Outer potential

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 Volta potential is defined as the difference between the electrostatic outer potentials of two condensed phases in equilibrium. The measurement of this and related quantities is performed using a system of voltaic cells. This technique, which in some applications is called the surface potential method, is one of the oldest but still frequently used experimental methods for studying phenomena at electrified solid and hquid surfaces and interfaces. The difficulty with the method, which in fact is common to most electrochemical methods, is lack of molecular specificity. However, combined with modem surface-sensitive methods such as spectroscopy, it can provide important physicochemical information. Even without such complementary molecular information, the voltaic cell method is still the source of much basic electrochemical data. 

The Volta potential, A very often called the contact potential, is the difference between the outer potentials of the phases, which are in electrochemical equilibrium in regard to the charged species, i.e., ions or electrons. Each two-phase electrochemical system, including a w/s system, may be characterized by the commonly known relation ... 

The surface potential of a liquid solvent s, %, is defined as the difference in electrical potentials across the interface between this solvent and the gas phase, with the assumption that the outer potential of the solvent is zero. The potential arises from a preferred orientation of the solvent dipoles in the free surface zone. At the surface of the solution, the electric field responsible for the surface potential may arise from a preferred orientation of the solvent and solute dipoles, and from the ionic double layer. The potential as the difference in electrical potential across the interface between the phase and gas, is not measurable. However, the relative changes caused by the change in the solution s composition can be determined using the proper voltaic cells (see Sections XII-XV). 

When the conductor as a whole is charged (i.e., has excess charge of one sign in its surface layer), an electrostatic field and a potential gradient will develop in the insulator region adjacent to it. The name of the outer potential, / f, of the conductor is used for the potential at a point a located in the insulator just outside the conductor. Since point a and the point of reference are located in the same phase, this potential can be measured. 

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. 

Consider the case of a junction between two different metals a and p. Generally, they will have different values of the Fermi energy and work function. Between the two metals, a certain Volta potential will be set up. This implies that the outer potentials at points a and b, which are just outside the two metals, are different. However, it will be preferable to count the Fermi levels or electrochemical potentials from a common point of reference. This can be either point a or point b. Since these two points are located in the same phase, the potential difference between them (the Vofta potential) can be measured. Hence, values counted from one of the points of reference are readily converted to the other point of reference when required. 

Besides the Galvani potential, another important interfacial potential is the Volta potential, Aj I, sometimes ealled the eontaet potential. Aj I is the differenee of the outer potentials of the phases, whieh are in eleetroehemieal equilibrium with regard to the eharged speeies, i.e., ions or eleetrons. As for any two-phase eleetroehemieal system, ineluding the w/s system, it may be eharaeterized by the eommonly known relation ... 

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. 

The result of the establishment of phase equilibrium is the formation of differences of inner and outer potentials of both phases. These differences are defined by the equations... 

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... 

Measurement yields both the differences between the outer potentials and the work functions (real potentials). If two phases oc an / with a common species (index i) come into contact, at equilibrium /, (< ) = (/ ), that is at(a) - <, (/ ) = ZiFApty. These quantities are mostly measured using the vibrating condenser, thermoionic, calorimetric, and photoelectric methods. 

The difference in the outer potentials between the metal and the electrolyte solution is measured similarly. In Fig. 3.6, phase jS will now designate an electrolyte solution in contact with the metal phase oc. Also here tue(a) = jue(cc ) and ip(oc ) = (/ ), and U is again expressed by Eq. (3.1.30) however, fie(oc) = as the communicating species between... 

A more general relation between potential and electronic pressure for a density-functional treatment of a metal-metal interface has been given.74) For two metals, 1 and 2, in contact, equilibrium with respect to electron transfer requires that the electrochemical potential of the electron be the same in each. Ignoring the contribution of chemical or short-range forces, this means that —e + (h2/ m)x (3n/7r)2/3 should be the same for both metals. In the Sommerfeld model for a metal38 (uniformly distributed electrons confined to the interior of the metal by a step-function potential), there is no surface potential, so the difference of outer potentials, which is the contact potential, is given by... 

Electrochemical interfaces are sometimes referred to as electrified interfaces, meaning that potential differences, charge densities, dipole moments, and electric currents occur. It is obviously important to have a precise definition of the electrostatic potential of a phase. There are two different concepts. The outer or Volta potential ij)a of the phase a is the work required to bring a unit point charge from infinity to a point just outside the surface of the phase. By just outside we mean a position very close to the surface, but so fax away that the image interaction with the phase can be ignored in practice, that means a distance of about 10 5 — 10 3 cm from the surface. Obviously, the outer potential i/ a U a measurable quantity. 

