Helmholtz, internal plane

Fig. 17.2. The distribution of charges at the internal wall of a silica capillary. x is the length in cm from the center of charge of the negative wall to a defined distance, 1 = the capillary wall, 2 = the Stern layer or the inner Helmholtz plane, 3 = the outer Helmholtz plane, 4 = the diffuse layer and 5 = the bulk charge distribution within the capillary.

By contrast, the charge of the solution, qs, is distributed in a number of layers. The layer in contact with the electrode, called the internal layer, is largely composed of solvent molecules and in a small part by molecules or anions of other species, that are said to be specifically adsorbed on the electrode. As a consequence of the particular bonds that these molecules or anions form with the metal surface, they are able to resist the repulsive forces that develop between charges of the same sign. This most internal layer is also defined as the compact layer. The distance, xj, between the nucleus of the specifically adsorbed species and the metallic electrode is called the internal Helmholtz plane (IHP). The ions of opposite charge to that of the electrode, that are obviously solvated, can approach the electrode up to a distance of x2, defined as the outer Helmholtz plane (OHP). 

Between the diffuse layer and the interface lies the Stern layer, i.e., layer of ions, which are not subjected to Brownian motion. Two levels are identified within it the internal with unhydrated ions and external with hydrated ions. Most of ions in the Stern layer are hydrated, so they caimot approach too closely the mineral surface. Because of this Helmholtz plane is drawn through the centers of immobile hydrated ions, and the thickness of Stern layer 8 is assumed equal to half of the median radius of hydrated ions (about 2 A). Electrostatic field in such layer is defined by the charge of mineral s surface, on the one hand, and by the charge of Helmholtz plane, on the other. It characterizes the density of electric permittance, which, according to equation (2.98), is equal to... 

The outer Helmholtz plane is limiting the Stern s layer and determines the shortest distance available for the hydrated ions from the solution. Inside the internal layer an internal Helmholtz plane is also distinguished which determines the centers of gravity of ions adsorbed on the surface of solid phase. 

In the case of charge transfer, which occurs in the double layer, the driving force is related to the internal potential difference across the double layer. More precisely, it is linked to the difference between the potentials of the metal and the electrolyte at the Helmholtz plane l... 

Having obtained the internal energy and the entropy, we can conclude that the canonical partition function of the system can completely define the system in the thermodynamic plane. We can therefore ejqtress any thermodynamic function using the canonical partition function, expressed as variables amount of matter N), volume (V) and temperature (7), i.e. the canonical variables associated with the Helmholtz function 7. ... 

As for the boundary conditions at the internal pore wall, it is assumed that r = Rp coincides with the position of the reaction or Helmholtz plane, that is, the plane of the closest approach of hydrated protons to the interface. Quantities are indicated at r = Rphy SL superscript s. Components of proton and oxygen fluxes normal to the reaction plane are related to the local faradaic current density by... 

The structure of the metal-solution interface can be represented by a series of capacitors (Figme B.1.4) with charges distributed over several planes metal surface, internal Helmholtz plane, external Helmholtz plane, and in the diffuse zone. This leads to the built-up of a difference in potential between the metal and the solution. This difference is generally called the absolute potential of the metal with respect to the solution, or Galvani potential. 

These results give access to the interfacial tension as a thermodynamic excess quantity of the force-free plane D-face. Note that the interfacial tension and the absolute adsorptions of aU components contribute to the interfacial energy, both the specific excess internal energy and the specific excess Helmholtz firee energy. At a first glance, this statement is very natural, indeed. In the literature, however, interfacial tension and interfacial energy are very often considered as synonyms. Clearly, this is wrong. 

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