Equation Lippmann-Helmholtz

Electrocapillary phenomena at the interface between two immiscible electrolyte solutions, which we will call the oil/water (O/W) interface for short, were studied first by Guastalla [1], then by Blank and Feig [2,3], Watanabe et al. [4, 5], Dupeyrat et al. [6, 7], Joos et al. [8,9], Gavach et al. [10-12], and Spumy [13]. Watanabe et al. applied the electrocapillary equations such as the Lippmann-Helmholtz equation to elucidate the double layer structure of the interface, whereas others [2,3,6,7] made a distinction between electrocapillarity and electroadsorption. Koryta et al. [14] have discussed the electric polarizability of the oil/water interface on the basis of the transfer Gibbs energies of ions from one solvent (the aqueous phase) to the other (the oil or organic phase). 

In 1873, Gabriel Lippmann (1845-1921 Nobel prize, 1908) performed extensive experiments of the electrocapiUary behavior of mercury and established his equation describing the potential dependence of the surface tension of mercury in solutions. In 1853, H. Helmholtz, analyzing electrokinetic phenomena, introduced the notion of a capacitor-like electric double layer on the surface of electrodes. These publications... 

Schofield Phil. Mag. March, 1926) has recently verified this relation by direct experiment. In order to appreciate the significance of this result, it is necessary to consider in more detail the electrical potential difference V and the manner in which it arises. Instead of regarding the phenomenon from the point of view of the Gibbs equation, it has been, until recently, more usual to discuss the subject of electro-capillarity from the conceptions developed by Helmholtz and Lippmann. These views, together with the theory of electrolytic solution pressure advanced by Nemst, are not in reality incompatible with the principles of adsorption at interfaces as laid down by Gibbs. 

Neither Gibbs equation nor that of Lippmann gives us any information as to the structure of the boundary layer. Helmholtz, as we saw, considered it to consist of a charge on the metal surface separated from a layer of ions of opposite sign situated at a small distance from the surface. He did not, however, enquire how these ions were kept separate from the surface or whether the charges should be considered as separated by a dielectric medium. 

In a true scattering problem, an incident wave is specified, and scattered wave components of ifr are varied. In MST or KKR theory, the fixed term x in the full Lippmann-Schwinger equation, f = x + / GqVms required to vanish, x is a solution of the Helmholtz equation. In each local atomic cell r of a space-filling cellular model, any variation of i// in the orbital Hilbert space induces an infinitesimal variation of the KR functional of the form 8 A = fr Govi/s) + he. This... 

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