Electric(al) Double Layer: Tutorial

Abstract

A tutorial of the Poisson-Boltzmann continuum model (Gouy-Chapman-stern-Grahame model) of the electric(al) double layer at the electrode interface is given. Starting from Coulomb law, Gauss theorem and Boltzmann statistical distribution, the method how to calculate the potential profile of the electric double layer is shown. We also show an example of the potential profile of the double layer of liquid|liquid interface. (Poisson Boltzmann () , Gouy Gouy(-Chapman [1, 2] 1 Stern[3] GCS(Gouy-Chapman-Stern) Grahame GCS [4] GCSG Poisson-Boltzmann GCSG 1 Basics The dielectric flux density D is related to the charge density ρ(r) divD = ∇ · D = ρ(r) (1) D = 0 E = − 0 ∇φ (2) 2 Here and 0 are the dielectric constant ((with no dimension) and electric permittivity of free space [ 8.854187817 ×10 −12 Fm −1 (= CV −1 m −1)], respectively. E and φ is the electric field (and the potential. Using the Gauss theorem V dr ∇ · D ρ = S D · dS (3) In the limit that the Gauss box 3 is very thin in z direction (thickness → 0) V drρ = Q box = n · [−D − + D + ]S (4) 1 Debye-Hückel [ P. Debye and E. Hückel (1923). "The theory of electrolytes. I. Lowering of freezing point and related phenomena". Physikalische Zeitschrift 24: 185?206.] 14 2 div D = ρ Appendix 3 We call the rectangular box, for which the Gauss law applies, "Gauss box". The z is defined as the distance from the electrified interface in the direction perpendicular to the interface.