Publication: New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants
Date
2024
Authors
Debord J.
Harel M.
Bollinger J.-C.
Koopal L.
Salvestrini S.
Chu K.H.
Journal Title
Journal ISSN
Volume Title
Publisher
American Chemical Society
Abstract
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.
Description
Keywords
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