Tunable rheology of dense soft deformable colloids

In the last two decades, advances in synthetic, experimental and modeling/simulation methodologies have considerably enhanced our understanding of colloidal suspension rheology and put the field at the forefront of soft matter research. Recent accomplishments include the ability to tailor the flow of colloidal materials via controlled changes of particle microstructure and interactions. Whereas hard sphere suspensions have been the most widely studied colloidal system, there is no richer type of particles than soft colloids in this respect. Yet, despite the remarkable progress in the field, many outstanding challenges remain in our quest to link particle microstructure to macroscopic properties and eventually design appropriate soft composites. Addressing them will provide the route towards novel responsive systems with hierarchical structures and multiple functionalities. Here we discuss the key structural and rheological parameters which determine the tunable rheology of dense soft deformable colloids. We restrict our discussion to non-crystallizing suspensions of spherical particles without electrostatic or enthalpic interactions.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Monodisperse conducting colloidal dipoles with symmetric dimer structure for enhancing electrorheology properties

This study introduces an electrorheological (ER) approach that allows us to obtain remarkably enhanced ER properties by using monodisperse colloidal dimer particles. Two sets of colloidal particles, which are spheres and symmetric dimers, were synthesized employing the seeded polymerization technique. The aspect ratio of dimer particles was ~1.43. Then, the surface of the particles was coated with polyaniline by using the chemically oxidative polymerization method. After preparation of the particle suspensions having the same particle volume and concentration, their ER behavior was investigated with changing the electric field strength. At the same experimental condition, both shear stress and shear yield stress of the dimer particle suspension remarkably increased, compared with those of the spherical particle suspension. This attributes to the fact that the shape anisotropy of suspending particles effectively led to increase in the dipole moment under the electric field, thus resulting in formation of a well-structured colloidal chains between the electrodes.     

Anomalous particle rotation and resulting microstructure of colloids in AC electric fields

We study the transition of ordered structures to disordered bands and vortices in colloidal suspensions subjected to AC electric fields. We map the critical frequencies and field biases at which particles form disordered bands and vortices. These results are interpreted based on the trajectory dynamics of particle pairs using blinking optical tweezers. Under conditions that vortices are observed, individual particle pairs rotate out of alignment with the field. The direction and magnitude of these interactions determine the orientation and average angular velocity of the band revolution. Increasing the frequency of the electric field reduces the anomalous rotation of the particles pairs, consistent with the frequency dependence of the suspension order-to-disorder transition. This anomalous rotation is consistent with a torque on doublets generated by the mutual polarization of particles and phase lag of the induced dipoles.     

Effect of Electrode Pattern on the Column Structure and Yield Stress of Electrorheological Fluids

For electrorheological (ER) suspensions, the aggregate structures of particles were observed in electric fields by the use of transparent cells with different electrode patterns. Although the suspension is dispersed to noninteracting particles without electric fields, many aggregates are formed on the electrode surface in electric fields. Since the dipole–dipole interactions cause chain structures of particles and equilibrium conformations of chains are always aligned with electric field, the aggregates indicate the presence of columns spanning the electrode gap. The particle concentration in columns which are developed between parallel-plate electrodes is about 22 vol %. In striped electrodes, the particles construct striped aggregates along the electrodes and no particles remain in the insulating region. The particle concentration in striped aggregates is about 35 vol %. The nonuniformity of electric field is responsible for the high particle concentration. The increase in particle concentration of column lead to the high yield stress of electrified suspension. Therefore, the ER performance of suspension as an overall response can be improved by the electrode design.     

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Electrorheological Response and Structure Growth of Colloidal Silica Suspensions

The electrorheological response and structure growth of colloidal silica suspension was studied with in situ measurements of the shear stress, electric conductivity, and dielectric permittivity of the suspension. The measurements were carried out under steady and sweep shears after the application of an electric field of alternative current (100 Hz) using silica particles with a diameter of 630 nm and a water content of 4.5 wt%. The measurements of the conductivity enabled the detection of structure growth formed by particle aggregation and clarified that the development of the particle aggregation enlarged the dielectric permittivity and the shear stress. Hysteretic behavior observed in the electrorheological response was explained by considering structure growth of the particle aggregation. The correlation equation for the shear stress and the dielectric permittivity obtained in our previous work (1) was found to be applicable to the present results. Copyright 2001 Academic Press.     

