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Cooperativity in Sorption Isotherms.

ABSTRACT: 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..

SUBMITTER: Shimizu S

PROVIDER: S-EPMC10552535 | biostudies-literature | 2023 Oct

REPOSITORIES: biostudies-literature

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Cooperativity in Sorption Isotherms.

Shimizu Seishi S Matubayasi Nobuyuki N

Langmuir : the ACS journal of surfaces and colloids 20230922 39

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). Th ...[more]

PMID: 37738037

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Project description:In the modern era, sol-gel plays a key role in the progress of a new generation of dispersive solid-phase microextractors (d-µ SPMEs) for the removal of organic and inorganic pollutants in complex matrices. Thus, the current study reports the use of sol-gel-functionalized polyurethane foams (PUFs) as a novel solid platform for complete extraction of chromium (VI) species from aqueous media. The planned protocol was based upon the complete extraction of the formed binary complex ion associates between the protonated ether and/or urethane groups of PUFs and chlorochromate anion [CrO3Cl]- aq in aqueous HCl (≥1M) medium in addition to H-bonding and the electrostatic π-π interaction that resulted between the CrO3Cl- and the silanol group (Si/ZrO2, Si-O-Zr) and siloxane (Si-O-Si) groups of the sol-gel. The impact of the analytical parameters (solution pH, natural mineral acids, shaking time, temperature, and chromium (VI) concentrations) was critically studied. At the optimal conditions, the uptake capacity of the established extractor (9.9 mg·g-1) was in agreement with the Langmuir adsorption capacity (12.08 mg·g-1) of the monolayer. The sorption data fitted well with the pseudo first-order kinetic model (R 2 = 0.9961) with an overall rate constant (k 1) of 0.081 min-1 and an equilibrium capacity (q e ) of 8.6 mg·g-1, which is in a good agreement with the experimental value (9.9 mg·g-1). The sorption of the oxyion [CrO3Cl]- aq onto the solid sorbent is an endothermic and spontaneous process as reflected from the values of ΔH (6.99 kJ·mol-1) and ΔG (-8.14 kJ·mol-1 at 293 K), respectively. The ΔS value (15.13 kJ·mol-1·K-1) reflects that the [CrO3Cl]- aq retention onto the sol-gel-treated PUFs sorbent proceeded in a more unplanned fashion. Sol-gel-treated PUFs sorbent-packed minicolumns were successfully used for the complete removal of trace levels of chromium (VI) species from water samples. Sorbed chromium (VI) species were recovered with NaOH (0.5 M) and analysed by spectrophotometry, which supports the utility of the sol-gel-treated PUFs as a low-cost solid extractor for water treatment.

Dataset Information

Cooperativity in Sorption Isotherms.

Publications

Cooperativity in Sorption Isotherms.

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