Adsorption excess functions

For easy reference the expressions for the various surface excess functions are collected in appendix 2. These thermodynamic amd statlstlccd equations constitute the framework onto which further elaborations are anchored. All thermodynamic interfacied excess functions, except 12 , depend on the choice of the dividing plane. Of course, none of the measurable quantities are sensitive to this choice. Charged interfaces are also covered, provided the charge is caused by the preferential adsorption of one of the ionic species. Then, the components i refer to electro-... 

So far the Gibbs adsorption isotherm represents the best foimded theoretical backgroimd for the calculation of the adsorption excess densities of surfactants. Statistical thermodynamics may enable us in future to calculate adsorption densities by accounting for the chemical structure of a surfactant. Beside the direct calculation of excess adsorption densities F with the help of r - log c-plots, relationships of F and the interfacial tension y as functions of the surfactant bulk concentration are very helpful. 

The fact that a consistent thermodynamic theory which in detail can account for both adsorption and surface tension at planar surfaces has not yet been established has been regarded by many physical chemists as rather unsatisfactory. The theory of capillary formulated by Gibbs gives, owing to the use of excess functions, general relations of a limited practical value. Different readers have drawn controversial conclusions when studying... 

Fischer et al, [122] proposed a model to predict the adsorption isotherm of krypton in porous material at supercritical temperature. In their study, a model pore of infinite length is formed by concentric cylindrical surfaces on which the centers of solid atoms are located. The interaction between an adsorbate and an individual center on the pore wall is described by the LJ 12-6 theory, and the overall potential is the integral of this interaction over the entire pore surface. With thermodynamic relations, Fischer et al. obtained the functional dependence of the saturation adsorption excess and the Henry s law constant on the pore structure. The isotherm was then produced by the interpolation between Henry s law range and saturation range. They tested their theory with the adsorption of krypton on activated carbon. It was shown that, with information on the surface area of the adsorbent and thermodynamic properties of the adso bate, their model gives more than quantitative agreement with experimental data. If a few experimental data such as the Henry s law constant at one temperature are available, the isotherms for all temperatures and pressures can be predicted with good quality. 

Further information is obtained if the amount of liquid adsorbed on the surface of the particle is also determined, permitting the combination of the data on heat of immersion with those on the amount of adsorbed liquid. Thus, molar adsorption enthalpies can be given for the characterization of the stabilizing adsorption layer [12-16]. A further benefit of adsorption excess isotherms is that it is possible to calculate from them the free enthalpy of adsorption as a function of composition. When these data are combined with the results of calorimetric measurements, the entropy change associated with adsorption can also be calculated on the basis of the second law of thermodynamics. Thus, the combination of these two techniques makes possible the calculation of the thermodynamic potential functions describing adsorption [14,17-19]. 

Different types of adsorption excess isotherms (U- and S-shaped functions) naturally yield different free enthalpy functions A21G = /(Xi), the course of which is characteristic of the minimum energy of wetting at the solid/liquid interface, a parameter diagnostic of the stability of the disperse system. 

Equation (15) can also be considered as a general form of adsorption (excess) isotherms applicable for liquid free surfaces. For example, let us suppose that the differential function of the measured relationship y versus a can be expressed in the following explicit form ... 

FIG. 36a Adsorption excess isotherm functions at afkT = 0 (perfect mixture) and different K equilibrium constants. 

The function of free energy of adsorption (usually obtained by integration of the adsorption excess isotherm function according to the Gibbs equation) also exhibits an inflection... 

The equlibrium between the bulk fluid and fluid adsorbed in disordered porous media must be discussed at fixed chemical potential. Evaluation of the chemical potential for adsorbed fluid is a key issue for the adsorption isotherms, in studying the phase diagram of adsorbed fluid, and for performing comparisons of the structure of a fluid in media of different microporosity. At present, one of the popular tools to obtain the chemical potentials is an approach proposed by Ford and Glandt [23]. From the detailed analysis of the cluster expansions, these authors have concluded that the derivative of the excess chemical potential with respect to the fluid density equals the connected part of the fluid-fluid direct correlation function (dcf). Then, it follows that the chemical potential of a fluid adsorbed in a disordered matrix, p ), is... 

Activated carbon filters remove a wide range of organic matter by adsorption onto the carbon bed. The bed may be derived from a number of different carbon sources, and the correct selection of bed type, capacity, and porosity is a specialized function. Activated carbon may be usefully employed in organic traps, complementing the resin bed, but its capacity and organic removal rate characteristics are flow-dependent. Excessive flows may compromise the rate of adsorption of organic matter. 

Charge transfer reactions at ITIES include both ET reactions and ion transfer (IT) reactions. One question that may be addressed by nonlinear optics is the problem of the surface excess concentration during the IT reaction. Preliminary experiments have been reported for the IT reaction of sodium assisted by the crown ether ligand 4-nitro-benzo-15-crown-5 [104]. In the absence of sodium, the adsorption from the organic phase and the reorientation of the neutral crown ether at the interface has been observed. In the presence of the sodium ion, the problem is complicated by the complex formation between the crown ether and sodium. The SH response observed as a function of the applied potential clearly exhibited features related to the different steps in the mechanisms of the assisted ion transfer reaction although a clear relationship is difficult to establish as the ion transfer itself may be convoluted with monolayer rearrangements like reorientation. 

An adsorption-desorption transition is illustrated schematically in Figure 1, where we plot a displacement isotherm, i.e. the adsorbed amount of a polymer as a function of the composition of a mixture of solvent and displacer. At the left in Figure 1, where the concentration of displacer is low, the polymer surface excess is positive. As we increase the proportion of displacer in the mixture, we observe a decrease in the adsorbed amount. At a certain composition the adsorbed amount of polymer becomes zero. The concentration at which the polymer surface excess just vanishes will be denoted as the critical displacer concentration cr. Beyond 4>cr, the surface excess of the polymer is negative (and very small if the polymer concentration is low). 

The investigations described in the preceding pages have been directed to one point Only the exact determination of the excess of dissolved substance in the surface layer at one particular concentration. There are, however, some further questions of great importance, the answers to which must be sought by other experimental methods. The first of these is does adsorption lead to a well-defined equilibrium in a short space of time the second is this equilibrium, assuming it to exist, a simple function of the concentration ... 

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