The Various Types of Potentials

Various kinds of potentials have been referred to in the course of this and the preceding chapter, and their interrelation is the subject of the present section. The chief problem is that certain types of potential differences are physically meaningful in the sense that they are operationally defined, whereas others that may be spoken of more vaguely are really conceptual in nature and may not be definable experimentally. 

The electrostatic potential within a phase, that is, l/e times the electrical work of bringing unit charge from vacuum at infinity into the phase, is called the Galvani, or inner, potential Similarly, the electrostatic potential difference 

The electrochemical potential is defined as the total work of bringing a species i from vacuum into a phase a and is thus experimentally defined. It.may be divided into a chemical work p , the chemical potential, and the electrostatic work ZiC0  

Since is experimentally measurable, it is convenient to define another potential, the real potential af  

Thus Pi, Xi, and J/ are experimentally definable, while the surface potential jump X, the chemical potential p, and the Galvani potential difference between two phases A0 = are not. While jl, is defined, there is a practical dif- 

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For purposes of comparison, it is possible to classify the various types of potential functions which may be represented by the functional form used in Eq. (3.32) with a few simple considerations. The restrictions we shall make are always to locate the origin in the minimum, or if more than one, in the deepest minimum second minima or inflection points are restricted to negative values of the coordinate Z and the positive values of Z always represent the most rapidly rising portion of the function. These restrictions do not eliminate any unique shape of potential function. Any other functions described by Eq. (3.32) are related to those already included by a simple translation of the origin or by rotation about the vertical axis. These operations, at most, change the eigenvalues by an additive constant. The different types of potential functions are summarized in Table 3.1. 

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