The inner and outer potential differ by the surface potential Xa — (fa — ipa- This is caused by an inhomogeneous charge distribution at the surface. At a metal surface the positive charge resides on the ions which sit at particular lattice sites, while the electronic density decays over a distance of about 1 A from its bulk value to zero (see Fig. 2.1). The resulting dipole potential is of the order of a few volts and is thus by no means negligible. Smaller surface potentials exist at the surfaces of polar liquids such as water, whose molecules have a dipole moment. Intermolecular interactions often lead to a small net orientation of the dipoles at the liquid surface, which gives rise to a corresponding dipole potential. 

For electrons in a metal the work function is defined as the minimum work required to take an electron from inside the metal to a place just outside (c.f. the preceding definition of the outer potential). In taking the electron across the metal surface, work is done against the surface dipole potential x So the work function contains a surface term, and it may hence be different for different surfaces of a single crystal. The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface. If the reference point for the Fermi level is taken to be the vacuum level instead, then Ep = —, since an extra work —eoV> is required to take the electron from the vacuum level to the surface of the metal. The relations of the electrochemical potential to the work function and the Fermi level are important because one may want to relate electrochemical and solid-state properties. 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

We should like to define a work function of an electrochemical reaction which enables us to calculate outer potential differences in the same way for a metal-solution interface, and this work function should also refer to the vacuum. For this purpose we consider a solution containing equal amounts of Fe3+ and Fe2+ ions in contact with a metal M, and suppose that the reaction is at equilibrium. We now transfer an electron from the solution via the vacuum to the metal in the following way ... 

The scale of electrochemical work functions makes it possible to calculate the outer potential difference between a solution and any electrode provided the respective reaction is in equilibrium. A knowledge of this difference is often important in the design of electrochemical systems, for example, for electrochemical solar cells. However, in most situations one needs only relative energies and potentials, and the conventional hydrogen scale suffices. 

The difference in the work functions causes the flow of electrons from the metal with the lower work function to that with the higher one, so that a surface dipole moment is created. This effect is similar to the establishment of an outer potential difference at the contact between two different metals (see Chapter 2). An adsorbate layer does not have a work function in the same... 

The relative position of the electronic level eo to the Fermi level depends on the electrode potential. We perform estimates for the case where there is no drop in the outer potential between the adsorbate and the metal - usually this situation is not far from the pzc. In this case we obtain for an alkali ion eo — Ep — where is the work function of the metal, and I the ionization energy of the alkali atom. For a halide ion eo — Ep = electron affinity of the atom. 

The intimate relationship between double layer emersion and parameters fundamental to electrochemical interfaces is shown. The surface dipole layer (xs) of 80SS sat. KC1 electrolyte is measured as the difference in outer potentials of an emersed oxide-coated Au electrode and the electrolyte. The value of +0.050 V compares favorably with previous determinations of g. Emersion of Au is discussed in terms of UHV work function measurements and the relationship between emersed electrodes and absolute half-cell potentials. Results show that either the accepted work function value of Hg in N2 is off by 0.4 eV, or the dipole contribution to the double layer (perhaps the "jellium" surface dipole layer of noble metal electrodes) changes by 0.4 V between solution and UHV. 

Figure 1. The upper curve is a cyclic esnersogram of a rotating oxide-coated Au electrode (outer potential 0 vs electrode potential U), measured with a Kelvin probe. (Here is plotted as 0 minus the ref. electrode Fermi level.) The lower curve is the electrolyte cyclic potentiogram (0S - (-U) vs U), by the same Kelvin probe. Data indicate that 0m 0g 3 50 mV at all times.

Double layer emersion continues to allow new ways of studying the electrochemical interphase. In some cases at least, the outer potential of the emersed electrode is nearly equal to the inner potential of the electrolyte. There is an intimate relation between the work function of emersed electrodes and absolute half-cell potentials. Emersion into UHV offers special insight into the emersion process and into double layer structure, partly because absolute work functions can be determined and are found to track the emersion potential with at most a constant shift. The data clearly call for answers to questions involving the most basic aspects of double layer theory, such as the role water plays in the structure and the change in of the electrode surface as the electrode goes frcm vacuum or air to solution. 

In general, the chemical potential of electrons, t., is characteristic of individual electron ensembles, but the electrostatic energy of-e< > varies with the choice of zero electrostatic potential. In electrochemistry, as is described in Sec. 1.5, the reference level of electrostatic potential is set at the outer potential of the electron ensemble. 

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