Dubinin-Radushkevich Polanyi potential

Semiernpirical Isotherm Models. Some of these models have been shown to have some thermodynamic inconsistencies and should be used with due care. They include models based on the Polanyi adsorption potential (Dubinin-Radushkevich, Dubinin-Astakhov, Radke-Prausnitz, Toth, UNI LAN. and BET). 

The Dubinin-Radushkevich (DR) equation was originally devised as an empirical expression of the Polanyi adsorption potential theory, and due to its simplicity it has been widely used to correlate adsorption data in many microporous sohds despite its failure in giving the correct Henry constant at extremely low pressures. This equation is based on the premise that adsorption in micropores follows a mechanism of pore filhng rather than the molecular layering and capillary condensation as proposed for mesoporous sofids. It has the form ... 

Based on the Polanyi potential theory, different approaches to describe the adsorption behavior of a purely microporous material (isotherm type I, Figure 21.25) have been undertaken by Dubinin and Stockli in collaboration with different other scientists. The simplest relationship that can be considered the base for all other variants is the Dubinin-Radushkevich equation [58] ... 

The DR isotherm remained known to a relatively small group of researchers until Hobson called attention to its applicability to non porous surfaces. In a letter to the Journal of Chemical Physics, Hobson, not without wonder, observed that the appearance of the Dubinin-Radushkevich equation in the present context (submonolayer adsorption of nitrogen on Pyrex) is surprising for two reasons. First, it is a particular equation within the Polanyi potential theory, which is a theory of condensation and might not be expected to apply to physical adsorption at very low coverage. Second, most of the adsorbents to which the Dubinin-Radushkevich equation have been applied have been porous, whereas our conclusion suggests that Pyrex is non-porous for nitrogen. Thus, unless and until a basic derivation for this equation is provided, it can only be considered as a useful empirical relation . 

The DR isotherm, initially proposed by Dubinin and Radushkevich for the description of adsorption on porous adsorbents, was found by Hobson to describe adsorption in submonolayer range on non-porous surfaces too. This empirical discovery was a challenge to theoreticians since the DR isotherm was expressed in terms of the Polanyi potential, which is expected not to apply to adsorption in the submonolayer range. 

This model for mixed adsorption (Grant and Manes 1966) is based upon the idea of equipotential energies among the components of the adsorbed mixture and is thus related to the Polanyi potential theory discussed in Section 3.3.5. As previously recorded, Dubinin and Radushkevich (1947) postulated a direct relation between the affinity coefficient Pi of a component i and the molar volume Vmt of the saturated pure liquid. The equipotential energy concept for two components is thus (eiiPi) = (ey/ft). Hence, by use of equation (3.18) for each component... 

The POLANYI-DUBININ adsorption potential theory is used to characterize the micropore network of zeolites (ref. 10). An isotherm at a given temperature T (expressed in volume adsorbed per activated zeolite mass unit, W, as a function of the relative pressure p/Pq) is treated in the DUBININ-RADUSHKEVICH model (ref. 11) (denoted D-R) in the linear form log W = f[(Tlog Po/p) ] ... 

Now let us overview the theoretical adsorption models for characterization of the pore structures according to the pore size range. For physical adsorption of the gas molecules on such microporous sohds as activated carbons and zeolites, Dubinin and Radushkevich developed an empirical equation, which describes the volume filling process in the micropoies. Their theory incorporates earlier work by Polanyi in regard to the adsorption potential ad defined as... 

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