Toward a Comprehensive Model

McGuire and Suffet [728] proposed the calculated net adsorption energy concept which is based on the solubility parameter of the adsorbate. They justified their approach by noting that the interactions involved in the adsorption of nonpolar and polar compounds onto a nonpolar [activated carbon] surface are, for the most part, governed entirely by the dispersion forces. Their results are summarized in Fig. 31. Even on a log-log plot, the r correlation coefficient is only 0.7. The authors cautioned against extrapolating such a correlation to predict the adsorption capacities of other neutral organic compounds. Clearly, incorporation of model parameters that quantify the chemistry of the carbon surface is necessary. 

Weber and Van Vliet [20] briefly described the Michigan Adsorption Design and Applications Model (MADAM), which includes both equilibrium and kinetic considerations, while Manes [729] advocated the use of the Polanyi adsorption potential theory, even to account for pH effects neither of these approaches includes a description of the role of carbon surface chemistry. 

31 Relationship between adsorption capacity for a range of organic compounds on activated carbon and the net adsorption energy. (Adapted from Ref. 728.) 

It is clear that there are quite a few possible theoretical approaches to the formulation of a comprehensive model for the adsorption processes discussed above. The most fundamental one would be based on the perturbation molecular orbital (PMO) theory of chemical reactivity [730,731] in which the wave functions of the products are approximated using the wave functions of the reactants. A key issue in the use of Klopman s PMO theory is the relative importance of the two terms in the expression for the total energy change of the system, Afpen. which is taken to be a good index of reactivity, [732,733]  

The question is whether the extent of adsorption is determined by charge control (AE, , i.e., coulombic or electrostatic interactions) or by orbital control i.e., attractive interactions between the filled orbitals of the adsorbate and the empty orbitals of the adsorbent). 

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ProchaskaJO, DiClemente CC Toward a comprehensive model of change, in Treating Addictive Behaviors Processes of Change. Edited by Miller WR, Heather N. New York, Plenum, 1986, pp 3-27... 

As indicated, modeling typically starts by defining an acid-base model for the sorbent (left-hand side of Fig. 10) and then proceeds to the interaction of other solutes with the sorbent (right-hand side of Fig. 10). Some parts of the different components toward a comprehensive model approach have already been discussed and associated problems have been mentioned. The availability of the information in the different boxes in Fig. 10 may constrain or increase the complexity of the model. Thus, the purpose of the modeling itself, which will have consequences on the experimental information gathered on a certain system, and the resulting amoimt of information are the important aspects, which determine how simple or complex a model may be. 

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