Modeling of Surface Heterogeneity of Microporous Adsorbents with LBET Approach

Abstract

A package of new isotherm equations aimed at examination of pore structure of sub- and microporous materials with respect to a surface heterogeneity is proposed. One considers adsorption of small nearly spherical molecules in irregular pores of molecular size. A generalized BET theory is exploited together with a thermodynamic description of the process and handling restrictions for multilayer adsorption (LBET approach). Realistic multivariant relationships linking a surface energy distribution with the pore size are proposed, and exponential distribution of the pore size is accepted. As a result, the heterogeneous adsorption equations (uLBET formulas) are derived, dedicated for irregular microporous systems. It was shown that they may be well-approximated with analytical BET-like formulas (the models of the LBET-type), enabling fast multivariant examination of real microporous materials. Such an examination provides complementary information on adsorption mechanisms, thus, allowing more reliable evaluation of the system parameters. Results of the new model's application to an empirical system (nitrogen adsorption on an activated carbon) are shown.

Complementary study of microporous adsorbents with DFT and LBET

“…In the LBET approach [9][10][11][12] adsorption is viewed as compressing of the adsorbate molecules to a volume V s , (a liquid-like reference state [13]), and then, moving them into rigid aggregates of empty cells (each of the same volume V s ) incorporated in the pores in a statistically predefined way. The aggregates represent total space of pores available for adsorption of considered molecules (see Fig.…”

“…The second approach, presented in more detail in earlier papers [9][10][11][12], combines the Flory-Huggins theory of mixtures [13] with BET-like description of adsorption process [14] in pores of irregular shape. Adsorption is viewed as creation of adsorbate clusters, starting from sites where local minima of adhesion energy are encountered.…”

“…In this approach no arbitrary assumptions on pore shapes are necessary, although the parameters representing directly the pore geometry effects are involved. These parameters allow deducing geometrical properties of pores [10,11]. The LBET model is recommended for the analysis of microporous and sub-microporous structures of irregular and diversified pore shapes [11,12].…”

High-Accuracy PVT Relationships for Compressed Fluids and Their Application to BET-like Modelling of CO2 and CH4 Adsorption

“…In particular, if ζ A ∈ (0, ζ Amax ) are uniformly distributed over all the sites, the total adsorption m a may be expressed by an appropriate integration of equation (30) (Duda and Milewska-Duda 2005). This leads to the following formula: (34) where B A is calculated using equations (31) and (32) with ζ A = ζ Amax , and B 0 like B A is ζ A = 0.…”

“…Nevertheless, it may suffer from bad conditioning of the numerical optimization procedures (due to over-parametrization) leading to less reliable evaluations of all the parameters (Duda and Milewska-Duda 2005).…”