Surface excess, concept

Effluent profiles obtained from a core-flood performed with a mixture of two surface-active components (C12 and C18) separated from a commercially available sulfobetaine are shown in Figure 24 (115). The points represent experimental data, and the lines were obtained by simulating the core-flood with a convection—dispersion—adsorption model that is based on the surface excess concept and takes into account monomer—micelle equilibrium (115). Because the mixture contains different homologues of the same surfactant, the ideal mixed micelle model... 

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. 

Therefore, the purpose of measuring surface excess is to provide material for testing models of the electrified interface. From these models, one can calculate the variation in the concentration of the surface excess of any species. The extent of agreement between the variation calculated thus and that determined from thermodynamic reasoning (see Section 6.5.7) determines the extent of validity of the model. This is why the concept of surface excess is so useful, despite its macroscopic nature. 

Third, a curious and subtle concept was explained, the concept of surface excess, r. This is not to be confused with adsorption, although the surface excess may become nearly identical to the total amount adsorbed under certain limiting conditions. The surface excess of a particular species is the excess of that species present in the surface phase relative to the amount that would have been present had there been no double layer. The surface excess, therefore, represents the accumulation or depletion of the species in the entire interphase region. Further, electrocapillaiy measurements and radiochemical experiments permit a direct experimental description of the surface excess of a species. 

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. 

When the solution consists of nearly pure alcohol, the quantities r M), and TiN> fall to zero, as would be expected on the ordinary man s concept of what surface excess means, which is probably something close to r( or r(M IY> does not fall to zero. 

Gibbs s adsorption equation. Guggenheim,2 developing some considerations put forward by Verschaffelt, has worked out the thermodynamics of surfaces, using a conception of the surface layer which is much more easily visualized physically than that used by Gibbs. Gibbs s surface excess is a very difficult quantity to interpret physically, as it is... 

To overcome this problem, Gibbs (1877) proposed an alternative approach. This makes use of the concept of surface excess to quantify the amount adsorbed. Comparison is made with a reference system, which is divided into two zones (A, of volume K3,0 and B, of volume V8,0) by an imaginary surface - the Gibbs dividing surface (or GDS) - which is placed parallel to the adsorbent surface. The reference system occupies the same volume V as the real system, so that ... 

Therefore, when studying interfacial reactions on rocks and soils, it must always be determined what the mechanism of the interfacial reaction is, and what kind of processes take place. Also, it must identify the dominant processes responsible for surface excess concentration. If this is not done, and the resultant process is evaluated without knowing it in conventional ways, incorrect thermodynamic data are obtained. The concepts of adsorption, ion exchange, and surface precipitation have to be clearly differentiated, as done previously. When the character of the process can be neglected, only surface accumulation is considered, and we can speak about sorption, including all of the surface processes. In this case, only aphenomenological description can be given, and no thermodynamics can be applied. 

All non-stoichiometric models adopt the electrical double layer concept and disagree with the stoichiometric hypothesis of an electroneutral stationary phase they emphasize the higher adsorbophilicity of the IPR compared to that of its counter ion a surface excess of IPR ions generates a primary charged layer and a charged interface. Like-sign co-ions are repelled from the surface while IPR counter ions are attracted by the charged surface. 

Fig. JH Illustration of the concept of the surface excess F, expressed in units of mol per square centimeter. The lines represent the concentrations of the two ions as a function of distance from...

It should be noticed that the model assumption in eq. (3.16) is rather arbitrary. The true state of charge of any adsorbed species is unknown from a thermodynamic point of view since a localization of electronic charge within the interphase would not change the total surface excess concentration, 7i(w), of the species i involved. According to the thermodynamic interphase concept presented here [3.54], experimentally observed deviations y z have only to be explained in terms of cosorption or competitive sorption... 

