Diffuse layer potential

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

Figure 3.16 The pair potential for rutile in ethylene glycol at infinite dilution as a function of diffuse layer potential. Background concentration 1 x 10 4 Ml ] electrolyte...

Diffuse layer potential = —50 mV and background electrolyte concentration... 

Three electroviscous effects have been noted in the literature.27 The primary electroviscous effect refers to the enhanced energy dissipation due to the distortion of the diffuse layer from spherical symmetry during flow. The analysis for low diffuse layer potentials has been clearly reviewed by van de Ven28 and the result for the intrinsic viscosity with Ka—> oo is ... 

Tables I and II contain electrochemical kinetic and related thermodynamic parameters for several transition-metal redox couples gathered at the mercury-aqueous interface. These systems were selected since the kinetics can be measured accurately under experimental conditions where the diffuse-layer potentials, , are small and/or could be estimated with confi-...

The distribution of excess charge of hydrated ions in the diffuse layer can be derived by using Poisson s equation, d% dx = - o(jc)/e, and Boltzmann s distribution equation, Ci(x) = Cys) exp -Zie )/ 7 , to obtain the relationship in Eqn. 5-3 between the interfacial charge, om, and the diffuse layer potential, ohp ... 

To a first approximation, the capacity of the diffuse layer in Eqn. 5-4 may be represented by an inverse parabolic function of the diffuse layer potential hp with its tnifiimum at the potential of zero charge, (4ohp = 0) the minimum capacity is given by Eqn. 5-5 ... 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

When analyzing data from a dissimilar system there are two potentials involved. In Fig. 3 we show theoretical force-separation curves for different pairs of potentials that when multiplied together give the same number. For constant charge systems there is very little difference between the curves produced by the different pairs of potentials. At large separations, where theory is lined to the experimental data to determine the diffuse layer potentials, there is little difference between the constant potential systems. Clearly, there is not a unique pair of diffuse layer potentials that fits the individual experimental force curves. Even when the constant potential interaction fits are considered, any differences between different potential pairs at small separations may be obscured if there is an extra non-DLVO short-range repulsion. For this reason it is necessary to have independently obtained values of the potentials of the materials for comparison. 

The work of Larson et al. (62) represented the first detailed study to show agreement between AFM-derived diffuse layer potentials and ((-potentials obtained from traditional electrokinetic techniques. The AFM experimental data was satisfactorily fitted to the theory of McCormack et al. (46). The fitting parameters used, silica and alumina zeta-potentials, were independently determined for the same surfaces used in the AFM study using electrophoretic and streaming-potential measurements, respectively. This same system was later used by another research group (63). Hartley and coworkers 63 also compared dissimilar surface interactions with electrokinetic measurements, namely between a silica probe interacting with a polylysine coated mica flat (see Section III.B.). It is also possible to conduct measurements between a colloid probe and a metal or semiconductor surface whose electrochemical properties are controlled by the experimenter 164-66). In Ref. 64 Raiteri et al. studied the interactions between... 

Our modeling approach was first used to describe the EDL properties of well-characterized, crystalline oxides ( 1). It was shown that the model accounts for many of the experimentally observed phenomena reported in the literature, e.g. the effect of supporting electrolyte on the development of surface charge, estimates of differential capacity for oxide surfaces, and measurements of diffuse layer potential. It is important to note that a Nernstian dependence of surface potential (iIJq) as a function of pH was not assumed. The interfacial potentials (4>q9 4> 9 in Figure 1) are... 

The inner potential drop across the ITIES, Aq2 0, is related to the rational potential [57], Aq 0r = E-Ep f., and the two diffuse layer potentials, each in the aqueous phase and in the organic phase, and 0°through... 

Figure 3.10 illustrates the same trends in terms of capacitances. In this example the asymmetry of the electrolyte has been varied at fixed concentration. In this plot the trends are more pronounced than in fig. 3.9. The new feature is that the capacity minimum no longer coincides with the zero point of the diffuse layer potential, but is shifted in the direction where the multivalent ion is the co-ion. (In fig. 3.9 the same can be seild of the position of the minimum slope.) The value y (min) where the capacitance minimum is located can be obtained by differentiating [3.5.34] with respect to y leading to the condition... 

The relation between the diffuse charge density o-j and the diffuse layer potential can be obtained from Eq. (6) and realising that according to Gauss law ... 

Attard, P., Antelmi, D., and Larson, I., Comparison of the zeta potential with the diffuse layer potential from charge titration, Langmuir, 16, 1542. 2000. 

Considerable effort has been made in recent years to improve the GC model. Early work [33] was carried out at the primitive level with the solvent represented as a dielectric continuum and the ions as hard spheres. The integral equation approach was one method applied to this problem. This work was followed by Monte Carlo studies [32]. The general result of these studies is that the GC model overestimates the magnitude of the diffuse layer potential drop (see fig. 10.18). 

Noting that the diffuse layer potential drop (j) is zero when Oad is equal to 0, this is also the potential due to the dipoles established by the adsorbed ions and their images in the metal. The corresponding dipole moment of the adsorbed ions is... 

Other adsorption isotherms have been used in the literature to analyze experimental data. However, it can usually be shown that they are limiting forms of the general isotherm derived here (equation (10.8.38)). For example, in early work the importance of the term in the diffuse layer potential (zj f ([) ) was not recognized. By using equation (10.8.7) for this contribution, the exact dependence of this term on Qni and Qad is obtained. Equation (10.8.7) can be simplified in limiting cases and the form of the isotherm without an explicit dependence on ([) obtained. 

As referred to earlier, the usual representation of effects of electrode potential on electrochemical reaction rates is through a modulating term pVF operating on AG° [Eq. (11)]. [Taking account of doublelayer structure, this term is written as )8( V - il/i)F where il/i is the diffuse-layer potential, but this is a trivial difference in the present context.] Change of potential, V, modifies the Fermi level energy by eV as in Eq. (10). In the usual transition-state treatment, this quantity, modified by the factor p, appears in the Arrhenius-Boltzmann exponent [-(AG - iSVF)/RT]. It is from this exponent that the conventional Tafel-slope quantity b arises, linear in T. 

The potential profile across the double layer is modified, including the value of the diffuse-layer potential, (/ i, for a given metal/solution p.d., A<. ... 

Figure 8. Schematic representation of an electrical double layer (EDL) surrounding a solid particle in aqueous solution, where tj/0 and

Among the six interfacial variables discussed in this section, the surface charge density oo, the surface potential (fo, and the potential at the OHP fd (usually called the diffuse layer potential), are most important in characterizing interfacial properties. The three remaining variables (i.e., ap, /p, and Od) can be estimated using Eqs. (5), (7), and (8) if oo, and /rf are known exactly. ao can be determined experimentally by the potentiometric titration method, and detailed explanation of the potentiometric titration is given, for example, by Yates [10]. The estimate of fo for the ceramic powder/aqueous solution interface is discussed in the next section, yd is perhaps the most important interfacial electrochemical parameter since it is closely correlated with the kinetic stability of a given colloidal suspension and it can be conveniently determined (approximately) experimentally. 

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