Surface excess, definition

We suppose that the Gibbs dividing surface (see Section III-5) is located at the surface of the solid (with the implication that the solid itself is not soluble). It follows that the surface excess F, according to this definition, is given by (see Problem XI-9)... 

More commonly used is another definition of Gibbs surface excesses, according to which r, is equal to the amount of substance j that must be added to the system (with a constant amount of the substance j = 0) so that the composition of the bulk phases will remain unchanged when the interface area is increased by unity. This definition can also be used when chemical reactions take place in the surface layer. In the case discussed here, the two definitions coincide. The set of surface excesses of all components is sometimes called the surface phase (in contrast to the real surface layer or interphase). 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

The definition of the electrosorption valence involves the total surface excess, not only the amount that is specifically adsorbed. It is common to correct the surface excess F, for any amount that may be in the diffuse double layer in order to obtain the amount that is specifically adsorbed. This can be done by calculating the excess in the... 

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... 

The definition of surface excess, on the other hand, starts with the concentration profile, but involves an integration between limits Kq. (6.65)]. Once the integration is done and limits are inserted, one obtains a number (so many moles per square centimeter) and loses all knowledge of the function c((x). In other words, after the integration is carried out and the surface excess evaluated, the concentration profile... 

Thus, surface tension changes have been related to changes in the absolute potential differences across an electrode/electrolyte interface and to changes in the chemical potential of all the species, i.e., to changes in solution composition. Only one other quantity is missing, the surface excess. This can be easily introduced by recalling the definition of surface excess [Eq. (6.66)], i.e.,... 

What is a Gibbs surface What are the definition and meaning of surface excess properties ... 

The extent of the surface-containing region is not specified by the definition of the surface excess. This region must contain all of the solution whose concentration differs from that of the bulk liquid and may contain any amount of bulk solution. The bulk solution makes no contribution to the value of the surface excess. No assumption is involved in the definition of surface excess as to whether either component forms a monolayer on the surface. 

The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined to show that the surface excess cannot be considered a surface concentration in the presence of an ionized monolayer on an impenetrable solid/liquid interface. 

Equation (3) has the same form as one of Gibbs s fundamental equations for a homogeneous phase, and owing to this formal similarity the term surface phase is often used. It must be remembered, however, that the surface phase is not physically of the same definiteness as an ordinary phase, with a precise location in space neither do the quantities c , if, mf refer to the total amounts of energy, entropy, or material components present in the surface region as it exists physioally they are surface excesses , or the amounts by which the actual system exceeds the idealized system in these quantities. Care must be taken not to confuse the exact mathematical expression, surface phase , with the physical concept of the surface layer or surface film. 

We now return to the definition of the surface excess chemical potential fta given by Equation (2.19) where the partial differentiation of the surface excess Helmholtz energy, Fa, with respect to the surface excess amount, rf, is carried out so that the variables T and A remain constant. This partial derivative is generally referred to as a differential quantity (Hill, 1949 Everett, 1950). Also, for any surface excess thermodynamic quantity Xa, there is a corresponding differential surface excess quantity xa. (According to the mathematical convention, the upper point is used to indicate that we are taking the derivative.) So we may write ... 

It should be borne in mind that all the data reported in the literature for mercury are values of the relative surface excess F , not the fractional coverage 0. In dilute solutions the relative surface excess is very nearly equal to the surface excess, in view of its definition, given by Eq. 28H... 

The surface excess T represents the total amount of the relevant species in a cylinder of unit cross section, extending from the interface into the bulk of the solution, less the amount that would have been in the same volume, had there been no interface. Fortunately, we do not have to determine how far exactly the interphase extends. The function (C - C ) is integrated to "infinity" - far enough into the bulk that its value has become negligible. It should be noted that on the scale of interest for interphases, "infinity" is not very far. In fact, it is less than 1 xm For the example just discussed, ( )(1 pm) = ( ) exp(—100). The definition of the surface excess is shown graphically in Fig. IH. 

In general, the phenomenological definition of specific adsorption depends on the model of the diffuse part of the double layer. However, at the potential of zero charge, the contribution of the nonspecific adsorption in the diffuse part of the double layer should be absent. According to the phenomenological definition of specific adsorption [53], at the point of zero charge it is said that there is specific adsorption if the measured surface excess of any ionic species is positive. 

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