Rheology of Dilute Suspensions of Hard Platelike Colloids

The concentration dependence of the viscosity is studied for suspensions of approximately hard, i.e., short-range repulsive, platelets. We combine rheological measurements on suspensions of sterically stabilized platelike colloids with dissipative particledynamics simulation for disks. This yields, for the first time, results for the intrinsic viscosity of (nearly) hard plate suspensions, as well as the second- and third-order φ (platelet volume fraction) coefficients in the viscosity. The intrinsic viscosity is used to calculate the number-average aspect ratio of the platelets, which is found to be 6.5 and 12 respectively for the two suspensions studied. The measured Huggins coefficients are intermediary between the theoretical value for hard spheres and hard rods. The combined results from viscosity measurements and simulations provide insight into the effect of Péclet number, particle model, and polydispersity on the viscosity of approximately hard platelet suspensions. Copyright 2001 Academic Press.     

Viscosity of hard sphere suspensions

A simple functional representation of the concentration dependence of the low-shear viscosity eta of hard sphere suspensions is proposed. The representation, which agrees with published literature at all volume fractions phi, has a hitherto-unremarked transition in its functional form at phi approximately 0.42 identical with phi(t). phi(t) is definitely less than the volume fraction 0.49 of the hard sphere melting transition.     

Adsorption behavior of oxyethylated surfactants at the air/water interface

The low-shear viscosity eta(0) of colloidal suspensions of acrylic latex or silica in aqueous gelatin has been measured at a temperature above the sol-gel transition. Measurements were made on dilution of a concentrated suspension with water or a gelatin solution. Thus, either the gelatin : colloid ratio was maintained or it was varied at constant aqueous gelatin concentration. Systems were studied with four lime-processed gelatins of different molecular weights at two concentrations of added salt. In addition, the latex particle size and the thickness of the adsorbed gelatin layer were measured by photon correlation spectroscopy (PCS) under dilute conditions. The dependence of the low-shear viscosity eta(0) on particle concentration was exponential and did not follow the well-established Krieger-Dougherty model for simple hard-sphere suspensions over the concentration range studied. A simple phenomenological model, eta(0)=eta(o)10(phi(e)/phi(s)), was found to predict the behavior well. Here, eta(o) is the viscosity of a gelatin solution of the corresponding solution concentration, phi(e) is proportional to the volume fraction of the particles, and phi(s) is a scaling factor, which was determined to have a value of 0.85. With this value of phi(s), the dimensions determined from PCS could be used to predict the viscosity values.     

Primary electroviscous effect in a moderately concentrated suspension of charged spherical colloidal particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernández, F. J.; Gómez-Merino, A. I.; García-Sánchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials zeta at the particle volume fraction phi < or = 0.3 for the case of nonoverlapping double layers, that is, at kappaalpha > 10 (where kappa is the Debye-Hückel parameter). A simple approximate analytic expression for p applicable for particles with large kappaalpha and arbitrary zeta is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi < or = 0.3, where the relative error is negligible for kappaalpha > or =100 and even at kappaalpha = 50 the maximum error is approximately 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.     

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction phi. For low rod concentrations, the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of phi with the slope alpha proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two-body hydrodynamic interactions are calculated using the so-called bead model in which the rod of aspect ratio p is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to p=1000. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than 5% from the model with filling. An analytical expression for alpha as a function of p is derived in the limit of very long rods. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.     

Dynamic Mobility of Particles with Thick Double Layers in a Nondilute Suspension

The dynamic mobility of a nondilute suspension of spherical particles is investigated in the case where the thickness of the electrical double layer around each particle is comparable to the particle radius. A formula is obtained for the O(φ) correction in a random suspension of particles with volume fraction φ, involving an integral over the dynamic mobility of a pair of spheres. This formula is then evaluated using both analytical approximations and numerical results previously obtained for the pair mobilities and valid for low surface potentials. The effect of double-layer thickness on the O(φ) coefficient is most pronounced at low frequencies, and lessens once the hydrodynamic penetration depth is smaller than the particle radius. Various approximations are considered that use the O(φ) result to predict the dynamic mobility in concentrated suspensions, and at high frequencies these approximations are shown to give results qualitatively different from those of recent cell models. Copyright 2000 Academic Press.     

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.     

