Thermodiffusion of interacting colloids. II. A microscopic approach

A microscopic approach is presented to describe the contribution to the thermal diffusion coefficient of colloids due to intercolloidal particle interactions. An exact expression for the leading-order virial coefficient of the thermal diffusion coefficient of interacting colloidal spheres is derived in terms of the intercolloidal pair-interaction potential and hydrodynamic interaction functions. This general expression is explicitly evaluated for hard-core interactions and for spheres with a short-ranged attractive potential. The derivation is based on a Smoluchowski equation that is generalized to include temperature gradients. For short-ranged attractive potentials, a negative Soret coefficient is predicted under certain conditions, when the depth of the attraction increases with increasing temperature.     

Colloidal Interaction at the Air-Liquid Interface

In this paper, we propose a model to analyze the stability of colloidal particles at the air-liquid interface. The proposed model for the colloidal particle interaction considers DLVO interactions and capillary, hydrophobic, and dipolar interactions between the particles. Typical values from the literature were assigned to most parameters included in the model. Numerical computation revealed the most important parameter in determining the total interaction is the density of dipoles at the external surface of the particles. We have found significant differences for the pair potential between hydrophobic and hydrophilic particles. Hydrophobic particles must aggregate in a principal minimum of the interaction potential curve while hydrophilic particles aggregate in a secondary minimum. Copyright 2000 Academic Press.     

Evanescent Wave Light Scattering A Fusion of the Evanescent Wave and Light Scattering Techniques to the Study of Colloids and Polymers Near the Interface

The evanescent wave light scattering technique, which is produced by a fusion of the evanescent wave technique and light scattering technique, is a very powerful and useful tool for investigation of colloidal particles and polymers near the surface and interfaces. We have developed two kinds of evanescent wave light scattering apparatuses. One is the evanescent wave dynamic light scattering (EVDLS) technique and the other is the evanescent wave light scattering microscope (EVLSM). By EVDLS, the diffusion behavior of a colloidal particle near the interface can be extracted quantitatively as a function of the distance from the interface. The diffusion coefficient was smaller than those for particles in bulk, reflecting electrostatic and hydrodynamic interactions. By EVLSM, the interaction potential profile between a colloidal particle and the surface in dispersion can be evaluated directly. EVLSM will play an important role in colloidal interaction studies, especially at a low ionic strength. It is also pointed out that a particle dynamics study is also possible by the EVLSM technique. A new field will be developed in colloid science and polymer science by application of the evanescent wave light scattering technique, i. e. a fusion of the evanescent light and a light scattering techniques.     

On the role of solute solvation and excluded-volume interactions in coupled diffusion

Coupled diffusion is observed in multicomponent liquid mixtures in which strong thermodynamic interactions occur. This phenomenon is described by cross terms in the matrix of multicomponent diffusion coefficients. This paper reports a theoretical analysis on the relative role of thermodynamic factors and Onsager cross-coefficients on cross-diffusion coefficients relevant to ternary mixtures containing macromolecules or colloidal particles in the presence of salting-out conditions. A new model based on frictional coefficients between solvated solutes is reported. This model predicts that the Onsager cross-coefficient is negative and contributes significantly to cross-diffusion coefficients even at infinite dilution for solutes with a large difference in size. These predictions are consistent with recent experimental results. The role of preferential solvation and excluded-volume interactions on the thermodynamic factors are also examined. Excluded-volume interactions are introduced through the use of the McMillan-Mayer thermodynamic framework after emphasizing some important aspects of diffusion reference frames and thermodynamic driving forces. Finally, new expressions for cross-diffusion coefficients are proposed.     

Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

Potential barrier gravitational field-flow fractionation based on the variation of the pH solution for the analysis of colloidal materials

Summary Potential barrier gravitational field-flow fractionation (PBGFFF) is a new technique for the separation and characterization of colloidal materials. It consists in changing the potential energy of interaction between the colloidal particles and the channel wall by varying the solution ionic strength or the Hamaker constant and the surface potential of the particles. In this work the PBGFFF technique based on the particles' surface potential variation, by varying the pH, is presented. Polydisperse colloidal particles of the sulphide CuZnS (with molar ratio Cu/Zn-10/90) are used as a model sample. Comparison of the results obtained by PBGFFF with those given by conventional gravitational fieldflow fractionation and laser counter measurements, shows that one could use PBGFFF not only for the separation and characterization of colloidal materials, but also for the investigation of the interactions between colloids and solid surfaces.     

