Cooperative Sorption on Porous Materials

Abstract

The functional shape of a sorption isotherm is determined by underlying molecular interactions. However, doubts have been raised on whether the sorption mechanism can be understood in principle from analyzing sorption curves via a range of competing models. We have shown recently that it is possible to translate a sorption isotherm to the underlying molecular interactions via rigorous statistical thermodynamics. The aim of this paper is to fill the gap between the statistical thermodynamic theory and analyzing experimental sorption isotherms, especially of microporous and mesoporous materials. Based on a statistical thermodynamic approach to interfaces, we have derived a cooperative isotherm, as a generalization of the Hill isotherm and our cooperative solubilization model, without the need for assumptions on adsorption sites, layers, and pore geometry. Instead, the statistical characterization of sorbates, such as the sorbate-interface distribution function and the sorbate number distribution, as well as the existence of statistically independent units of the interface, underlies the cooperative sorption isotherm. Our isotherm can be applied directly to literature data to reveal a few key system attributes that control the isotherm: the cooperative number of sorbates and the free energy of transferring sorbates from the saturated vapor to the interface. The sorbate− sorbate interaction is quantified also via the Kirkwood−Buff integral and the excess numbers.

Surface Area Estimation: Replacing the Brunauer–Emmett–Teller Model with the Statistical Thermodynamic Fluctuation Theory

“… 15 Addressing this difficult question requires further work. However, we would like to point out, based on our previous work on adsorption on porous materials, 21 , 23 , 24 that N 22 may still play a crucial role in connecting the gradient of an isotherm to the number of sorbates that sorb cooperatively. N 22 changes with a 2 ( Figures 7 b and 8 b) and plays a central role in understanding how a macroscopic isotherm is composed of different sorption processes.…”

“…This contradiction was resolved by the current authors using statistical thermodynamics (Figure ). − A general isotherm, which contains the BET and GAB models as its special cases, has been derived from a Maclaurin expansion of the sorbate–sorbate interaction (quantified via the Kirkwood–Buff integral) at the dilute limit, incorporating up to sorbate pair and triplet contributions (Figure b,c). This has fulfilled “the need to examine the limitations of the BET method and in particular to attempt to define the conditions which govern its application”; the wide applicability of the BET or GAB comes from the sorbate pair and triplet contribution instead of the planar multilayer assumption, rationalizing why the BET and GAB models are widely applicable beyond their original assumptions .…”

General cluster sorption isotherm: surface area determination

“…The latter has been formally derived and applied to the description of protein-ligand interactions by Klotz in 1946. 20 Both the derivation by classical 20 or statistical thermodynamics 21,22 is possible. For an open system the number of n adsorbed molecules per primary sorption site is unlimited.…”

Porous PVA-g-SPA/PVA-SA Catalytic Composite Membrane via Lyophilization for Esterification Enhancement

“…Excellent separation performance and high catalytic activity are indispensable for catalytic composite membranes. Generally, hydrophilic polymer materials, such as poly­(vinyl alcohol) (PVA), sodium alginate (SA), and CS, are used as the separation layer. ,− The catalytic layer is prepared by adding catalysts into the membrane material via blending and grafting. Li et al prepared a catalytic layer by grafting polystyrene sulfonic acid onto PVA and directly coating it on the separation layer.…”