Effect of pH and Salt on Rheological Properties of Aerosil Suspensions

Ionic strength and pH will influence the zeta potential of suspended particles, and consequently particle interactions and rheological properties as well. In this study the rheological properties and aggregation behaviour of Aerosil particles dispersed in aqueous solutions with various pH and salt concentration were studied. The potential energy was estimated by the DLVO theory and short range hydration forces and compared to the experimentally determined zeta potential. The strongest attraction between particles occurs at the isoelectric point (pH 4) and resulted in large aggregates, which gave relatively higher values of viscosity, yield stress, moduli, and shear thinning effects. The relative viscosity as a function of volume fraction was fitted to the Krieger and Dougherty model for all the suspensions. Oscillation measurements showed that the suspensions display elastic behaviour at low pH and viscous behavior at high pH. Furthermore, suspensions with high salt content had higher storage moduli. A power law dependency of storage moduli with volume fraction could be used to indicate the interaction strength between particles.     

Isotropic-nematic phase transition of nonaqueous suspensions of natural clay rods

A novel model system for studying the behavior of hard colloidal rods is presented, consisting of sterically stabilized particles of natural sepiolite clay. Electron microscopy and scattering results confirmed that the organophilic clay particles were individual, rigid rods when dispersed in organic solvents. With a length-to-diameter ratio of approximately 27, the particles showed nematic ordering for volume fractions phi > 0.06. Polarizing microscopy revealed that the phase separation process involved nucleation, growth, and coalescence of nematic domains. The phase volumes and particle concentrations in the coexisting phases were determined. The dependence of these quantities on the total concentration of the suspension agrees well with Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] isotropic-nematic phase transition theory extended to bidisperse and polydisperse rod systems, and with previous experimental results for rigid rodlike particles. Particle size distributions were obtained by analyzing transmission electron microscopy images. A significant fractionation with respect to rod length (but not diameter) was observed in the coexisting isotropic and nematic phases. The relative polydispersity of both daughter phases was distinctly smaller than that of the parent suspension. The phase behavior of these daughter fractions agrees well with the predictions for hard spherocylinders of corresponding aspect ratios. An isotropic-nematic-nematic phase equilibrium was seen to develop in phase separated samples after 1 month standing and is ascribed to the effect of polydispersity and possibly gravity. The second nematic phase appearing is dominated by very long rods.     

Structure of colloid silica determined by viscosity measurements

The viscosity of nanosized colloid silica suspensions, used as binders in the investment casting, was determined as a function of their weight fraction reaching 52%. A new capillary viscometer was used whose construction eliminated sedimentation effects. The experiments have been carried out at fixed pH 10.0 and controlled ionic strength. It was found that for a low silica concentration range (weight fraction below 5%) the suspension viscosity increased more rapidly than the Einstein theory predicts. This anomalous behavior could not be explained in terms of the primary electroviscous effect predicted to be a few orders of magnitude smaller as observed. This discrepancy was accounted for by postulating a fuzzy, gel-like structure of colloid silicas used in our experiments. Hence, the apparent hydrodynamic radius of silica particles in aqueous suspensions was found to be larger than the primary particle size in accordance with previous observations. Based on this postulate, an apparent density of the silica sols was found to be 1.32-1.37 g/cm(3) instead of 2.2-2.32 g/cm(3) as determined from the suspension dilution method. This behavior was interpreted in terms of the core/shell model with high shell porosity, reaching 85%. Similarly, for higher concentration ranges, silica viscosity increased more rapidly with increased sol concentration than predicted by the Batchelor model derived for hard particles. The deviation was attributed to the secondary electroviscous effect stemming from the electrostatic interactions among silica particles in sheared suspensions. This effect has quantitatively been interpreted in terms of Russel's theory. On the other hand, for the high concentration range the experimental results were well accounted for by the Dougherty-Krieger model. By exploiting our experimental findings a sensitive method of determining the structure and apparent density of silica sols in aqueous media was proposed.     

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.     

On the viscosity of composite suspensions of aluminum and ammonium perchlorate particles dispersed in hydroxyl terminated polybutadiene--New empirical model

