Temperature Dependence of Sorption

Seishi Shimizu,Nobuyuki Matubayasi

doi:10.1021/acs.langmuir.1c01576

Seishi Shimizu, Nobuyuki Matubayasi

Open Access

https://doi.org/10.1021/acs.langmuir.1c01576

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Journal: Langmuir	Publication Date: Sep 9, 2021
Citations: 14	License type: CC BY 4.0

Affiliation: University of York, Osaka University

Abstract

Understanding how sorption depends on temperature on a molecular basis has been made difficult by the coexistence of isotherm models, each assuming a different sorption mechanism and the routine application of planar, multilayer sorption models (such as Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-de Boer (GAB)) beyond their premises. Furthermore, a common observation that adsorption isotherms measured at different temperatures fall onto a single "characteristic curve" when plotted against the adsorption potential has not been given a clear explanation, due to its ambiguous foundation. Extending our recent statistical thermodynamic fluctuation theory of sorption, we have generalized the classical isosteric theory of sorption into a statistical thermodynamic fluctuation theory and clarified how sorption depends on temperature. We have shown that a characteristic curve exists when sorbate number increment contributes purely energetically to the interface, whereas the correlation between sorbate number and entropy drives the temperature dependence of an isotherm. This theory rationalizes the opposite temperature dependence of water vapor sorption on activated carbons with uniform versus broad pore size distributions and can be applied to moisture sorption on starch gels. The adsorption potential is a convenient variable for sorption in its ability to unify sorbate-sorbate fluctuation and the isosteric thermodynamics of sorption.

Highlights

Understanding how sorption depends on temperature is an important question in basic and applied sciences alike.[1−3] This paper aims to answer this question on a molecular scale via statistical thermodynamics.[4−7] This question may seem simple yet has been made complicated
The isotherms from different temperatures very commonly fall onto a single “characteristic curve” when plotted against the adsorption potential.[39−41] Ambiguity surrounding the theoretical foundation of the potential theory has long prevented a clear identification of the underlying mechanism
The classical isosteric thermodynamics of sorption has been reformulated within a general framework of the statistical thermodynamic fluctuation theory in combination with an assumption regarding the finite-ranged nature of the interface.[4]

Summary

Introduction

Understanding how sorption depends on temperature is an important question in basic and applied sciences alike.[1−3] This paper aims to answer this question on a molecular scale via statistical thermodynamics.[4−7] This question may seem simple yet has been made complicated. Studying sorption was made complicated by the coexisting of 80+ different isotherm models, each assuming a different sorption mechanism including how it depends on temperature.[8−14] Here, we demonstrate that temperature dependence has been explained differently from model to model and there are even disagreements within the same model as to which parameters are temperature-dependent. The Langmuir model[15] contains two parameters, the Langmuir constant and the saturation loading.[16] The Langmuir constant is linked to adsorption enthalpy via the van’t Hoff equation,[17] and generally agreed to be temperature-dependent.[1,3] an agreement has not been reached regarding when the saturation loading is temperature-independent[18,19] or temperature-dependent.[16,20,21]

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