Fundamentals of Adsorption Equilibria

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

The situation is more complex for liquid-solid equilibria. The surface tension of solids is not readily measured. In liquid-solid equilibria the adsorbate always has to compete, at least with the solvent which is in large excess, for access to the solid sirrface, a phenomenon that does not take place in gas-solid equilibria imder the conditions prevailing in gas chromatography [5]. As a consequence, most of our imderstanding of liquid-solid equilibria remains empirical. 

The fundamental references in gas-solid adsorption are the works by Fowler and Guggenheim [12], Everett [13], and Hill [14,15], and the books by Young and Crowell [16], de Boer [17], Kiselev [4], and more recently by Ruthven [18] and T6th [19], who gives a clear, logical, and simple presentation of this topic. We present first a few theoretical results obtained in the study of gas-sohd adsorption, results that have been extended semiempirically to liquid-solid adsorption [18]. Then, we describe the various isotherm models that have been used in the study of retention mechanisms in liquid chromatography. 

In the case of adsorption, the fundamental equation summarizing the first and the second law of thermodynamics as applied to the adsorbed component may be 

Differentiation of Eq. 3.4 and subtracting Eq. 3.1 from this differential gives  

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This chapter has addressed the fundamentals of adsorption equilibria of a pure component. A number of fundamental equations have been discussed. Although they are successful in describing some experimental data, they are unfortunately unable to describe experimental data of practical solids. This is usually attributed to the complexity of the solid, and to some extent the complexity of the adsorbate molecule. There are two approaches adopted to address this problem. One is the empirical approach, which we will address in Chapter 3, and the other involves the concept of heterogeneity of the system whether this heterogeneity is from the solid or from the adsorbate or a combination of both. This second approach is addressed in some detail in Chapter 6. 

In Chapter 2, we discussed the fundamentals of adsorption equilibria for pure component, and in Chapter 3 we presented various empirical equations, practical for the calculation of adsorption kinetics and adsorber design, the BET theory and its varieties for the description of multilayer adsorption used as the yardstick for the surface area determination, and the capillary condensation for the pore size distribution determination. Here, we present another important adsorption mechanism applicable for microporous solids only, called micropore filling. In this class of solids, micropore walls are in proximity to each other, providing an enhanced adsorption potential within the micropores. This strong potential is due to the dispersive forces. Theories based on this force include that of Polanyi and particularly that of Dubinin, who coined the term micropore filling. This Dubinin theory forms the basis for many equations which are currently used for the description of equilibria in microporous solids. 

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