From Langmuir isotherm to Brunauer–Emmett–Teller isotherm

Abstract

Developed for multilayer adsorption, the Brunauer-Emmett-Teller (BET) isotherm considers the adsorption of the first layer as an equilibrium chemical reaction between adsorbate molecules and adsorption sites and the adsorption of the second and subsequent layers as a condensation-evaporation process. Following the recent development of an activity-based formulation for the Langmuir isotherm for monolayer adsorption, we present an activity-based formulation for the BET isotherm in which species concentrations are replaced with species activities. Capturing the adsorbent surface heterogeneity for the adsorption of the first layer, the resulting thermodynamic BET isotherm is shown to accurately represent pure component adsorption isotherms over the relative pressure range of zero to unity or prior to the onset of capillary condensation. The thermodynamic BET isotherm should facilitate accurate estimation of monolayer adsorption capacity and the corresponding adsorbent surface area.

Slowly Removing Surface Ligand by Aging Enhances the Stability of Pd Nanosheets toward Electron Beam Irradiation and Electrocatalysis

“…The gradual desorption of PVP from Pd NSs during aging can be explained using the Langmuir isotherm, which is generally used to describe the behavior of an adsorbate on a solid surface. [19] Here the PVP molecules can be regarded as the adsorbate and the Pd NS as the solid surface. The equilibrium fraction (θ) of surface sites occupied up by the adsorbate can be expressed as Equation 1:…”

Phosphate adsorption characteristics of ‘nanoclay’ separated from Indonesian volcanic tuffs

“…Application of the Langmuir model results in adsorption maxima (qe) and adsorption energy (K) parameters (Islam et al 2021), while Freundlich, BET, and D-R model results in empirical constant (1/n) and Freundlich constant (Kf) parameters (Kim and Kim 2020), adsorption capacity at the first adsorptive layer (qmono) parameter (Vyawahare et al 2022), adsorption maxima (qe) and transfer energy (E) parameters (Azouaou et al 2010;Ragadhita and Nandiyanto 2021), respectively.…”

“…Therefore, the qmono obtained in this study was certainly lower than qe. However, the qmono parameter provided by BET model is more accurate in describing adsorption characteristics of an adsorbent compared to those of Langmuir, Freundlich, and D-R model because in establishing the best-fit linear equation both the initial and final or equilibrium concentrations of the sorbate are incorporated in BET model (Brunauer et al 1938;Vyawahare et al 2022), while the other equations incorporate only the initial sorbate concentration.…”

Improvement of temperature profiles using variable heat of adsorption in modeling H 2 /CO 2 breakthrough experiments

“…Vyawahare et al developed an activity‐based formulation for the Brunauer‐Emmett‐Teller isotherm in which species concentrations are replaced with species activities. The formulation can accurately estimate the monolayer adsorption capacity and the adsorbent surface area 11 . Yang et al experimented on the adsorption and desorption of two‐component gas (H 2 /CO 2 and H 2 /CO) in zeolite under different adsorption pressures, studied the kinetics of adsorption and desorption and obtained the optimal adsorption and desorption pressure conditions in the PSA process 12 .…”

“…The formulation can accurately estimate the monolayer adsorption capacity and the adsorbent surface area. 11 Yang et al experimented on the adsorption and desorption of two-component gas (H 2 /CO 2 and H 2 /CO) in zeolite under different adsorption pressures, studied the kinetics of adsorption and desorption and obtained the optimal adsorption and desorption pressure conditions in the PSA process. 12 Lee et al optimize the structure based on the traditional adsorption bed and propose the concept of a ring-shaped bed.…”