Star double layer

Schematic representation of the star model of the electrochemical double layer. M = electrode metal, equivalent = outer Helmholtz surface, a / 2 = radius of the solvated ions, x = distance to the metal surface, Δφ = potential difference, ζ = position coordinate with ζ = x - a / 2.

The star double layer is a double layer that is described in the electrolyte by two areas: the so-called rigid layer made up of (possibly solvated) ions lying on the electrode and the diffuse layer that is adjacent to it and extends far into the electrolyte. According to the theory that Otto Stern published in 1924, this charge distribution creates a potential that increases or decreases exponentially in the rigid layer and exponentially in the diffuse layer.

The star bilayer model builds on the earlier Helmholtz and Gouy-Chapman bilayer models by combining the two models.

Potential curve according to the star model

The calculation of the potential curve is analogous to the calculation in the context of the Debye-Hückel theory . It is advantageous to use the location coordinate

${\displaystyle \zeta =x-d=x-{\frac {a}{2}}}$

With

• the distance from the electrode surface and ${\displaystyle x}$
• the radius and the diameter of the ion. ${\displaystyle d}$ ${\displaystyle a}$

The potential profile in the diffuse part of the double layer is then described by the equation

${\displaystyle \varphi (\zeta )-\varphi _{L}=(\varphi _{aH}-\varphi _{L})e^{-\zeta /\beta }}$

With

• the “thickness” of the diffuse double layer (more precisely: the distance at which the potential drops to the 1 / e-th part). is identical to the " radius of the ion cloud " defined in the Debye-Hückel theory . ${\displaystyle \beta }$ ${\displaystyle \beta =\kappa ^{-1}}$
• the potential inside the electrolyte and ${\displaystyle \varphi _{L}}$
• the potential for . ${\displaystyle \varphi _{aH}}$ ${\displaystyle \zeta =0}$

All in all, according to the star model, one obtains for the potential profile in the entire double layer:

${\displaystyle {\varphi (x)={\begin{cases}\varphi _{M}&{\text{für }}x\leq 0\\\varphi _{M}+(\varphi _{aH}-\varphi _{M})\cdot {\dfrac {x}{d}}&{\text{für }}0\leq x\leq d\\\varphi _{L}+(\varphi _{aH}-\varphi _{L})e^{-(x-d)/\beta }&{\text{für }}x\geq d\\\varphi _{L}&{\text{für }}x\rightarrow \infty \end{cases}}}}$

Individual evidence

1. ↑ Otto Stern: On the theory of the electrolytic double layer . In: German Bunsen Society for Applied Physical Chemistry, Erich Müller (Hrsg.): Journal for Electrochemistry . tape 30 , no. 21-22 . Wiley ‐ VCH Verlag, November 1924, ISSN  0372-8323 , p. 508-516 , doi : 10.1002 / bbpc.192400182 ( online at the Electrochemical Science and Technology Information Resource (ESTIR) of the Electrochemical Society [PDF]).
2. ↑ ^{a b c} Gerd Wedler: Textbook of physical chemistry . 5th edition. Wiley-VCH, Weinheim 2004, ISBN 3-527-31066-5 , 2.7.7 The electrical double layers, p. 435-440 .