Double layer potential

Surface potential Stern potential Zeta potential Double>layer thickness (reciprocal Debye length)... 

Z(a>) - Ra Rct + (1 - jymo-w and produce an electrochemical "spectrum as charge transfer-potential, double layer capacity-potential, ohmic resistance-potential, and Warburg coefficient-potential plots. Together with the current-potential curve, these present a useful representation of the steady-state electrochemical behaviour. 

Two solutions, 1M hydrochloric acid + 0.01 M PdCl2 (A) and O.lM hydrochloric acid + 0.91 M perchloric acid + 0.01 M PdCl2 (B), have been analysed in Fig. 17(a) and (b) by impedance-potential measurements, to give standard rate constant-potential, double layer capacity-potential, and current-potential curves for a particular reaction mechanism, in this case for the PdCl+ complex... 

Chapters 10 and 11 are devoted entirely to aspects of colloid stabihty. First, the essential concepts of the electrical and van der Waals forces between colloid particles are presented with special emphasis on the concepts of the zeta potential, double-layer thickness and Hamaker constants. Then, the DLVO theory for colloidal stability is presented. This is a major tool in colloid chemistry and we discuss how stability is affected by manipulating the parameters of by the classical DLVO theory. Chapter 11 closes with a presentation of kinetics of colloid aggregation and structure of aggregates. Chapters 12 and 13 are about emulsions and foams, respectively - two important categories of colloid systems where DLVO and other principles of colloid and surface science are apphed. In this case, DLVO is often not sufficient. Steric forces and solvation effects are not covered by the classical DLVO and their role in colloid stabihty is also discussed in Chapter 12. 

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. 

By analogy with the Helmholtz condenser formula, for small potentials the diffuse double layer can be likened to an electrical condenser of plate distance /k. For larger yo values, however, a increases more than linearly with o, and the capacity of the double layer also begins to increase. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Here, the only surface adsorption is taken to be that of the charge balancing the double-layer charge, and the electrochemical potential change is equated to a change in o- Integration then gives... 

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

Fig. V-12. Variation of the integral capacity of the double layer with potential for 1 N sodium sulfate , from differential capacity measurements 0, from the electrocapillary curves O, from direct measurements. (From Ref. 113.)...

The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

Much use has been made of micellar systems in the study of photophysical processes, such as in excited-state quenching by energy transfer or electron transfer (see Refs. 214-218 for examples). In the latter case, ions are involved, and their selective exclusion from the Stem and electrical double layer of charged micelles (see Ref. 219) can have dramatic effects, and ones of potential imfKntance in solar energy conversion systems. 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

Referring to Section V-2, the double-layer system associated with a surface whose potential is some value j/o requires for its formation a free energy per unit area or a t of... 

The great advantage of the RDE over other teclmiques, such as cyclic voltannnetry or potential-step, is the possibility of varying the rate of mass transport to the electrode surface over a large range and in a controlled way, without the need for rapid changes in electrode potential, which lead to double-layer charging current contributions. 

The first case is relevant in the discussion of colloid stability of section C2.6.5. It uses the potential around a single sphere in the case of a double layer that is thin compared to the particle, Ka 1. Furthennore, it is assumed that the surface separation is fairly large, such that exp(-K/f) 1, so the potential between two spheres can be calculated from the sum of single-sphere potentials. Under these conditions, is approximated by [42] ... 

In the second case, a thick double layer, Ka 1 (low ionic strength), is assumed. Wlren the surface potential is low, 1, a reasonable approximation is given by... 

As a furtlier example for tire meaning of ex situ investigations of emersed electrodes witli surface analytical teclmiques, results obtained for tire double layer on poly crystalline silver in alkaline solutions are presented in figure C2.10.3. This system is of scientific interest, since tliin silver oxide overlayers (tliickness up to about 5 nm) are fonned for sufficiently anodic potentials, which implies tliat tire adsorjDtion of anions, cations and water can be studied on tire clean metal as well as on an oxide covered surface [55, 56]. For tire latter situation, a changed... 

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