Electrolytes diffuse double layer

The capacity of the electrolytic diffuse double layer is often ignored when Mott-Schottky plots are used to characterize semiconductor-electrol3ffe interfaces. Under what conditions is this assumption justified ... 

The total potential drop Apotential drop at the metal/oxide interface, the potential drop in the oxide, the potential drop in the Helmholtz layer and the potential drop in the electrolyte (diffuse double layer) ... 

The quantity 1 /k is thus the distance at which the potential has reached the 1 je fraction of its value at the surface and coincides with the center of action of the space charge. The plane at a = l//c is therefore taken as the effective thickness of the diffuse double layer. As an example, 1/x = 30 A in the case of 0.01 M uni-univalent electrolyte at 25°C. 

The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

We shall use the familiar Gouy-Chapman model (3 ) to describe the behaviour of the diffuse double lpyer. According to this model the application of a potential iji at a planar solid/electrolyte interface will cause an accumulation of counter-ions and a depletion of co-ions in the electrolyte near the interface. The disposition of diffuse double layer implies that if the surface potential of the planar interface at a 1 1 electrolyte is t ) then its surface charge density will be given by ( 3)... 

B , while for an n-type semiconductor the reverse is true. An analog to the SCR in the semiconductor is an extended layer of ions in the bulk of the electrolyte, which is present especially in the case of electrolytes of low concentration (typically below 0.1 rnolh1). This diffuse double layer is described by the Gouy-Chap-man model. The Stern model, a combination of the Helmholtz and the Gouy-Chapman models, was developed in order to find a realistic description of the electrolytic interface layer. 

The charge at the surface of a solid (including any adsorbed species) will be balanced by a countercharge in the electrolyte the double layer as a whole is electrically neutral. The countercharges remain in the vicinity of the surface-adsorbed charge but, due to thermal motion, do not accumulate at the surface but move in a more or less diffuse cloud surrounding the particle. The extent to which this layer... 

A corrected and more general analysis of the primary electroviscous effect for weak flows, i.e., for low Pe numbers (for small distortions of the diffuse double layer), and for small zeta potentials, i.e., f < 25 mV, was carried out by Booth in 1950. The result of the analysis leads to the following result for the intrinsic viscosity [rj] for charged particles in a 1 1 electrolyte ... 

This same relationship is the starting point of the Debye-Hiickel theory of electrolyte nonideality, except that the Debye-Hiickel theory uses the value of V2 p required for spherical symmetry. It is interesting to note that Gouy (in 1910) and Chapman (in 1913) applied this relationship to the diffuse double layer a decade before the Debye-Hiickel theory appeared. 

The charge density, Volta potential, etc., are calculated for the diffuse double layer formed by adsorption of a strong 1 1 electrolyte from aqueous solution onto solid particles. The experimental isotherm can be resolved into individual isotherms without the common monolayer assumption. That for the electrolyte permits relating Guggenheim-Adam surface excess, double layer properties, and equilibrium concentrations. The ratio u0/T2N declines from two at zero potential toward unity with rising potential. Unity is closely reached near kT/e = 10 for spheres of 1000 A. radius but is still about 1.3 for plates. In dispersions of Sterling FTG in aqueous sodium ff-naphthalene sulfonate a maximum potential of kT/e = 7 (170 mv.) is reached at 4 X 10 3M electrolyte. The results are useful in interpretation of the stability of the dispersions. 

The characteristics of the diffuse electric double layer at a completely polarized interface, such as at a mercury/aqueous electrolyte solution interface are essentially identical with those found at the reversible interface. With the polarizable interface the potential difference is applied by the experimenter, and, together with the electrolyte, specifically adsorbed as well as located in the diffuse double layer, results in a measurable change in interfacial tension and a measurable capacity. 

Figure 1. Schematic Diffuse double layer formed as a result of anion adsorption, showing the effect of negative adsorption of similions on the bulk concentration. A. Initial electrolyte concentration. B. Final electrolyte concentration. C. Final concentration if there were no negative adsorption of similions...

It is postulated that one of the ions of the adsorbed 1 1 electrolyte is surface active and that it forms an ionized monolayer at the solid/liquid interface. All counterions are assumed located in the diffuse double layer (no specific adsorption). Similions are negatively adsorbed in the diffuse double layer. Since the surface-containing region must be electrically neutral, the total moles of electrolyte adsorbed, n2a, equals the total moles of counterions in the diffuse double layer which must be equal to the sum of the moles of similions in the diffuse double layer and the charged surface, A[Pg.158]

Another important feature is the relative size of the diffusion layer with respect to the double layer. The diffusion-layer dimensions are proportional to the size of the electrode, and can approach the size of the double layer with electrodes of molecular dimensions [95]. This can also occur in other situations explored with microelectrodes. For example, in solutions of very dilute electrolyte, the diffuse double layer extends several nanometers into solution [62]. Alternatively, very fast cyclic voltammetry results in a very small diffusion layer, which may be of dimensions similar to the double layer [46]. In all these situ-... 

D.C. Grahame, Diffuse double layer theory for electrolytes of unsymmetrical valence types, J. Chem. Phys. 21 (1953) 1054-1060. 

The addition of the inert electrolyte affords other advantages. The most important point is that the conductivity of the solution increases (and thus the ohmic drop decreases through a decrease of the resistance of the cell, Rccw see Sect. 1.9). Moreover, the diffuse double layer narrows, being formed mainly by the ions of the inert electrolyte (with a sharp potential drop over a very short distance from the electrode surface). This makes the capacitance more reproducible and the Frumkin effects less obtrusive. Activity coefficients of the electroactive species are also less variable (and, therefore, quantities like formal potentials and rate constants), since... 

The treatment of the diffuse double layer outlined in the last section is based on an assumption of point charges in the electrolyte medium. The finite size of the ions will, however, limit the inner boundary of the diffuse part of the double layer, since the centre of an ion can only... 

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