown that magnetodipole interparticle interactions lead to a manyfold increase in the susceptibility; however, no evidence of the spontaneous transition of ferrocolloids to the magnetoordered state are disclosed. For ferrocolloids with a dispersion medium having a low melting point, the loss of fluidity and transition to the solidified state at temperatures above the melting point are revealed. The independence of the solidification temperature on the magnetic phase concentration and strong temperature dependence on the type of stabilizer make it possible to suggest that the transition is associated with molecular interactions. The solidification of a magnetic fluid is accompanied by the appearance of a peak on the temperature dependence of susceptibility in all cases when large particles are present in a colloidal solution, and the relaxation of particle magnetic moment is due to thermal motion of the particles.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 2, 2005, pp. 218–230.Original Russian Text Copyright © 2005 by Pshenichnikov, Lebedev.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

Interactions between Silica Colloids with Magnetite Cores: Diffusion, Sedimentation and Light Scattering

The magnetic and Van der Waals attraction between uncharged silica spheres with a magnetic core has been studied using sedimentation and static and dynamic light scattering techniques. Specifically the effect of the interactions on the concentration dependence of the sedimentation velocity, diffusion, and the apparent radius of gyration was investigated. It was found experimentally that the concentration dependence is decreased significantly as a result of the Van der Waals and magnetic attractions and even may change sign in comparison to the hard-sphere case. Calculations of the (linear) concentration dependence for weak interactions predict this decrease and also indicate that for the silica-magnetite particles the second virial coefficient passes a maximum with increasing silica layer thickness. Copyright 1999 Academic Press.     

Correlation of viscoelastic properties of stable and flocculated suspensions with their interparticle interactions

This review starts with a general introduction on the properties of concentrated suspensions. The distinction between “dilute”, “solid” and “concentrated” suspensions is given in terms of the balance between Brownian, hydrodynamic and interparticle interactions. A section is given on interparticle interactions and their combinations. The four different types of interactions, namely hard-sphere, electrostatic, steric and van der Waals are described. The flocculation of both electrostatically and sterically stabilized suspensions is also discussed. The next section covers the principles of rheological measurements. Transient (static), dynamic (oscillatory), shear wave propagation and steady state measurements are described. The last part of the review deals with the viscoelastic properties of concentrated suspensions. Four different systems were described and examples were given: (a) Suspensions with hard-sphere interactions; (b) Stable systems with soft (electrostatic) interaction; (c) Sterically stabilised systems; (d) Flocculated and coagulated systems. Both weakly and strongly flocculated systems were discussed.In the above review, particular emphasis was given to the relationship between the viscoelastic properties of concentrated suspensions and their interparticle interactions. As far as was possible, the results obtained from rheological measurements were quantitatively analysed in terms of such interparticle forces. The review demonstrated that such correlation is generally followed and this illustrated the powerful use of rheology for studying interparticle interactions.     

Small-angle neutron scattering study of concentrated colloidal dispersions: the interparticle interactions between sterically stabilized particles

Small-angle neutron scattering (SANS) was used to investigate the interparticle interactions in concentrated dispersions of colloidal silica stabilized either by steric or by electrostatic repulsive interactions. In 10 mM NaCl, an adsorbed PEO layer is required to prevent flocculation, and particles are stabilized by steric repulsions. The adsorbed layer was made invisible to neutrons by contrast matching with the aqueous continuous phase. Dispersions of the same particles at the same concentrations but in the absence of added salt and adsorbed PEO were also studied. In both cases, the SANS spectra of concentrated dispersions show a peak at low Q, which is due to interparticle interactions: a structure factor. The SANS data can be described rather well by a homogeneous spherical form factor and a structure factor based on the Hayter-Penfold/Yukawa potential model. The steric potential was compared to the electrostatic potential obtained by fitting the SANS data of the bare silica dispersions. The steric potential shows a greater dependence on the particle volume fraction, which we ascribe to the penetration and compression of the adsorbed PEO layer as the particles approach.     

Thermodiffusion of interacting colloids. II. A microscopic approach

A microscopic approach is presented to describe the contribution to the thermal diffusion coefficient of colloids due to intercolloidal particle interactions. An exact expression for the leading-order virial coefficient of the thermal diffusion coefficient of interacting colloidal spheres is derived in terms of the intercolloidal pair-interaction potential and hydrodynamic interaction functions. This general expression is explicitly evaluated for hard-core interactions and for spheres with a short-ranged attractive potential. The derivation is based on a Smoluchowski equation that is generalized to include temperature gradients. For short-ranged attractive potentials, a negative Soret coefficient is predicted under certain conditions, when the depth of the attraction increases with increasing temperature.     

