Structure of a colloidal suspension confined in a planar slit

Computer simulations and mode-coupling theory of glass-forming confined hard-sphere fluids

We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated using the full system of matrix-valued integro-differential equations. We investigate several dynamical properties of supercooled liquids including scattering functions, frequency-dependent susceptibilities, and mean-square displacements. Close to the glass transition, we find quantitative agreement between the coherent scattering function predicted from theory and that evaluated from simulations, which enables us to make quantitative statements on caging and relaxation dynamics of the confined hard-sphere fluid.

Structural properties of liquids in extreme confinement

We simulate a hard-sphere liquid in confined geometry where the separation of the two parallel, hard walls is smaller than two particle diameters. By systematically reducing the wall separation we analyze the behavior of structural and thermodynamic properties, such as inhomogeneous density profiles, structure factors, and compressibilities when approaching the two-dimensional limit. In agreement with asymptotic predictions, we find for quasi-two-dimensional fluids that the density profile becomes parabolic and the structure factor converges toward its two-dimensional counterpart. To extract the compressibility in polydisperse samples a perturbative expression is used which qualitatively influences the observed nonmonotonic dependence of the compressibility with wall separation. We also present theoretical calculations based on fundamental-measure theory and integral-equation theory, which are in very good agreement with the simulation results.

Thickness of the particle-free layer near charged interfaces in suspensions of like-charged nanoparticles

When a suspension of charged nanoparticles is in contact with a like-charged water-solid interface, next to this interface a particle-free layer is formed. The present study provides reliable measurements of the thickness of this particle-free layer with three different techniques, namely optical reflectivity, quartz crystal microbalance (QCM), and direct force measurements with atomic force microscopy (AFM). Suspensions of negatively charged nanoparticles of different size and type are investigated. When the measured layer thickness is normalized to the particle size, one finds that this normalized thickness shows universal inverse square root dependence on the particle volume fraction. This universal dependence can be also derived from Poisson-Boltzmann theory for highly asymmetric electrolytes, whereby one has to assume that the nanoparticles represent the multivalent coions.

Structural and Double Layer Forces between Silica Surfaces in Suspensions of Negatively Charged Nanoparticles

Direct force measurements between negatively charged silica microparticles are carried out in suspensions of like-charged nanoparticles with atomic force microscopy (AFM). In agreement with previous studies, oscillatory force profiles are observed at larger separation distances. At smaller distances, however, soft and strongly repulsive forces are present. These forces are caused by double layer repulsion between the like-charged surfaces and can be quantitatively interpreted with the Poisson-Boltzmann (PB) model. However, the PB model must be adapted to a strongly asymmetric electrolyte to capture the nonexponential nature of these forces. Thereby, the nanoparticles are modeled as highly charged co-ions, while the counter ions are monovalent. This model permits extraction of the effective charge of the nanoparticles, which is well comparable to the one obtained from electrophoresis. The PB model also explains the presence of a particle-free layer close to the interface.

Tagged-particle dynamics in confined colloidal liquids

We present numerical results for the tagged-particle dynamics by solving the mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show that neither the microscopic dynamics nor the type of intermediate scattering function qualitatively changes the asymptotic dynamics in vicinity of the glass transition. In particular, we find similar characteristics of confinement in the low-frequency susceptibility spectrum which we interpret as footprints of parallel relaxation. We derive predictions for the localization length and the scaling of the diffusion coefficient in the supercooled regime and discover a pronounced nonmonotonic dependence on the confinement length. For dilute liquids in the hydrodynamic limit we calculate an analytical expression for the intermediate scattering functions, which is in perfect agreement with event-driven Brownian dynamics simulations. From this, we derive an expression for persistent anticorrelations in the velocity autocorrelation function (VACF) for confined motion. Using numerical results of the cMCT equations for the VACF we also identify a crossover between different scalings corresponding to a transition from unconfined to confined behavior.

Stability mechanisms for plate-like nanoparticles immersed in a macroion dispersion

An integral equation theory and Monte Carlo simulations are applied to study a model macroion solution confined between two parallel plates immersed in a 1:1 electrolyte and the macroions' counterions. We analyze the cases in which plates are: (a) uncharged; (b) when they are like-charged to the macroions; (c) when they are oppositely charged to the macroions. For all cases a long range oscillatory behavior of the induced charge density between the plates is found (implying an overcompensation/undercompensation of the plates' charge density) and a correlation between the confined and outside fluids. The behavior of the force is discussed in terms of the macroion and ion structure inside and outside the plates. A good agreement is found between theoretical and simulation results.

