Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.     

Adsorption of weakly charged polyelectrolytes onto oppositely charged spherical colloids

The adsorption of a long weakly charged flexible polyelectrolyte in a salt solution onto an oppositely charged spherical surface is investigated. An analytical solution for Green's function is derived, which is valid for any sphere radius and consistently recovers the result of a planar surface in the limit of large sphere radii, by substituting the Debye-Hückel potential via the Hulthén potential. Expressions for critical quantities like the critical radius and the critical surface charge density are provided. In particular, we find a universal critical line for the sphere radius as a function of the screening length separating adsorbed from desorbed states. Moreover, results for the monomer density distribution, adsorbed layer thickness, and the radius of gyration are presented. A comparison of our theoretical results with experiments and computer simulations yields remarkably good agreement.     

Active colloids in complex fluids

We review recent work on active colloids or swimmers, such as self-propelled microorganisms, phoretic colloidal particles, and artificial micro-robotic systems, moving in fluid-like environments. These environments can be water-like and Newtonian but can frequently contain macromolecules, flexible polymers, soft cells, or hard particles, which impart complex, nonlinear rheological features to the fluid. While significant progress has been made on understanding how active colloids move and interact in Newtonian fluids, little is known on how active colloids behave in complex and non-Newtonian fluids. An emerging literature is starting to show how fluid rheology can dramatically change the gaits and speeds of individual swimmers. Simultaneously, a moving swimmer induces time dependent, three dimensional fluid flows that can modify the medium (fluid) rheological properties. This two-way, non-linear coupling at microscopic scales has profound implications at meso- and macro-scales: steady state suspension properties, emergent collective behavior, and transport of passive tracer particles. Recent exciting theoretical results and current debate on quantifying these complex active fluids highlight the need for conceptually simple experiments to guide our understanding.     

Formation and properties of positively charged colloids based on polyelectrolyte complexes of biopolymers

Formation of colloids based on polyelectrolyte complexes (PECs) was mainly studied with synthetic polyelectrolytes. In this study, we describe the elaboration of positively charged PEC particles at a submicrometer level obtained by the complexation between two charged polysaccharides, chitosan as polycation and dextran sulfate (DS) as polyanion. The complexes were elaborated by dropwise addition of default amounts of DS to excess chitosan. Quasi-elastic light scattering was used to investigate in detail the influence of the characteristics of components (chain length, degree of acetylation) and parameters linked to the reaction of complexation (molar mixing ratio, ionic strength, concentration in polymer) on the sizes and polydispersity of colloids. Chain length of chitosan is the major parameter affecting the dimensions of the complexes, high molar mass chitosans leading to the largest particles. Variations of hydrodynamic diameters of PECs with the molar mass of chitosan are consistent with a mechanism of particle formation through the segregation of the neutral and then hydrophobic blocks of the polyelectrolyte complexed segments. Resulting particles display probably a structure constituted by a neutral core surrounded by a chitosan shell ensuring the colloidal stabilization. Such a structure was evidenced by measurements of electrophoretic mobilities revealing that the positive charge of particles was decreasing with pH, in relation with the neutralization of excess glucosamine hydrochloride moieties.     

Theory of repulsive charged colloids in slit-pores

Using classical density functional theory (DFT) we analyze the structure of the density profiles and solvation pressures of negatively charged colloids confined in slit pores. The considered model, which was already successfully employed to study a real colloidal (silica) suspension [S. H. L. Klapp et al., Phys. Rev. Lett. 100, 118303 (2008)], involves only the macroions which interact via the effective Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a hard core interaction. The solvent enters implicitly via the screening length of the DLVO interaction. The free energy functional describing the colloidal suspension consists of a hard sphere contribution obtained from fundamental measure theory and a long range contribution which is treated using two types of approximations. One of them is the mean field approximation (MFA) and the remaining is based on Rosenfeld's perturbative method for constructing the Helmholtz energy functional. These theoretical calculations are carried out at different bulk densities and wall separations to compare finally to grand canonical Monte Carlo simulations. We also consider the impact of charged walls. Our results show that the perturbative DFT method yields generally qualitatively consistent and, for some systems, also quantitatively reliable results. In MFA, on the other hand, the neglect of charge-induced correlations leads to a breakdown of this approach in a broad range of densities.     

Thermodiffusion of charged colloids: single-particle diffusion

An expression for the single-particle thermal diffusion coefficient of a charged colloidal sphere is derived on the basis of force balance on the Brownian time scale in combination with thermodynamics. It is shown that the single-particle thermal diffusion coefficient is related to the temperature dependence of the reversible work necessary to build the colloidal particle, including the core, the solvation layer, and the electrical double layer. From this general expression, an explicit expression for the contribution of the electrical double layer to the single-particle thermal diffusion coefficient is derived in terms of the surface charge density of the colloidal sphere, the electrostatic screening length, and its core radius, to within the Debye-Hückel approximation. This result is shown to explain experimental data, for both thin and thick double layers. In addition, a comparison with other theories is made.     

The electrokinetic behavior of charged non-spherical colloids

The response of charged colloids to electric fields is determined by combined phenomena occurring first in the electric double layer to then develop into long-range perturbations of ion concentration, local fields, and solvent flows. When particles are non-spherical, the loss of symmetry affects the short- and long-ranged processes modifying their behavior as observed through their electrophoretic mobility, dielectric permittivity, and electro-optical response. Recent measurements and theoretical developments have revealed phenomena characteristic for non-spherical particles, such as the doubling of the relaxations in the dielectric spectra, the appearance of torque-inducing hydrodynamic flows, and the anomalous perpendicular alignment. In this article we discuss in a unifying frame the recent experimental and theoretical progresses about the electrokinetic behavior of charged non-spherical colloids.     

