Sorption: A Statistical Thermodynamic Fluctuation Theory.

Seishi Shimizu,Nobuyuki Matubayasi

doi:10.1021/acs.langmuir.1c00742

Seishi Shimizu, Nobuyuki Matubayasi

Open Access

https://doi.org/10.1021/acs.langmuir.1c00742

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Abstract

Can the sorption mechanism be proven by fitting an isotherm model to an experiment? Such a question arises because (i) multiple isotherm models, with different assumptions on sorption mechanisms, often fit an experimental isotherm equally well, (ii) some isotherm models [such as Brunauer–Emmett–Teller (BET) and Guggenheim–Anderson–de Boer (GAB)] fit experimental isotherms that do not satisfy the underlying assumptions of the model, and (iii) some isotherms (such as Oswin and Peleg) are empirical equations that do not have a well-defined basis on sorption mechanisms. To overcome these difficulties, we propose a universal route of elucidating the sorption mechanism directly from an experimental isotherm, without an isotherm model, based on the statistical thermodynamic fluctuation theory. We have shown that how sorbate–sorbate interaction depends on activity is the key to understanding the sorption mechanism. Without assuming adsorption sites and planar layers, an isotherm can be derived, which contains the Langmuir, BET, and GAB models as its special cases. We have constructed a universal approach applicable to adsorption and absorption, solid and liquid sorbents, and vapor and liquid sorbates and demonstrated its efficacy using the humidity sorption isotherm of sucrose from both the solid and liquid sides.

Highlights

Sorption isotherms play an important role in all aspects of our daily lives from food,[1−3] clothing,[4] and building,[5−7] as well as in diverse scientific areas, such as biomolecules and colloids,[8] activated carbons,[9,10] nanoparticles,[11] and aerosols.[12]
There are more than 80 different isotherm models published so far, each lying on a spectrum between empirical and physical.[13−18] The empirical models do not have a well-defined physical basis, and despite their practical value, insights on the adsorption mechanism may not be gained by fitting such a model to an experimental isotherm
In applying our general statistical thermodynamic theory, we have focused on relatively simple sorption isotherms that can be modeled via expanding the Kirkwood−Buff integral around a2 → 0, taking up to sorbate three-body interactions that are, influenced by the presence of the sorbent

Summary

Introduction

Sorption isotherms play an important role in all aspects of our daily lives from food,[1−3] clothing,[4] and building,[5−7] as well as in diverse scientific areas, such as biomolecules and colloids,[8] activated carbons,[9,10] nanoparticles,[11] and aerosols.[12]. There are more than 80 different isotherm models published so far, each lying on a spectrum between empirical and physical.[13−18] The empirical models (such as the Oswin[19] and Peleg20,21) do not have a well-defined physical basis, and despite their practical value, insights on the adsorption mechanism may not be gained by fitting such a model to an experimental isotherm. The physical models [such as the Langmuir,[22] Brunauer−Emmett−Teller (BET),[23,24] and Guggenheim− Anderson−de Boer (GAB)25−27] are founded on assumed adsorption mechanisms, such as adsorption sites, layers, their numbers, and binding constants.[13−18] some of the most popular physical models have been applied routinely beyond their basic assumptions and premises.[20] Doubts have been raised whether the goodness of fit is a sufficient criterion to judge the correctness of a sorption mechanism because different types of models can fit an experimental isotherm well.[20,28] In the face of these difficulties, the objective of this paper is threefold:

Objectives

Results

Conclusion