Inner potential difference

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. 

An electrostatic potential difference, called the inner potential difference, arises across the interface of two contacting phases. This inner potential difference consists of a potential gA/ac) due to an interfacial charge (charge on both sides of the interface), Oa/b> aiid a potential gj /snip) due to an interfacial dipole, dipA/B, as shown in Eqn. 4-3 ... 

The inner potential difference between two contacting phases is cafied in electrochemistry the Galvani potential difference, and the outer potential difference is called the Volta potential difference. The outer potential difference corresponds to what is called the contact potential between the two phases. We call, in this test, the inner potential difference across an interface the interfacial potential. 

The outer potential difference between two contacting phases can be measured because it is a potential difference between two points in the same vacuum or gas phase outside the free surfaces of the two phases. On the other hand, the inner potential difference can not be measured, because the potential measuring probe introduces its interfacial potential that differs with the two phases and thus can not be canceled out this gives rise to an unknown potential in the potential measurement. 

The interface at which the interfacial charge,, is zero is called the interface of zero charge or the zero charge interface. The inner potential difference across the zero charge interface is determined by the interfacial dipole only, thus, it is characteristic of the contacting interface of the two phases as indicated in Eqn. 4-6 ... 

Fig. 4-7. Ihe inner potential difference, d n/s, and the outer potential difference, dtpu/s, between a solid metal M and an aqueous solution S (a) charged interface where = gwauip) gwsio), (b) zero charge interface where - gM/scsp).

For the interface of zero charge the inner potential difference is given by... 

Fig. 4- Electron energy levels of two different metals A and B in (a) isolated state and in (b) contact state e s electron energy a,= real potential of electrons in metal ty = Fermi level of electrons in metal MtJB = inner potential difference AtpA/B = outer potential difference.

Since the electrochemical potential of electrons in metals is a function of the inner potential of the metal (P ca) = p. - where electron transfer is in equilibrium is represented by the difference in the chemical potential of electrons between the two metal phases A and B is shown in Eqn. 4-8 ... 

In the case of ion transfer equilibrium at the electrode interface M/S, the ion level, Pi(M>, in the electrode equals the ion level, Pioj, of hydrated ions in the solution as shown in Fig. 4-9. The inner potential difference, is hence... 

As is shown in Eqn. 4-3, the inner potential difference across the interface M/S consists of a chaise-induced potential and a dipole-induced potential =... 

It follows from Eqn. 4—13 that the electron level o u/av) in the electrode is a function of the chemical potential p.(M) of electrons in the electrode, the interfacial potential (the inner potential difference) between the electrode and the electrolyte solution, and the surface potential Xs/v of the electrolyte solution. It appears that the electron level cx (ii/a/v) in the electrode depends on the interfacial potential of the electrode and the chemical potential of electron in the electrode but does not depend upon the chemical potential of electron in the electrolyte solution. Equation 4-13 is valid when no electrostatic potential gradient exists in the electrolyte solution. In the presence of a potential gradient, an additional electrostatic energy has to be included in Eqn. 4-13. 

The term used for this total potential difference across an electrified interface is the Galvani potential or inner potential difference, and the symbol used is d< >. 

The argument just presented can be extended to the differences of the various potentials. The outer potential difference A f can be measured (Klein and Lange Appendix 6.1) the surface potential difference A% cannot and therefore the inner potential differences d< ) = d y + Ax also cannot be experimentally obtained. 

Is the Inner Potential Difference an Absolute Potential Difference ... 

As explained in Section 6.3.11, the inner potential difference—A( )—seems to encompass all the sources of potential differences across an electrified interface—Ax and A jf—and therefore it can be considered as a total (or absolute ) potential across the electrode/electrolyte interface. However, is the inner potential apractical potential First, the inner potential cannot be experimentally measured (Section 6.3.11). Second, its zero point or reference state is an electron at rest at infinite separation from all charges (Sections 6.3.6 and 6.3.8), a reference state impossible to reach experimentally. Third, it involves the electrostatic potential within the interior of the phase relative to the uncharged infinity, but it does not include any term describing the interactions of the electron when it is inside the conducting electrode. Thus, going back to the question posed before, the inner potential can be considered as a kind of absolute potential, but it is not useful in practical experiments. Separation of its components, A% and A f, helped in understanding the nature of the potential drop across the metal/solution interface, but it failed when we tried to measure it and use it to predict, for example, the direction of reactions. Does this mean then that the electrochemist is defeated and unable to obtain absolute potentials of electrodes ... 

