Equation Cohen-Kisarov

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

Figure 1. Test of Cohen-Kisarov equation, case of CO -l 3X and C Hi-5A systems...

However, one may observe that in Equation 4 the saturation of the adsorbent (W = W0, q = qm) is reached for a value of p approaching infinity—i.e., - — oo although Polanyi s theory predicts saturation for e = 0. Conversely, substitution of e = 0 into Equation 7 yields for W, a value slightly lower than Wo (the difference lying between 3 and 10%, depending upon the cm /A value). This peculiarity of the Cohen-Kisarov equation gives rise to the theoretical question of its validity at high pressure however this question is of little practical importance compared with the lack of accuracy in the experimental determination of W0. 

Comparison Between the Cohen-Kisarov and Dubinin-Radushkevich Equations. In a plot of log q vs. e2 the experimental points for one adsorption isotherm on zeolite frequently do not give a straight line, which would verify the Dubinin-Radushkevich equation. In this case, two distinct lines of different slopes are found (4). 

Let us assume that an experimental isotherm is perfectly described by the Cohen-Kisarov equation. When plotting the experimental points with the previous coordinates, three different cases may occur (1) if cmlA < 2, a case which was not yet found ((4) and Table I), the curve exhibits a constant convex curvature towards the ordinate axis (2) if cm /A > 2, the curve exhibits two distinct inflection points (Figure 3) where the experimental curve may easily be confused with the tangent to the inflection point, thus explaining the previous observations (3) if cm /A decreases to a value of 2, these inflection points are unified to give a large linear section, and the Dubinin-Radushkevich equation behaves as a limiting case of the Cohen-Kisarov equation. 

Figure 8. Log 6 vs. ( /eM)2 for isotherms perfectly described by the Cohen-Kisarov equation, with different values of the parameter eM/A ( ) Inflection point...

Figure 4. Log W vs. e2 for the C02-H-Mordenite system full line theoretical curve according to the Cohen-Kisarov equation...

Equation 3 was verified experimentally (3) over wide ranges of temperature and equilibrium pressure for the adsorption of various vapors on active carbons with different parameters for the microporous structure. For adsorption on zeolites, this equation fitted the experimental results well only in the range of high values of 0 (4, 5, 6, 7). Among other equations proposed for the characteristic curve (4, 5, 8, 9, 10) we chose to use the Cohen (4) and Kisarov s (10) equation, which starts from the following adsorption isotherm equation ... 

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