Role of Electrostatic Repulsion on the Viscosity of Bidisperse Silica Suspensions

The flow behavior of bidisperse aqueous silica suspensions has been studied at different electrolyte concentrations as a function of shear rate, total volume fraction of the particles, and volume ratio of small to large particles. It is shown that the range of the electrostatic repulsion plays an important role in determining the viscosity of the suspension. Binary mixtures of particles of longer range repulsive forces showed higher viscosities than the suspensions of shorter range electrostatic interactions. Bimodal suspensions of long-range interactions showed non-Newtonian behavior over wider ranges of shear due to the deformation of the ionic cloud around the particles, which is larger in these systems. The viscosity of bimodal suspensions used in this study was scaled with respect to the viscosity of the related monosized systems and the viscosity of one bimodal suspension at a fixed total volume fraction of the particles, employing our earlier scaling method. The model normalizes the effect of colloidal forces by introducing a scaling factor that collapses the data into a single curve for bimodal suspensions of a particular size ratio, and it is shown that the model is valid for systems with both short-range and long-range repulsive forces. Copyright 1999 Academic Press.     

Structure and rheological behavior of highly charged colloidal particles in a cylindrical pore I. Effect of pore size

In this work we performed nonequilibrium Brownian dynamics (NEBD) computer simulations of highly charged colloidal particles in diluted suspension under a parabolic flow in cylindrical pores. The influence of charged and neutral cylindrical pores on the structure and rheology of suspensions is analyzed. A shear-induced disorder-order-disorder-like transition was monitored for low shear rates and small pore diameters. We calculate the concentration profiles, axial distribution functions, and axial-angular pair correlation functions to determine the structural properties at steady state for a constant shear flow for different pore sizes and flow strengths. Similar behavior has been observed in a planar narrow channel in the case of charged interacting colloidal particles (M.A. Valdez, O. Manero, J. Colloid Interface Sci. 190 (1997) 81). The mobility of the particles in the radial direction decreases rapidly with the flow and becomes practically frozen. The flow exhibits non-Newtonian shear thinning behavior due to interparticle interactions and particle-wall interaction; the apparent viscosity is lower as the pore diameter decreases, giving rise to an apparent slip in the colloidal suspension. The calculated slip velocity was higher than that obtained in a rectangular slit under shear flow.     

Electrorheological fluids as colloidal suspensions

An increase in suspension stress transfer by many orders of magnitude upon application of an external electric field is commonly referred to as the electrorheological response. Suspensions displaying this behavior are often composed of a nonaqueous dispersion of colloidal particles. In this review, the current understanding of the origin of electrorheology is described in the context of a fundamental discussion of the colloidal forces relevant to these suspensions. We show that many of the observed phenomena can be described in terms of colloidal and electric field induced interparticle interactions. The field induced arrangement of a suspension, where columns of particles are formed along field lines, is intimately related to its rheological response. A review of particle interaction potential energies of both colloidal and electric origin provides basic scaling relationshios useful in understanding structural alterations and leads naturally to a discussion of models of a suspension's rheological response. Poorly understood areas such as the effect of charge carriers in the continuous phase and particle size, shape and chemistry are delineated to indicate areas deserving further research.     

Interparticle interactions in concentrated suspensions and their bulk (rheological) properties