A coarse-grained explicit solvent simulation of rheology of colloidal suspensions

We use a simple extension of the dissipative particle dynamics (DPD) model to address the dynamical properties of macrosolutes immersed in complex fluid solvents. In this approach, the solvent particles are still represented as DPD particles, thereby retaining the time and length scale advantages offered by the DPD approach. In contrast, the solute particles are represented as hard particles of the appropriate size. We examine the applicability of this simulation approach to reproduce the correct hydrodynamical characteristics of the mixture. Our results focus on the equilibrium dynamics and the steady-state shear rheological behaviors for a range of volume fractions of the suspension, and demonstrate excellent agreement with many published experimental and theoretical results. Moreover, we are also able to track the glass transition of our suspension and the associated dynamical signatures in both the diffusivities and the rheological properties of our suspension. Our results suggest that the simulation approach can be used as a one-parameter model to examine quantitatively the rheological properties of colloidal suspensions in complex fluid solvents such as polymeric melts and solutions, as well as allied dynamical phenomena such as phase ordering in mixtures of block copolymers and particles.     

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.     

Electro-optic characteristics of optically interacting beta-FeOOH particles

In this article the influence of multiple light scattering on the basic electro-optic parameters of optically dense colloidal particles is analyzed. The model system is an aqueous suspension of monodisperse ellipsoidal beta-FeOOH particles that displays large electric light scattering variations, including sign reversal, at very low particle volume fractions (two orders of magnitude below the critical concentration of particle electric interactions). The scaling method permits the relative variations in particle electric polarizability to be followed and its relaxation frequency to be determined. Particle rotational relaxation frequency and the phase shift of the responses at this frequency are obtained by the alternating component of the effects. Characteristic field intensity curves in the low-frequency range are used to follow the relative changes induced by the slow electrokinetic effect. The experimental results show that, despite the drastic variations in the effects with volume fraction, the basic electro-optic parameters are independent of multiple scattering and can be adequately determined for any particle concentration, excluding a narrow range in the vicinity of the electro-optic sign reversal. The investigation demonstrates that the dependence of the frequency behavior of aqueous beta-FeOOH on particle volume fraction reported in the literature is due not to optical interactions but to variation of particle surface electric state in the process of dilution.     

Negative electrorheological behavior in suspensions of inorganic particles

An investigation is described on the electric-field-induced structures in colloidal dispersions. Both rheological determinations and direct microscopic observations are used with that aim. The starting point of this study is the so-called electrorheological (ER) effect, consisting of the mechanical reinforcing of a fluid or suspension due to formation of chains of molecules or particles after being polarized by the action of the field. One macroscopic manifestation of this phenomenon is the transformation of the fluid from a typically Newtonian behavior to a viscoelastic material, with finite yield stress and high elastic modulus. The systems investigated were suspensions of elongated goethite (β-FeOOH) particles in silicone oils with varying amounts of silica nanoparticles. The results showed the rather unusual behavior known as "negative ER effect", which can be best described by saying that the application of an electric field reduces the yield stress and the elastic modulus, that is, produces destruction of structures rather than their build up. The negative behavior is also found for suspensions of other inorganic powders, including hematite and quartz. On the contrary, the usual positive ER response is found for suspensions of cellulose and montmorillonite clay. The same happens if goethite suspensions are prepared in high volume fractions, high-viscosity fluids, or both. All of the results found are compatible with the so-called interfacial model of electrorheology: the reduction of the yield stress of goethite suspensions when the applied field is high enough is the consequence of particle migration toward the electrodes because of charge injection and subsequent electrophoresis. The migration leaves the gap between the electrodes devoid of particles and explains the decrease in yield stress. The addition of silica nanoparticles contributes to reduce the strength of this effect by hindering the charging and making it necessary to increase the field strength to observe the negative effect. The model appears to also be applicable to cellulose, although the positive response found for such particles is explained by their large size: larger diameters bring about larger attraction forces between particles, leading to a tendency to produce strong aggregates. This is likely to occur in suspensions of colloids which, because of their relatively high electrical conductivity, tend to acquire charge even in such nonpolar liquids as silicone oils.     

