Surface Activity Coefficients

In a second paper Kazakevich and Eltekov consider the problem in terms of a layer of finite thickness, a treatment equally applicable to adsorption by microporous bodies where the adsorption volume is constant. They define a new system of activity coefficients (U and for both bulk and adsorbed phases write 

However, the condition that the adsorption space shall remain full, i.e. on exchange 1 mole of component 1 of molar volume ui is replaced by vjv2 moles of component 2, does not seem to have been taken account of. In effect the terms include surface tension terms which do not cancel so that is not a constant. The correct formulation in terms of volume fractions will still 

This reformulation of the problem does not appear to have any significant advantage over the more conventional methods. 

Oscik and Goworek discuss the calculation of activity coefficients by equations (8) and (9). For systems of molecules of the same size the two methods should be equivalent. The authors have analysed the experimental data of Lu and Lama for the adsorption from benzene+cyclohexane mixtures by silica gel. The graphically presented results indicate that the curves derived from equation (8) and (9) deviate considerably from one another. However, since no details are given of the values assumed for the molar areas it is not possible to identify the origin of these discrepancies, which because of the close similarity of the sizes of the molecules concerned, are unexpected. Madan has used equation (9) to calculate the activity coefficients of benzene and acetic acid adsorbed from their mixtures by tin oxide gel 0 — 160 m g ). The results look surprising and consideration of the behaviour of ln(Y2/yT) shows that the two sets of activity coefficients are thermodynamically inconsistent, presumably as a result of a computational error. 

A third method of determining activity coefficients suggested by Oscik and Goworek is based on measurements of enthalpies of immersion. 

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It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

Non-ideality due to lateral interactions can be treated in two ways, by introducing surface activity coefficients in the adsorption isotherms or expressing the free energy of adsorption as a function of coverage, on the basis that the free energy of adsorption varies with coverage [94]. 

The exponential term can be thought of as a surface activity coefficient (Dzombak and Morel, 1990) that corrects the apparent acidity constants for surface charge effects. 

One can see that the thickness of the oil layers does not remain constant upon dilution. This is a consequence of the nonlinearity of the system of eqs 17, which takes into account the partition of the alcohol between oil, water, and interface and the dependence of the surface activity coefficients on the surface concentrations of all the components. Figure 6c, in which the product between the repeat distance d and 4> as a function of

deviations from the ideal dilution law during the water dilution, alcohol and surfactant molecules leave the interface, and this shrinks its area. 

The models applying the law of mass actions (Gaines and Thomas 1953 Howery and Thomas 1965 Argersinger et al. 1950 Ekedahl et al. 1950 Hogfeldt 1950) introduce the term of surface activity coefficient. 

All models, however, have the same deficiency, that is, the concentrations in the solid and solution can be measured experimentally however, the surface activity coefficients, the surface electric work, as well as the energy distribution function can only be estimated. It means that the models are adapted to the experimental data and the best-fitted model is used, and therefore the selected model has no thermodynamically significant meaning (Cemik et al. 1995). In this chapter, these problems will be illustrated and discussed. 

To estimate the surface activity coefficients, several different approaches have been suggested. For example, the surface can be considered heterogeneous, containing j kinds of homogeneous part with known ratios and equilibrium constants. In this case, the selectivity coefficient can be described by a power series (Barrer and Klinowski 1972) ... 

The other interpretation of surface activity coefficients supposes that the interactions between the pairs of the exchanging and exchanged ions (Me, - Mex, Me2-Me2, and Mex - Me2, respectively) are not equivalent, so the surface activity is necessarily the function of surface composition (Hogfeldt 1984, 1988 Konya et al. 1989). This is the Hogfeldt three-parameter model, in which the selectivity coefficient depends on the surface molar factions of the ions and their interactions, as follows ... 

Various empirical and chemical models of metal adsorption were presented and discussed. Empirical model parameters are only valid for the experimental conditions under which they were determined. Surface complexation models are chemical models that provide a molecular description of metal and metalloid adsorption reactions using an equilibrium approach. Four such models, the constant capacitance model, the diffuse layer model, the triple layer model, and the CD-MUSIC model, were described. Characteristics common to all the models are equilibrium constant expressions, mass and charge balances, and surface activity coefficient electrostatic potential terms. Various conventions for defining the standard state activity coefficients for the surface species have been... 

At the end of this section, let us consider a general expression, which allows us to obtain the surface activity coefficient Yij directly from the surface pressure isotherm tt/fi). From the Gibbs adsorption isotherm, dn = T djUi, it follows that... 

For surface phases the electrostatic effects are usually considered directly, using models with different numbers of layers for the positions of different ions relative to the solid surface [1-3], leading to the capacitance parameter. A description of surface activity coefficients is given by Liu et al. [4]. 

A serious problem is the fact that for most models the number of model parameters is great and the information obtained from the experiments comparatively poor. Many parameters have to be taken from other sources or have to be estimated (or even disregarded, because it is supposed that they have small influence in an estimation). Activity coefficients in the liquid phase are usually omitted by using a "sufficient" concentration of background electrolyte. The surface activity coefficients are usually not mentioned at all. In most models only one type of adsorption... 

Several other papers on the evaluation of surface activity coefficients have appeared, among them that by Levchenko and Kirichenko,who have studied the competitive adsorption of benzene and p-toluidine by active carbon from dilute aqueous solutions. The abstract does not give details. Thomas and Eon in a paper discussed more fully later give surface activity coefficients for the three binaries derived from acetone, carbon tetrachloride, and benzene adsorbed by silica gel. They comment that the functions yTixJ) bear no resemblance to the corresponding bulk functions. 

A theoretical analysis of these experiments is presented by Dekany, Nagy, and Schay and by Dekany and Nagy. In their presentations the assumptions involved are not all stated explicitly, and some of these seem to be mutually incompatible. The following somewhat more complete argument is suggested, which brings out these points more clearly. First it is assumed, with the authors, that the molecules are the same size and that the ratio of the surface activity coefficients can be taken as unity. If adsorption occurs independently on the two types of site A, B, with adsorption equilibrium constants for alcohol adsorption Xa and Kb, respectively, then the surface mole fractions of alcohol on the two types of site are... 

We can check that Equation 4.23 is equivalent to the van der Waals surface tension isotherm in Table 4.2 for a nonionic surfactant. Furthermore, combining Equations 4.23 and 4.24, we obtain the Butler Equation 4.16, but this time with another expression for the surface activity coefficient... 

Everett [43] discusses experimental evaluation methods for flie activity coefficient, but offers no explicit activity coefficient equations in closed analytical form. Hence, in applications of Eq. (412) in the literature, the surface activity coefficients (and frequently the solution activity coefficients) are set to unity. While Eq. (412) is an adsorption equation based on rigorous fliermodynamics, its application has always been as an ideal adsorption equation. Substitution of activity coefficient equations, described in Section ll.E and Chapter 4, into Eq. (412) would extend its applicability to nonideal adsorption. 

While ideal adsorption is frequently a bad assumption for real systems, the difficulty of evaluating the activity coefficients (particularly surface activity coefficients) makes such an assumption popular with many authors. In addition to ignoring nonideality, many GP treatments do not have explicit pH dependence. However, as shown in previous sections, explicit pH dependence in surface-site complexation adsorption equations depends on proper surface-site mass balance equations, not activity coefficients. 

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