Heating-induced freezing and melting transitions in charged colloids

We examine influence of temperature on the phase behavior of dilute aqueous dispersions of charged colloidal silica and polystyrene particles. They undergo either freezing or melting transitions with increasing temperature. Freezing occurs in the case of low-charge, low-salt colloids, and melting is observed in the case of high-charge, high-salt colloids. All of these phase transitions are thermoreversible. These intriguing behaviors can be qualitatively explained in terms of the decrease in the permittivity of water at elevated temperatures.     

Phase diagrams of binary mixtures of oppositely charged colloids

Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semiquantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.     

Thermal-diffusive behavior of a dilute solution of charged colloids

Thermal diffusion of a dilute solution of charged silica colloidal particles (Ludox) is studied by a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length and the surface charge density of the colloids. The latter is varied by means of variation of the pH. The experimental Soret coefficients are compared with several theoretical predictions. The surface charge density is independently obtained from electrophoresis measurements, the size of the colloidal particles is obtained from electron microscopy, and the Debye length is calculated from ion concentrations. The only adjustable parameter in the comparison with theory is therefore the intercept at zero Debye length, which measures the contribution to the Soret coefficient of the solvation layer and possibly the colloid core material.     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Electrophoretic properties of highly charged colloids: a hybrid molecular dynamics/lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.     

Complexation and coacervation of polyelectrolytes with oppositely charged colloids

Polyelectrolyte-colloid coacervation could be viewed as a sub-category of complex coacervation, but is unique in (1) retaining the structure and properties of the colloid, and (2) reducing the heterogeneity and configurational complexity of polyelectrolyte-polyelectrolyte (PE-PE) systems. Interest in protein-polyelectrolyte coacervates arises from preservation of biofunctionality; in addition, the geometric and charge isotropy of micelles allows for better comparison with theory, taking into account the central role of colloid charge density. In the context of these two systems, we describe critical conditions for complex formation and for coacervation with regard to colloid and polyelectrolyte charge densities, ionic strength, PE molecular weight (MW), and stoichiometry; and effects of temperature and shear, which are unique to the PE-micelle systems. The coacervation process is discussed in terms of theoretical treatments and models, as supported by experimental findings. We point out how soluble aggregates, subject to various equilibria and disproportionation effects, can self-assemble leading to heterogeneity in macroscopically homogeneous coacervates, on multiple length scales.     

Coarse-graining intermolecular interactions in dispersions of highly charged colloids

Effective pair potentials between charged colloids, obtained from Monte Carlo simulations of two single colloids in a closed cell at the primitive model level, are shown to reproduce accurately the structure of aqueous salt-free colloidal dispersions, as determined from full primitive model simulations by Linse et al. (Linse, P.; Lobaskin, V. Electrostatic Attraction and Phase Separation in Solutions of Like-Charged Colloidal Particles. Phys. Rev. Lett.1999, 83, 4208). Excellent agreement is obtained even when ion-ion correlations are important and is in principle not limited to spherical particles, providing a potential route to coarse-grained colloidal interactions in more complex systems.     

Properties of charged non-aqueous colloids in a low conductivity regime

Extensive investigation of the properties on non-aqueous charged colloids was undertaken utilizing quasi-elastic light scattering, optical and electrical transients and electrical platecuts. For the first time all basic physical properties of low conductivity colloids were measured. These include size, mobility and charge of colloidal particles, mobilities and concentration of counterions and excess ions, and also size and charge stability. It is shown that highly charged nonaqueous colloids are attainable in a low dielectric media despite of a low degree of dissociation of ionizable species. The importance of space charge conditions is identified and their universal scaling law illustrated for these low conductivity colloids. Ions of one polarity predominate in the double layer, and thus classical treatments of electrophoresis may not apply to these colloids.     

Screening effects on structure and diffusion in confined charged colloids

Using molecular dynamics computer simulations we investigate structural and dynamic (diffusion) properties of charged colloidal suspension confined to narrow slit pores with structureless, uncharged walls. The system is modeled on an effective level involving only the macroions, which interact via a combination of a soft-sphere and a screened Coulomb potential. The aim of our study is to identify the role of the range of the macroion-macroion interaction controlled by the inverse Debye screening length, kappa. We also compare to bulk properties at the same chemical potential as determined in parallel grand canonical Monte Carlo simulations. Our results reveal a significant influence of the interaction range which competes, however, with the influence of density. At liquidlike densities a decrease of range yields a decreasing mobility (and a corresponding enhancement of local structure) in the bulk system, whereas the reverse effect occurs in narrow slits with thickness of a few particle diameter. These differences can be traced back to the confinement-induced, and kappa-dependent, reduction of overall density compared to the bulk reservoir. We also show that an increase of kappa softens the oscillations in the normal pressure as function of the wall separation, which is consistent with experimental observations concerning the influence of addition of salt.     

Re-entrant melting and freezing in a model system of charged colloids

We studied the phase behavior of charged and sterically stabilized colloids using confocal microscopy in a low polarity solvent (dielectric constant 5.4). Upon increasing the colloid volume fraction we found a transition from a fluid to a body centered cubic crystal at 0.0415+/-0.0005, followed by reentrant melting at 0.1165+/-0.0015. A second crystal of different symmetry, random hexagonal close packed, was formed at a volume fraction around 0.5, similar to that of hard spheres. We attribute the intriguing phase behavior to the particle interactions that depend strongly on volume fraction, mainly due to the changes in the colloid charge. In this low polarity system the colloids acquire charge through ion adsorption. The low ionic strength leads to fewer ions per colloid at elevated volume fractions and consequently a density-dependent colloid charge.