In the paper applicability of BET approach to modeling of adsorption of small nearly spherical molecules in submicro-and microporous sorbents is discussed. The BET assumptions are analyzed from physical point of view, and properly generalized to handle geometrical as well as energetic conditions for multilayer adsorption in microporous structures. A formal description of multilayer adsorption is derived, by using the thermodynamic approach, with any energy profile across the layers being admitted. To get an analytical formula describing the process one proposes to assume an exponential distribution of pore capacity, and apply the BET equation with limited number of layers. Formal properties of the obtained formula, referred to as LBET model, are carefully examined and compared with those of Dubinin-Radushkievith and BET equations. The examination showed that the LBET model describes adequately adsorption process on materials of submicroporous and microporous structure with dominant fraction of small micropores. It provides reliable information on the porous surface capacity and on the first layer adsorption energy. It gives also a semiquantitative characterization of pore volume distribution. Application of the LBET model to interpretation of sorption isotherms of water and methanol on a hard coal and of carbon dioxide on activated carbon is presented.
The paper presents a properties study of the new LBET class models for heterogeneous multilayer adsorption and its applicability to analysis of microporous carbonaceous adsorbents in comparison to the selected classical equations. This paper shows that the LBET formulas give a good insight into the pore size distribution and dominant pore shape. Moreover, they provide more reliable evaluation of material surface area than the popular classical equations. This research constitutes a significant development and completion of the author's earlier works and provides a basis for the evaluation of reliability of parameters calculated for real systems.
Herein, a comprehensive analysis of DFT methods as a tool for evaluating the impact of the nature of the activating agent on the porous structure of activated carbons derived from hazelnut shells is given. The study was based on the use of NLDFT, QSDFT, and 2D-NLDFT methods applied to nitrogen adsorption isotherms, and the results were compared with those formerly obtained by using DR, BET, and LBET methods. Analyses conducted with NLDFT, QSDFT, and 2D-NLDFT revealed a very strong dependence of the results on assumptions about the specific pore model, which calls into question the reliability and credibility of these methods. However, if one takes into account the measurement errors that may during the determination of the adsorption isotherms, as well as the difficulty of selecting a representative sample in a batch of materials (most often non-homogeneous) to be analysed, some imperfections of the DFT methods become acceptable. The analyses in question revealed some limitations of the LBET method which became obvious when the analysis concerned bimodal porous materials with a considerable proportion of mesopores. In such cases, the LBET method, which was formerly designed for analysing microporous materials, may become less reliable.
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