The nonpolarizable interface has been defined above (Section 6.3.3) as one which, at constant solution composition, resists any change in potential due to a change in cell potential. This implies that (3s Ma< )/3V)jl = 0. However, the inner potential difference at such an interface can change with solution composition hence, Eq. (6.89) can be rewritten in the form of dM7ds< > = (RT/ZjF) d In a, which is the Nemst equation [see Eq. (7.51)] in differential form for a single interface. 

Second, the inner potential difference across a double layer, d(J), was defined. It was determined that this inner potential can be resolved into two contributions. One of them, the outer potential difference or A jJ, emerged from the chaiges in the electrode and/or in the solution, and was found to be a measurable quantity. The other potential, the surface potential difference or A%, was due to the oriented dipoles existing on one... 

Calculate the inner potential difference across (a) anNa 7Na+ standard reversible... 

Once we know the value of the inner potential difference, — 0, we can correlate A using Equations (10) and (11) and then calculate the variation of y with due to the presence of the electrical double layers. In the present model, we simply neglect — < °, which is known to be small and shows no strong dependence on [24]. 

The PEVD system used in this investigation is schematically shown in Eigure 36. A Na -p/ P -alumina disc, 16 mm in diameter and 5 mm in thickness, was used as the solid electrolyte with a working electrode on one side and both counter and reference electrodes on the other. To simplify data interpretation, the same electrode material, a Pt thick film, was used for all three electrodes, so the measured potential difference could be directly related to the average inner potential difference between the working and reference electrode. In order to make good electrical and mechanical contact, Pt meshes, with spot-welded Pt wires, were sintered on the Pt thick films as electron collectors and suppliers. 

The conversion of u into the zeta potential depends on the molecular structure of the double layer of the colloid surface. The zeta potential is smaller than the surface potential because it reflects the inner potential difference across that portion of the electrochemical double layer which does not migrate in an applied field. 

Galvani (inner) potential difference between two phases i, j... 

Since the discussion here concerns interfaces, it is also important to consider the potential differences which arise between the boundaries of two phases a and p. The inner potential difference, which is known as the Galvani potential difference, can be defined as... 

The difference in the inner potentials of the two phases at an electrochemical interface, the inner potential difference or Galvani potential difference, cannot be measured directly. The difference between the outer potentials of the two phases is called the Volta potential difference, and is measured by the Kelvin Probe technique, as described in Sect. 7.8 in this volume. 

As described earlier, the s/e interface is electrified, that is, charge is separated at the interface. According to Gauss law, the charge separation is accompanied by an inner-potential difference between the semiconductor and the electrolyte. Consequently, in the absence of any electrochemical process, the s/e interface acts as a capacitor, the capacitance of which may... 

R.H.-independent signal output has been achieved in thefour-probe type sensor shown in Fig. 36.4, where two additional Ag probes are inserted in the proton conductor bulk (AA) beneath the Pt electrodes. One of the Pt electrodes is covered by a layer of AA sheet, which acts as a sort of gas diffusion layer. The short-circuit current flowing between the two Pt electrodes is proportional to H2 concentration but dependent on R.H., just as in the previous amperometric sensor. On the other hand, the difference in potential between the two Ag probes (inner potential difference, AE g) with the outer Pt electrodes short-circuited is shown to be not only proportional to H2 concentration but also independent of R.H. as shown in Fig. 36.3b and Table 36.2. This mode of sensing has no precedence, and is noted as a new method to overcome the greatest difficulty in using proton conductor-based devices, i.e. their R.H. dependence. 

Fig. 36.3. (a) Dependence of short-circuit current (/) of the amperometric proton-conductor sensor on H2 concentration, and (b) dependence of (inner potential difference) of the four-probe type sensor on Hj concentration in air at different relative humidity (25 (reprinted by permission of The Electrochemical Society, Inc,),... 

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