Gibbs-Lippmann equation

For solutions of simple electrolytes, the surface excess of ions can be determined by measuring the interfacial tension. Consider the valence-symmetrical electrolyte BA (z+ = —z = z). The Gibbs-Lippmann equation then has the form... 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

The fact that the electrocapillary quantities are measured relative to their value in the base electrolyte can also be expressed in the formulation of the Gibbs-Lippmann equation. If quantities referred to the base electrolyte are primed and quantities referred to the studied surface-active substance are denoted by the subscript 1, then... 

The appearance of peaks on the differential capacity curves can be derived from this potential dependence in the following manner. The Gibbs-Lippmann equation (see Eq. 4.2.23) gives... 

On the other hand, equilibrium at the polarized interface is described by the Gibbs-Lippmann equation (5.9). Here, the equilibrium potential eq, surface concentration Xj Fj of all adsorbing species, their bulk electrochemical potential fa, and the resulting interfacial charge Qi are linked rather less explicitly to surface tension y. 

A notable difference between these two relationships is that the Gibbs-Lippmann equation contains one more independent variable parameter, the interfacial charge. It cannot be determined directly. Several unsuccessful attempts to design chemical sensors (e.g., the immunosensor) based on the measurement of adsorbed surface charge have been made. There are no ideally polarized interfaces that are sufficiently ideal to allow such direct measurement of interfacial charge. 

See also - electrocapillarity, - electrocapillary curve, -r Gibbs-Lippmann equation, - Wilhelmy plate (slide) method, - ring method, - Lippmann capillary electrometer. 

Esin-Markov coefficient — Various cross-differential relationships can be obtained from the - Gibbs-Lippmann equation because it is a complete differential. For instance,... 

Free surface charge density -> Gibbs-Lippmann equation... 

The Gibbs-Duhem equation is used in several cases in electrochemistry, e.g., in the derivation of - Gibbs adsorption equation or -> Gibbs-Lippmann equation since Eq. (4) can be extended by surface work ... 

Gibbs-Lippmann equation — The relationship between the - interfacial tension (y) and the surface excess quantities was derived by -> Gibbs, J. W. At constant temperature (T) and external pressure (/ )... 

See also - electrode surface area, -> Gibbs-Lippmann equation, - interfacial tension, -> interface between two liquid solvents, -> interface between two immiscible electrolyte solutions -> Lippmann capillary electrometer, -> Lippmann equation -> surface, -> surface analytical methods, - surface stress. 

Ring method — Method to determine the - interfacial tension in liquid-gas systems introduced by Lecomte du Noiiy [i]. It is based on measuring the force to detach a ring or loop of a wire from the surface of a liquid. The method is similar to the -> Wilhelmyplate method when used in the detachment mode [ii]. See also -> electrocapillarity, -r electrocapillary curve, -> Gibbs-Lippmann equation, - Wilhelmy plate (slide) method, - drop weight method, - Lippmann capillary electrometer. 

The general thermodynamic approach yields the - Gibbs-Lippmann equation (- electrocapillary) for the nonpolarizable [v] and ideally polarizable [ix] ITIES. For the interface between the electrolyte solutions of RX in w and SY in o, see also - interface between two immiscible electrolyte solutions, this equation has the form [x]... 

Gibbs-Lippmann equation, drop weight method, -> ring method, Lippmann capillary electrometer, -> Wilhelmy. 

See also capillarity, adhesion, double layer, Dupre equation, Gibbs-Lippmann equation, electrocapillary equation, -> electrokinetic effects, Lipp-mann equation, Lippmann capillary electrometer, point of zero charge, Young equation, Wilhelmy... 

See also -> electrode surface area, Gibbs-Lippmann equation, -> interfacial tension, interface between... 

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