Double layer: counter ions thickness

Z = Valence of counter ions, assumed symmetrical e = electronic charge 0 = surface potential k = double layer thickness 7r, T have their usual meanings... 

For a 1-1 electrolyte the double layer thickness is, therefore, about 1 nm for a 101-1 mol dm-3 solution and about 10 nm for a 1Q 3 mol dm-3 solution. For unsymmetrical electrolytes the double layer thickness can be calculated by taking z to be the counter-ion charge number. 

At comparable thicknesses of the dipole and diffuse layers their coupling becomes important and has so far been underestimated. However, the Debey length increases with decreasing electrolyte concentration and the diffuse layer becomes independent. The counter-ion distribution in the inner part of the double layer can be described as localised or non-localised adsorption dependent on some conditions. 

The last effect to be described here is film elasticity In case of ionic surfactants the aqueous phase in the double layers contain dissolved counter ions of the surfactants. When the ionic density increases, the repulsive forces of equally charged ions become substantial, see Fig. 11. The repulsive forces are also responsible for a certain elasticity of double layers. The thickness of double layers in the well-known coloured air bubbles lies between 1,000 and 10,000 A. It can be determined by the order of interferential colours The process is very dynamic and fluctuates over the surface area. Under certain conditions the drainage reaches an end at a metastable state (so called black films ) giving the lamella or bubble a limited time of existence ... 

An understanding of electro-osmosis goes back to Schmoluchowski (Figure 10.14). An electrically charged surface (surface potential 0 exposed to a layer of almost pure water develops a double layer (surface -h counter-ions), the thickness of which is the screening radius where the counter-ions collect. 

The double layer extension is determined by the electrolyte concentration and the valency of the counter ions, as given by the reciprocal of the Debye-Huckel parameter (1 /k) - referred to as the thickness of the double layer,... 

In reality, the counter charge arises from the ions in the electrolyte which can approach the surface only up to a distance which corresponds with the thickness of the Helmholtz double layer dn. The result is an increase of the potential drop between the electrolyte and the bulk of the semiconductor by a voltage... 

Note that the ionic valency, z includes the sign of the ion charge. For example, S04 has z = -2 and Ca " has z = +2. The atomic valency, on the other hand, refers to the number of possible bonds an atom can form with other atoms and is always positive. The term K (as opposed to is called the Debye-Hiickel parameter. The Debye length, is often referred to as the thickness of the double layef even though the region of varying potential is of the order of 3/k to 4/k (Hunter, 1993). The Stem layer is, in most cases, much smaller than the diffuse layer and is of the order of the counter-ion diameter. 

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