Cooperative Sorption on Heterogeneous Surfaces

Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory

Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.

Porous sulfur polymers for effective aqueous-phase organic contaminant removal

Sulfur polymers produced through 'inverse vulcanization' exhibit various attributes, such as photocatalytic activity and a high capacity to adsorb heavy metals. Nevertheless, there is a lack of research investigating the use of sulfur polymers as materials for the removal of organic contaminants. In this work, porous sulfur polymers (PSPs) were synthesized from elemental sulfur and 1,3-diisopropenylbenzene, with porosity introduced via salt templating. The result is a material that can strongly adsorb and chemically neutralize a model organic contaminant (caffeine). PSPs show adsorption up to 5 times higher than a leading adsorption material (activated carbon). Furthermore, either the adsorption or degradation processes can govern the removal efficiency depending on the synthesis parameters of PSPs. This is the first-ever report demonstrating sulfur polymers as effective materials for removing emerging contaminants from water. The versatile synthesis of sulfur polymers offers variation, which means that there is much more to explore in this exciting research area.

Replacing the Langmuir Isotherm with the Statistical Thermodynamic Fluctuation Theory

In the age of all-atom simulations, primitive isotherm models, such as Langmuir, BET, and GAB, are still used widely for analyzing experimental data. However, their routine applications to complex materials are not in line with their underlying assumptions (i.e., statistically independent adsorption sites with no interfacial structural changes), which manifests as the temperature dependence of the monolayer capacity. Our proposal is to replace these models with the statistical thermodynamic fluctuation theory because the ABC isotherm derived from it (i) contains these primitive models as its special cases, (ii) is applicable to any interfacial geometry, and (iii) is linked to molecular distribution functions, sharing the same language as simulations. Rectifying the inability of the primitive isotherm models to handle attractive and repulsive interactions consistently leads to a reconsideration of how physical interpretations should be attributed to the isotherms of empirical origin (e.g., Freundlich).

Cooperativity in Sorption Isotherms

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Sorption from Solution: A Statistical Thermodynamic Fluctuation Theory

Given an experimental solid/solution sorption isotherm, how can we gain insight into the underlying sorption mechanism on a molecular basis? Classifying sorption isotherms, for both completely and partially miscible solvent/sorbate systems, has been useful, yet the molecular foundation of these classifications remains speculative. Isotherm models, developed predominantly for solid/gas sorption, have been adapted to solid/solution isotherms, yet how their parameters should be interpreted physically has long remained ambiguous. To overcome the inconclusiveness, we establish in this paper a universal theory that can be used for interpreting and modeling solid/solution sorption. This novel theory shares the same theoretical foundation (i.e., the statistical thermodynamic fluctuation theory) not only with solid/gas sorption but also with solvation in liquid solutions and solution nonidealities. The key is the Kirkwood-Buff χ parameter, which quantifies the net self-interaction (i.e., solvent-solvent and sorbate-sorbate interactions minus solvent-sorbate interaction) via the Kirkwood-Buff integral in the same manner as the solvation theory and, unlike the Flory χ, is not limited to the lattice model. We will demonstrate that the Kirkwood-Buff χ is the key not only to isotherm classification but also to generalizing our recent statistical thermodynamic gas (vapor) isotherm, which is capable of fitting most of the solid/solution isotherm types.

Understanding Sorption Mechanisms Directly from Isotherms

Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.