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184 CHAPTER 2

Fig. 2.74. Schematic representation of the trans-
fer of electrons from metal to the conduction band
of water before and after the breakdown. The
current-potential relation leading to breakdown
involves a plateau in which current hardly in-
creases as potential approaches breakdown.
(Reprinted from M. Szklarczyk, R. Kainthla, and
J. O’M. Bockris, J. Electrochem. Soc., 136: 2512,
1989.)

energy levels are full and transport by electrons is therefore nonexistent. This valence
band region is separated from the conductance band by what is called an energy gap;
i.e., between the energy of the band of electron levels that conducts and the band that
does not, there is a region in which no electrons exist. However, energetically above
the top of the gap in the conduction band, electrons can conduct freely and with a
mobility millions of times above that of ions in solution.
A theory put forward by Szklarczyk et al. suggests that the high applied potential
(and high resulting field strength in solution) are secondary reflections of the effect
they cause on the fundamental Fermi energy level of electrons in this metal. Here are
most of the available electrons in a metal. Should it be possible to lift this electron-
emitting level in the electrode to sufficiently high levels, the level of the conduction
band in water (seen as a semiconductor) would be reached (Fig. 2.73). This would be
the critical event for breakdown, for if electrons in the metal attained such an energy,
they would enter the conduction band of water and behave as electrons in the
conduction band of a semiconductor, traveling too rapidly to react chemically with

46
Distance = (speed)(time). Suppose one allows twice the diameter of water (~ 600 pm) for the distance
between the center of a water molecule and that in which an electron could affect a water chemically, and
0.1 of the speed of light for the velocity of passage of a streamer. Then where is
the time the water has to recognize an electron; s leaves waterunaffected as faras thevibrational
and rotational levels are concerned. Even the electrons in water move only about 1/100 of a diameter in
such a short time.