A new model system for diffusion NMR studies of concentrated monodisperse and bidisperse colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.     

Measuring colloidal interactions with confocal microscopy

We use confocal laser scanning microscopy to measure interactions in colloidal suspensions. By inverting the radial distribution function, determined by tracking the particle coordinates, we obtain the effective interaction between the colloidal particles. Although this method can be applied to arbitrary colloidal interactions, here we demonstrate its efficacy with two well-known systems for which accurate theories are available: a colloid-polymer mixture and binary hard spheres. The high sensitivity of this method allows for the precise determination of complex interactions, as exemplified, for example, by the accurate resolution of the oscillatory effective potential of the binary hard sphere system. We argue that the method is particularly well suited for the determination of attractive forces.     

Spontaneous formation of mesostructures in colloidal monolayers trapped at the air-water interface: a simple explanation

The spontaneous formation of loosely bound ordered aggregates, foam, voids, chains, striations, and loops (see Figure 1a), called mesostructures hereafter, has been observed in colloidal monolayers trapped at the air-water interface. The distance between particles in these mesostructures is of the order of the particle radius (micrometers), implying that the colloidal interaction potential has a minimum at such distances, which could induce the phase separation of colloidal monolayers in dense and dilute regions. This is at odds with the accepted theory (Derjaguin-Landau-Verwey-Overbeek (DLVO)) of colloidal interactions, which predicts a secondary minimum at distances of nanometers between pairs of interacting particles. Moreover, the introduction of capillary, hydrophobic, and dipolar interactions between particles in an extended DLVO theory is not able to explain the spontaneous formation of mesostructures either. Recently, a great deal of effort has focused on understanding the mechanism behind the phenomenon of long-range attraction between colloidal particles confined in interfaces. In particular, this attraction has been employed to explain the spontaneous formation of mesostructures. Here, we show that the appearance of our mesostructures is due to the contamination of colloidal monolayers by silicone oil (poly(dimethylsiloxane)), which arises from the coating of the needles and syringes used to deposit and spread the particle solution at the air-water interface. The difference in the interfacial tension of water and silicone oil accounts for the formation of the experimentally observed mesostructures.     

On the stability of concentrates. Non-aqueous dispersions

It is demonstrated that the depth of the potential well between two colloidal particles which interact via van der Waals interactions can be minimized if they are covered with a shell of adsorbed surfactant molecules whose Hamaker constant is near to that or the liquid medium. This result is used to explain some experimental observations (I. Sushumna, R.P. Gupta and E. Ruckenstein, J. Mater. Res., 7 (1992) 2884) which indicate that long-chain fatty acids with an alkyl side chain of 5–10 carbon atoms located far from the head group of the surfactant lead to lower paste viscosities than those without side chains or with longer side alkyl chains. It is also suggested that, in concentrated suspensions, the collective interactions when the pair interaction is attractive can lead to an effective repulsion component between two neighboring particles, and that this effect may contribute to the stability of the concentrated dispersions.     

Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power q of the interparticle distance, and the attractive part varying with an inverse power p. We consider the combinations (12,11) (model I), (12,6) (model II), and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configurational entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configurational entropy, knowledge of the high temperature activation energies in order to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior.     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Energy of interaction in colloids and its implications in rheological modeling

This work deals with the problem of deriving theoretical connections between rheology and interparticle forces in colloidal suspensions. The nature of interparticle forces determines the colloidal structure (crystalline order due to long range repulsive forces, flocculation due to attractive forces, etc.) and hence, the flow behavior of suspensions. The aim of this article is to discuss how these interactions enter the modeling of rheometric functions, in particular, the shear viscosity. In this sense, the main interactions commonly appearing in colloids are reviewed, as well as the role they play in phase transition behavior. Then, a series of approaches relating the interaction potential to viscosity is examined. The results of applying these models to experimental data are also discussed. Finally, examples of viscosity modeling for different interaction potentials are given, by using the structural model proposed previously by the authors. The possibility of relating the flow behavior of colloidal suspensions to the interaction between particles offers new perspectives for the study and technical applications of these systems.     

