New results from the contact theorem for the charge profile for symmetric electrolytes

Abstract

In this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwell electrostatic tensor and a new electrostatic property defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed.

Evidence for a second, local contact condition for a planar electric double layer containing size and valency asymmetric ions

“…A relation for the charge profile would be valuable in, for instance, surface electrochemistry. An exact second contact condition was advanced by Holovko, Badiali, and di Caprio (HBC) [6,7] for the RPM double layer, which for equal diameter z : z valency electrolytes reads…”

Response to “Comment on ‘Contact conditions for the charge in the theory of the electrical double layer’ ” [J. Chem. Phys. 128, 117101 (2008)]

“…In this case, it was shown in Ref. 10 that g coion ͑d / 2͒ → 0. This implies that in this limit, J = a.…”

“…10 After Eq. ͑8͒, it should read "g Ϯ ͑z͒ is the singlet distribution function for coions" instead of "g Ϯ ͑z͒ is the singlet distribution function for counterions."…”

A modified Poisson–Boltzmann study of the singlet ion distribution at contact with the electrode for a planar electric double layer

“…This was derived by Holovko, Badiali and di Caprio4,5 (HBC), and Holovko and di Caprio6 starting from the Bogoliubov–Born–Green–Yvon (BBGY) hierarchy of equations7. For a double layer containing a restricted primitive model (RPM) electrolyte (the ions of the PM are now restricted to having a common diameter), and for symmetric valency salts – our interest in this paper, their relation is particularly simple, viz., $$g_{\text{diff}}(d/2)=-z\mathrm{e}\mathrm{\beta }{\displaystyle \underset{d/2}{\overset{\infty }{\int }}{g}_{\text{sum}}false(xfalse)\frac{\mathrm{normald}\mathrm{normal\psi }false(xfalse)}{\mathrm{normald}x}\mathrm{normald}x}$$ where g sum ( x ) = (1/2)( g ctr ( x ) + g co ( x )), g diff ( x ) = (1/2)( g ctr ( x ) − g co ( x )), the subscripts ‘ctr’ and ‘co’ denoting counter- and coions, respectively.…”