Modern Electrochemistry 2A

9.1. SETTING THE SCENE (p. 1455-1456)

When Galvani and, separately, Volta, made their first hesitant electrochemical experiments, in the eighteenth century, the electricity with which they dealt was not understood. Faraday's laws of 1834 (relating the amount of metal deposited in electrolysis to the amount of electricity passed) hinted at a particulate nature for electricity, and by 1897 J. J. Thompson had measured electric charge to mass ratio (e/m) for the charged "cathode corpuscles" he found in gas discharge tubes. By 1912, Millikan had measured the charge, on such particles, so that their mass was also known. The realization that the passage of electricity consists of the flow of these "electrons" is less than 100 years old.

The electron is the quintessential particle in electrochemistry. But it has turned out that its properties bear within them a mystery, the nature of which is still debated. For Davidson and Germer (1927), and then G. P. Thompson (1928) found that the corpuscles that J. J. Thompson (1897) had measured possessed a Jekyl and Hyde character. Material corpuscles they could be (with definite mass and charge) but lo!-they could also behave as if they were waves.

Earlier on, in 1901, experimental results on the variation of the intensity of radiation from hot black bodies as a function of the wavelengths emitted by the radiation led Planck to suggest that energy itself went about as "quanta," bits of energy, the amount of energy in each bit being related to the frequency of the radiation concerned. Bohr's 1913 interpretation of the H atom spectra then involved an assumption to which he needed to fit the facts: only certain frequencies of radiation were "allowed." The radiations emitted from hot atoms consisted of a number of spectral lines having frequencies of and etc. The positions in the atoms issuing radiation at these specific frequencies are called quantum states. Electrons could be in these states, but not in others.

By 1926, just in time for Davidson and Germer's 1927 experiment, Schrödinger put into mathematical form an idea due to de Broglie (1924). It was that the sometimes wavelike character of electrons could be the basis of the quantum states. The waves had to "fit into" the space available (e.g., the distance between two nuclei in a solid), and it was this need to fit and make a "standing wave" that made only certain states-certain wavelengths (or energies)-possible. All this material is described in introductory textbooks of physics and chemistry. However, it is interesting to recall the headlines here because the very first application to a chemical theme of the ideas of waves in quantum mechanics was to explain how electrons were emitted from, or accepted by, electrodes. This was the achievement of Ronald Gurney,1 the first physical electrochemist, and much of this chapter is based on developments that sprang from his seminal paper of 1931. In this paper, he related electric currents across the electrode solution interface to the tunneling of electrons through energy barriers formed between the electrode and the ions or molecules in the first layer next to the electrode (possessing "electronic states").

Our chapter has two broad themes. In the first, we will consider some aspects of quantum states relevant to electrochemical systems. In the second, the theme will be the penetration of the barrier and the relation of the current density (the electrochemical reaction rate) to the electric potential across the interface. This concerns a quantum mechanical interpretation of Tafel's experimental work of 1905, which led (1924- 1930) to the Butler-Volmer equation.