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It has been shown [55] that it is possible to distinguish between the two adsorption regimes based upon the magnitude of the exponent (1/m). In particular, adsorption occurs according to the van der Waals mechanism if 1/m < 1/3, whereas it occurs by the capillary condensation (or capillary wetting) mechanism if 1/m > 1/3.

6.3.3 Fractal Analogue of the Dubinin-Astakhov Adsorption Isotherm

The DR isotherm describing adsorption in a single pore is a special case of a more general isotherm known in the literature as the Dubinin-Astakhov (DA) isotherm [35, 62]:

where n can assume values from 1 to 6 [59, 62]. In the case of microporous carbons with cylindrical pores, the values of n are usually in the range from 1 to 2. For molecular sieves and clay minerals (slit-like pores), they are close to 2, whereas for zeolites possessing pores in quite complex networks the value of n can be as high as 6.

The isotherm described by Equation (6.48) can be extended to the case of porous adsorbents whose pore-size distribution is governed by Equation (6.41). In Equation (6.40), it is possible to replace the integrand 0DR(x; R) of Equation (6.39) with 0DA(x; R) of Equation (6.48) to obtain [35]

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