Gouy-Chapman layer thickness

Hottenliuis et al. studied Ag (100) surface. They made a comparison between ex situ images and in situ images. " To interpret their results they postulated a resolution increase in dependence on electrolyte concentration and its limitation to the Gouy-Chapman layer thickness. 

Fig. 2. Schematic diagram of a suspended colloidal particle, showing relative locations of the Stem layer (thickness, 5) that consists of adsorbed ions and the Gouy-Chapman layer (1 /k) which dissipates the excess charge, not screened by the Stem layer, to 2ero ia the bulk solution (108). In the absence of a...

The semiconductor occupies the region to the right of the vertical solid line representing the interface (jc = 0). To the left of it, there is the Helmholtz layer formed by ions attracted to the electrode surface, and also by solvent molecules its thickness, L, is the order of the size of an ion. The space-charge region in the solution (the Gouy-Chapman layer) is adjacent to the Helmholtz layer from the electrolyte side. 

The ensemble Helmholtz layer/Gouy-Chapman layer constitutes the electrochemical double layer. Its thickness is in the order of a few tens of Angstroms. This layer is generally represented by the series combination of two capacitances relative to the diffuse and compact layers, Cdia and Qomp- The capacity of the double layer, Cd, is thus equal to ... 

The reciprocal value is a measure for the thickness of the Gouy-Chapman layer. 

Contributions from double layer effects to the distribution of ionic species and electrical potential are also typically disregarded in the SECCM model as the thickness of the Gouy-Chapman layer in the presence of relatively high electrolyte concentrations is very small compared to the simulation domain (meniscus and probe) size. This allows the application of the electroneutrality condition throughout the simulation domain ... 

The Gouy-Chapman theory relates electrolyte concentration, cation valence, and dielectric constant to the thickness of this double layer (see Equation 26.2). This theory was originally developed for dilute suspensions of solids in a liquid. However, experience confirms that the principles can be applied qualitatively to soil, even compacted soil that is not in suspension.5... 

According to the Gouy-Chapman model, the thickness of the diffuse countercharge atmosphere in the medium (diffuse double layer) is characterised by the Debye length k 1, which depends on the electrostatic properties of the... 

Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to (a) Gouy-Chapman model and (b) Stern model, where /q and are surface and Stern potentials, respectively, and d is the thickness of the Stern layer...

As the electrode surface will, in general, be electrically charged, there will be a surplus of ionic charge with opposite sign in the electrolyte phase in a layer of a certain thickness. The distribution of jons in the electrical double layer so formed is usually described by the Gouy— Chapman—Stern theory [20], which essentially considers the electrostatic interaction between the smeared-out charge on the surface and the positive and negative ions (non-specific adsorption). An extension to this theory is necessary when ions have a more specific interaction with the electrode, i.e. when there is specific adsorption of ions. 

As in the Gouy-Chapman model, the more concentrated the electrolyte the less the importance of the thickness of the diffuse layer and the more rapid the potential drop. At distance xH there is the transition from the compact to the diffuse layer. The separation plane between the two zones is called the outer Helmholtz plane (OHP) the origin of the inner Helmholtz plane will be discussed below. 

Fig. 3. Schematic representation of the double layer structure at the nitrobenzene-water interface at 25 C. The full curve illustrates the potential distribution at Aq 0 = 0.2 V for the interface between a 0.1 M solution of Pn4NPh4B in nitrobenzene and a 0.05 M aqueous solution of LiCl at 25 °C. The thickness of the inner layer is assumed to be 1 nm and the potential distribution is calculated using the Gouy-Chapman theory. (Reprinted from [61]. Copyright Elsevier Seience Publishers, Amsterdam).

The outer surface of the Stern layer is the shear surface of the micelle. The core and the Stern layer together constitute what is termed the kinetic micelle. Surrounding the Stern layer is a diffuse layer called the Gouy-Chapman electrical double layer, which contains the aN counterions required to neutralise the charge on the kinetic micelle. The thickness of the double layer is dependent on the ionic strength of the solution and is greatly compressed in the presence of electrolyte. 

In the Stern-Gouy-Chapman (SGC) theory the double layer is divided into a Stern layer, adjacent to the surface with a thickness dj and a diffuse (GC) layer of point charges. The diffuse layer starts at the Stern plane at distance d] from the surface. In the most simple case the Stern layer is free of, charges. The presence of a Stern layer has considerable consequences for the potential distribution across the Stern layer the potential drops linearly from the surface potential V s to the potential at the Stern plane, V>d- Often is considerably lower than especially in the case of specific adsorption (s.a.). 

The determination of the real surface area of the electrocatalysts is an important factor for the calculation of the important parameters in the electrochemical reactors. It has been noticed that the real surface area determined by the electrochemical methods depends on the method used and on the experimental conditions. The STM and similar techniques are quite expensive for this single purpose. It is possible to determine the real surface area by means of different electrochemical methods in the aqueous and non-aqueous solutions in the presence of a non-adsorbing electrolyte. The values of the roughness factor using the methods based on the Gouy-Chapman theory are dependent on the diffuse layer thickness via the electrolyte concentration or the solvent dielectric constant. In general, the methods for the determination of the real area are based on either the mass transfer processes under diffusion control, or the adsorption processes at the surface or the measurements of the differential capacitance in the double layer region [56],... 

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