State diagram for the electrostatic adsorption of charged colloids on confining walls: simulation and theory

We study the structure of charged colloidal suspensions under confinement and determine a state diagram for the occurrence of electrostatic adsorption onto the confining walls, an effect that results in the accumulation of particles on the bounding surfaces and that could be relevant in experiments. We use Monte Carlo simulations to quantify this structural transition and perform theoretical calculations based on integral equations. Overall, our results provide a guide for experimentalists dealing with charged colloidal systems to determine the relevance of this purely electrostatic effect.

Particle migration induced by confinement of colloidal suspensions along the gravitational direction

We confine charged spheres in cells with the smallest dimension along the direction of gravity ĝ. The particles are density mismatched with the surrounding medium and sediment along ĝ with typical Péclet numbers of Pe approximately 10(-3). After a certain time, we find that the number of particles N increases near both upper and lower plates until a characteristic time tau is reached; above this time N plateaus. We attribute the observed phenomenology to collective particle motions driven by gravity and mediated by hydrodynamic interactions; these could yield formation of swirls made of particles with correlated velocities that could eventually drive the particles towards the upper plate. The characteristic time for these migrations scales with plate-to-plate separation Lz as tau approximately Lz1.2, exactly as the characteristic decay time of velocity fluctuations in sedimentation processes [S. Y. Tee, Phys. Rev. Lett. 89, 054501 (2002)], despite that in these experiments the smallest cell dimension is perpendicular to ĝ and 7<Pe<50. In the absence of gravitational field, the observed particle migrations disappear, emphasizing the key role played by gravity in these experiments.

Entropic forces in dilute colloidal systems

Depletion forces can be accounted for by a contraction of the description in the framework of the integral equations theory of simple liquids. This approach includes, in a natural way, the effects of the concentration on the depletion forces, as well as energetic contributions. In this paper we systematically study this approach in a large variety of dilute colloidal systems composed of spherical and nonspherical hard particles, in two and in three dimensions, in the bulk and in front of a hard wall with a relief pattern. We show by this way the form in which concentration and geometry determine the entropic interaction between colloidal particles. The accuracy of our results is corroborated by comparison with computer simulations.

Structure and Adsorption of A Hard-Core Multi-Yukawa Fluid Confined in A Slitlike Pore: Grand Canonical Monte Carlo Simulation and Density Functional Study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: Grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.

Structure of Inhomogeneous Attractive and Repulsive Hard-Core Yukawa Fluid: Grand Canonical Monte Carlo Simulation and Density Functional Theory Study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.

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

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

Transformation from Rogers-Young approximation to the density functional approach for nonuniform fluids: numerical recipe

A numerical recipe is devised to extend the methodology [J. Chem. Phys. 112, 8079 (2000)] to nonhard-sphere nonuniform fluids where analytical expressions for the functional relationship of the bridge function as a function of indirect correlation function do not exist, the numerical recipe is also based on the universality of the free-energy density functional. As an example, the recipe is employed to calculate the density profile of a colloidal suspension near a single charged hard wall and the hard-sphere Yukawa fluid near a single hard wall and a single hard wall with an attractive tail, the agreement of the predictions of the theory with the simulation data is good. The difference of the present methodology from that of the weighted density approximation is discussed.

Energetic contributions to wall-particle depletion forces

Recently, depletion forces were accounted for by a contraction of the description based on the integral equations theory of simple liquids [Phys. Rev. E 61, 4095 (2000)]. The extension of those results to the case of inhomogeneous systems is reported here. Besides, the energetic contributions to the wall-particle depletion forces are studied, as they arise as soon as charge is put on some of the components of a binary mixture of hard spheres on the front of a hard wall. By charging the small particles the amplitude of the depletion attraction between wall and large particles is reduced, and can even become a repulsion. A similar effect is observed if an attractive interaction between wall and small particles is present.

Axial and angular correlations between colloidal particles in narrow cylindrical pores

In this work we present a study of the local structure of a model colloidal suspension highly confined inside a cylindrical pore. Such a study is based in Monte Carlo computer simulations, using the repulsive part of the Derjaguin-Landau-Verwey-Overbeek potential as the pair interaction between particles. The structural properties calculated here are the concentration profile n(rho), the axial pair correlation function g(z), and the axial-angular pair correlation function g(z,straight phi). The behavior of these quantities is analyzed as a function of the density of colloidal particles in the restricted space, and as a function of the size of the pore.