The interparticle interactions in concentrated suspensions are described. Four main types of interactions can be distinguished: (i) "Hard-sphere" interactions whereby repulsive and attractive forces are screened. (ii) "Soft" or electrostatic interactions determined by double layer repulsion. (iii) Steric repulsion produced by interaction between adsorbed or grafted surfactant and polymer layers. (iv)and van der Waals attraction mainly due to London dispersion forces. Combination of these interaction energies results in three main energy-distance curves: (i) A DLVO type energy-distance curves produced by combination of double layer repulsion and van der Waals attraction. For a stable suspension the energy-distance curve shows a "barrier" (energy maximum) whose height must exceed 25kT (where k is the Boltzmann constant and T is the absolute temperature). (ii) An energy-distance curve characterized by a shallow attractive minimum at twice the adsorbed layer thickness 2δ and when the interparticle-distance h becomes smaller than 2δ the energy shows a sharp increase with further decrease of h and this is the origin of steric stabilization. (iii) an energy-distance curve characterized by a shallow attractive minimum, an energy maximum of the DLVO type and a sharp increase in energy with further decrease of h due to steric repulsion. This is referred to as electrosteric repulsion. The flocculation of electrostatically and sterically stabilized suspensions is briefly described. A section is devoted to charge neutralization by polyelectrolytes and bridging flocculation by polymers. A distinction could be made between "dilute", "concentrated" and "solid suspensions" in terms of the balance between the Brownian motion and interparticle interaction. The states of suspension on standing are described in terms of interaction forces and the effect of gravity. The bulk properties (rheology) of concentrated suspensions are described starting with the case of very dilute suspensions (the Einstein limit with volume fraction Φ≤0.01), moderately concentrated suspensions (0.2>Φ≥0.1) taking into account the hydrodynamic interaction and concentrated suspensions (Φ>0.2) where semi-empirical theories are available. The rheological behavior of the above four main types of interactions is described starting with "hard-sphere" systems where the relative viscosity-volume fraction relationship could be described. The rheology of electrostatically stabilized suspensions was described with particular reference to the effect of electrolyte that controls the double layer extension. The rheology of sterically stabilized systems is described using model polystyrene suspensions with grafter poly(ethylene oxide) layers. Finally the rheology of flocculated suspensions was described and a distinction could be made between weakly and strongly flocculated systems.     

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.     

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.     

Hamaker 2: A Toolkit for the Calculation of Particle Interactions and Suspension Stability and its Application to Mullite Synthesis by Colloidal Methods

For modern processing of ceramics at the nanoscale, the influence of interparticle interactions in the suspended state becomes increasingly important. The Hamaker 2 program has been developed for the rapid prediction of these interactions, allowing us to gain important understanding of the often delicate balance of forces in ceramic powder suspensions. This article discusses the theoretical foundation of the implemented models and shows the benefit of this predictive approach applied to mullite production by colloidal methods.     

Mixing of partially fluorinated carboxylic acids with their hydrocarbon analogs at the air-water interface

Rheological behavior of surfactant-stabilized colloidal dispersions of silica particles under extreme conditions (low pH, high ionic strength) has been investigated in relation to interparticle forces and stability of the dispersion. The surfactant used as the dispersing agent was C(12)TAB, a cationic surfactant. Stability analysis through turbidity measurements indicated that there is a sharp increase in the stability of the dispersion when the surfactant concentration is in the range of 8 to 10 mM in the system. The state of the dispersion changes from an unstable regime to a stable regime above a critical concentration of C(12)TAB in the system. In the case of interaction forces measured between the silica substrate and AFM tip, no repulsive force was observed up to a surfactant concentration of 8 mM and a transition from no repulsive forces to steric repulsive forces occurred between 8 and 10 mM. Rheological measurements as a function of C(12)TAB concentration indicated a significant decrease in the viscosity and linear viscoelastic functions of the dispersion over the same range of surfactant concentration (8 to 10 mM C(12)TAB), showing a strong correlation between the viscosity behavior, interparticle forces, and structure development in the dispersion.     

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.     

DLVO AND NON-DLVO SURFACE FORCES AND INTERACTIONS IN COLLOIDAL DISPERSIONS

Some aspects of DLVO and non-DLVO forces in colloidal systems are over-viewed. The influence of long range interactions on some kinetic properties of dispersions, as Brownian diffusion, is discussed. It is shown, both theoretically and experimentally, that the electrostatic repulsion increases the collective diffusivity. The film stratification and oscillatory structure forces in colloidal suspensions are considered within the framework of an uniform approach The presence of small colloidal species (e. g. micelles or polymer molecules) may lead to several maxima and minima in the disjoining pressure isotherm. The particular case of interacting emulsion droplets is examined accounting for the interfacial deformability. The droplet deformation acts as a soft repulsion but affects also the remaining contributions to the interaction energy due to changes of the droplet shape. A general procedure for calculating the inter-droplet interaction energy, as well as the equilibrium film radius and thickness in a doublet of droplets, is suggested. The energy of interaction between charged colloidal particles, due to correlations of the density fluctuations in the electric double layer is also studied. It is found that this effect may lead to attraction greater than the van der Waals contribution, especially when multivale counter ions are present.     

