New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants
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 i...
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2025
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my.uniten.dspace-365272025-03-03T15:42:53Z New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants Debord J. Harel M. Bollinger J.-C. Koopal L. Salvestrini S. Chu K.H. 7005677021 7006218434 35546414700 7006913453 6602767451 7402453718 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. Final 2025-03-03T07:42:53Z 2025-03-03T07:42:53Z 2024 Article 10.1021/acs.langmuir.4c00862 2-s2.0-85194256811 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85194256811&doi=10.1021%2facs.langmuir.4c00862&partnerID=40&md5=c50a7ca9503c824d9381c2315145b312 https://irepository.uniten.edu.my/handle/123456789/36527 40 23 12070 12077 American Chemical Society Scopus |
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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 |
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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 Debord J. Harel M. Bollinger J.-C. Koopal L. Salvestrini S. Chu K.H. New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
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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. |
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7005677021 |
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7005677021 Debord J. Harel M. Bollinger J.-C. Koopal L. Salvestrini S. Chu K.H. |
| format |
Article |
| author |
Debord J. Harel M. Bollinger J.-C. Koopal L. Salvestrini S. Chu K.H. |
| author_sort |
Debord J. |
| title |
New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
| title_short |
New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
| title_full |
New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
| title_fullStr |
New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
| title_full_unstemmed |
New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants |
| title_sort |
new sorption isotherms derived from a gamma distribution of binding constants |
| publisher |
American Chemical Society |
| publishDate |
2025 |
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1825816275722436608 |
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13.244109 |