Collective Dynamics in Quasibidimensional Colloidal Suspensions

The Journal of Chemical Physics, 2002

We use an integral equation scheme to obtain self-consistently the effective interaction between colloids in salt-free charged colloidal suspensions. The colloid-counterion direct correlation function ͑DCF͒ is obtained for the fixed colloid-colloid pair structure by solving the corresponding hypernetted-chain equation ͑HNC͒. This DCF is then used to formulate an effective colloid-colloid pair potential for which the one-component reference hypernetted-chain equation is solved. Both processes are iterated until self-consistency is achieved. Counterion-counterion correlations are considered linear and uncoupled from the rest of the correlations. The method is based on a similar treatment utilized in liquid metals ͓Phys. Rev. B 61, 11400 ͑2000͔͒ and provides equivalent results to those obtained using the standard multicomponent HNC equation for mixtures of charged hard spheres. The theory proves rather accurate when compared with molecular dynamic simulations of charged hard and soft spheres for colloidal charges of up to 300. We study in detail the existence of net attractions between colloids in certain cases ͑especially in the presence of divalent and trivalent counterions͒ and how this attraction may lead to phase instability. The problem of the lack of solution of the integral equation for more realistic cases ͑larger charges͒ is also discussed.

The Journal of chemical …, 2010

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.

The Journal of Chemical Physics, 2002

We report the results of studies, using digital video microscopy, of the spatial distribution of particles in a quasi-one-dimensional colloidal liquid. The system studied consists of a water suspension of silica particles with diameter ϭ1.58 m confined in a 3 mϫ3 mϫ2 mm silicone elastomer channel. The measured spatial distributions have been characterized by the nearest-neighbor distribution function and the pair correlation function, and the pair correlation function has been inverted, using the hypernetted chain approximation, to yield the effective colloid-colloid interaction. The effective colloid-colloid interaction is found to have an attractive potential well with depth of ϳ0.3k B T at a colloid-colloid separation RϷ1.18. Molecular-dynamics simulations of the nearest neighbor and pair correlation functions carried out using the empirically determined colloid-colloid interaction are in very good agreement with the experimental data. The experimental data obtained rule out any important charge-charge contribution to the measured colloid-colloid interaction. It is suggested that because the host liquid does not wet the channel wall, and the colloid particles are tightly confined in the long narrow channel, capillary forces determine the effective colloid-colloid interaction. This suggestion is consistent with the determination ͑also reported͒ that the effective colloid-colloid interaction in a quasi-two-dimensional suspension of the same particles is different from that in the quasi-one dimensional suspension.

We present a general method for constructing effective pair interaction potentials in colloidal systems, which results from a contraction of the description of colloidal mixtures based on the integral equations theory of simple liquids. In order to illustrate its applicability, we calculate the entropy driven potentials in mixtures of hard spheres, as well as the screened coulombic interactions between charged particles. The accuracy of our results is pointed out by comparison with computer simulations for the case of entropy driven potentials and experimental data for the case of charged colloids.

Physical Review E, 2010

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to twodimensional gravity. In particular it is a non-integrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points towards their experimental realizations via colloidal suspensions.

Advances in Colloid and Interface Science, 2007

The interaction forces acting between colloidal particles in suspensions play an important part in determining the properties of a variety of materials, the behaviour of a range of industrial and environmental processes. Below we briefly review the theories of the colloidal forces between particles and surfaces including London-van der Waals forces, electrical double layer forces, solvation forces, hydrophobic forces and steric forces. In the framework of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, theoretical predictions of total interparticle interaction forces are discussed. A survey of direct measurements of the interaction forces between colloidal particles as a function of the surface separation is presented. Most of the measurements have been carried out mainly using the atomic force microscopy (AFM) as well as the surface force apparatus (SFA) in the liquid phase. With the highly sophisticated and versatile techniques that are employed by far, the existing interaction theories between surfaces have been validated and advanced. In addition, the direct force measurements by AFM have also been useful in the explaining or understanding of more complex phenomena and in engineering the products and processes occurring in many industrial applications.

2001

These lecture notes address some recent advances in our understanding of macroionic interactions inspired in part by the evolution of new techniques for studying macroions' dynamics.