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.     

Stability of polydimethylsiloxane-magnetite nanoparticle dispersions against flocculation: interparticle interactions of polydisperse materials

The colloidal stability of dispersions comprised of magnetite nanoparticles coated with polydimethylsiloxane (PDMS) oligomers was investigated theoretically and experimentally. Particle-particle interaction potentials in a theta solvent and in a good solvent for the PDMS were predicted by calculating van der Waals, electrostatic, steric, and magnetic forces as functions of interparticle separation distances. A variety of nanoparticle sizes and size distributions were considered. Calculations of the interparticle potential in dilute suspensions indicated that flocculation was likely for the largest 1% of the population of particles. Finally, the rheology of these complexes over time in the absence of a solvent was measured to probe their stabilities against flocculation as neat fluids. An increase in viscosity was observed upon aging, suggesting that some agglomeration occurs with time. However, the effects of aging could be removed by exposing the sample to high shear, indicating that the magnetic fluids were not irreversibly flocculated.     

Flow-Induced Anisotropy in Mixtures of Associative Polymers and Latex Particles

The effect of associative polymers on the structure and rheological behavior of colloidal suspensions is discussed. Adding associative polymer is known to increase the viscosity of the suspensions. At high shear rates the increase is close to what could be expected on the basis of the hydrodynamic effects of the added polymer. At low shear rates the viscosity increases much more. Small-angle light scattering (SALS) during flow is used here to investigate the underlying structural mechanisms. The SALS patterns indicate that the associative polymer changes the particulate structure: characteristic butterfly patterns appear even at relatively low particle volume fractions. They are not present in the suspensions without associative polymer. The patterns indicate that fluctuations in particle concentration are more pronounced in the flow direction than in the vorticity direction and that anisotropic particulate structures with an orientation along the vorticity direction develop. The evolution of their characteristic length scale during flow has been followed over time. Changing the hydrophilic part of the polymer from polyacrylamide to polyacrylic acid induces stronger associative interactions. In the suspensions this results in a reduction of the relative viscosity rather than an increase. The difference in degree of associativity between the polymers also has an effect on the SALS patterns in the suspensions both at rest and during flow. The rheology as well as the SALS suggest the presence of a strong polymer network in the second system. The competition between adsorption of the associative polymer on the particles with the intermolecular associations between the polymer chains seems to be responsible for the observed differences. Copyright 2000 Academic Press.     

Structure of electrorheological fluids under an electric field and a shear flow: experiment and computer simulation

It is known that macroscopic properties of colloidal suspensions are often determined by the microstructure of the particles in the suspensions, depending on the interparticle, Brownian, and hydrodynamic (if any) forces. We take electrorheological (ER) fluids as an example. By using a computer simulation and an experimental approach, we investigate the structure of ER fluids subjected to both an electric field and a shear flow. The microstructure evolution from random structure, to chains, and then to stable lamellar patterns, observed in the experiments, agrees very well with that obtained in the simulations. It is shown that the formation of such lamellar patterns originates from the difference between the dipole moment induced in the particles suspended in the ER fluids without shear and the one with shear. The results on the relaxation process of structural formation and the internal structure of layers are also presented. Thus, it seems possible to achieve various structures and hence desired macroscopic properties of colloidal suspensions by adjusting external fields and, simultaneously, a shear flow.     

