A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 17
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Consider, for example, a spherical mercury dropof 0.5 mm radius. Changing its potential requires only about 5 X 10~ 14 C/V (about300,000 electrons/V), if it is suspended in air or in a vacuum (21).2.2.2Interactions Between Conducting PhasesWhen two conductors, for example, a metal and an electrolyte, are placed in contact, thesituation becomes more complicated because of the coulombic interaction between thephases. Charging one phase to change its potential tends to alter the potential of the neighboring phase as well. This point is illustrated in the idealization of Figure 2.2.2, whichportrays a situation where there is a charged metal sphere of macroscopic size, perhaps amercury droplet 1 mm in diameter, surrounded by a layer of uncharged electrolyte a fewmillimeters in thickness.
This assembly is suspended in a vacuum. We know that theSurrounding vacuumElectrolyte layerwith no net chargeMetal withcharge quGaussian surfaceFigure 2.2.2 Cross-sectional view of theinteracti56on between a metal sphere anda surrounding electrolyte layer. TheGaussian enclosure is a sphere containingthe metal phase and part of the electrolyte.2.2 A More Detailed View of Interfacial Potential Differences57Mcharge on the metal, q , resides on its surface.
This unbalanced charge (negative in thediagram) creates an excess cation concentration near the electrode in the solution. Whatcan we say about the magnitudes and distributions of the obvious charge imbalances insolution?Consider the integral of equation 2.2.3 over the Gaussian surface shown in Figure2.2.2. Since this surface is in a conducting phase where current is not flowing, % at everypoint is zero and the net enclosed charge is also zero. We could place the Gaussian surface just outside the surface region bounding the metal and solution, and we would reachthe same conclusion.
Thus, we know now that the excess positive charge in the solution,sq , resides at the metal-solution interface and exactly compensates the excess metalcharge. That is,«7S= " <(2.2.4)This fact is very useful in the treatment of interfacial charge arrays, which we have al9ready seen as electrical double layers (see Chapters 1 and 13).Alternatively, we might move the Gaussian surface to a location just inside the outerboundary of the electrolyte. The enclosed charge must still be zero, yet we know that thenet charge on the whole system is 0м. A negative charge equal to 0м must therefore resideat 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 agiven distance from the center. As the test charge is brought from the right side of the diagram, it is attracted by the charge on the outer surface of the electrolyte; thus negativework is required to traverse any distance toward the electrolyte surface in the surrounding vacuum, and the potential steadily drops in that direction. Within the electrolyte, % iszero everywhere, so there is no work in moving the test charge, and the potential is constant at </>s. At the metal-solution interface, there is a strong field because of the doublelayer there, and it is oriented such that negative work is done in taking the positive testcharge through the interface.
Thus there is a sharp change in potential from ф^ to фмover the distance scale of the double layer.10 Since the metal is a field-free volume, theDistanceVacuumFigure 2.2.3 Potential profile throughthe system shown in Figure 2.2.2.Distance is measured radially from thecenter of the metallic sphere.9Here we are considering the problem on a macroscopic distance scale, and it is accurate to think of qs asresiding strictly at the metal—solution interface.
On a scale of 1 fxva or finer, the picture is more detailed. Onefinds that g s is still near the metal-solution interface, but is distributed in one or more zones that can be as thickas 1000 A (Section 13.3).10The diagram is drawn on a macroscopic scale, so the transition from фБ to фм appears vertical. The theory ofthe double layer (Section 13.3) indicates that most of the change occurs over a distance equivalent to one toseveral solvent monolayers, with a smaller portion being manifested over the diffuse layer in solution.58Chapter 2.
Potentials and Thermodynamics of Cellspotential is constant in its interior. If we were to increase the negative charge on themetal, we would naturally lower ф м , but we would also lower <£s, because the excessnegative charge on the outer boundary of the solution would increase, and the test chargewould be attracted more strongly to the electrolyte layer at every point on the paththrough the vacuum.The difference фм — (/>s, called the interfacial potential difference, depends on thecharge imbalance at the interface and the physical size of the interface. That is, it dependson the charge density (C/cm2) at the interface.
Making a change in this interfacial potential difference requires sizable alterations in charge density. For the spherical mercurydrop considered above (A = 0.03 cm 2 ), now surrounded by 0.1 M strong electrolyte, onewould need about 10~6 С (or 6 X 10 12 electrons) for a 1-V change. These numbers aremore than 107 larger than for the case where the electrolyte is absent. The difference appears because the coulombic field of any surface charge is counterbalanced to a very largedegree by polarization in the adjacent electrolyte.In practical electrochemistry, metallic electrodes are partially exposed to an electrolyte and partially insulated.
For example, one might use a 0.1 cm 2 platinum disk electrode attached to a platinum lead that is almost fully sealed in glass. It is interesting toconsider the location of excess charge used in altering the potential of such a phase.
Ofcourse, the charge must be distributed over the entire surface, including both the insulatedand the electrochemically active area. However, we have seen that the coulombic interaction with the electrolyte is so strong that essentially all of the charge at any potential willlie adjacent to the solution, unless the percentage of the phase area in contact with electrolyte is really minuscule.11What real mechanisms are there for charging a phase at all? An important one is simply to pump electrons into or out of a metal or semiconductor with a power supply ofsome sort.
In fact, we will make great use of this approach as the basis for control over thekinetics of electrode processes. In addition, there are chemical mechanisms. For example,we know from experience that a platinum wire dipped into a solution containing ferricyanide and ferrocyanide will have its potential shift toward a predictable equilibriumvalue given by the Nernst equation. This process occurs because the electron affinities ofthe two phases initially differ; hence there is a transfer of electrons from the metal to thesolution or vice versa.
Ferricyanide is reduced or ferrocyanide is oxidized. The transfer ofcharge 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 totalcharge 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 chemical effects on the solution are unnoticeable.
By this mechanism, the metal adapts to thesolution and reflects its composition.Electrochemistry is full of situations like this one, in which charged species (electrons or ions) cross interfacial boundaries. These processes generally create a net transferof 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 concepts (see Section 2.3 and Chapter 3).Actually, interfacial potential differences can develop without an excess charge on either phase.
Consider an aqueous electrolyte in contact with an electrode. Since the electrolyte interacts with the metal surface (e.g., wetting it), the water dipoles in contact withthe metal generally have some preferential orientation. From a coulombic standpoint, thissituation is equivalent to charge separation across the interface, because the dipoles are1]As it can be with an ultramicroelectrode. See Section 5.3.2.2 A More Detailed View of Interfacial Potential Differences* 59not randomized with time. Since moving a test charge through the interface requireswork, the interfacial potential difference is not zero (23-26). 122.2.3Measurement of Potential DifferencesWe have already noted that the difference in the inner potentials, Аф, of two phases incontact is a factor of primary importance to electrochemical processes occurring at the interface between them.
Part of its influence comes from the local electric fields reflectingthe large changes in potential in the boundary region. These fields can reach values ashigh as 107 V/cm. They are large enough to distort electroreactants so as to alter reactivity, and they can affect the kinetics of charge transport across the interface. Another aspect of Аф is its direct influence over the relative energies of charged species on eitherside of the interface. In this way, Аф controls the relative electron affinities of the twophases; hence it controls the direction of reaction.Unfortunately, Аф cannot be measured for a single interface, because one cannotsample the electrical properties of the solution without introducing at least one more interface. It is characteristic of devices for measuring potential differences (e.g., potentiometers, voltmeters, or electrometers) that they can be calibrated only to registerpotential differences between two phases of the same composition, such as the twometal contacts available at most instruments.
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