Electric Double Layer, Lateral Fields

Schwarz theory provides a practical tool for analyzing measured data, but the theory has been criticized for neglecting the diffusion of ions in the bulk solution near the surface. Efforts have been made by, among others, Dukhin, Fixman and Chew, and Sen to employ Gouy-Chapman theory on particle suspensions, but the resulting theories are very complex and difficult to use on biological materials. Mandel and Odijk (1984) have given a review of this work. 

Simplified models that use the Gouy-Chapman theory have been presented by, for example, Grosse and Foster (1987), but the assumptions made in their theory limits the utility of the model. 

Hydration of ions is due to the dipole nature of water. In the case of a cation in water, the negative (oxygen) end of the neighboring water molecules will be oriented toward the ion, and a sheet of oriented water molecules will be formed around the cation. This sheet is called the primary hydration sphere. The water molecules in the primary hydration sphere will furthermore attract other water molecules in a secondary hydration sphere, which will not be as rigorous as die primary sphere. Several sheets may likewise be involved until at a certain distance the behavior of the water molecules will not be influenced by the ion. 

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What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

In addition, there are techniques developed in other fields of colloid science, which are not directly related to classical electrochemistry. In surface force experiments, for instance, the distance dependence of the electric double layer is measured precisely. This will be discussed later. 

The stability of inverse micelles has been treated by Eicke (8,9) and by Muller (10) for nonaqueous systems, while Adamson (1) and later Levine (11) calculated the electric field gradient in an inverse micelle for a solution in equilibrium with an aqueous solution. Ruckenstein (5) later gave a more complete treatment of the stability of such systems taking both enthalpic (Van der Waals (VdW) interparticle potential, the first component of the interfacial free energy and the interparticle contribution of the repulsion energy from the compression of the diffuse part of the electric double layer) and entropic contributions into consideration. His calculations also were performed for the equilibrium between two liquid solutions—one aqueous, the other hydrocarbon. 

Charged particles in weak electrolytes have associated with them an electrical double layer. When these particles settle under gravity the double layer is distorted with the result that an electrical field is set up that opposes motion. This effect was first noted by Dorn [74] and was studied extensively by Elton et. al. [75-78] and later by Booth [79,80]. 

In the first part of this century, electrochemical research was mainly devoted to the mercury electrode in an aqueous electrolyte solution. A mercury electrode has a number of advantageous properties for electrochemical research its surface can be kept clean, it has a large overpotential for hydrogen evolution and both the interfacial tension and capacitance can be measured. In his famous review [1], D. C. Grahame made the firm statement that Nearly everything one desires to know about the electrical double layer is ascertainable with mercury surfaces if it is ascertainable at all. At that time, electrochemistry was a self-contained field with a natural basis in thermodynamics and chemical kinetics. Meanwhile, the development of quantum mechanics led to considerable progress in solid-state physics and, later, to the understanding of electrostatic and electrodynamic phenomena at metal and semiconductor interfaces. 

One year later, Brust and Schiffrin [28,29] published a method for AuNPs synthesis which has a considerable impact on the overall field in less than a decade because it allowed the facile synthesis of thermally stable and air-stable AuNPs of reduced dispersity and controlled size for the first time. In this method, the gold colloids are sterically stabilized by organic molecules having thiol, amide or acid groups in contrast to the citrate reduction method where the gold colloids are kinetically stabilized in aqueous solutions by an electrical double layer [28,29], The main advantage of the Brust method is that the gold particles behave in a way as chemical compounds. These AuNPs can be repeatedly isolated and... 

Later work has thrown doubts on these all too simple interpretations of the relation between charge and stability, but nevertheless the general idea, that the stability of hydrophobic sols is governed by the charge or more generally, by the electrical double layer of the particles, still survives and has. lost nothing of its importance in the field of hydrophobic colloids. 

The electrochemical double layer offers the exceptional possibility of investigating the Stark effect at very high electric fields. Some important progress has been made in the theoretical treatment of the problem. Experimental data of potential effects upon the frequency and/or the intensity of vibrational modes must discriminate between the pure electric field effect and the secondary effect of potential on the coverage and, consequently, on the lateral interactions. 

This confirmation of the Smoluchowski derivation also illustrates why it is generally valid at high Ka (outside the relatively thin double layer, general hydrodynamics applies with zero electric field) and why the outcome is independent of a ( ( is independent of a). Smoluchowski already anticipated that the equation therefore remains valid for other than spherical geometries (Including hollow and irregularly formed surfaces) provided xa 1. This was later confirmed by Morrison ),... 

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