Rheological behavior of silica suspensions in aqueous solutions of associating polymer

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups. The aqueous solutions show viscoelastic responses above some critical concentrations because a three-dimensional structure is formed by association of hydrophobic groups. When the associating polymers are added to silica suspensions at low concentrations, the flocculation is induced by bridging mechanisms, and the flow of suspensions become shear-thinning. For suspensions prepared with polymer solutions in which the associating network is developed, the viscosity decreases, shows a minimum, and then increases with increasing particle concentration. The viscosity decrease may arise from the breakdown of associating network due to adsorption of polymer chains onto the silica surfaces. As the particle concentration is increased, the polymer concentration in solution is decreased, and finally, all polymer chains are adsorbed on the surfaces. Beyond this point, the partial coverage of particle surfaces takes place and strong interactions are generated between particles by polymer bridging. Since the stable suspensions are converted to highly flocculated systems, the viscosity is increased and the flow becomes shear-thinning. The concentration effect of silica particles on the viscosity behavior of suspensions can be explained by a combination of viscosity decrease in solution due to polymer adsorption and viscosity increase due to flocculation.     

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.     

Manipulating forces between surfaces: applications in colloid science and biophysics

It is the forces between the microscopic constituents of materials which to a large extent determine the macroscopic properties. For example, it is the differences in bonding between the carbon atoms which determines the different physical properties of carbon and graphite. The same is true in colloidal systems. In colloidal systems, there are three common types of long-range interactions between particles: van der Waals forces, electrical double layer forces and steric forces. In this paper, examples as to how these forces can be modified and even manipulated will be given. To convincingly demonstrate these effects, it is necessary to measure these interaction forces. We have achieved this by using the principles of atomic force microscopy (AFM). The principle is simple, a small particle, 5-30 microm, is attached onto a small weak cantilever spring. The interaction between this particle and another particle or a surface is measured by monitoring the deflection of the spring as the two particles are moved together. In this paper, I shall give examples of direct measurements of van der Waals, electrical double layer and steric forces and show how they can be modified and how these modifications affect the properties of bulk suspensions. Similar principles are involved in the interactions of biological materials. However, nature is much cleverer than man such that many of the macromolecules on cell surfaces are able to specifically recognise only one other molecule. An example of this recognition-type interaction, namely, cholera toxin interacting with the glycolipid Gm1, will also be presented. Finally, the adhesion of cells to surfaces of different surface chemistries has been determined; this is of significance in many fields ranging from fouling of filtration membranes on the one hand to the biocompatibility of surgical implants on the other.     

Dynamic effects on colloidal electric interactions

Dynamic behaviors are abundant in field-responsive colloidal suspensions. Being beyond the usual point-dipole approximation, we develop a multiple image method of dipoles for two dynamic unequal colloidal dielectric spherical particles, which can be perfectly reduced to those for two static conducting particles. The method is applied to investigate colloidal electric interparticle forces under various conditions of dynamics. As a result, we find that the force can be enhanced, reduced, or even changed from attraction to repulsion, or vice versa. Some other interesting results are also reported. Our theoretical results are compared favorably with existing experimental observations. Therefore, it becomes possible to achieve desired colloidal structures by adjusting colloidal interactions by choosing appropriate dynamic phenomena.     

Recent developments in the measurement of interparticle forces

In the last twenty years there has been an explosion of experimental work devoted to determining the forces between colloidal particles. There have been considerable experimental and theoretical advances. In this review we shall concentrate on the experimental aspects. Currently there is no technique which directly measures the interaction between two individual particles as a function of their separation. Particle - particle forces can only be inferred. In this paper we review the experimental procedures which have been used to determine the nature and range of interparticle forces in this indirect way. The many different experimental techniques which have been developed are outlined and typical data presented. The relative merits and demerits of each technique is discussed and the way forward to measuring particle - particle interactions directly is proposed.     

Electrorheological properties and microstructure of silica suspensions

We present experimental and theoretical results on the electrorheological response and microstructure of colloidal suspensions composed of silica nanoparticles dispersed in a silicon oil, as a function of electric field strength and silica water content. Using small-angle neutrons scattering experiments, we determined the evolution of the static structure factor of the suspensions when an electric field is applied. Experimental data were fitted with model calculations using the Percus-Yevick solution for Baxter's hard-sphere adhesive potential. The obtained stickiness parameter is directly related to the polarization interactions that depend on the water content of silica particles. The influence of the polarization interparticle potential on the rheology of the silica dispersions was investigated in a second time. A microscopic theory for the shear viscosity of adhesive hard-sphere suspensions was successfully used which describes the steady shear viscosity of suspension in terms of the fractal concept.