Abstract
The fundamentals of the statistical mechanical theory of the electric double layer are discussed in relation to the choice of the independent electric variable. It is shown that the grand canonical ensemble theory implies the use of the potential as the independent electric variable. The notion of a constant charge ensemble is then introduced as a particular case of the grand canonical ensemble. The differential capacity is expressed unambiguously by charge fluctuation in the grand canonical ensemble theory, while the analogous formula in the constant charge ensemble theory can be interpreted as a surface excess of polarizability, which cannot be resolved unambiguously into absolute quantities: dipole moment fluctuation and thickness of the interface. The implication of the choice of the independent electric variable for the so-called polarization catastrophe is discussed.
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