New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants

• Main Authors: Debord J., Harel M., Bollinger J.-C., Koopal L., Salvestrini S., Chu K.H.
• Other Authors: 7005677021
• Format: Article
• Published: American Chemical Society 2025
• Subjects: Adsorption isotherms; Probability distributions; Sorption; sorbent; Binding constant; Cooperativity; Energy distributions; Exponential integrals; Freundlich; Gamma distribution; Hills' equations; Langmuir equation; Sorption isotherms; Stieltjes transform; article; association constant; controlled study; hypobaric pressure; isotherm; Binding energy

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new ?Gamma isotherms? are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global ?Gamma-Langmuir? isotherm retrieves Henry?s law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global ?Gamma-Hill? isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions. ? 2024 American Chemical Society.