Adsorption dividing surface

Brunauer and co-workers [129, 130] found values of of 1310, 1180, and 386 ergs/cm for CaO, Ca(OH)2 and tobermorite (a calcium silicate hydrate). Jura and Garland [131] reported a value of 1040 ergs/cm for magnesium oxide. Patterson and coworkers [132] used fractionated sodium chloride particles prepared by a volatilization method to find that the surface contribution to the low-temperature heat capacity varied approximately in proportion to the area determined by gas adsorption. Questions of equilibrium arise in these and adsorption studies on finely divided surfaces as discussed in Section X-3. 

The adsorption T depends on the position of the Gibbs dividing surface and it is therefore convenient to define a new function, the relative adsorption, that is not dependent on the dividing surface. The absorption of component i at the interface is defined by eq. (6.3) as... 

The advantage of this expression is that although the adsorption of each component depends on the Gibbs dividing surface, the right-hand side is independent of its position. We can thus define the relative adsorption of component B with respect to component A ... 

Figure 6.21 Schematic illustration of the concentration of component A across an interface. The Gibbs dividing surface is positioned such that it gives zero adsorption of component A since the algebraic sum of the two shaded areas with opposite sign is zero.

Since r -1 is independent of the position of X, we can choose the position of X to correspond to rA = 0, as illustrated for a schematic two-dimensional interface in Figure 6.21. The two shaded areas, above and below the interface, are equal and give zero adsorption of A. Recall that it is only for planar surfaces that the position of the Gibbs dividing surface is arbitrary, and in the following we will restrict our treatment to planar surfaces only. 

Gibbs approach, for treating surfactant adsorption, 24 134-138 Gibbs dividing surface, 24 135 Gibbs-Duhem equation, 3 744 24 134, 135, 672, 677... 

Determination of adsorption of any component is made under the condition of a special location of the dividing surface, which corresponds to This surface is referred to as equimolecular for component i. 

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 deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

The standard approach for describing surfactant adsorption at the gas-liquid interface is based on the Gibbs methodology [16]. The Gibbs dividing surface was introduced and is mathematically defined by the interface line that divides the surface excess of the solvent into two equal parts with opposite signs, and the total surface excess of the solvent is, therefore, equal... 

In the following, the Lucassen-Reynders dividing surface is used to obtain a number of significant adsorption models. 

Raman spectra of adsorbed species, when obtainable, are of great importance because of the very different intensity distributions among the observable modes (e.g., the skeletal breathing frequency of benzene) compared with those observed by infrared spectroscopy and because Raman spectra of species on oxide-supported metals have a much wider metal oxide-transparent wavenumber range than infrared spectra. Such unenhanced spectra remain extremely weak for species on single-crystal surfaces, but renewed efforts should be made with finely divided catalysts, possibly involving pulsed-laser operation to minimize adsorbate decomposition. Renewed efforts should be made to obtain SER and normal Raman spectra characterizing adsorption on surfaces of the transition metals such as Ni, Pd, or Pt, by use of controlled particle sizes or UV excitation, respectively. 

NMR is a widely used and important technique for molecular structure determination as applied to bulk materials, where it competes, often advantageously, with vibrational spectroscopy. However, a lack of sensitivity has limited its application to the study of adsorption on high-area finely divided surfaces. Also, certain metals with bulk magnetic properties—e.g., Fe, Co, and Ni (but not the other group Vlll transition metals)—cannot be studied by the technique as their magnetism causes very broad and weak resonances from adsorbed species. 

Here II = yo - y is the surface pressure, k the Boltzmann constant, and (Oo the solvent molecule molecular area. An important feature of Eq. (6) is that it involves solvent characteristics only. The (Oo value depends on the choice of the position of the dividing surface. Assuming the solvent adsorption to be positive, the equation was proposed30 which relates the surface excesses H of the solvent (subscript i = 0) and dissolved species (i > 1) with any molecular area (fy ... 

If, however, a dividing surface exists which separates the adsorbent completely from the adsorbate, so that throughout the adsorption reaction no material, electrons, etc., can cross this dividing surface, we can considerably restrict the number of possible types of interaction. When such a surface exists, we can apply equations of the Polanyi (18) or Guggenheim (10) type [essentially variants of... 

In general, the adsorption reaction will not resemble a mechanical reaction if the dividing surface largely ceases to exist because of solution of the gas throughout the solid, material of the solid dissolving directly or indirectly in the adsorbate,... 

In general the values of rA and rB depend on the position chosen for the Gibbs dividing surface. However, two quantities, TB(A) and rB(n) (and correspondingly wBa(A) and nB°(n)), may be defined in a way that is invariant to this choice (see [l.e]). TB(A) is called the relative surface excess concentration of B with respect to A, or more simply the relative adsorption of B it is the value of rB when the surface is chosen to make rA = 0. rB(n) is called the reduced surface excess concentration of B, or more simply the reduced adsorption of B it is the value of rB when the surface is chosen to make the total excess r = rt = 0. 

However, this is not always true. Complications arise, for example, if the adsorbent undergoes some form of elastic deformation or if the pore structure is modified as a result of the adsorption process. We adopt this convention in order to simplify the thermodynamic treatment. Similarly, we assume that the area of the Gibbs dividing surface is equal to the constant surface area of the adsorbent. We must not forget that we have made these simplifying assumptions when we come to interpret experimental data - especially if there is any indication of low pressure hysteresis. 

It follows from the discussion of the quantitative expression of adsorption in Chapter 2 that the most appropriate demarcation between the gas and the adsorbed phase is the Gibbs dividing surface (GDS). This enables us to express the adsorption data in terms of the surface excess and avoids having to determine (or assume) the absolute thickness of the adsorbed layer. 

The next question is where should we locate the Gibbs dividing surface For several reasons it is most convenient to locate the GDS as closely as possible to the solid surface. By doing so we can minimize the effect of operational temperature and facilitate the comparison of adsorption data. 

Both have the advantage of giving a sample volume (and therefore a location of the dividing surface) which is, by definition, perfectly reproducible from one adsorption bulb to another and from one laboratory to another. Even if not always realistic, it is a sound convention, if the aim is to obtain reproducible measurements and calculations and is consistent with the spirit of the Gibbs representation. It is, for these reasons, certainly well suited for the study of reference materials. Of course, this approach would replace Step 3 in the procedure described above, whereas Steps 1 and 2 would remain necessary. 

Here U x,y,z) is the energy of an atom at an arbitrary point (x,y,z) over the surface zc x,y) is the Gibbs dividing surface with respect to which the adsorption is determined. (This surface is implicitly determined in experiments by helium calibration.) Kh is connected with the Gibbs adsorption on area by the relation Kh = NakTfp. Finally, k x, y) in Eq. (6) may be called the two-dimensional density of the Henry s Law constant. This function is shown in Fig. 2, which was taken from Ref. [39]. 

Talu, O. and Myers, A.L. (2001). Molecular simulation of adsorption Gibbs dividing surface and comparison with experiment. AIChEJ., 47, 1160-8. 

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