The Concept of Surface Excess

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. 

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 ... 

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). 

However, the incorporation of perfluoroalkyl groups into a material is not necessarily a guarantee that low surface tensions will be obtained. The surface of a PTFE material is comprised mainly of —CF2— groups, which is the composition of the bulk. The surface composition of FAs is often quite different from the bulk. The concept of surface activity is one that must be considered in order to formulate materials for optimum repellency or low surface tension. For pragmatic reasons, commercial fabric and carpet repellents are based on perfluoroalkyl chain-containing FAs. Not only is the amount of fluorine less in these materials than in PTFE, but the surface tensions are often lower. This can only imply that there is an excess of fluorinated material at the surface. The concept of surface excess or activity can be seen from a simplified form of the Gibbs equation " ... 

Minka and Myers (8) have extended the concept of surface excess and selectivity to multicomponent mixtures. They applied a theory of an ideal adsorbed phase to predict the adsorption behavior of ternary mixtures from adsorption measurements in binary systems. Having binary data in the form of Equation (10) a ternary isotherm is calculated as follows ... 

Adsorption from liquid solution is more complicated than that from the gas phase. In a two-component liquid solution, both the solvent and the solute will be adsorbed to different extents. Usually the adsorption of the solute is of interest. The experimental procedure and expression for the amount adsorbed both differ from those used for gas adsorption. The basis for expressing the amount adsorbed from liquids is the concept of surface excess given by Gibbs in 1878. Gibbs surface excess is the difference in the amount of a given component in the surface layer (per unit surface area) over that in the bnlk Uqnid. 

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... 

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. 

The curved meniscus on a liquid, the head on a pint of beer and the effectiveness of soap are all phenomena that can be rationalized using the concept of surface energy. The basic idea that there is an excess energy in the surface of a solid or liquid can be accepted by considering the formation of the surface by breaking the bonds across what are to become the two surfaces formed. The energy to break these bonds is the surface energy. 

Abstract The quantities and relationships of capillary theory are summarized in a consistent formalism. Its constituents are the canonical thermo statics of the excess quantities, the interpretation of the surface tension according to deformation theory, and the formalism of parametric theory. A generalized concept of surface excess quantities is established by introducing the... 

The closed and logically consistent set of tools of capillary theory is completed by the generalized concept of surface excess quantities, by introducing the factors and defining the individual quantities. It has also to be considered that the deformation quantities can be introduced into the theory only if the changes of the phase volumes are restricted. 

Following the concepts of H. Helmholtz (1853), the EDL has a rigid structnre, and all excess charges on the solntion side are packed against the interface. Thus, the EDL is likened to a capacitor with plates separated by a distance 5, which is that of the closest approach of an ion s center to the surface. The EDL capacitance depends on 5 and on the value of the dielectric constant s for the medium between the plates. Adopting a value of 5 of 10 to 20 nm and a value of s = 4.5 (the water molecules in the layer between the plates are oriented, and the value of e is much lower than that in the bulk solution), we obtain C = 20 to 40 jjE/cm, which corresponds to the values observed. However, this model has a defect, in that the values of capacitance calculated depend neither on concentration nor on potential, which is at variance with experience (the model disregards thermal motion of the ions). 

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. 

Usually, alkalis and alkaline earths are released in excess of silica, and dissolved aluminum is the least abundant. This observed non-stoichiometry suggested that silica and aluminum were being preferentially retained in some solid phase relative to alkalis and alkaline earths. Such preferential retention, manifested as non-stoichiometric dissolution, was long thought to be consistent with the concept of some kind of residual surface layer. 

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

The vast majority of small-amplitude methods are based on small-amplitude potential excitations with potential control of the surface concentrations. In earlier chapters, the relationship between surface concentration and electrode potential was explored and the concept of concentration profiles was presented. Whenever there is a flux of electrons at the electrode surface, the concentration profiles of at least two species will exhibit nonzero slopes at the electrode surface, as the electrochemical conversion of one member of a couple into another takes place and mass transport processes act to reestablish a uniform concentration distribution. These processes occur irrespective of whether the current flux arises from a potential or current excitation of the cell. In either case, they result in a perturbation from the previously existing concentration profile. The initial surface concentrations (which existed prior to the application of the new perturbation) are often termed the dc surface concentrations. It is useful to note that at any time, the distance integral of the concentration excess or defect is directly proportional to the charge passed due to that per-... 

It is now time to reconsider the simple case of a two-phase system that contains two different types of molecules. If molecules of phase a are polar and molecules of phase [3 are nonpolar, the introduction of amphiphilic molecules that are capable of associating with either one of the two bulk phase molecules will result in an accumulation at the interface. Hence, these molecules will have a true excess concentration at the interface. Figure D3.5.4 illustrates that once surfactants adsorb at interfaces, the concentration within the interface may be larger than in any of the other phases. In order to predict the influence that these adsorbed surfactant molecules can have on the properties of the bulk system, interfacial chemists must be able to quantify the number of molecules that are adsorbed at the interface, that is, they must be able to measure the interfacial coverage. Unfortunately, it is extremely difficult, if not impossible, to directly measure the concentration of surface-active molecules adsorbed in a two-dimensional plane. This is where the thermodynamic concepts discussed earlier prove to be very useful, because a relationship between the interfacial coverage (G) and the interfacial tension (y) can be derived. 

Recent applications of CPSA descriptors include QSAR investigations of the genotoxicity of thiophene derivatives (Mosier et al., 2003) as well as of secondary and aromatic amines (Mattioni et al., 2003) and a study to classify phenols with respect to toxic modes of action (Aptula et al., 2003). A somewhat different route has been explored with the concept of dynamic molecular surface areas (Lipkowitz et al., 1989) that represent Boltzmann-weighted means of surface areas of different conformations within a preset energy window (e.g., within an excess of 10.5 kJ/mol above the lowest energy found for the particular molecule). Following this strategy, so-called dynamic polar... 

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... 

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. 

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