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.     

Diffusing wave spectroscopy study of the colloidal interactions occurring between casein micelles and emulsion droplets: comparison to hard-sphere behavior

Understanding the underlying processes that govern interparticle interactions in colloidal systems is fundamental to predicting changes in their bulk properties. In this paper we discuss the colloidal behavior of casein micelles and protein-stabilized fat globules individually and in a mixture. The colloidal interactions were observed by transmission diffusing wave spectroscopy. The turbidity parameter, l*, and the diffusion coefficients of the samples studied were measured experimentally and compared to the theoretically calculated parameters for a hard-sphere system. The light scattering properties of casein micelles (volume fraction phi = 0.1-0.2) dispersed in milk permeate showed no deviation from the theoretically predicted model. Whey protein isolate (WPI)-stabilized emulsions (phi = 0.025-0.1) prepared either in milk permeate or in 5 mM imidazole buffer at pH 6.8 showed a behavior identical to that of the hard-sphere model. Similarly to the WPI-stabilized fat globules, the sodium caseinate (NaCas)-stabilized emulsions (phi = 0.025-0.1) prepared in milk permeate also showed resemblance to the theory. In contrast, NaCas-stabilized emulsions prepared in 5 mM imidazole buffer exhibited some discrepancy from the theoretically calculated parameters. The deviation from theory is attributed to the enhanced steric stabilization properties of these droplets in a low ionic strength environment. When recombined milks made from concentrated milk and WPI- and NaCas-stabilized droplets prepared in permeate (phi = 0.125-0.2) were studied, the experimental data showed a significant deviation from the theoretical behavior of a hard-sphere model due to mixing of two different species.     

Mesoscale constitutive modeling of magnetic dispersions

A constitutive model for dispersions of acicular magnetic particles has been developed by modeling the particles as rigid dumbbells dispersed in a solvent. The effects of Brownian motion, anisotropic hydrodynamic drag, a steric force in the form of the Maier-Saupe potential, and, most importantly, a mean-field magnetic potential are included in the model. The development is similar to previous models for liquid-crystalline polymers. The model predicts multiple orientational states for the dispersion, and this phase behavior is described in terms of an orientational order parameter S and an average alignment parameter J; the latter is introduced because the magnetic particles have distinguishable direction due to polarity. A transition from isotropic to nematic phases at equilibrium is predicted. Multiple nematic phases-both prolate and oblate-are predicted in the presence of steady shear flow and external magnetic field parallel to the flow. The effect of increasing magnetic interparticle interactions and particle concentration is also presented. Comparisons with experimental data for the steady shear viscosity show very good agreement.     

Anisotropic colloidal particles in critical fluids

We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluid mixture. The orientation-dependent long-ranged universal interactions mediated by the critical solvent between a particle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to the correlation length and interparticle distances. Exact results are obtained using a "small particle operator expansion." The amplitudes of the isotropic and anisotropic operators in the expansion depend on the size and aspect ratio of the dumbbell or lens and are determined by density profiles in the Ising model at the critical point in a wedge geometry with symmetry-breaking fixed-spin boundary conditions. Dumbbells and ellipsoids with a symmetry preserving surface are also considered.     

Stabilization of magnetorheological suspensions by polyacrylic acid polymers

This work is devoted to the synthesis and stabilization of magnetorheological suspensions constituted by monodisperse micrometer-sized magnetite spheres in aqueous media. The electrical double-layer characteristics of the solid/liquid interface were studied in the absence and presence of adsorbed layers of high molecular weight polyacrylic acids (PAA; Carbopol). Since the Carbopol-covered particles can be thought of as "soft" colloids, Ohshima's theory was used to gain information of the surface potential and the charge density of the polymer layer. The effect of the pH of the solution on the double-layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The stability of the suspensions was experimentally studied for different pH and polymer concentrations, and in the absence or presence of a weak magnetic field applied. The stability of the suspensions was explained using the classical DLVO theory of colloidal stability extended to account for hydration, steric, and magnetic interactions between particles. Diagrams of potential energy vs interparticle distance show the predominant effect of steric, hydrophilic/hydrophobic, and magnetic interactions on the whole stability of the system. The best conditions to obtain stable suspensions were found when strong steric and hydrophilic repulsions hinder the coagulation between polymer-covered particles, simultaneously avoiding sedimentation by the thickening effect of the polymer solution. When a not too high molecular weight PAA was employed in a low concentration, the task of a long-time antisettling effect compatible with the desired magnetic response of the fluid was achieved.     

