Basics for adsorption isotherms

From the point of view of microporous structure, adsorbents (i.e., nanoporous carbons) are classified as homogeneous (uniform) and heterogeneous (non-uniform). Adsorption on uniformly microporous carbons is often described by the Dubinin-Radushkevich (DR) or the Dubinin-AstaJdiov (DA) equations however, it should be mentioned that there is no a rigorous analytical equation for gas adsorption in carbons with uniform micropores. 

The Dubinin-Radushkevich (DR) equation, proposed in 1947 [110], undoubtedly occupies a central position in the theoiy of physical adsorption of gases and vapors on microporous solids (the theoiy of volume filling of micropores TVFM) [93], The amount adsorbed in micropores dm,-is  

Here B is the temperature-independent structural parameter associated with the micropore sizes, and is the similarity coefficient, which reflects the adsorbate properties [93]. Eq. (36) is commonly used for description of gas and vapor adsorption on microporous active carbons [13, 93, 111]. 

A more general expression in TVFM is that proposed by Dubinin and Astakliov [93,112], which is known as the DA equation  

In Eqs. (36), (37) and (38) a i represents the amount adsorbed in micropores at relative pressure p/p and temperature T, is the limiting volume of adsorption or the volume of micropores and Vm is the molar volume of the adsorbate. 

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According to Gibbs we obtain surface excess quantities as the basic for adsorption isotherms and surface rheology. For flat or only slightly curved surfaces one can define the surface excess quantity convenient for discussion of a particular problem. It is assiuned that this freedom... 

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