The Correlation Functions of a Suspension of Large Particles in Amorphous Polybutadiene: A Molecular Dynamics Simulation Study

The correlation functions of a suspension of Lennard-Jones large particles in a model 1,4-cis-polybutadiene solvent have been investigated by molecular dynamics simulations. We present the effects of temperature, the degree of polymerization, and the solvent/large particle density on the effective interactions between the large particles and the solvent. It is found that as the temperature increases, the structure between solvent-solvent, solvent-large particle, and large-large particle decreases. Additionally, as the bulk density or the chain length is increased, the attractive part of the large-large interaction becomes weaker and small. We believe that in part, this is due to the polymer having collapsed onto itself and entangling the large particles and lessening their interaction until they are actually in contact. Increasing the length of the polymer also entangles the large particles. However, we believe that this may be a general feature that is a characteristic of a polymer solvent containing macroscopically large colloidal particles even though entanglement should be of less significance. Copyright 2000 Academic Press.     

DLVO AND NON-DLVO SURFACE FORCES AND INTERACTIONS IN COLLOIDAL DISPERSIONS

Some aspects of DLVO and non-DLVO forces in colloidal systems are over-viewed. The influence of long range interactions on some kinetic properties of dispersions, as Brownian diffusion, is discussed. It is shown, both theoretically and experimentally, that the electrostatic repulsion increases the collective diffusivity. The film stratification and oscillatory structure forces in colloidal suspensions are considered within the framework of an uniform approach The presence of small colloidal species (e. g. micelles or polymer molecules) may lead to several maxima and minima in the disjoining pressure isotherm. The particular case of interacting emulsion droplets is examined accounting for the interfacial deformability. The droplet deformation acts as a soft repulsion but affects also the remaining contributions to the interaction energy due to changes of the droplet shape. A general procedure for calculating the inter-droplet interaction energy, as well as the equilibrium film radius and thickness in a doublet of droplets, is suggested. The energy of interaction between charged colloidal particles, due to correlations of the density fluctuations in the electric double layer is also studied. It is found that this effect may lead to attraction greater than the van der Waals contribution, especially when multivale counter ions are present.     

Engineering DNA-mediated colloidal crystallization

DNA is a powerful and versatile tool for nanoscale self-assembly. Several researchers have assembled nanoparticles and colloids into a variety of structures using the sequence-specific binding properties of DNA. Until recently, however, all of the reported structures were disordered, even in systems where ordered colloidal crystals might be expected. We detail the experimental approach and surface preparation that we used to form the first DNA-mediated colloidal crystals, using 1 mum diameter polystyrene particles. Control experiments based on the depletion interaction clearly indicate that two standard methods for grafting biomolecules to colloidal particles (biotin/avidin and water-soluble carbodiimide) do not lead to ordered structures, even when blockers are employed that yield nominally stable, reversibly aggregating dispersions. In contrast, a swelling/deswelling-based method with poly(ethylene glycol) spacers resulted in particles that readily formed ordered crystals. The sequence specificity of the interaction is demonstrated by the crystal excluding particles bearing a noninteracting sequence. The temperature dependence of gelation and crystallization agree well with a simple thermodynamic model and a more detailed model of the effective colloidal pair interaction potential. We hypothesize that the surfaces yielded by the first two chemistries somehow hinder the particle-particle rolling required for annealing ordered structures, while at the same time not inducing a significant mean-force interaction that would alter the self-assembly phase diagram. Finally, we observe that particle crystallization kinetics become faster as the grafted-DNA density is increased, consistent with the particle-particle binding process being reaction, rather than diffusion limited.     

A light scattering study of concentrated dispersions in nonaqueous media

Interparticle interactions between colloidal poly(methylmethacrylate) particles stabilised by poly(12-hydroxystearic acid) in non-aqueous media have been investigated using time-average light scattering. The problem of multiple scattering was avoided by using a binary mixture of solvents such that the colloidal particles were optically matched. This enabled the static structure factor to be measured and from the small scattering vector expansion the osmotic pressure to be determined. The softness of the pairwise interaction potential has been exposed using the Chandler-Weeks-Anderson perturbation theory. However, it is concluded that dispersions of the type studied can be reasonably well approximated by a hard sphere fluid model.