The main result of the thermodynamic treatment in Section 8.6 is that the interphase between a 3D Me-S bulk alloy phase and an electrolyte phase can be described by relative specific surface excess quantities, q, Tand Fi with f = IC and X, analogous to the interphase concept of an ideally polarizable substrate S in contact with the electrolyte phase (Section 8.2). 

On further consideration of the above construct, it is clear that the value of the surface energy (essentially a macroscopic thermodynamic concept) is dependent upon how the surface, near-surface, and bulk regions are defined (i.e., how the particle is subdivided). For this reason, it is perhaps useful to set aside the surface excess terminology for a moment and focus on the key issues surface energy is probably often size dependent, and surface sites contribute excess energy to a material. 

The case of most interest above is clearly a > 0, that is 6 > SL. Roughly speaking, this means that the attraction between adsorbent and adsorbate molecules is greater than the attraction between adsorbate molecules themselves (the liquid wets the solid). The amount of adsorption decreases as a —> 0 (Fig. 6) when a = 0 there is no adsorption at all up to x = 1, at which point there is sudden condensation. When a < 0, questions of supersaturation and film instability arise which are discussed in detail by Frenkel (69) the concept of surface excess must be used and the adsorption is negative for p < pa (see Sec. IV.5.a). 

It is seen that the surface excess free energy is not fully developed immediately since at small separations the surface molecules are still to some extent under the influence of those on the opposite faces [Figure 2.5(b)]. One may say that the surface excess free energy, and hence the interfacial tension of the surfaces, depends on their separation we shall have occasion to use this concept in later chapters. 

The surface excess obtained by the second-harmonic generation in the concentration range below the CMC, however, changes with concentration in contradiction to the usual interpretation of surface tension data. Moreover, the absolute values of the adsorption determined by two experimental methods differ by one order of magnitude. These discrepancies were explained by means of the concept of a depth-dependent distribution of surfactant molecules [66]. Different distributions can lead to identical adsorption values. The surface excess determined by the second-harmonic generation can be attributed only to the very top layer, whereas the values obtained from surface tension techniques are apparently more sensitive to the near-surface layer. 

The foregoing thermodynamic concepts can be illustrated in a qualitative, yet revealing, fashion as follows. Consider two parallel flat interfaces separated by an infinite distance. Suppose, arbitrarily, the segment density distribution increases linearly with distance from the interface until it reaches the bulk value at a distance W, as shown in Fig. 17.18a. If is the bulk polymer concentration (in appropriately chosen units), the surface excess (in its simplest form) at each interface is simply Wc-ifl — Wci = — Wc p.. For two interfaces, the surface excess is thus - Wc-. ... 

The quantitative description of adsorption as a purely macroscopic phenomenon is achieved through the concept of relative surface excess This quantity,... 

The positive adsorption of metal cations by the solid phases in soil can involve the formation of either inner-sphere or outer-sphere surface complexes, or the simple accumulation of an ion swarm near the solid surface without complex formation. These adsorption mechanisms are implied in the development of the concept of surface charge balance (Eq. 3.3) and were illustrated, for the case of surface complex formation, in Figs. 1.8 and 1.10. The quantitative relationship between these mechanisms and measured surface excesses of metals on soil minerals is taken up in Chap. 5. In the present section, emphasis is placed on the qualitative... 

This is a simple concept respiration will increase as a respcmse to oxygen to maintain an O2 concentration of zero at the cell surface. Excess oxygen stops nitrogenase activity (see Fig. 11) and bacterial growth. On the other hand, bacterial growth on fixed nitrogen is not inhibited by excess O2 in... 

If the concept of partial charge is introduced into the electrocapillary equation one gets the following result for the relative surface excess of the adsorbed ion ... 

The principles given above allow one to derive an expression relating theoretical concepts of surface excess concentration and adsorption to experimentally obtainable quantities. But what is the practical importance of those ideas In fact, the phenomenon of adsorption at interfaces, tied to the resultant effects of such adsorption, carries with it a multitude of important consequences (some good and some bad) for many technological and biological processes. 

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