The Canadian Journal of Chemical Engineering, 2008

Charged nano-colloidal particles self-assemble and display ordered arrays or other structures at liquid interfaces. We used Monte Carlo (MC) simulations to examine the effect of long-range repulsive collective inter-particle interactions on structural transitions from liquid-like to crystallike. We used the asymptotic pair interaction potential proposed by Hurd (J. Phys. A. Math Gen 18, L1055 (1985)), which includes both the screened Coulombic contribution and the dipole-dipole interaction. The effects of the collective inter-particle interactions on the interfacial 2-D colloid structure formation were quantified by the radial distribution function and the potential of the mean force. The MC simulations agreed with the experimentally observed particle structural transitions at both the air-water and oil-water interfaces. The effects of the particle charge and interfacial coverage on the 2-D structure formation were analyzed. The significance of the results lies in their potential applications in inducing 2-D structural transitions in interfacial colloids to form ordered structures; this controls the emulsion and foam stability, and aids in the fabrication of patterned materials with desirable properties. Les particules nano-colloïdales s'auto-assemblent et montrent des dispositions ordonnées ou d'autres structures aux interfaces liquides. On a eu recours à des simulations de Monte Carlo (MC) pour examiner l'effet des interactions collectives répulsives de longue durée sur les transitions structurelles de la forme de type liquide à la forme de type cristaux. On a utilisé le potentiel d'interaction par paires asymptotiques proposé par Hurd (J. Phys. A. Math Gen 18, L1055 (1985)), qui inclut la contribution de Coulomb et l'interaction dipôle-dipôle. Les effets des interactions interparticulaires collectives sur la formation des structures colloïdales interfaciales en 2-D ont été quantifiés par la fonction de distribution radiale et le potentiel de la force moyenne. Les simulations MC concordent avec les transitions structurelles des particules observées expérimentalement aux interfaces air-eau et huile-eau. Les effets de la charge des particules et de la récupération interfaciale sur la formation des structures en 2-D ont été analysés. La pertinence des résultats repose sur leurs applications potentielles lorsque des transitions structurelles en 2-D sont induites dans les colloïdes interfaciaux pour former des structures ordonnées; ceci permet de contrôler l'émulsion et la stabilité de la mousse et aide à la fabrication de matériaux structurés avec les propriétés souhaitables.

Le Journal de Physique IV, 2000

The paper summarizes recent theoretical work on the effective interactions between charge-stabilized, spherical colloidal particles. Despite the purely repulsive nature of the effective pair potential, fluid-fluid phase separation is shown to occur at very low salt concentrations, due to a frequently forgotten "volume" term. A longrange attractive component to the pair interaction is predicted when the colloidal particles are confined by charged surfaces (e.g. in slit or pore geometries), in agreement with recent experimental findings. The importance of excluded volume and solvent effects is briefly discussed. 1. Colloids and ions Polymeric or mineral colloidal particles carrying ionizable surface radicals will release counterions when suspended in a solvent of high dielectric constant E , like water; these counterions, together with ions from any electrolyte, will form electric double-layers in the vicinity of the highly charged colloid surfaces. The double-layers are characterized by ion density profiles showing a strong enhancement of local counterion density and a depletion of coions. The colloidal particles may be mesoscopic globular objects, like proteins or synthetic polystryrene balls, lamellar objects, like clay platelets, which are rather rigid, and flexible membranes, or rod-like objects like the tobacco mosaic virus (TMV) or semi-flexible DNA molecules. The latter are an example of charged polymers, or polyelectrolytes that are considered elsewhere in these Proceedings [I]. The present paper is restricted to rigid spherical or lamellar colloidal particles. The statistical description of the very asymmetric three-component system involving highly charged colloidal particles (henceforth referred to as polyions), microscopic co-and counterions (microions) and solvent molecules, poses a challenging problem. The three key length scales are the characteristic size a of the polyions (e.g. the diameter), the thickness of the double-layer, expected to be of the order of the Debye screening length A, of the microions, and the correlation length d of the solvent, which is of the order of the diameter of the solvent molecules. Under most physical conditions these length scales are well separated, i.e. : making it natural to look for a coarse-grained statistical description. The second inequality justifies modelling the solvent by a mere dielectric continuum (E) ; this is the common "primitive model" of electrochemistry, and will be adopted until further notice. The first inequality in (1) may be put to good use to derive effective interactions between polyions within the mean field Poisson-Boltzmann (PB) theory. A linearized version of PB theory leads to the well known DLVO effective pair potential between two spherical polyions [2,3]:

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

Computer simulations and theory are used to systematically investigate how the effective force between two big colloidal spheres in a sea of small spheres depends on the basic (big-small and small-small) interactions. The latter are modeled as hardcore pair potentials with a Yukawa tail which can be either repulsive or attractive. For a repulsive small-small interaction, the effective force follows the trends as predicted by a mapping onto an effective nonadditive hardcore mixture: both a depletion attraction and an accumulation repulsion caused by small spheres adsorbing onto the big ones can be obtained depending on the sign of the big-small interaction. For repulsive big-small interactions, the effect of adding a small-small attraction also follows the trends predicted by the mapping. But a more subtle "repulsion through attraction" effect arises when both big-small and small-small attractions occur: upon increasing the strength of the small-small interaction, the effec...