By William Geraint V. Rosser
Creation to Statistical Physics (Mathematics and Its purposes) [Paperback
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Extra resources for An introduction to statistical physics (1982), Edition: 1st
For example, treating the data for Hg/H2 O-NaF interface in Fig. 2 leads to Fig. 001 M, were used for c1 , while c2 was taken each time equal to the maximum concentration. The points thus found are shown together with the corresponding experimental dispersion. On the one hand, it is sufﬁcient to accept one of the Grahame’s hypotheses, the one on the independence of the compact-layer capacitance of the electrolyte concentration, in order to relate the δC −1 value to the characteristics of the diffuse layer, that is, the change of its inverse capacitance [Cdiff (σ, c)]−1 , with concentration, at a ﬁxed value of the electrode charge: δC −1 ≡ [Cdiff (σ, c1 )]−1 − [Cdiff (σ, c2 )]−1 (23b) On the other hand, if we also accept the second postulate of the Grahame theory, then Cdiff (σ, c) can be calculated with the use of the GC model, Eq.
The simplest interpretation of the compact-layer capacitance is represented by the Helmholtz model of the slab ﬁlled with a dielectric continuum and located between a perfect conductor (metal surface) and ‘‘the outer Helmholtz plane’’ considered as the distance of the closest approach of surface-inactive ions. Experimental determination of its thickness, zH , may be based on Eq. (12). Moreover, its dielectric permittivity, εH , is often considered as a constant across the whole compact layer. Then its value can be estimated from the values of the compact-layer capacitance, for example, it gives about 6 or 10 (depending on the choice of zH ) for mercury–water interface, that is, a value that is much lower than the one in the bulk water, 80.
1. The error bars were calculated from those in the capacitance versus potential curves (Fig. 001 M, within the whole potential interval, as it is discussed in the text. Fig. 2 If one relies on the validity of the GC model for the diffuse-layer properties, one can use Eq. (20) to calculate the values of the compact-layer capacitance, CH , from experimental data for C and theoretical formula (21a) for CGC . This operation performed for all available values of the charge and the electrolyte concentration results in Fig.