Gouy-Chapman double layer

The model of the Gouy-Chapman double layer is a further development of the simple model of an electrical double layer according to Helmholtz . What is new here is that the thermal movement of the solvent molecules and the ions are taken into account, which refute the idea of ​​a rigid ion layer in Helmholtz's model. This thermal movement leads to the formation of a diffuse layer that is more extensive than a molecular layer. A statistical distribution of the ions is assumed, as was postulated later in the Debye-Hückel theory (Debye-Hückel-Onsager theory). In accordance with these considerations, there is an exponential drop in potential across the diffuse layer. Since the ions are assumed to be point-shaped in this theory, they can get as close as desired to the surface of the phase in question. This description does not suffice for the real case of ions with their own expansion. A further development of the double layer theory, which takes this case into account, is the Stern double layer according to Otto Stern .

The Gouy-Chapman double layer is named after the French physicist Louis Georges Gouy and the British physical chemist David Leonard Chapman . Gouy, who had published a detailed study of Brownian motion as early as 1888 and was therefore familiar with the motion of molecules and ions in solutions, published his article on the double layer in 1909/1910. Chapman published his work in 1913.

Charge and double layer capacitance

The charge of the electrode and that in the electrolyte depends on the model of the diffuse double layer in a binary electrolyte, in which the cation has the charge + | z | and the anion the charge - | z | reduces potential and concentration as follows:

${\displaystyle q_{m}=-q_{d}=2{\sqrt {2\varepsilon RTc}}\;\;\sinh {\left({\frac {zF(\varphi -\varphi _{0})}{2RT}}\right)}}$.

${\displaystyle q_{m}}$	Charge density in the metal surface
${\displaystyle q_{d}}$	Total charge distributed in the electrolyte per electrode area
${\displaystyle \varepsilon }$	Solvent permittivity ; ${\displaystyle \varepsilon =\varepsilon _{0}\varepsilon _{r}}$
${\displaystyle R=k_{\mathrm {B} }\cdot N_{\mathrm {A} }}$	Universal gas constant
${\displaystyle T}$	Absolute temperature (K)
${\displaystyle c}$	Concentration of the electrolyte = concentration of the anions = concentration of the cations
${\displaystyle k_{\mathrm {B} }}$	Boltzmann constant
${\displaystyle N_{\mathrm {A} }}$	Avogadro's constant
${\displaystyle F=N_{\mathrm {A} }\cdot e}$	Faraday constant
${\displaystyle z}$	Charge number
${\displaystyle e}$	Elemental charge
${\displaystyle \varphi }$	Potential of the electrode (measured against a reference electrode)
${\displaystyle \varphi _{0}}$	Zero charge potential of the electrode (measured against the same reference electrode)

The differential double-layer capacitance C zu is obtained by deriving the charge density according to the potential φ

${\displaystyle C=-\left({\frac {\mathrm {d} q_{d}}{\mathrm {d} \varphi }}\right)=zF{\sqrt {\frac {2\varepsilon c}{RT}}}\;\;\cosh {\left({\frac {zF(\varphi -\varphi _{0})}{2RT}}\right)}}$.

This function has a minimum at the zero charge potential, which is also observed experimentally for dilute solutions. In practice, the measurement of the double-layer capacitance of dilute solutions is used to determine the zero charge potential of solid electrodes.

Importance of the Gouy-Chapman model

The model of a pure diffuse charge layer only applies to very small concentrations, e.g. B. less than 1 mM, and lower potentials, d. H. the potential must not deviate from the zero charge potential by more than approx. 60 mV. Therefore, the model has only a very limited scope, in which it is also very useful. The Gouy-Chapman model is especially important because the formalism of the calculations and a significant part of the results can be easily transferred to the Stern model.

literature

• Gerd Wedler: Textbook of physical chemistry , 5th edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004, ISBN 3-527-31066-5 .

Individual evidence

1. ↑ Louis-Georges GOUŸ 1854-1926 - Physicien, enseignant, chercheur. Portraits de personnalités ardéchoises. Jean-Yves Gourdol, April 10, 2014, archived from the original on April 27, 2014 ; Retrieved November 6, 2014 (French). 
2. ↑ Louis Georges Gouy: Sur la constitution de la charge électrique à la surface d'un electrolyte . In: Comptes Rendus de l'Académie des sciences . tape 149 , 1909, pp. 654–657 ( online on the Gallica website - bibliothèque numérique de la Bibliothèque nationale de France ).
3. ↑ Louis Georges Gouy: Sur la constitution de la charge électrique à la surface d'un electrolyte . In: Journal De Physique . tape 9 , no. 1 , 1910, pp. 457–468 , doi : 10.1051 / jphystap: 019100090045700 ( online at hal.archives-ouvertes.fr of the Center pour la Communication Scientifique Directe CCSD ).
4. ^ David Leonard Chapman: A Contribution to the Theory of Electrocapillarity . In: Philosophical Magazine Series 6 . tape 25 , no. 148 , 1913, pp. 475-481 , doi : 10.1080 / 14786440408634187 ( online on the Electrochemical Science and Technology Information Resource ESTIR site of the Electrochemical Society (ECS) [PDF]).