Dynamical test of interaction potentials for colloidal suspensions

Accessing the free expansion of a crystalline colloidal drop by optical experiments

We study poly-crystalline spherical drops of an aqueous suspension of highly charged colloidal spheres exposed to a colloid-free aqueous environment. Crystal contours were obtained from standard optical imaging. The crystal spheres first expand to nearly four times their initial volume before slowly shrinking due to dilution-induced melting. Exploiting coherent multiple-scattering by (110) Bragg reflecting crystals, time-dependent density profiles were recorded within the drop interior. These show a continuously flattening radial density gradient and a decreasing central density. Expansion curves and density profiles are qualitatively consistent with theoretical expectations based on dynamical density functional theory for the expansion of a spherical crystallite made of charged Brownian spheres. We anticipate that our study opens novel experimental access to density determination in turbid crystals.

Role of diffusion in crystallization of hard-sphere colloids

Vital for a variety of industries, colloids also serve as an excellent model to probe phase transitions at the individual particle level. Despite extensive studies, origins of the glass transition in hard-sphere colloids discovered about 30 y ago remain elusive. Results of our numerical simulations and asymptotic analysis suggest that cessation of long-time particle diffusivity does not suppress crystallization of a metastable liquid-phase hard-sphere colloid. Once a crystallite forms, its growth is then controlled by the particle diffusion in the depletion zone surrounding the crystallite. Using simulations, we evaluate the solid-liquid interface mobility from data on colloidal crystallization in terrestrial and microgravity experiments and demonstrate that there is no drastic difference between the respective mobility values. The insight into the effect of vanishing particle mobility and particle sedimentation on crystallization of colloids will help engineer colloidal materials with controllable structure.

Glass-transition properties of Yukawa potentials: from charged point particles to hard spheres

The glass transition is investigated in three dimensions for single and double Yukawa potentials for the full range of control parameters. For vanishing screening parameter, the limit of the one-component plasma is obtained; for large screening parameters and high coupling strengths, the glass-transition properties cross over to the hard-sphere system. Between the two limits, the entire transition diagram can be described by analytical functions. Unlike other potentials, the glass-transition and melting lines for Yukawa potentials are found to follow shifted but otherwise identical curves in control-parameter space.

Heterogeneous crystallization in colloids and complex plasmas: the role of binary mobilities

Both charged colloidal suspensions and complex (dusty) plasmas represent classical many-body strongly coupled Coulomb systems. Here we discuss their basic properties and focus on their heterogeneous crystallization from an undercooled melt. In particular, a model with different mobilities is proposed which is realizable in binary mixtures of charged particles. Within this binary-mobility model, the crystallization behaviour near a structured wall is explored by Brownian dynamics computer simulations. As a result, the propagation velocity of the crystal-fluid interface is a nonmonotonic function of the mobility ratio (if expressed in terms of an averaged mobility).

The metastable states of foam films containing electrically charged micelles or particles: experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case - surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson-Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.

Micro-rheology on (polymer-grafted) colloids using optical tweezers

Optical tweezers are experimental tools with extraordinary resolution in positioning (± 1 nm) a micron-sized colloid and in the measurement of forces (± 50 fN) acting on it-without any mechanical contact. This enables one to carry out a multitude of novel experiments in nano- and microfluidics, of which the following will be presented in this review: (i) forces within single pairs of colloids in media of varying concentration and valency of the surrounding ionic solution, (ii) measurements of the electrophoretic mobility of single colloids in different solvents (concentration, valency of the ionic solution and pH), (iii) similar experiments as in (i) with DNA-grafted colloids, (iv) the nonlinear response of single DNA-grafted colloids in shear flow and (v) the drag force on single colloids pulled through a polymer solution. The experiments will be described in detail and their analysis discussed.

Twenty years of confined colloids: from confinement-induced freezing to giant breathing

The physics of colloidal suspensions confined in slits and cavities has significantly advanced during the last twenty years. In particular, freezing transitions in confinement have been addressed by theory and simulations and experimental realizations were proposed to confine colloidal particles to two dimensions. After reviewing this progress, we discuss the generalization to time-dependent confinement which leads to nonequilibrium situations. This is elaborated further for unstable situations where the particles can leave the confinement. In particular, the completely overdamped Brownian motion of a colloidal particle in a time-dependent harmonic trap is considered. The analytically soluble model of a time-dependent quadratic potential is used to extract the dynamical properties of the potential if the potential undergoes periodic switching from a confining harmonic potential to an unstable one. The amplitudes of the oscillating particle response can strongly grow in time, which we refer to as 'giant breathing'. This giant breathing process occurs also in anharmonic potentials and is verifiable in real-space experiments of colloids in laser-optical fields.

Forces between single pairs of charged colloids in aqueous salt solutions

Forces between single pairs of negatively charged micrometer-sized colloids in aqueous solutions of monovalent, divalent, or trivalent counter-ions at varying concentrations have been measured by employing optical tweezers. The experimental data have been analyzed by using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and a numerical solution of the Poisson-Boltzmann (PB) equation. With monovalent counterions, the data are well described by the DLVO and PB theories, suggesting that the DLVO theory is adequate to describe the colloidal forces at these conditions. At higher counter-ion valence, the approximations within the two theories become evident.

