Double layers, origin

Figure 2.12 Simple capacitor model of electrode-solution interface as a charged double layer (original Helmholtz model). Negatively charged surface. Positively charged ions are attracted to the surface, forming an electrically neutral interphase.

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

Lyklema J (1995) Electric double layers, origin, thermodynamics, models, applications. In Fundamentals of interface and colloid science, vol D. Academic/ Elsevier, Chap 3... 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

The reader already familiar with some aspects of electrochemical promotion may want to jump directly to Chapters 4 and 5 which are the heart of this book. Chapter 4 epitomizes the phenomenology of NEMCA, Chapter 5 discusses its origin on the basis of a plethora of surface science and electrochemical techniques including ab initio quantum mechanical calculations. In Chapter 6 rigorous rules and a rigorous model are introduced for the first time both for electrochemical and for classical promotion. The kinetic model, which provides an excellent qualitative fit to the promotional rules and to the electrochemical and classical promotion data, is based on a simple concept Electrochemical and classical promotion is catalysis in presence of a controllable double layer. 

The parameter a in Equation (11.6) is positive for electrophobic reactions (5r/5O>0, A>1) and negative for electrophilic ones (3r/0Oelectrochemical promotion behaviour is frequently encountered, leading to volcano-type or inverted volcano-type behaviour. However, even then equation (11.6) is satisfied over relatively wide (0.2-0.3 eV) AO regions, so we limit the present analysis to this type of promotional kinetics. It should be remembered thatEq. (11.6), originally found as an experimental observation, can be rationalized by rigorous mathematical models which account explicitly for the electrostatic dipole interactions between the adsorbates and the backspillover-formed effective double layer, as discussed in Chapter 6. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

Figure 6.13. The electron distribution in the model metal jellium gives rise to an electric double layer at the surface, which forms the origin of the surface contribution to the work function. The electron wave function reaches...

Consider an atom approaching the surface in Fig. 6.23. If the upper level of the atom originally contained an electron, then upon adsorption it will transfer part of this electron density to the metal and become positively charged. This is the case with alkali atoms. The atom forms a dipole with the positive end towards the outside, which counteracts the double layer that constitutes the surface contribution to the work function of the metal (Fig. 6.13). Thus alkali atoms reduce the work function of a metal surface simply because they all have a high-lying s electron state that tends to donate charge to the metal surface. 

The origin of the observed correlation was not established, and the relation was not interpreted as causal. It could be argued that a sustained elevated potential due to as-yet unknown microbial processes altered the passive film characteristics, as is known to occur for metals polarized at anodic potentials. If these conditions thickened the oxide film or decreased the dielectric constant to the point where passive film capacitance was on the order of double-layer capacitance (Cji), the series equivalent oxide would have begun to reflect the contribution from the oxide. In this scenario, decreased C would have appeared as a consequence of sustained elevated potential. 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

The question arises of the extent to which the build-up of an electrode potential may significantly alter the original concentration of the solution in which the electrode is placed. Let us take the example of a silver electrode. Once the electrode has been immersed in an Ag+ solution, part of the Ag+ ions will be discharged by precipitation of the corresponding amount of Ag and to an extent such that the Nemst potential has been reached. In fact, a double layer at the electrode/solution interface has been formed whose structure cannot be as precisely described as has appeared from the model proposed by... 

In the closely related coulostatic method based on injection of a charge from a small condenser into an electrode in equilibrium with a redox system. The resulting time dependence of the electrode potential originates from the discharging of the electrical double layer by electrode reactions... 

The Gouy-Chapman theory relates electrolyte concentration, cation valence, and dielectric constant to the thickness of this double layer (see Equation 26.2). This theory was originally developed for dilute suspensions of solids in a liquid. However, experience confirms that the principles can be applied qualitatively to soil, even compacted soil that is not in suspension.5... 

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

As regards the origin of the double layer the Helmholtz theory gives no information, but several other theories have been formulated. Modem electrical theories suppose every conducting substance to contain large numbers of negatively charged ions, called electrons, which are exactly alike no matter in what substance they are found. When two s.T. 5... 

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