Molecular insight into the formation of adsorption clusters based on the zeta isotherm

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..

Determination of the surface properties and adsorption states of nanoporous materials using the zeta adsorption isotherm

The adsorption process of porous materials has always been a popular field of research in interfacial physics, and the surface physical parameters of materials can be obtained from their adsorption characteristics, which has a great influence on the performance of materials. Based on the zeta adsorption isotherm, we propose a method based on the zeta adsorption isotherm to predict the entire adsorption process of porous materials and determine material surface properties from the measured isotherm data in the heterogeneity-free range. We applied the zeta constants of the silica adsorption system to the corresponding adsorption isotherm of the porous material. The results showed that the predicted adsorption isotherms are in good agreement with the experimental measurements before pore filling and can effectively identify the pressure ratios at the beginning and end of pore filling. In the region of high-pressure ratios, the Kelvin equation was utilized to calculate the pressure ratio at a contact angle of 0°. The surface parameters of the materials were determined by geometrically calculating the variation of the adsorption amount and the desorption isotherms in the high-pressure ratio range were calculated from these surface parameters. The predicted desorption isotherms can well reflect the adsorption process of silica porous materials in the region of a high-pressure ratio. In addition, for the surface parameters of the materials, the specific surface area calculated from the adsorption and desorption isotherms, respectively, differed by less than 7.9%, and the reliability of the method was verified by comparing the results with those of the argon adsorption systems.