Читать книгу Electroanalytical Chemistry - Gary A. Mabbott - Страница 24

One can gain a lot of insight about electrochemical processes from approximating the behavior of an electrified interface with that of a capacitor. For example, it is interesting to think about how many charges are involved in creating a voltage across the boundary between two phases. An estimate can be made by modeling the electrical double layer as a simple capacitor where the solid metal constitutes one plate of the capacitor and the solution at the OHP (plus the diffuse region) serves as the second plate (Figure 1.10). (A similar argument can be made for other types of phase boundaries, such as between two ion‐containing liquids.)

Figure 1.10 The electrical double layer can be modeled as a capacitor where the charge Q is the charge on one plate.

Consider how much charge would be required to create an interface potential difference of 1.0 V. For the sake of discussion, consider a metal surface that has a net positive charge. The magnitude of charge, Q, that a capacitor accumulates on each side of the interface for a given voltage, V, separating the two plates is given by Eq. (1.21) [5].

(1.21)

where the proportionality constant, C, is the capacitance of the dielectric medium separating the plates. (Here is the reason that the model is an over‐simplification. The double layer actually has a capacitance that varies with both the electrolyte concentration and with the double layer potential. However, this model does give results that set some upper limits. That is useful.) Empirically, the capacitance of the interface between a metal electrode in an aqueous salt solution is typically in the range of 10–40 μF/cm² [9]. For convenience, a value at the midpoint of that range will be used, i.e. 25 μF/cm² or 25 × 10⁻⁶ C/(V cm²), to estimate the charge in this example. (Notice that the units on the value for the capacitance indicate that total charge depends on the electrode area.)

(1.22)

Because there are 9.6485 x 10⁴ C/mole of charge:

(1.23)

The calculation indicates that 2.5 × 10⁻¹⁰ mol of anions will be required to charge the double layer to a potential of 1.0 V. Thus, on a mole basis, the number of ions required to charge the solution side of the interface is tiny. For comparison, consider the number of moles of anions present next to a square electrode 1 cm on a side. Consider the chloride ions in a volume of 1 cm³ solution of 0.1 M NaCl.

(1.24)

(1.25)

Charging the electrode to 1.0 V would require less than 0.0003% of the chloride ions from the surrounding milliliter of solution to be recruited into the double layer. Clearly, that amount represents a negligible loss to the Cl⁻ concentration in the neighboring solution.

For every potential difference that appears across the double layer, there is a corresponding arrangement of charge. If the number of charges changes, the double layer potential changes. Likewise, if one is applying a voltage to the interface, then one must move electrons and ions to establish any new arrangement of charge. Because the movement of charge constitutes a current, then a current will exist until the new arrangement of charge is established. This phenomenon is called the double layer charging current. It can be a problem in some voltammetry experiments, because the signal current may be much smaller than the double layer charging current. In applied potential techniques one is usually interested in measuring the current that is related to the amount of analyte that is being oxidized or reduced at the electrode interface. The signal current associated with the oxidation or reduction of a chemical species is called a Faradaic current because the charge exchanged between the electrode and the electroactive species in solution is proportional to the number of moles of analyte that is oxidized or reduced according to Faraday's law (Q = ∫ i dt = nFN). The double layer charging current is non‐Faradaic; it represents a background component that one must remove from the signal in order to perform quantitative analyses. Methods for circumventing the double layer charging current are described in Chapter 5 on controlled potential techniques.