Dubinin-Astakhov analysis

No current theory is capable of providing a general mathematical description of micropore fiUirig and caution should be exercised in the interpretation of values derived from simple equations. Apart from the empirical methods described above for the assessment of the micropore volume, semi-empirical methods exist for the determination of the pore size distributions for micropores. Common approaches are the Dubinin-Radushkevich method, the Dubinin-Astakhov analysis and the Horvath-Kawazoe equation [79]. 

Membrane pore diameter estimated from the Dubinin-Astakhov analysis [20]. 

That is the reason why lower pore size membranes working by molecular-sieving mechanism have been tested with a view to perform continuous operations. The use of a zeolite membrane (pore diameter estimated from the Dubinin-Astakhov analysis [20] 1.1 nm) provided an interesting rejection of 0.98 [10] (see Table 7.1). In that case, caffeine adsorption was weak and zeolite membrane could not be easily fouled with the solute. Transport was mainly controlled by molecular sieving, as indicated by the good rejection rate also obtained with other molecules (e.g., lauric acid) having molecular weight close to caffeine. 

On the other hand, for the microporous carbons with pore size distribution (PSD) with pore fractality, the pore fractal dimensions56,59,62 which represent the size distribution irregularity can be theoretically calculated by non-linear fitting of experimental adsorption isotherm with Dubinin-Astakhov (D-A) equation in consideration of PSD with pore fractality.143"149 The image analysis method54,151"153 has proven to be also effective for the estimation of the surface fractal dimension of the porous materials using perimeter-area method.154"159... 

Textural characterisation of the samples was carried out by measuring apparent density (mercury at 0.1 MPa), mercury porosimetry and N2 and CO2 adsorption isotherms, at -196 and 0 °C, respectively. The apparent surface areas of the samples were obtained by using the BET equation [5]. The micropore size analysis was performed by means of the t-plot and the Dubinin-Astakhov methods [6]. 

The difficulty in the case of microporous materials stems from the porefilling mechanism. For this reason, the surface area of such materials is often determined by other methods than BET, which is based on layer formation. From the Dubinin equation the micropore volume Wo can be converted to the surface area. The as isotherm comparison method is an independent method for estimating the micropore volume and the surface area (20). The reference isotherm is a plot of the measured isotherm normalized by the amount of gas adsorbed at a fixed relative pressure, typically at p/po = 0.4. High resolution as analysis (21) yields more information about the characteristic texture of the adsorbent. Further methods (MP (22), -plot (23), Dubinin-Astakhov (11), Dubinin-Stockli (12), and so on) are also available for more reliable estimates of the micropore volume and surface area. 

Dubinin and Astakhov [117] put forward a more general form of Eq. (38), termed the DA equation, in which the square exponent is replaced with an empirical constant with a value between 2 and 6. No physical basis was identified, however, for selecting the value of the exponent. To cast the DR equation into a form more suitable for PSD analysis of heterogeneous microporous solids, Stoeckli [118] suggested an integral form of Eq. (38) involving a structure distribution function 7(B) for the micropore PSD,... 

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