Electrostatic interactions between colloidal particles

N. Sun, J.Y. Walz, A model for calculating electrostatic interactions between colloidal particles of arbitrary surface topology. J. Colloid Interface Sci. 234(1), 90-105 (2001). doi 10.1006/jcis. 2000.7248... 

A substantial fraction of colloid studies refer to charged colloids in water or other solvents under conditions in which electrostatic interactions between colloidal particles are certain to be present. We note several of these, while recognizing that polyelectrolyte effects are generally beyond the scope of this volume. Fluorescence recovery after photobleaching was employed by Imhof, et al. to obtain the self-diffusion coefiBcient of silica spheres in LiCl dimethylformamide(16). Imhof, et al. s spheres were substantially charged Dg fell nearly tenfold with increasing... 

N. Sun and J. Y. Walz, J. Colloid Interface Sci., 234, 90 (2001). A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology. 

Figure 6.3. Schematic potential energy curve describing the interactions between colloidal particles. The overall potential is a sum of an electrostatic repulsive term which arises due to any charged groups on the surface of the particle and the attractive van der Waals term.

Polyelectrolyte molecules affect in a more complicated manner than the neutral ones the bridging interactions between colloidal particles because they influence through their dissociation the electrical potential of the electrical double layer [24 27] which, in turn, affects the conformation of the chains and the overall electrostatic interaction. 

On the basis of the disjoining pressure (44), an electrostatic part of the pair interaction between colloidal particles can be computed as... 

The classical DLVO (Derjaguin-Landau-Verwey-Overbeek) theory (Derjaguin and Landau, 1941 Yerwey and Overbeek, 1948) states that the stability of a colloidal system essentially depends on two independent interactions between colloidal particles van der Waals attractions and electrostatic repulsion ... 

The preceding section illustrates the variety of phenomena that may be observed in polymer-colloid-solvent mixtures. Polymer dissolved in a colloidal suspension is in some ways similar to ionic solutes responsible for electrostatic effects. Interactions between colloidal particles and polymer generate nonuniform distributions of polymer throughout the solution. Particle-particle interactions alter the equilibrium polymer distribution, producing a force in which sign and magnitude depend on the nature of the particle-polymer interaction. The major difference between polymeric and ionic solutions lies in the internal degrees of freedom of the polymer. Thus, a complete treatment of particle-polymer interactions requires detailed consideration of the thermodynamics of polymer solutions. 

The physical stability of a colloidal system is determined by the balance between the repulsive and attractive forces which is described quantitatively by the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. The electrostatic repulsive force is dependent on the degree of double-layer overlap and the attractive force is provided by the van der Waals interaction the magnitude of both are a function of the separation between the particles. It has long been realized that the zeta potential is a good indicator of the magnitude of the repulsive interaction between colloidal particles. Measurement of zeta potential has therefore been commonly used to assess the stability of colloidal systems. 

The second part is devoted to adsorption of polyelectrolytes at interfaces and to flocculation and stabilization of particles in adsorbing polymer solutions. A recent theory of the electrostatic adsorption barrier, some typical experimental results, and new approaches for studying the kinetics of polyelectrolyte adsorption are presented in the first chapter of this part. In the following chapters, results are collected on the electrical and hydrodynamic properties of colloid-polyelectrolyte surface layers, giving information on the structure of adsorbed layers and their influence on the interactions between colloidal particles examples and mechanisms are analyzed of polyelectrolyte-induced stabilization and fragmentation of colloidal aggregates ... 

On the basis of work done in the years just before World War II, Deijaguin and Landau [26] were able to explain in 1941 many of the complex phenomena involved in aggregative stability on the basis of forces of interaction between colloidal particles, namely the van der Waals-London forces of attraction and the electrostatic forces of repulsion. In the meantime, as a result of theoretical investigations and calculations performed in the years 1940-1944 and without the benefit of much of the literature that appeared during the war years, Verwey and Overbeek [7] formulated a theory of stability of lyophobic colloids and published it as a book in 1948. Because their... 

The experimentally relevant system of an electrically charged 2D colloid has been addressed with the model of identical, electrically charged, spherical particles at the interface between a dielectric fluid and an electrolyte (e.g., air/water). The direct electrostatic interaction between the particles is given asymptotically by a dipole-dipole repulsion (see Figure 2.1), described by a potential f/jep [59-61]. The electric field also exerts a vertical force on the particles and an electric... 

To calculate the electrostatic force, we first derive an expression for the Gibbs energy of an electric double layer. The energy of an electric double layer plays a central role in colloid science, for instance, to describe the properties of charged polymers (polyelectrolytes) or the interaction between colloidal particles. Here, we only give results for diffuse layers because it is simpler and in most applications only the diffuse layer is relevant. The formalism is, however, applicable to other double layers as well. 

In 1997, a Chinese research group [78] used the colloidal solution of 70-nm-sized carboxylated latex particles as a subphase and spread mixtures of cationic and other surfactants at the air-solution interface. If the pH was sufficiently low (1.5-3.0), the electrostatic interaction between the polar headgroups of the monolayer and the surface groups of the latex particles was strong enough to attract the latex to the surface. A fairly densely packed array of particles could be obtained if a 2 1 mixture of octadecylamine and stearic acid was spread at the interface. The particle films could be transferred onto solid substrates using the LB technique. The structure was studied using transmission electron microscopy. 

When two similarly charged colloid particles, under the influence of the EDL, come close to each other, they will begin to interact. The potentials will detect one another, and this will lead to various consequences. The charged molecules or particles will be under both van der Waals and electrostatic interaction forces. The van der Waals forces, which operate at a short distance between particles, will give rise to strong attraction forces. The potential of the mean force between colloid particle in an electrolyte solution plays a central role in the phase behavior and the kinetics of agglomeration in colloidal dispersions. This kind of investigation is important in these various industries ... 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

The electrostatic stabilization theory was developed for dilute colloidal systems and involves attractive van dcr Waals interactions and repulsive double layer interactions between two particles. They may lead to a potential barrier, an overall repulsion and/or to a minimum similar to that generated by steric stabilization. Johnson and Morrison [1] suggest that the stability in non-aqueous dispersions when the stabilizers are surfactant molecules, which arc relatively small, is due to scmi-stcric stabilization, hence to a smaller ran dcr Waals attraction between two particles caused by the adsorbed shell of surfactant molecules. The fact that such systems are quite stable suggests, however, that some repulsion is also prescni. In fact, it was demonstrated on the basis of electrophoretic measurements that a surface charge originates on solid particles suspended in aprotic liquids even in the absence of traces of... 

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