Helmholtz displays

It is important to stress that the activity coefficients (and the concentrations) in equation 16.18 refer to the species close to the surface of the electrode, and so can be very different from the values in the bulk solution. This is portrayed in figure 16.6, which displays the Stern model of the double layer [332], One (positive) layer is formed by the charges at the surface of the electrode the other layer, called the outer Helmholtz plane (OHP), is created by the solvated ions with negative charge. Beyond the OHP, the concentration of anions decreases until it reaches the bulk value. Although more sophisticated double-layer models have been proposed [332], it is apparent from figure 16.6 that the local environment of the species that are close to the electrode is distinct from that in the bulk solution. Therefore, the activity coefficients are also different. As these quantities are not... 

This result is formally identical to the expression for the total capacity displayed by two capacitors in series [Fig. 6.66(c)]. The conclusion therefore is that an electrified interface has a total differential capacity that is given by the Helmholtz and Gouy capacities in series. Let s examine two extreme cases. 

It will prove useful in the sequel to use the hertz potentials (Born and Wolf, 1980, pp. 76-84) to describe the electromagnetic field. The hertz potentials also satisfy the homogeneous vector Helmholtz equation in free space. The advantage of the hertz potentials is that they display much higher symmetry than the conventional vector and scalar potentials. Furthermore, they may be written in a form that displays the paraxial approximation of quasioptics directly. 

Helmholtz energy is displayed as the natural energy function of its natural variables T and V. The geometry of the equilibrium surface is expressed by the coefficients of the differentials. 

---