Interactions Between Conducting Phases

2.1 BASIC ELECTROCHEMICAL THERMODYNAMICS 2.1.1 Reversibility

2.2 A MORE DETAILED VIEW OF INTERFACIAL POTENTIAL DIFFERENCES

2.2.2 Interactions Between Conducting Phases

When two conductors, for example, a metal and an electrolyte, are placed in contact, the situation becomes more complicated because of the coulombic interaction between the phases. Charging one phase to change its potential tends to alter the potential of the neigh- boring phase as well. This point is illustrated in the idealization of Figure 2.2.2, which portrays a situation where there is a charged metal sphere of macroscopic size, perhaps a mercury droplet 1 mm in diameter, surrounded by a layer of uncharged electrolyte a few millimeters in thickness. This assembly is suspended in a vacuum. We know that the

Surrounding vacuum

Metal with charge qu

Electrolyte layer with no net charge

Gaussian surface

Figure 2.2.2 Cross-sectional view of the interacti56on between a metal sphere and a surrounding electrolyte layer. The Gaussian enclosure is a sphere containing the metal phase and part of the electrolyte.

2.2 A More Detailed View of Interfacial Potential Differences 57 charge on the metal, qM, resides on its surface. This unbalanced charge (negative in the diagram) creates an excess cation concentration near the electrode in the solution. What can we say about the magnitudes and distributions of the obvious charge imbalances in solution?

Consider the integral of equation 2.2.3 over the Gaussian surface shown in Figure 2.2.2. Since this surface is in a conducting phase where current is not flowing, % at every point is zero and the net enclosed charge is also zero. We could place the Gaussian sur- face just outside the surface region bounding the metal and solution, and we would reach the same conclusion. Thus, we know now that the excess positive charge in the solution, qs, resides at the metal-solution interface and exactly compensates the excess metal charge. That is,

«7S = " < (2.2.4)

This fact is very useful in the treatment of interfacial charge arrays, which we have al- ready seen as electrical double layers (see Chapters 1 and 13).9

Alternatively, we might move the Gaussian surface to a location just inside the outer boundary of the electrolyte. The enclosed charge must still be zero, yet we know that the net charge on the whole system is 0м. A negative charge equal to 0м must therefore reside at the outer surface of the electrolyte.

Figure 2.2.3 is a display of potential vs. distance from the center of this assembly, that is, the work done to bring a unit positive test charge from infinitely far away to a given distance from the center. As the test charge is brought from the right side of the di- agram, it is attracted by the charge on the outer surface of the electrolyte; thus negative work is required to traverse any distance toward the electrolyte surface in the surround- ing vacuum, and the potential steadily drops in that direction. Within the electrolyte, % is zero everywhere, so there is no work in moving the test charge, and the potential is con- stant at </>s. At the metal-solution interface, there is a strong field because of the double layer there, and it is oriented such that negative work is done in taking the positive test charge through the interface. Thus there is a sharp change in potential from ф^ to фм

over the distance scale of the double layer.10 Since the metal is a field-free volume, the

Distance

Vacuum Figure 2.2.3 Potential profile through the system shown in Figure 2.2.2.

Distance is measured radially from the center of the metallic sphere.

9Here we are considering the problem on a macroscopic distance scale, and it is accurate to think of qs as residing strictly at the metal—solution interface. On a scale of 1 fxva or finer, the picture is more detailed. One finds that gs is still near the metal-solution interface, but is distributed in one or more zones that can be as thick as 1000 A (Section 13.3).

10The diagram is drawn on a macroscopic scale, so the transition from фБ to фм appears vertical. The theory of the double layer (Section 13.3) indicates that most of the change occurs over a distance equivalent to one to several solvent monolayers, with a smaller portion being manifested over the diffuse layer in solution.

58 Chapter 2. Potentials and Thermodynamics of Cells

potential is constant in its interior. If we were to increase the negative charge on the metal, we would naturally lower ф^м, but we would also lower <£^s, because the excess negative charge on the outer boundary of the solution would increase, and the test charge would be attracted more strongly to the electrolyte layer at every point on the path through the vacuum.

The difference ф^м — (/>^s, called the interfacial potential difference, depends on the charge imbalance at the interface and the physical size of the interface. That is, it depends on the charge density (C/cm²) at the interface. Making a change in this interfacial poten- tial difference requires sizable alterations in charge density. For the spherical mercury drop considered above (A = 0.03 cm²), now surrounded by 0.1 M strong electrolyte, one would need about 10~⁶ С (or 6 X 10¹² electrons) for a 1-V change. These numbers are more than 10⁷ larger than for the case where the electrolyte is absent. The difference ap- pears because the coulombic field of any surface charge is counterbalanced to a very large degree by polarization in the adjacent electrolyte.

In practical electrochemistry, metallic electrodes are partially exposed to an elec- trolyte and partially insulated. For example, one might use a 0.1 cm² platinum disk elec- trode attached to a platinum lead that is almost fully sealed in glass. It is interesting to consider the location of excess charge used in altering the potential of such a phase. Of course, the charge must be distributed over the entire surface, including both the insulated and the electrochemically active area. However, we have seen that the coulombic interac- tion with the electrolyte is so strong that essentially all of the charge at any potential will lie adjacent to the solution, unless the percentage of the phase area in contact with elec- trolyte is really minuscule.¹¹

What real mechanisms are there for charging a phase at all? An important one is sim- ply to pump electrons into or out of a metal or semiconductor with a power supply of some sort. In fact, we will make great use of this approach as the basis for control over the kinetics of electrode processes. In addition, there are chemical mechanisms. For example, we know from experience that a platinum wire dipped into a solution containing ferri- cyanide and ferrocyanide will have its potential shift toward a predictable equilibrium value given by the Nernst equation. This process occurs because the electron affinities of the two phases initially differ; hence there is a transfer of electrons from the metal to the solution or vice versa. Ferricyanide is reduced or ferrocyanide is oxidized. The transfer of charge continues until the resulting change in potential reaches the equilibrium point, where the electron affinities of the solution and the metal are equal. Compared to the total charge that could be transferred to or from ferri- and ferrocyanide in a typical system, only a tiny charge is needed to establish the equilibrium at Pt; consequently, the net chem- ical effects on the solution are unnoticeable. By this mechanism, the metal adapts to the solution and reflects its composition.

Electrochemistry is full of situations like this one, in which charged species (elec- trons or ions) cross interfacial boundaries. These processes generally create a net transfer of charge that sets up the equilibrium or steady-state potential differences that we observe.

Considering them in more detail must, however, await the development of additional con- cepts (see Section 2.3 and Chapter 3).

Actually, interfacial potential differences can develop without an excess charge on ei- ther phase. Consider an aqueous electrolyte in contact with an electrode. Since the elec- trolyte interacts with the metal surface (e.g., wetting it), the water dipoles in contact with the metal generally have some preferential orientation. From a coulombic standpoint, this situation is equivalent to charge separation across the interface, because the dipoles are

1 ] As it can be with an ultramicroelectrode. See Section 5.3.

2.2 A More Detailed View of Interfacial Potential Differences * 59 not randomized with time. Since moving a test charge through the interface requires work, the interfacial potential difference is not zero (23-26).12