Inner potential

The electrostatic potential within a phase, that is, l/e times the electrical work of bringing unit charge from vacuum at infinity into the phase, is called the Galvani, or inner, potential Similarly, the electrostatic potential difference... 

Figure 8. Schematic potential distribution across a bipolar membrane under increased anodic polarization. 15 At the neutral layer, dehydration proceeds in accordance with anodic polarization. and A are the inner potential and membrane potential, respectively. (Reproduced from N. Sato, Corrosion 45,354,1989, Fig. 27 with permission from NACE International.)...

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

The energy of an ion in a given medium depends not only on chemical forces but also on the electrostatic held hence the chemical potential of an ion j customarily is called its electrochemical potential and labeled fi. The electrostatic potential energy of an ion j when reckoned per mole is given by ZjF, where / is the electrostatic (inner) potential of the phase containing the ion a plus sign for cations and a minus sign for anions. Hence, the electrochemical potential can be written as the sum of two terms ... 

No potential gradient exists within the conductor hence the conductor s inner potential /( is Ihe potential at any point A inside the conductor. The potential dilference between points A and a, defined as... 

For measurements of the Volta potentials, one uses a special feature of the electrostatic capacitor. In fact, when the two sides of a capacitor do not (as usual) consist of identical conductors but of different ones, the charge on the capacitor plates, according to the capacitor relation, is not related to the difference between the inner potentials of the two conductors but to their Volta potential (to the difference between the outer potentials). Knowing the value of capacitance of the capacitor and measuring the charge that flows when the plates are made part of a suitable circuit, one can thus determine the Volta potential. 

The presence of an electrical potential drop, i.e., interfacial potential, across the boundary between two dissimilar phases, as well as at their surfaces exposed to a neutral gas phase, is the most characteristic feature of every interface and surface electrified due to the ion separation and dipole orientation. This charge separation is usually described as the formation of the ionic and dipolar double layers. The main interfacial potential is the Galvani potential (termed also by Trasatti the operative potential), which is the difference of inner potentials (p and of both phases. It is a function only of the chemical... 

Kakiuchi [41] has examined the transport mechanism in some detail. He considers the interface as a region of thickness k in which friction is considerably larger than in the bulk. The transferring ion has different electrochemical potentials = 1, 2) in the two bulk phases as usual, they can be decomposed into their chemical and their electrostatic parts /x,- = /x,- -t-zeo, where z is the charge number of the ion. When the system is in equilibrium, and the concentration of the ion is the same in the two solutions, then the difference in the inner potential is given by ... 

It has become fairly common to adopt the manufacture of combinations of internal reference electrode and its inner electrolyte such that the (inner) potential at the glass electrode lead matches the (outer) potential at the external reference electrode if the glass electrode has been placed in an aqueous solution of pH 7. In fact, each pH glass electrode (single or combined) has its own iso-pH value or isotherm intersection point ideally it equals 0 mV at pH 7 0.5 according to a DIN standard, as is shown in Fig. 2.11 the asymmetry potential can be easily eliminated by calibration with a pH 7.00 0.02 (at 25° C) buffer solution. 

In contrast to differences in the inner potentials (the Galvani potential difference), the difference in the outer potentials A pip (the Volta potential difference or the contact potential) and the real potential or, can be measured. The real potential <, is defined as... 

As was demonstrated in Section 3.1.2, the energy of the Fermi level is identical with the electrochemical potential of an electron in the metal. A change in the inner potential of the electrode phase by Apotential difference of an external voltage source by AE = A0,... 

The cell potential is the difference in electrical potential (inner potential) between the right-hand and left-hand mercury terminals ... 

The inner potential bulk property. Even though it cannot be measured, it is still a useful concept, particularly for model calculations. Differences in the inner potential of two phases can be measured, if they have the same chemical composition. The surface potential a is a surface property, and may hence differ at different surfaces of a... 

In adding a charged particle work is done against the inner potential , and it may be useful to separate this out and write ... 

Since the redox couple and the reference system experience the same inner potential fa0i, we have ... 

To be specific we consider a planar electrode in contact with a solution of a z — z electrolyte (i.e., cations of charge number z and anions of charge number -z). We choose our coordinate system such that the electrode surface is situated in the plane at x = 0. The inner potential (x) obeys Poisson s equation ... 

Strictly speaking the exponents should not contain the inner potential 4> but the so-called potential of mean force, but this subtlety is only important at high electrolyte concentrations and high potentials, where other weaknesses of this theory also become important. Substituting Eqs. (3.3) and (3.2) into Eq. (3.1) gives ... 

The partitioning of ions is not so simple, since each solution must be electrically neutral (with the exception of a thin boundary layer at the interface). As an example we consider the case where a single salt is partitioned between the two phases for simplicity we assume that the cation and the anion have the same charge number . We denote the cation by the index +, and the anion by -. Applying the equilibrium condition Eq. (12.1) to both ions gives for the difference in inner potentials ... 

All quantities in Eq. (12.6) are measurable The concentrations can be determined by titration, and the combination of chemical potentials in the exponent is the standard Gibbs energy of transfer of the salt, which is measurable, just like the mean ionic activity coefficients, because they refer to an uncharged species. In contrast, the difference in the inner potential is not measurable, and neither are the individual ionic chemical potentials and activity coefficients that appear on the right-hand side of Eq. (12.3). 

Although the inner potential difference is not measurable in principle, it would be useful to have at least good estimates. We can see from Eq. (12.3) that this problem is equivalent to determining the difference in the chemical potential of individual ions. If we knew the standard Gibbs energies of transfer of the ions ... 

There are other ways of estimating inner potential differences. Gi rault and Schiffrin [4] assume that the difference in the inner potential is negligible at the pzc, because the interface consists of an extended layer where both solvents mix, so that any dipole potentials will be small. The resulting scale of Gibbs energies of transfer agrees reasonably well with the TPAs+/TPB scale, if the small difference in the radii of these ions is accounted for. 

In a real experiment one uses at least four electrodes (see Fig. 12.2), one counter and one reference electrode on each side, and measures the difference in potential between the two reference electrodes. In principle each reference electrode could be referred to the vacuum scale using the same procedure that was outlined in Chapter 2. However, in practice the required data are not available with sufficient accuracy. Of course, the voltage between the two reference electrodes characterizes the potential difference between the two phases uniquely. It can be converted to an (estimated) scale of inner potential differences by using the energies of transfer of the ions involved. 

The inner potentials have to be calculated by solving the Poisson-Boltzmann equations for the potentials this is done in Appendix A. 

The two reference electrodes and the interface between the two solution are in electronic equilibrium, so that we can express the differences in the inner potential through the differences in the chemical potentials. We denote the chemical potential of the two metal electrodes as hm, those of the two reference systems as / ef and and those of the two redox couples as /u4edox and /ij edox We obtain ... 

Since systems that are in the same phase experience the same inner potential, we can write this as ... 

Figure 12.5 Electron transfer at ITIES. A is the total drop in the inner potential, Aeff is the part that is effective in the reaction.

The difference s in the inner potentials is not directly measurable however, if the solution is in contact with a suitable reference electrode, its inner potential with respect to this electrode is fixed, and d 4>m — 4>s) — d, where (j) is the electrode potential. The resulting equation is known as the electrocapillary equation ... 

---