A Model for Multilayer Adsorption of Small Molecules in Microporous Materials

Abstract

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.

Application of multiple sorption model to estimation of CO2sequestration capacity or CH4recovery in polish hard coals

“…Sorption isotherms of CO2 and CH4 measured up to 3.4 MPa were used for evaluation of the computed set of isotherms. The MSM model was described in previous articles [12][13][14]. The results that were obtained are presented on Figures and Tables 2 and 3.…”

Characterization of hard coal properties applying multiple sorption model with parameters determined from qualitative approach to adsorption mechanism identification

“…Hence, absorption-adsorption phenomena may be seen as mixing of sorbate particles (6) with individual components of the carbonaceous material (1-5). In order to examine such sorption system, a consistent approach so called MSM, was elaborated in Author's team (Milewska-Duda et al 2000;Milewska-Duda and Duda 1993). In particular, coming from general equilibrium thermodynamics, sorption system in MSM is considered comparing to a standard state of pure liquid-like sorbate and dry sorbent.…”

“…2), separately for each indicated subprocess of the adsorptiveabsorptive nature and adsorptive or absorptive nature, only. Hence, let us consider energy of sorbate molecule deposition, expressed by the dimensionless energetic parameter χ ac , as a separation of the sorbate molecule from its liquid-like reference state (i.e., evaporation) at the first stage, creation of a hole (i.e., room) for this molecule within the sorbent matter (expansion) and placing the molecule in the created hole (condensation) in second and third stage, respectively (Milewska-Duda et al 2000;Duda 1997, 1993).…”

“…(4) was recently strongly developed in Author's team, both as a completion of MSM, as well as individual numerical tool aimed at identification of materials porous structure, referred as LBET class adsorption models. The LBET approach is far generalization of classical BET formulae enabling as well to consider, multilayer adsorption in bigger pores and also a non-BET stacks formation Milewska-Duda et al 2000).…”

A qualitative approach to adsorption mechanism identification on microporous carbonaceous surfaces

“…: (Duda et al 2013;Milewska-Duda et al 2000;Milewska-Duda and Duda 2001). In such a view a key parameter is an effective adhesion energy E adh , related to a measurable monolayer adsorption energy Q A with a Huggins formula (Flory 1953):…”