Helmholtz layer

Scheme of a Helmholtz layer and a corresponding double layer. In the example, the metal carries a positive excess charge, which is balanced by the charge of the anions in the layer on the electrolyte side.

A Helmholtz layer is a narrow area within an electrolyte that is directly adjacent to an electrode and that carries an excess charge. This is possible if the sum of the charges on the cations is not equal to the sum of the charges on the anions in this area. In the simplest case there are monovalent cations and monovalent anions in different numbers. The Helmholtz layer only includes ions that either lie directly on the electrode without a hydration shell or that are maximally separated from the electrode by a hydration shell. The Helmholtz layer is only a part of the entire electrochemical double layer , the diffuse part of which can extend far into the electrolyte.

The Helmholtz double layer consists of the above-mentioned Helmholtz layer and the oppositely charged layer in the electrode.

The inner Helmholtz plane is a plane parallel to the electrode surface through the centers of gravity of the ions directly adjacent to the electrode without a hydration shell . Such ions are called specifically adsorbed. The outer Helmholtz plane is a plane parallel to the electrode surface through the centers of the ions, the hydration shells of which lie directly on the electrode surface; they are not specifically adsorbed.

Because of the fixed distances between the Helmholtz levels and as a contrast to the diffuse part of the double layer, the Helmholtz double layer is also called a rigid double layer . But that does not mean that the ions do not move: They diffuse both in the plane and in exchange with the diffuse double layer. In the context of Otto Stern's model , the Helmholtz layers are also called the inner star layer.

Scheme of a Helmholtz layer made of cations and a Helmholtz double layer with a negative charge in the metal. The cations are hydrated; H. water molecules are bound to each cation.

Historical

The term “double layer” comes from Hermann von Helmholtz . Without explicitly referring to the electrode-electrolyte interface, he wrote in 1853: “In the following, an electrical double layer will always only mean two layers that are on the opposite sides of a surface at an infinitely small distance in front of it, and one of which is just as many positive In a work published in 1879, Helmholtz explains that on “metallic electrodes in an electrolyte”, “electrical double layers form on the electrode surfaces, the electrical moment of which corresponds to the current potential jump between the relevant electrode and the liquid ". In 1882 Helmholtz published a study of the double layer with the mercury drop electrode , in which he wrote: "Expansion of the surface thins the existing electrical double layer and thus reduces the potential difference between mercury and electrolytes."

The terms "inner" and "outer" level were created and coined by the American chemist David C. Grahame , who worked at Amherst College. He also pointed out that in the case of small cations and large anions, the “inner” plane with the specifically adsorbed ions can lie outside the “outer” plane with the hydrated cations.

Calculation of the potential curve

Scheme of the potential curve in an idealized Helmholtz double layer: constant in the electrode and in the electrolyte, linear in the Helmholtz layer.

For the relationship between the space charge density ρ and the potential φ , if one considers the potential as a function of the coordinate x perpendicular to the electrode surface, the Poisson's equation applies

${\displaystyle {\frac {\partial ^{2}\varphi }{\partial x^{2}}}=-{\frac {4\pi \rho }{\varepsilon }}}$.

Since there is no charge density between the electrode surface and the inner Helmholtz plane, ρ = 0 applies there. The Laplace equation follows from this

${\displaystyle {\frac {\partial \varphi }{\partial x}}={\text{const}}}$.

This means that the potential between the electrode surface and the inner Helmholtz plane changes linearly.

There is also no charge inside the metal ( ρ = 0). Even inside the electrolyte, despite the anions and cations, the mean charge density is zero ( ρ = 0); in these cases the change is not only constant but zero. Using these boundary conditions, one obtains for the potential curve:

${\displaystyle {\varphi (x)={\begin{cases}\varphi _{M}&{\text{für }}x\leq 0\\(\varphi _{L}-\varphi _{M})\cdot {\dfrac {x}{d}}+\varphi _{M}&{\text{für }}0\leq x\leq d\\\varphi _{L}&{\text{für }}d\leq x\end{cases}}}}$

Diameter of the layer and electric field strength

Helmholtz wrote about the diameter of the layer: "Kohlrausch's investigations into the capacity of platinum surfaces during the electrolysis of water result in the mean distance between such layers equal to 2,475,000th of a millimeter, assuming the polarization is evenly distributed over both plates". This is a distance d of 0.40 nm. This agrees quite well with typical ionic radii, e.g. B. 0.17 nm for chloride, 0.18 nm for bromide. The effective diameter of the sulfate ion is given as 0.40 nm, that of the hydrated sodium ion Na ⁺ as 0.45 nm.

Most simple ions have radii in the 0.1 nm to 1 nm range, even when they are hydrated. It is therefore also expected that the distance between the electrode and the Helmholtz plane is in the range from 0.1 nm to 1 nm. Electrochemical voltages cannot exceed a few volts because of the decomposition voltage of the respective electrolyte, which is 1.23 V for water. With a voltage of 0.1 V to 1 V, electrical field strengths in the range from 10 ⁸ to 10 ¹⁰ V / m result. These values ​​are above the dielectric strength of many materials, e.g. B. that of glass is only 10 ⁷  V / m, that of water 7 10 ⁷  V / m. This means that the dielectric strength values ​​obtained from macroscopic experiments cannot easily be applied on an atomic scale. The stresses occurring here are small due to the small distances.

Individual evidence

1. ↑ Hermann von Helmholtz: About some laws of the distribution of electrical currents in physical conductors, with application to animal electrical experiments . In: JC Poggendorff (Ed.): Annals of Physics and Chemistry . Third row. tape 89 . Publisher by Johann Ambrosius Barth, Leipzig 1853, p. 211–233 , doi : 10.1002 / andp.18531650603 ( online on the pages of Gallica - Bibliothèque nationale de France [accessed October 10, 2014]).
2. ↑ Hermann von Helmholtz: Studies on electrical boundary layers . In: G. Wiedemann (Ed.): Annals of Physics and Chemistry . tape 243 , no. 7 . Publisher by Johann Ambrosius Barth, Leipzig 1879, p. 337–382 , doi : 10.1002 / andp.18792430702 ( online on the Gallica - Bibliothèque nationale de France pages [accessed October 10, 2014]).
3. ↑ Hermann von Helmholtz: About galvanic polarization of mercury and related new experiments by Mr. Arthur König . From: Monthly reports of the Berlin Academy of November 3, 1881. In: Wissenschaftliche Abhandlungen. First volume. Publisher by Johann Ambrosius Barth, Leipzig 1882, p. 925-938 ( online on the pages of ECHO - Cultural Heritage Online ).
4. ^ R. Levine, An Interpretation of the Stern Inner Region at a metal / aqueous electrolyte interface, in: The Electrochemical Double Layer, Edited by Carol Korzeniewski, BE Conway, The Electrochemical Society, Inc., Pennington
5. ↑ ^{a b} Carl H. Hamann, Wolf Vielstich: Elektrochemie . 3. Edition. Wiley-VCH, 1998, ISBN 978-3-527-27894-7 , pp. 108-109 .
6. ↑ ^{a b} Ionic Radii and Diameters from Several Sources. Retrieved October 13, 2014 .