Electrical double layer, colloid particle

Figure 7.11. Representation of negatively charged hydrophobic colloidal particles surrounded in solution by positively charged counter-ions, forming an electrical double layer. (Colloidal particles suspended in water can have either a negative or a positive charge.)...

Splelman L A and Friedlander S K 1974 Role of the electrical double layer In particle deposition by convective diffusion J. Colloid. Interfaoe. Sol. 46 22-31... 

Spielman, L. A. and FRIEDLANDER, S. K. J. Colloid and Interface. Sci. 46 (1974) 22. Role of the electrical double layer in particle deposition by convective diffusion. 

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. 

Martmez-Pedrero R, Tirado-Miranda M., Schmitt A., and Callejas-Femandez J. 2007. Structure and stability of aggregates formed by electrical double-layered magnetic particles. Colloids Surf. A 306 158-165. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

Loeb, AL Overbeek, JTG Wiersema, PH, The Electrical Double Layer Around a Spherical Colloid Particle, Computation of the Potential, Charge Density, and Free Energy of the Electrical Double Layer Around a sperical Colloid Particle M.I.T. Press Cambridge, MA, 1961. Lorentz, HA, Wied, Ann. 11, 70, 1880. 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

Each colloid particle is surrounded with an electric double layer. 

Another possibility that could explain the effect of illumination is a change in the electric double layer surrounding the CdSe particles, either adsorbed on the substrate or in the solution, which could lower a potential barrier to adsorption and coalescence, as suggested previously for film formation from Se colloids under illumination [93]. Partial coalescence would reduce the blue spectral shift due to size quantization. However, the spectral shape is not expected to undergo a fundamental change in this case. The photoelectrochemical explanation therefore appears more reasonable. 

Diffusion, of molecular species as well as colloidal particles, plays perhaps a more dominant role in many topics of interest to us. For example, without diffusion of ions we will not have the diffuse electrical double layers next to charged surfaces (discussed in Chapter 11). At the colloidal level, diffusion plays a central role in the transport and collision of particles in colloidal stability (discussed in Chapter 13). There are many more such examples. 

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. 

Electrostatic and electrical double-layer forces play a very important role in a number of contexts in science and engineering. As we see in Chapter 13, the stability of a wide variety of colloids, ranging from food colloids, pharmaceutical dispersions, and paints, to colloidal contaminants in wastewater, is affected by surface charges on the particles. The filtration efficiency of submicron particles can be diminished considerably by electrical double-layer forces. As we point out in Chapter 13, coagulants are added to neutralize the electrostatic effects, to promote aggregation, and to enhance the ease of separation. 

For studying the stability of colloidal particles in suspension (Chapter 13) or for determining the potential at the surface of particles (Chapter 12), one often needs expressions for potential distributions around small particles that have curved surfaces. Solving the Poisson-Boltzmann equation for curved geometries is not a simple matter, and one often needs elaborate numerical methods. The linearized Poisson-Boltzmann equation (i.e., the Poisson-Boltzmann equation in the Debye-Hiickel approximation) can, however, be solved for spherical electrical double layers relatively easily (see Section 12.3a), and one obtains, in place of Equation (37),... 

Hunter, R. J., Zeta Potentials in Colloid Science Principles and Applications, Academic Press, London, 1981. (Advanced level. The focus of this book is on the role of electrical double layers and zeta potential on electrophoresis and electroviscous effects. This volume presents some details on electrical double layers around nonspherical particles not discussed in the present book.)... 

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