The rheological properties of fuel suspensions with various solid loadings up to close their maximum packing fraction and suspending media having different viscosities are investigated using the rotational viscometer at relatively low shear rates in which suspensions behave as Newtonian fluids. Aluminum (Al) and ammonium perchlorate (AP) particles are major solid components of any solid fuel system which should be distributed uniformly inside a polymeric binder based on hydroxyl terminated polybutadiene (HTPB). The experimental data generated in this investigation indicates that the relative viscosity of the suspensions is independent of viscosity of polymer binder, but in addition to solid content, geometrical aspects of the solid particles affect strongly the relative viscosity of suspensions. Maximum packing fraction of filler is found to be suitable quantitative measure of filler characteristics such as size, size distribution, shape and structure. Consequently, it is revealed that the relative viscosity of fuel suspension is a unique function of reduced volume fraction (Phi). Based on analogy of viscosity enhancement of reactive resin with cure conversion and suspension with filler content, an empirical model with two adjustable parameters originated from resin gelation model is suggested. According to this model and experimental results obtained in this investigation, a generalized model is proposed to describe the relative viscosity as a function of solid content in which the adjustable parameters are found to be general constants. The generalized model which is expressed as mu(r) = (1-Phi)(0.3 Phi-2) is found to be quite accurate to predict the experimental data. Furthermore, the applicability and accuracy of the generalized model are evaluated using the viscosity data of some suspension systems reported in the literature.     

Cell model calculation for electrokinetic phenomena in concentrated suspensions: an Onsager relation between sedimentation potential and electrophoretic mobility

Cell model calculations for the electrophoretic mobility, electrical conductivity and sedimentation potential in concentrated suspensions of colloidal particles with low zeta potentials are reviewed with particular emphasis on an Onsager relation between sedimentation potential and electrophoretic mobility. A general Onsager relation is derived on the basis of the thermodynamics of irreversible processes. This relation, which involves the ratio of the electrical conductivity K* of the suspension to the conductivity Kinfinity in the absence of the particles, reproduces the Onsager relation derived from cell model calculations at low zeta potentials, where K*/Kinfinity becomes (1 - phi)/(1 + phi/2), phi being the particle volume fraction.     

Influence of poly(ethylene oxide) brushes on the rheological properties of MgO colloidal suspensions in water

A combined experimental and multiscale simulation study of the influence of polymer brush modification on interactions of colloidal particles and rheological properties of dense colloidal suspensions has been conducted. Our colloidal suspension is comprised of polydisperse MgO colloidal particles modified with poly(ethylene oxide) (PEO) brushes in water. The shear stress as a function of shear rate was determined experimentally and from multiscale simulations for a suspension of 0.48 volume fraction colloids at room temperature for both bare and PEO-modified MgO colloids. Bare MgO particles exhibited strong shear thinning behavior and a yield stress on the order of several Pascals in both experiments and simulations. In contrast, simulations of PEO-modified colloids revealed no significant yielding or shear thinning and viscosity only a few times larger than solvent viscosity. This behavior is inconsistent with results obtained from experiments where modification of colloids with PEO brushes formed by adsorption of PEO-based comb-branched chains resulted in relatively little change in suspension rheology compared to bare colloids over the range of concentration of comb-branch additives investigated. We attribute this discrepancy in rheological properties between simulation and experiment for PEO-modified colloidal suspensions to heterogeneous adsorption of the comb-branch polymers.     

Rheology of polystyrene latexes with adsorbed and free gelatin

The rheology of monodisperse polystyrene latex particles of two different particle radii (26 and 67 nm) has been studied with a range of concentrations of the polyampholyte gelatin. Gelatin contributes to the rheology by adsorption to the particles and by thickening the continuous phase. High viscosities and strong shear thinning are measured for low volume fractions of latex. A procedure is presented to deconvolute the effects of free and bound gelatin by applying simple hard-sphere models. This procedure allows us to estimate the effective size of the gelatin-covered particles as well as the continuous-phase gelatin concentration and viscosity. The layer thicknesses from rheology agree well with those from PCS. The effect of varying particle volume fraction, ionic strength, pH and gelatin and surfactant concentration on the rheology of these suspensions is presented. For the smaller latex, the adsorbed layer occupies a greater fraction of the effective volume. Increasing free polymer concentration reduces the adsorbed-layer thickness. The reduced critical shear stress increases with the suspension viscosity for suspensions of the 26 nm latex but is constant for the 67 nm latex. At very high shear (>2000 s⁻¹), the suspensions show excess shear thinning over that expected from a hard-sphere model. This excess thinning is attributed to deformation of the adsorbed gelatin layer under high shear stress and interpreted in terms of an empirical interparticle potential.     

