Accuracy of Dubinin-Astakhov (DA) and Dubinin-Radushkevich (DR)
IntroductionClay can be used in several applications due to its physical and chemical properties, such as large specific surface area, cation exchange capacity and adsorptive affinity for inorganic and organic ions from aqueous solution and water. Among the clays, bentonite is considered as a main candidate in the removal of pollutants such as lead and other heavy metal ions. Bentonite consists mostly of microcrystalline particles of montmorillonite which belongs to 2:1 clay minerals meaning that it has two tetrahedral sheets sandwiching a central octahedral sheet [1][2][3][4]. Since the existence of huge deposits of bentonite, there is a great potential for its utilization in removing various dilute pollutants and adsorption technology including the removal of heavy metal ions [5][6][7][8] [18][19][20]. To apply bentonite in adsorption, the textural properties including surface area, pore size, micropore volume and mesopore volume must be determined. The textural properties of porous materils are very often determined by gas (N 2 ) adsorption isotherm data [8,21,22].The empirical form of an adsorption isotherm was recognized as early as 1926 by Freundlich [23], and was later derived theoretically from the Langmuir equation [24] extended to heterogeneous surfaces considered to be a composite surface, composed of many homogeneous patches [25]. By adopting the Langmuir mechanism, but introducing a number of simplifying assumptions, the Brunauer-Emmet-Teller (BET) equation was subsequently derived for multilayer adsorption [26]. It is unquestionable that together with the concept of multilayer adsorption (leading to the BET equation) the theory of volume filling of micropores is one of the most stimulating concepts occupying the principal position in adsorption science [27]. Developed formerly, and based on the Weibull distribution of adsorption potential, the proposed equation by M. M. Dubinin [28] was considered to be a semi-empirical one. The fundamental relations are the Dubinin-Astakhov and Dubinin-Radushkevich equations [28,29]. The surface area, mesopore volume and micropore volume of such porous materials can be evaluated by means of BET, BJH [30] and both HK [31] and density functional theory (DFT)