Lippmann’s equation

Lippmann s equation is thus shown to be completely valid in spite of the shortcomings of the simple double-layer theory. 

This, combined with Lippmann s equation, which we have seen has received experimental confirmation in many ways, leads to the result 6 = 96-5 X 10 r. 

Lippmann s equation may thus be regarded as identical with that of Gibbs expressed in the form given to it by Warburg. 

Teiectrons being measured in grm. equivalents per sq. cm. If I be replaced by its equivalent in coulombs per. sq. cm. we obtain Lippmann s equation... 

It thus appears that the surface concentration calculated with the aid of Gibbs equation is equal on the one hand to minus the surface charge found by Lippmann s equation from the slope of the electro-capillary curve and on the other hand to minus the number of grm. equivalents of mercurous ions taken up by an expanding mercury surface or thrown off a contracting one in the course of the N emst ionic transfer. 

Equation (13) is generally called Lippmann s equation, having been first deduced by him from consideration of the quantity of electricity on... 

The relation between the change of tension, at constant applied potential, and the change of potential at constant interfacial tension, for a given change in concentration of any component, in either phase, can be obtained at once from Lippmann s equation, since... 

The experimental verification of Lippmann s equation has been carried out in three ways. Pellat4 showed that in an experiment such as that indicated in Fig. 53, where mercury drops continuously from a fine jet and reunites in a... 

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... 

The title of this subsection refers to a recent paper by Kylstra and Joachain investigating double poles of the S matrix [25]. Their paper is based on the time-dependent Lippmann-Schwinger equation. Since the Hamiltonian is periodic in time the use of the Floquet theorem permits one to apply the time-independent theory of scattering. As in Ref. [25] we consider two quasi bound states (n = 2). Instead of starting from an Hamiltonian periodic in time (semi-classical approximation) we use a time-independent model. The laser field is assumed to be quantized and as a result the total Hamiltonian describing the atom in the laser field is time-independent (see chapter VI of Ref. [13]) Our aim is twofold To reproduce the results of Ref. [25] and, more generally, to illustrate the relevance of simple models to describe collision... 

Conversion of values of y into capacities is done by double differentiation in relation to the electrostatic potential difference A0 between its value in the metal, 0M, and that in the solution, (j)s. The first derivative gives the charge on the interface, and is the Lippmann equation... 

The additional charge and the corresponding additional surface tension are time-dependent quantities in which the equilibrium between the bulk and the interface is not established. The irreversible contribution can be separated from the reversible by considering the time dependence, if the experimental time scale allows for such a test. Time-dependent effects can be observed by impedance measurements at different frequencies. For gold, as an example, impedance measurements showed spectra characteristic for equilibration processes at least over a time scale of 0.1 ms to 100 s. Gold also shows a surface reconstruction depending on the potential [148]. Fortunately, the variation of the interfacial strain with potential is usually so small that the original Lippmann equation (41) for a solid is practically the same as for a liquid electrode 1149]. 

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