Surface excess, definition measurement

Surface chemists, who are used to these sorts of problems, have defined a quantity called the surface excess, a measure of surface concentration per unit area which can be related to macroscopic, measurable thermodynamic variables such as the change in interfacial tension. The surface excess, denoted P, of a soluble surfactant is defined as the excess amount per unit area present in a finite section through the surface (i.e., including some of each phase) compared to the amount that would be present in an identical section of the aqueous bulk phase containing the same number of moles of water as the surface section. It can be shown that such a definition implies the existence of a plane such that the excess of water present in the fuzzy air phase above is balanced by the depleted amount of water in the fuzzy water phase below. The surface excess of the water is thus taken as zero. If this plane is taken as the zero of a depth scale into the bulk solution and c(x) is the profile of concentration of a surface-adsorbed species, it can be shown that ... 

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). 

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. 

The solution of the dividing plane problem is that the adsorptions are not referred to a zero value of one of the two components, but that Tj " cmd are introduced where is the surface excess of 1 per unit cirea over the amoimt of 1 in a reference system of uniform composition with Xj = (1 - x) and x =x. This is the excess that is measured in surface excess isotherms and which determines the surface tension. The definitions are... 

It is important to note that in order to calculate the amount adsorbed n, the amount of liquid in the adsorbed phase, (n ), must be known. Since this quantity is not subject to a direct measurement it should be recognized that the amount adsorbed is not a unique variable and that it always should be related to a specific definition of the adsorbed phase or to a specific experimental technique used for separating the solid and the adsorbed phase from the bulk liquid phase. This point is quite obvious from Figure 1 as a shift in the dividing line between adsorbed and bulk phases would not change the value of the surface excess, but the amount adsorbed would be changed. 

The Gibbs equation expresses the equilibrium between the surfactant molecules at the surface or interface and those in the bulk solution. It is a particularly useful equation since it provides a means by which the amount of surfactant adsorbed per unit area of the surface, the surface excess , may be calculated. The direct measurement of the surface excess provides almost insuperable experimental problems and hence the Gibbs equation is widely used as an alternative method of determining this quantity. In the derivation of this equation a definite boundary between the bulk of the solution and the interfacial layer is imagined (see Fig. 1.3). The real system containing the interfacial layer is then compared to this reference system in which it is assumed that the properties of the two bulk phases remain unchanged up to the dividing surface. 

We often know the nature of the absorbing species (absorbate) and its concentration in solution. We also know the potential of the electrode. Sometimes we can measure the surface excess T (a definition of which is given in Chapter 4) which is related to the surface concentration L. Two items make the list of the desired quantities or functions how does the nature and concentration of adsorbate and the potential of the electrode influence L and what is the value of L The function which relates L to solution concentration c, to the nature of the species and to potential is called adsorption isotherm... 

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