Surface excess of ions

For solutions of simple electrolytes, the surface excess of ions can be determined by measuring the interfacial tension. Consider the valence-symmetrical electrolyte BA (z+ = —z = z). The Gibbs-Lippmann equation then has the form... 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

First let us note that experiment revealed long ago that not all ions prefer the bulk to the interface [8]. Gibbs adsorption equation predicts that the surface tension increases with the electrolyte concentration when the total surface excess of ions is negative. The conventional picture, that the ions prefer the bulk, is probably due to Langmuir, who noted that the increase in the surface tension of aqueous solutions of simple salts with increasing concentration can be explained by assuming a surface layer of pure solvent with a thickness of about 4 A [9]. However, because the aqueous solutions of some simple acids (such as HC1) possess surface tensions smaller than that of pure water [8], Gibbs adsorption equation indicates a positive total... 

The surface tension depends on the potential (the excess charge on the surface) and the composition (chemical potentials of the species) of the contacting phases. For the relation between y and the potential see - Lipp-mann equation. For the composition dependence see -> Gibbs adsorption equation. Since in these equations y is considered being independent of A, they can be used only for fluids, e.g., liquid liquid such as liquid mercury electrolyte, interfaces. By measuring the surface tension of a mercury drop in contact with an electrolyte solution as a function of potential important quantities, such as surface charge density, surface excess of ions, differential capacitance (subentry of... 

The spatial distribution of potential near the interface is accompanied by changes in electrolyte concentrations that produce surface excesses of ions. In each phase, the surface excess Fi of an ion i can be divided into two components in the inner layer FJ and in the diffuse layer F ... 

The surface excesses of ions 1 and 2 in the diffuse layer are caused only by the coulombic interaction of these ions with the net charge (ctm + cri), hence, =x/(l — x). Under these condition, the sum of two last terms inside the brackets of Eq. (31) is equal to zero, so that... 

The surface potential at the interfacial layer is controlled by the surface excess of ions, their charges and polariTation, packing density, and dipole moment or induced dipole moment it can be determined by special techniques, that is, the vibrating plate method, combined with a Kelvin probe. Experimental data together with the most suitable prediction models may include the ion concentration in the bulk or ionic strength, and, when dealing with a monolayer, the ion number density in the monolayer, the monolayer thickness, and ion diameter. 

We have seen in this section that information on the surface excess of ions is experimentally available, provided one uses the correct reference electrode. We illustrated the correlation between energy of hydration of ions and their adsorbability, we also established that specific adsorption is probably not due to formation of chemical bonds. We saw that specific adsorption of anions is quite general, but cations adsorb only if they are rather large the extent of adsorption and its dependence on the solution activity and the electrode potential have remained without a generally accepted explanation. 

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid-liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. 

The representation of surface groups as diprotic weak acids is appealing because it includes a modest degree of complexity (two acidity constants), allows convenient representation of the condition of zero surface excess of hydrogen ion, and is still quite manageable mathematically. However, it must be borne in mind that this model is still a grossly simplified representation of the actual surface. It remains to be shown that this simplification is significantly better than any other simplification. 

The role of supporting electrolyte in adsorption processes is sometimes unclear. The adsorption of mannitol and sucrose on the Hg electrode from NaF and NaCl solutions shows that CT ions exert small, though observable, effects on the differential capacity curves (the saturation coverage and surface excess are slightly different in both solutions). Unexpectedly, at low surface excess of sucrose, the adsorption of sucrose is greater in the NaCl than in the NaF solution. At high surface excesses, the opposite situation is observed. 

Negative adsorption occurs when a charged solid surface faces an ion in an aqueous suspension and the ion is repelled from the surface by Coulomb forces. The Coulomb repulsion produces a region in the aqueous solution that is depleted of the anion and an equivalent region far from the surface that is relatively enriched. Sposito (1984) characterized this macroscopic phenomenon through the definition of the relative surface excess of an anion in a suspension, by... 

Were it supposed that at an interface the density of each component changed abruptly at an imaginary geometrical surface, being constant on either side into the interior of each phase, the amount of each component actually present in the system would differ from that calculated on this basis by an amount depending on the position chosen for this dividing surface. By a suitable choice, however, the surface excess of any one component can be made to vanish, and in the present system it is convenient to so choose it, that there is no surface excess or deficit of metallic ions at the interfoce, since these are the one constituent present in both phases. In accordance with this convention all the metallic ions in the system are assigned to one or other of the bulk phases. 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

In Eq. 38, the partial surface coverage, 0i, of the surfactant is defined as 01 = ri/Foo, where Ao is the surface excess of surfactant at saturation. K is the adsorption constant, which is a function of the surfactant and counterion adsorptions. The dependence is usually linear, yielding K = Ki + K20.1, where Ki and A are the equilibrium adsorption constants of the surfactant ions and their counterions. 

Fig. 3 The natural logarithms of true rate constants of Cd(ll)/Cd(Hg) system versus -

Ocko etal. [57, 58] have studied adsorption of bromide on Au(lOO) using in situ surface X-ray diffraction (SXD) in combination with electrochemical measurements. Low surface excess of bromide ions at Au(100)-(hex) caused a lifting of the... 

Surface Excess of Cs and Cl Ions in a Mercury-1.0 N CsCI Interphase as a Function of Applied Potential... 

The surface excess of a species i is obtained from the plot of interfacial tension versus mean activity of the electrolyte taken under conditions of constant applied cell potential V. By considering various applied potentials, one can get the surface excess r+ and T and thus the excess-charge densities q = z+FT+ and q = Z FT, due to the positive and negative ions, as a function of the applied potential... 

This result may now be simplified by invoking some previous results. Recalling curve 2 from Figure 7.14, we know that the surface excess of the X ions is likely to be a small negative number that we shall set equal to zero as a first approximation. With this approximation, Equation (58) becomes... 

When the surface excess of anions exceeds that of cations, dy/dE is positive, as is observed in Figure 7.23a. Negative values of dy/dE correspond to larger surface excesses of cations, as shown by Figure 7.23b. Finally, the condition dy/dE = 0 corresponds to equal amounts of positive and negative adsorbed charge, that is, surface neutrality. Note that this is not the same as saying no ions are adsorbed. The slope of the electrocapillary curve measures the... 

Equation (4.2) shows to what extent positive ions are repelled from the surface producing a deficit of (+) ions, and Eq. (4.3) shows to what extent negative ions are attracted to the surface producing an excess of (-) ions. The net charge per unit volume at the point x, q(x) in the double layer region is given by... 

The election of a reference electrode sensitive to one of the ions of the electrolyte leads to the appearance in Eq. (1.71) of the surface excess of the other. Equation (1.71) is usually named as Lippman s electrocapillary equation. 

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