Motion of a colloidal sphere with interfacial self-electrochemical reactions induced by a magnetic field

The motion of a spherical colloidal particle with spontaneous electrochemical reactions occurring on its surface in an ionic solution subjected to an applied magnetic field is analyzed for an arbitrary zeta potential distribution. The thickness of the electric double layer adjacent to the particle surface is assumed to be much less than the particle radius. The solutions of the Laplace equations governing the magnetic scalar potential and electric potential, respectively, lead to the magnetic flux and electric current density distributions in the particle and fluid phases of arbitrary magnetic permeabilities and electric conductivities. The Stokes equations modified with the Lorentz force contribution for the fluid motion are dealt by using a generalized reciprocal theorem, and closed-form formulas for the translational and angular velocities of the colloidal sphere induced by the magnetohydrodynamic effect are obtained. The dipole and quadrupole moments of the zeta potential distribution over the particle surface cause the particle translation and rotation, respectively. The induced velocities of the particle are unexpectedly significant, and their dependence on the characteristics of the particle-fluid system is physically different from that for electromagnetophoretic particles or phoretic swimmers.     

Electric field processing to control the structure of poly(vinylidene fluoride) composite proton conducting membranes

A novel method is reported for controlling the structure of poly(vinylidene fluoride) (PVdF) composite proton conducting membranes. When proton conducting Nafion or zirconium phosphate sulfophenylenphosphonate (ZrPSPP) particles are dispersed in a mixed colloidal suspension with PVdF particles, the proton conducting particles selectively respond to an applied electric field. Under appropriate conditions, the proton conducting particles are induced to assemble into chains that rapidly grow to span the gap between electrodes as the electric field is applied. By removing the solvent and melting the PVdF phase while applying the electric field, composite membranes were formed that have field-induced structure. In comparison to randomly structured composites, the electric field-processed Nafion/PVdF or ZrPSPP/PVdF composite membranes showed improved proton conductivity, water sorption, selectivity for protons over methanol, and controlled surface area changes upon swelling with water. The transport and mechanical properties of the electric field-processed composite membranes suggest the potential for improved performance in direct methanol fuel cells.     

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.     

Two-dimensional crystallization of microspheres by a coplanar AC electric field

The particle-field and particle-particle interactions induced by alternating electric fields can be conveniently used for on-chip assembly of colloidal crystals. Two coplanar electrodes with a millimeter-sized gap between them are used here to assemble two-dimensional crystals from suspensions of either latex or silica microspheres. When an AC voltage is applied, the particles accumulate and crystallize on the surface between the electrodes. Light diffraction and microscopic observations demonstrate that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is turned off, and the process can be repeated many times. The diffraction patterns from all consecutively formed crystals are identical. This assembly is driven by forces that depend on the electric field gradient, and a model is proposed involving a combination of dielectrophoresis and induced dipole chaining. The organization of large two-dimensional crystals allows characterization of the electrostatic interactions in the particle ensembles. The process can be controlled via the field strength, the frequency, and the viscosity of the liquid media. It could be used to make rudimentary optical switches or to separate mixtures of particles of different sizes.     

AC electrokinetic templating of colloidal particle assemblies: effect of electrohydrodynamic flows

The use of spatially nonuniform electric fields for the contact-free colloidal particle assembly into ordered structures of various length scales is a research area of great interest. In the present work, numerical simulations are undertaken in order to advance our understanding of the physical mechanisms that govern this colloidal assembly process and their relation to the electric field characteristics and colloidal system properties. More specifically, the electric-field driven assembly of colloidal silica (d(p) = 0.32 and 2 μm) in DMSO, a near index matching fluid, is studied numerically over a range of voltages and concentration by means of a continuum thermodynamic approach. The equilibrium (u(f) = 0) and nonequilibrium (u(f) ≠ 0) cases were compared to determine whether fluid motion had an effect on the shape and size of assemblies. It was found that the nonequilibrium case was substantially different versus the equilibrium case, in both size and shape of the assembled structure. This dependence was related to the relative magnitudes of the electric-field driven convective motion of particles versus the fluid velocity. Fluid velocity magnitudes on the order of mm/s were predicted for 0.32 μm particles at 1% initial solids content, and the induced fluid velocity was found to be larger at the same voltage/initial volume fraction as the particle size decreased, owing to a larger contribution from entropic forces.     

Colloid vibration potential and ion vibration potential in a dilute suspension of spherical colloidal particles

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.