Comment on “On the ‘simple check’ of electrocapillarity” by AY Gokhshtein

Comment on “Simple thermodynamic derivation of the electrocapillary equations” by L. Makkonen [Surf. Sci. 635 (2015) 61–63]

“…of Eq. (10) actually equals zero, as here the surface charge density q is a single-value function of the potential E (q = kE) and q is independent of A [5,6]. This is in agreement with the Lippmann's remark that q is a function of E independent of A [11], but this important fact is not even mentioned in [1].…”

“…However, this conclusion contradicts the fact that the so called the first and second Gokhshtein equations are only artificially distorted forms of the Lippmann equation and any discussions of their validity do not make sense [5].…”

“…of Eq. (6) equals zero [5,6]. In turn, the Lippmann equation does not require checks of its validity as shown in detail in the review [7].…”

“…Of course, in a general case, this derivative can be non-zero, as, for example, in the case of a spherical conductive body immersed in a dielectric medium, where q is, indeed, a function of two independent variables E and A. Meanwhile, if such body is immersed in an electrolyte, then the surface electric double layer is formed, and the potential drop is the same as in the parallelplate capacitor, i.e., q is independent of A [5,6].…”

“…Since the generalized forces are functions of the corresponding generalized coordinates, the potential E must be the state function of independent state variables Q and A, i.e., E(Q, A). It happens in the majority of problems in electrostatics, e.g., in the case of a spherical conductive body immersed in a dielectric medium, but it does not happen in the case of a double electric layer [5,6], where the variables A and Q = qA are not independent, which does not satisfy the recipe for obtaining Maxwell relations [8], as discussed earlier [5][6][7]9,10]. Actually, in a double electric layer the potential E is a single-value function of the surface charge density q, i.e., q = kE, and q is independent of A just as it takes place in a parallel-plate capacitor [5,6].…”