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.     

Hard structured particles: suspension synthesis, characterization, and compressibility

Hard interactions are developed on three grades of fumed silica by eliminating interparticle forces and sterically stabilizing the particles by attaching an organic coating to the surface of the particles, suspending them in an index-matching solvent and screening the electrostatics. These hard-structured particles are studied to understand the effects of the particle's microstructure on suspension properties without the influence of interparticle forces other than volume exclusion, Brownian, and hydrodynamic interactions. Light and X-ray scattering studies of low-volume-fraction suspensions suggest that the fumed silicas consist of primary particle of radius of gyration R(g1) approximately equals 16 nm and aggregate size R(g2) approximately 50 nm and mass fractal dimension D(f) approximately equals 2.2. Osmotic compressibilities of these suspensions are measured as a function of particle concentration exploring the packing mechanism of fumed silica. While there is minimal detectable change in the primary particle size, R(g2) varies by approximately 15%, providing insight into how suspension properties are related to particle size. As expected of hard particles with the same microstructure, the concentration dependence on the osmotic pressure superimposes with volume fraction of solids. The comparison of fumed-silica-suspension measurements to the known behavior of hard-sphere suspensions demonstrates the effects of particle geometry on suspension properties with indications of interpenetration of the fumed silica due to their open geometry.     

Steric interactions between physically adsorbed polymer-coated colloidal particles: soft or hard?

The steric interaction potential between colloidal particles imparted by adsorbed polymer layers is directly related to their structure. Due to the complexity of these interfacial structures, the steric potential may behave differently at different interparticle separations. In this study, we proposed a combined model of the equivalent hard-sphere model (EHS) and the Hayter-Penfold/Yukawa model (HPY) to describe the steric potential due to adsorbed homopolymers on colloidal particles. The EHS potential describes the dense train/small-loop region and the HPY potential the more diffuse tail/long-loop region. The steric potential was extracted from the structure factors measured by small-angle neutron scattering (SANS). It was found that this combined model gave better agreement with experimental data than either of its component models alone. This study also shows that the adsorbed polymer layer in a good solvent partially collapses when the layers approach one another, which is also supported by an NMR solvent relaxation study.     

Dynamical arrest, percolation, gelation, and glass formation in model nanoparticle dispersions with thermoreversible adhesive interactions

We report an experimental study of the dynamical arrest transition for a model system consisting of octadecyl coated silica suspended in n-tetradecane from dilute to concentrated conditions spanning the state diagram. The dispersion's interparticle potential is tuned by temperature affecting the brush conformation leading to a thermoreversible model system. The critical temperature for dynamical arrest, T*, is determined as a function of dispersion volume fraction by small-amplitude dynamic oscillatory shear rheology. We corroborate this transition temperature by measuring a power-law decay of the autocorrelation function and a loss of ergodicity via fiber-optic quasi-elastic light scattering. The structure at T* is measured using small-angle neutron scattering. The scattering intensity is fit to extract the interparticle pair-potential using the Ornstein-Zernike equation with the Percus-Yevick closure approximation, assuming a square-well interaction potential with a short-range interaction (1% of particle diameter). (1) The strength of attraction is characterized using the Baxter temperature (2) and mapped onto the adhesive hard sphere state diagram. The experiments show a continuous dynamical arrest transition line that follows the predicted dynamical percolation line until ? ≈ 0.41 where it subtends the predictions toward the mode coupling theory attractive-driven glass line. An alternative analysis of the phase transition through the reduced second virial coefficient B(2)* shows a change in the functional dependence of B(2)* on particle concentration around ? ≈ 0.36. We propose this signifies the location of a gel-to-glass transition. The results presented herein differ from those observed for depletion flocculated dispersion of micrometer-sized particles in polymer solutions, where dynamical arrest is a consequence of multicomponent phase separation, suggesting dynamical arrest is sensitive to the physical mechanism of attraction.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.