Electrostatic double layer work

The classic 1948 Verwey-Overbeek text is well worth studying even today. E. J. W. Verwey and J. Th. G. Overbeek, Theory of the Stability ofLyophobic Colloids (Dover, Mineola, NY, 1999 originally published by Elsevier, New York, 1948). In 1967 Verwey told me that their studies were done in secret while Nazi soldiers controlled the Philips Laboratories where he and Overbeek pretended to do assigned work. Because they could publish nothing during the war, the world was eventually blessed with a coherent monograph that has defined much of colloid research ever since. This text is especially valuable for its sensitive, systematic treatment of electrostatic double layers. 

Research has shown that a solute with a diameter closer to that of zeolite pore dimension showed higher adsorption (close fit mechanism). An important consideration for applying zeolites in drinking water treatment practice is that their size exclusion and close fit adsorption mechanism makes them effective for the removal of specific solutes. [4]. Because the Si Al ratio allows for tuning of the surface properties and the resultant electrostatic double layer such membranes could also be tuned for specific ion-selective applications, but further work is needed to fully understand the connection between zeolite chemistry and membrane performance. Osewe (2014) investigated the dissipation half-life of malathion as affected by the largest window opening for FAU, MOR, and ZSM-5s zeolites [16]. 

Despite these arguments and the conceptual attractiveness of the procedure which is sketched in Fig. 1 convincing evidence for the relevance of a particular gas phase adsorption experiment can only be obtained by direct comparison to electrochemical data The electrode potential and the work function change are two measurable quantities which are particularly useful for such a comparison. In both measurements the variation of the electrostatic potential across the interface can be obtained and compared by properly referencing these two values 171. Together with the ionic excess charge in the double layer, which in the UHV experiment would be expressed in terms of coverage of the ionic species, the macroscopic electrical properties of the interracial capacitor can thus be characterized in both environments. 

If one defines the electrostatic potential of phase, 4, as the work necessary to carry the unit charge from infinity to within this phase, all the layers of the double layer can be assigned a phase potential. In Figure 26 the variation in the potential profile within the double layer is shown. 

The electrical double layer has been dealt with in countless papers and in a number of reviews, including those published in previous volumes of the Modem Aspects of Electrochemistry series/ The experimental double layer data have been reported and commented on in several important works in which various theories of the structure of the double layer have been postulated. Nevertheless, many double layer-related problems have not been solved yet, mainly because certain important parameters describing the interface cannot be measured. This applies to the electric permittivity, dipole moments, surface density, and other physical quantities that are influenced by the electric field at the interface. It is also often difficult to separate the electrostatic and specific interactions of the solvent and the adsorbate with the electrode. To acquire necessary knowledge about the metal/solution interface, different metals, solvents, and adsorbates have been studied. 

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

During the 1930 s a clearer idea of the role of the electrical double layer in stabilising colloidal particles began to emerge, particularly in the work of Verwey (5), Kruyt (6) and Derjaguin (7). In 1938 in a classic paper Langmuir (8) showed that when an overlap of double layers occurred, with two flat plates whose surfaces were at the same electrostatic potential, then a repulsion pressure was developed between them. 

The role of electrostatic repulsion in the stability of suspensions of particles in non-aqueous media is not yet clear. In order to attempt to apply theories such as the DLVO theory (to be introduced in Section 5.2) one must know the electrical potential at the surface, the Hamaker constant, and the ionic strength to be used for the non-aqueous medium these are difficult to estimate. The ionic strength will be low so the electric double layer will be thick, the electric potential will vary slowly with separation distance, and so will the net electric potential as the double layers overlap. For this reason the repulsion between particles can be expected to be weak. A summary of work on the applicability or lack of applicability of DLVO theory to non-aqueous media has been given by Morrison [268],... 

The concept of double layer structure is far from being well established and evaluated. The models presented above give emphasis to electrostatic considerations. Chemical models have been developed that consider the electronic distribution of the atoms in the electrode, which is related to their work function. This was only possible after experimental... 

To get the interaction potential we must first evaluate the free energy of formation of the electrical double layer between two charged bodies. This is defined as the work done in charging up the surfaces. The process by which uniformly charged surfaces are charged up from a neutral reference state has been discussed by Yerwey and Overbeek [4], who have shown that the electrostatic work of charging a surface is given by the simple formula... 

The vast majority of work on particle-surface electrostatic interactions has neglected any effects due to particle motion. However, both theoretical [31,32] and experimental work [33-35] have been done on the problem of a charged particle interacting with a charged wall in a linear shear flow. In the theoretical treatment, it is assumed that the double layer thickness is small compared to both the particle diameter and the surface-to-particle gap. Hence, changes in the pressure and potential profiles in the gap caused by motion can be written as small perturbations to their equilibrium profiles. In the region outside the small double layers, the fluid velocity v and perturbation pressure dp are governed by Stokes equations... 

Up till about 1921, it was often supposed that the potential could be identified with the single potential difference at the phase boundary. Freundlich and his collaborators1 showed that this is quite impossible, since the variation with concentration, and the influence of adsorbed substances, are entirely different in the two cases sometimes indeed the two potentials may have different signs. The phase boundary potential, if defined as the Volta potential, is the difference between the energy levels of the charged component, to which the phase boundary is permeable, inside the two phases when these are both at the same electrostatic potential. We have seen that it is difficult, or impossible, to define the phase boundary potential in any other way (see 2 and 3). It includes the work of extraction of the charged component from each phase, and this includes the part of the double layer which according to Stern s theory is fixed. The potential is merely the potential fall in the mobile, diffuse part of the double layer, and is wholly within one phase. 

Theories of colloid stability based on electrostatics go way back beyond the DLVO theory, to the Gouy-Chapman theory of the electrical double layer proposed in the early 1910s and the Stem theory of counterion condensation proposed in 1924. There was much weighty speculation about the counterion distribution around colloidal particles throughout the 20th century, but nobody succeeded in measuring it until our work in 1997. This work is described in detail in Chapter 8. 

Few outer-sphere electrode reactions have precursor-state concentrations that are measurable [21] so that it is usual to estimate wp and ws from double-layer models. The simplest, and by far the most commonly used, treatment is the Frumkin model embodied in eqns. (8) and (8a) whereby, as noted in Sect. 2.2, the sole contributor to wp and ws is presumed to be electrostatic work associated with transporting the reactant from the bulk solution to the o.H.p. at an average potential Gouy-Chapman (GC) theory [58],... 

Variation in the metal surface composition is, then, generally expected to yield large variations in the observed rate constant for inner-sphere pathways since the reaction energetics will be sensitive to the chemical nature of the metal surface. For outer-sphere reactions, on the other hand, the rate constants are anticipated to be independent of the electrode material after correction for electrostatic work terms provided that adiabatic (or equally non-adiabatic) pathways are followed. Although a number of studies of the dependence of the rate constants for supposed outer-sphere reactions on the nature of the electrode material have been reported, relatively few refer to sufficiently well-defined conditions where double-layer corrections are small or can be applied with confidence [111-115]. Several of these studies indeed... 

Since anions and cations adsorb at oxide electrodes positive and negative to the pzc, respectively, electrostatic work terms (double layer corrections) should contribute to the activation free energy barrier for adsorbed electroactive ions depending on the position of the reaction site. Not much attention has been paid to this phenomenon yet. Trasatti and co-workers... 

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