Nucleation kinetics in deionized charged colloidal model systems: a quantitative study by means of classical nucleation theory

We have studied the nucleation kinetics of charged colloidal model systems under salt free conditions crystallizing in bcc structure covering a wide range of particle number densities 18 microm(-3) < or =n< or =66.3 microm(-3). We employed direct video-microscopic observation of individual nucleation events to obtain time resolved nucleation rate densities. Polarization microscopy and static light scattering on the resulting solids in combination with Avrami theory is used to determine the steady state nucleation rate at high undercoolings. The final nucleation rate densities J from different methods are observed to be consistent with each other. By increasing the difference in the chemical potential between melt and crystal Delta mu about one order of magnitude J increases from 10(9)m(-3)s(-1) to 10(17)m(-3)s(-1) over approximately seven orders of magnitude. The data can be well analyzed and interpreted using classical nucleation theory (CNT) leading to a linearly increasing melt-crystal surface tension. Surprisingly, the reduced surface tension is about one order of magnitude larger compared to other system (metals; hard sphere colloids). The critical radius of the crystal nuclei is decreasing down to a very small value of 1.5 coordination shells. The determined kinetic prefactors are up to 10 orders of magnitude smaller than the prefactor calculated by CNT.

Electrophoretic flow behaviour and mobility of colloidal fluids and crystals

We report on measurements of the electrophoretic mobility mu of charged colloidal spheres in the deionized state, where the suspensions show fluid or crystalline order. In the fluid state, parabolic flow profiles are observed due to electro-osmotic solvent flow. In the crystalline state, complex flow profiles occur due to additional crystal cohesion. The mobility mu then may inferred from the flow velocity averaged over the complete cell cross section as performed in our home built super-heterodyne Doppler velocimeter. For two particle species of 68 and 122 nm diameter we measured mu as a function of particle concentration. Starting from a plateau value at low concentration, mu decreases approximately logarithmically with increased concentration. Interestingly, the decrease of mu is not affected by the phase transition, indicating that electro-kinetic properties may be viewed as single particle properties even in the case of structure formation. Moving further along this line of thought, we show that this behaviour may indeed be captured near quantitatively by an ad hoc combination of charge renormalization calculations and the Standard Electro-kinetic Model originally designed for isolated, non-interacting particles. From this coincidence, we may conclude that (i) counter-ion condensation behind the hydrodynamic slip plane is the dominant effect of finite particle concentrations and leads to a decrease of the effective particle charge and (ii) an increased colloid concentration can be understood in terms of an elevated total ion concentration and that (iii) it can thus be reduced to a modification of the screening parameter, such that the problem can be mapped onto a single particle theory for an infinite electrolyte.

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).

Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles

As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.

Lane formation in colloidal mixtures driven by an external field

The influence of an external field on a binary colloidal mixture performing Brownian dynamics in a solvent is investigated by nonequilibrium computer simulations and simple theory. In our model, one half of the particles are pushed into the field direction while the other half of them are pulled into the opposite direction. For increasing field strength, we show that the system undergoes a nonequilibrium phase transition from a disordered state to a state characterized by lane formation parallel to the field direction. The lanes are formed by the same kind of particles moving collectively with the field. Lane formation accelerates particle transport parallel to the field direction but suppresses massively transport perpendicular to the field. We further show that lane formation also occurs in a time-dependent oscillatory field. If the frequency of the external field exceeds a critical value, however, the system exhibits a transition back to the disordered state. Our results can be experimentally verified in binary colloidal suspensions exposed to external fields under nonequilibrium conditions.

Influence of solvent granularity on the effective interaction between charged colloidal suspensions

We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard-sphere solvent. Apart from molecular oscillating forces for nearly touching colloids that arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerably reduced as compared to the prediction based on the primitive model. When these forces are repulsive, the long-distance behavior can be described by an effective Yukawa pair potential with a solvent-renormalized charge. As a function of colloidal volume fraction and added salt concentration, this solvent-renormalized charge behaves qualitatively similar to that obtained via the Poisson-Boltzmann cell model, but there are quantitative differences. For divalent counterions and nanosized colloids, on the other hand, the hydration may lead to overscreened colloids with mutual attraction while the primitive model yields repulsive forces. All these new effects can be accounted for through a solvent-averaged primitive model (SPM) which is obtained from the full model by integrating out the solvent degrees of freedom. The SPM was used to access larger colloidal particles without simulating the solvent explicitly.

Eccentric poisson-boltzmann cell model

We solve the nonlinear Poisson-Boltzmann equation around a charged colloidal sphere in an electrolyte that is confined in a cell. The colloid has an eccentric position inside the confining sphere. This models the situation in a highly concentrated charge-stabilized colloidal suspension, where a single colloid simultaneously interacts with the whole cage of neighboring colloids. We calculate the ion density profiles, the free energy, and the osmotic pressure as a function of the shifting position. We express the total force acting on the particle as a sum of pair contributions and compare the resulting pair interaction potential law with the standard Derjaguin-Landau-Verwey-Overbeck expression.

Chemical Charge Regulation and Charge Renormalization in Concentrated Colloidal Suspensions

This article discusses the charging behavior of particles in a colloidal suspension allowing for a simple model reaction at the surface of the colloidal particles that regulates the total number Z(f) of free counterions. This number is to be distinguished from an effective number of charges Z* calculated in the Wigner-Seitz cell model to determine the interaction between the colloidal particles. We discuss the problem in terms of the full free energy of the system. The number of free counterions Z(f) as a function of the structural charge of the colloid is derived from the minimum of this free energy. Our results are compared with experimental data. Copyright 1999 Academic Press.