Dubinin Equation for Potential Theory

Dubinin and coworkers investigated the effect of surface structure on the absorbability of different gases and adsorption of different solutes from solutions on active carbons, and observed that over a wide ranges of values of adsorption, the characteristic curves of different vapors on the same adsorbent were related to each other. In fact, it was observed that if the adsorption potential s, corresponding to a certain volume of adsorption space W, on the characteristic curve for one vapor was multiplied by a constant, the adsorption potential corresponding to the same value of W on the characteristic curve of another vapor was obtained. Thus, we obtain 

Dubinin and Radushkevich suggested that for microporous active carbons (or porous materials), volume of adsorption space can be expressed as a Gaussian function of the corresponding adsorption potential W=W (s), so that the characteristic curve for microporous active carbons can be written as 

Affinity Coefficient jBfor Some Vapors and Gases on Active Carbon (From 47) 

Source Dubinin, M.M. and Timofeev. D.P., DokL Akad, Nauk., SSSR, 54, 1946. With permission. 

Equation 2.99 shows that a plot of In W against (In- ) should give a straight line with Slope D and intercept W . Dubinin plotted results of a large number of adsorbates such as nitrogen, and benzene, saturated hydrocarbons on active carbons and found that the equation was valid over the range 1 x 10 to 0.2 relative vapor pressure in those cases where the solid was truly microporous. 

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