Determination Of The Activated Carbon Structural Heterogeneity On The Basis Of Stoeckli
DETERMINATION OF THE ACTIVATED CARBON STRUCTURAL HETEROGENEITY ON THE BASIS OF STOECKLI
AND DUBININ – STOECKLI EQUATIONS
B.J. Trznadel, P. Kowalczyk
Military Institute of Chemistry and Radiometry, 00-910 Warsaw, Poland
Activated carbons possess micropores, mesopores, and macropores. Macropores play the main role in mass transfer phenomena from gaseous phase to meso- and micropores. The presence of micropores and mesopores affects sorption properties of an adsorbent. The most important characteristic of adsorbent is pore sizes distribution, mainly micropore size distribution (MPSD). Several methods of evaluation of MPSD have been proposed previously (Jaroniec and Madey, 1988). The basis of determination of MPSD is solving of integral equation in the form proposed by Stoeckli:
(1)
Assuming MPSD as Gaussian distribution function and the Dubinin–Radushkevich equation as a kernel of Eq.(1) one can obtain well known equation of Dubinin and Stoeckli (DS, 1980):
(2)
Nickolov and Mehandjiev(1995) proposed the simplification of Eq.(2). The simplified equation (SE) can be written in linear form as:
(3)
Stoeckli solved Eq.(1). He used the equation of Dubinin–Astahov (1971) (n=3) as a kernel and gamma-type size distribution function and obtained solution in the form:
(4)
where:
(5)
This work has two objectives. The first one is the new proposal of solving Stoeckli\’s equation (4-5) by the use the least square method. The second one is the quantitative evaluation of dispersion of structural parameters in batch of activated carbon production.
Eight samples (designated S1-S8) of activated carbon of AG-5 type purchased from HPSDD (Hajnówka, Poland) were used in experiments. The benzene vapour adsorption-desorption isotherms at 293K were carefully acquisited by gravimetric methods using McBain-Bakr vacuum balance. Fig.1 presents a whole range of adsorption pressure and Fig.2 the parts of isotherms up to the beginning of the hysteresis loop as the DR plots. The shape of the isotherms indicates they are of IV type according to UPAC classification. The presence of micropore and mesopore structures is evident. The experimental isotherms were corrected for adsorption on the mesopore surface.
Four numerical algorithms, for solving of Stoeckli’s equation (4-5), are proposed here. The base of our proposal is the minimisation of functional:
(6)
where:
(7)
It was found that each kind of algorithm leads to similar values of the structural parameters. Moreover, the calculated MPSDs show the resemblance in their character. The comparison between the obtained results and the MPSDs determined on the basis of the DS and the SE equations proofs the correctness of proposed algorithms. It seems that our proposal gives useful tool for evaluation of MPSD on the basis of the single adsorption isotherm.
The presented here results indicate the indisputable presence of the dispersion of structural parameters in production batch of examined activated carbon. It seems that it is an effect of residence time distribution in the activation reactor.
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