Aqueous suspensions of natural swelling clay minerals. 2. Rheological characterization

We report in this article a comprehensive investigation of the viscoelastic behavior of different natural colloidal clay minerals in aqueous solution. Rheological experiments were carried out under both dynamic and steady-state conditions, allowing us to derive the elasticity and yield stress. Both parameters can be renormalized for all sizes, ionic strength, and type of clay using in a first approach only the volume of the particles. However, applying such a treatment to various clays of similar shapes and sizes yields differences that can be linked to the repulsion strength and charge location in the swelling clays. The stronger the repulsive interactions, the better the orientation of clay particles in flows. In addition, a master linear relationship between the elasticity and yield stress whose value corresponds to a critical deformation of 0.1 was evidenced. Such a relationship may be general for any colloidal suspension of anisometric particles as revealed by the analysis of various experimental data obtained on either disk-shaped or lath- and rod-shaped particles. The particle size dependence of the sol-gel transition was also investigated in detail. To understand why suspensions of larger particles gel at a higher volume fraction, we propose a very simplified view based on the statistical hydrodynamic trapping of a particle by an another one in its neighborhood upon translation and during a short period of time. We show that the key parameter describing this hydrodynamic trapping varies as the cube of the average diameter and captures most features of the sol-gel transition. Finally, we pointed out that in the high shear limit the suspension viscosity is still closely related to electrostatic interactions and follows the same trends as the viscoelastic properties.     

Effective static and high-frequency viscosities of concentrated suspensions of soft particles

We obtain an analytic expression that allows to determine the static η and high-frequency η(∞) viscosities as function of the volume fraction φ of a concentrated suspension of soft spherical particles in a liquid of viscosity η(0). The particles consist of a hard core of radius a covered by a porous layer of thickness d. Suspensions of hard spheres and homogeneous porous particles are limiting cases of the model. The proposed expression incorporates the results for the intrinsic viscosity obtained on the basis of a cell model [H. Ohshima, Langmuir 26, 6287 (2010)] into a recently obtained relation for the effective viscosity of concentrated colloidal suspensions [C. I. Mendoza and I. Santamari?a-Holek, J. Chem. Phys. 130, 044904 (2009); J. Colloid. Interface Sci. 346, 118 (2010)]. In this model, the correlations between the particles due to crowding effects are introduced through an effective volume fraction φ(eff) which is then used as integration variable in a differential effective medium procedure. The final expression is simple, accurate, and allows to collapse all the data in a universal master curve that is independent of the parameters characterizing the system. The only difference between the static and high-frequency cases is that in the later case φ(eff) also incorporates hydrodynamic interactions arising from the so-called relaxation term. We have tested the accuracy of our model comparing with experimental results for spherical polymeric brushes and simulations for the high-frequency viscosity of homogeneous porous particles. In all cases the agreement with the data is extremely good.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

Stability of the aqueous suspensions of nanotubes in the presence of nonionic surfactant

Stability of aqueous suspensions of multiwalled carbon nanotubes (MWNTs) and their percolation behavior are investigated. Nanotubes of aqueous suspensions show a strong tendency to aggregation and networking into electroconductive clusters. The percolation threshold of the electrical conductivity is rather low and of order phi approximately 0.01 (where phi is the volume fraction), which can be explained by the high aspect ratio of MWNTs. Strong influence of the nonionic surfactant Triton X-305 on the colloidal stability of aqueous suspensions of MWNTs is observed. Addition of surfactant exerts a stabilizing effect at surfactant concentration C(s) proportional to the weight concentration C of MWNTs, C(s) approximately C mol/dm3. The transient behavior of electrical conductivity in the aqueous suspensions is explained by fractal aggregation processes. The fractal dimension is shown to be sensitive to the surfactant concentration C(s).     

Polymer depletion-induced instability of silica suspensions in the presence of flexible and semiflexible polymers

Polymer depletion-induced instability of silica suspensions in dilute toluene solutions of flexible polystyrene (PS) or semiflexible poly(hexyl isocyanate) (PHIC) was investigated by direct observation and oscillatory moduli measurements as functions of silica volume fraction and polymer molecular weight. Addition of the respective polymers to the gelled silica suspensions induces a gel settling. Below the silica volume fraction phi=4 vol%, PS chains compress the volume of the sediment silica phase, whereas PHIC chains expand it and play a role in swelling agents. Thus, PHIC chains lead to the formation of aggregates in the silica suspensions that are larger and less compact than those formed by the PS chains. On the other hand, above phi=4 vol% where the silica suspension occurs gelation, the effect of nonadsorbing polymers on changes in the volume of the silica phase is opposite. Moreover, polymer depletion interaction results in a mechanically stronger gelled phase, leading to the storage modulus G' values larger than those without polymer, but the effects of polymer concentration and polymer molecular weight on the G' values are not clear.