Probing adsorbent heterogeneity using Toth isotherms

Abstract

The binding affinity distribution is a fingerprint of the adsorbent heterogeneity. In chromatographic separations, the affinity distribution determines the molecular recognition capability of the stationary phases. In gas storage and...

Acid Gas Removal by Superhigh Silica ZSM-5: Adsorption Isotherms of Hydrogen Sulfide, Carbon Dioxide, Methane, and Nitrogen

“…The Langmuir adsorption isotherm is another adsorption isotherm that simply assumes that adsorption takes place at specific homogeneous sites. The Langmuir equation is as follows (eq ): The maximum number of adsorption sites on the adsorbent surface is expressed by q m in terms of mmol·g –1 or g·g –1 , and b , as an adsorbent property, is the binding affinity of the adsorption sites. According to the Langmuir equation, if P is infinitely inclined, the total capacity of the monolayer is completed, and the Langmuir equation is thermodynamically inconsistent because it has been proven that according to Gibbs thermodynamics, a plateau in the high-pressure range cannot exist …”

Potential Application of Alternative Materials for Organic Pollutant Removal

“…where q e (mg g −1 ) and C e (mg L −1 ) are adsorbed amount and adsorbate concentrations at equilibrium; q m , q S , and q To (mg g −1 ) are the maximum adsorbed amount to Langmuir, Sips, and Toth, respectively, where the maximum adsorbed amount is influenced according to the concentration of biochar (Bardestani et al, 2019;Zhang, Meng, et al, 2019); K L is Langmuir constant (L mg −1 ); k F is the Freundlich constant ((mg g −1 ) (mg L −1 ) −1/n ) which indicates the relative adsorption/desorption capacity of the adsorbent in relation to the bonding energy; n is the constant related to the adsorption intensity that should be between 1 and 10, where it usually indicates physical adsorption (Dasgupta et al, 2018;Enaime et al, 2017); n s is the heterogeneity factor, where if n s = 1, the model is reduced to the Langmuir equation and if n s < 1, there is an increase in heterogeneity, that is, the model approaches Freundlich (Kumar et al, 2019;Shahri et al, 2018); n TO is the heterogeneity parameter, which can assume a value between 0 and 1; for n TO = 1 the Langmuir model is obtained (characteristic for representing homogeneous surfaces) and if n TO ≠ 1 represents a heterogeneous surface; and b TO is the constant of the Toth isotherm (Al-Ghouti & D.A. Da'ana, 2020;Kumar et al, 2021).…”

Enhanced thermal stability and adsorption performance of MIL-53(Fe)@montmorillonite

“…The L-F equation, a kind of semi-empirical equation based on introducing the Langmuir equation into the Freundlich equation in exponential form for describing the surface heterogeneity of the adsorbent, could be applied to analyze data of adsorption (Batebi et al, 2021). For the more, in order to make up for the deficiency of the Freundlich equation, a semi-empirical Toth equation could also be applied (Kumar et al, 2021). Here, the isotherm parameters of MB were analyzed by different isotherm models, such as nonlinear form of Langmuir (Eq.…”

“…The L-F equation is a semi-empirical equation that introduces the Langmuir equation into the Freundlich equation in exponential form to describe the surface heterogeneity of the adsorbent (Batebi et al, 2021). To make up for the deficiency of the Freundlich equation, the semi-empirical Toth equation was also tested (Kumar et al, 2021). These equations are as follows:…”