Electrostatic interactions/forces colloids

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 ... 

FIGURE 8.25 The stability of a sol (a suspension of colloidal particles) may be evaluated from the balance of repulsive (electrostatic) interaction forces and attractive (dispersive) interaction forces, e.g., by applying the DLVO theory (Equation 8.103). If a potential energy barrier exists the system is stable (left). If the barrier is removed, the coagulation of the particles is contolled by diffusion alone. (Courtesy of Jean Le Bell.)... 

A detailed study by Grieser and co-workers [169] of the forces between a gold-coated colloidal silica sphere and a gold surface reveals the preferential adsorption of citrate ions over chloride to alter the electrostatic interaction. 

Vakarelski et al. [88] also investigated the adhesive forces between a colloid particle and a flat surface in solution. In their case they investigated a sihca sphere and a mica surface in chloride solutions of monovalent cations CsCl, KCl, NaCl, and LiCl. The pH was kept at 5.6 for all the experiments. To obtain the adhesive force in the presence of an electrostatic interaction, they summed the repulsive force and the pull-off force (coined foe by the authors ) to obtain a value for the adhesive force that is independent of the electrostatic component. 

Double-layer forces are commonly used to induce repulsive interactions in colloidal systems. However, the range of electrostatic forces is strongly reduced by increasing the ionic strength of the continuous phase. Also, electrostatic effects are strong only in polar solvents, which is a severe restriction. An alternative way to create long-range repulsion is to adsorb macromolecules at the interface between the dispersed and the continuous phase. Polymer chains may be densely adsorbed on surfaces where they form loops and tails with a very broad distribution of sizes... 

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 forces also play an important role in the conformation and structure of macromolecules such as polymers, polyelectrolytes, and proteins. The self-assembly of proteins from disks to virus is triggered by electrostatic interactions between neighboring subunits. In the case of polyelectrolytes (polymer molecules with charges) and charged colloids, transport behavior such as rheology is also affected significantly by charge effects, as we have already seen in Chapter 4. 

A variety of methods have been demonstrated for crystallizing monodispersed spherical colloids (such as polymer beads and silica spheres) into long-range ordered lattices. Some of the commonly used ones include sedimentation, self-assembly via repulsive electrostatic interaction, ordering via attractive capillary forces, and crystallization under physical confinement. 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

Electrostatic. Virtually all colloids in solution acquire a surface charge and hence an electrical double layer. When particles interact in a concentrated region their double layers overlap resulting in a repulsive force which opposes further approach. Any theory of filtration of colloids needs to take into account the multi-particle nature of such interactions. This is best achieved by using a Wigner-Seitz cell approach combined with a numerical solution of the non-linear Poisson-Boltzmann equation, which allows calculation of a configurational force that implicitly includes the multi-body effects of a concentrated dispersion or filter cake. 

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. 

For well-dispersed colloid systems, particle electrophoresis has been the classic method of characterization with respect to electrostatic interactions. However, outside the colloidal realm, i.e., in the rest of the known world, the measurement of other electrokinetic phenomena must be used to characterize surfaces in this respect. The term electrokinetic refers to a number of effects induced by externally applied forces at a charged interface. These effects include electrophoresis, streaming potential, and electro-osmosis. 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

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