Interpreting the hydrogen adsorption on organic groups functionalized MOF-5s by statistical physics model

Adsorption of Methane on Shale: Statistical Physics Model and Site Energy Distribution Studies

“…It can be found in Figure that the density of receptors N m for all shale samples decreases monotonically with increasing temperature. This is due to the effect of thermal agitations: the adsorption process is exothermic as a result of binding energy of CH 4 molecules disturbed and destroyed or disanchored by the thermal collisions . In addition, the size of formed aggregated CH 4 molecules increases with temperature by a stereographic effect, and the aggregation of methane molecules has an effect on neighboring receptors …”

“…The adsorption energy is an important parameter which can be applied to characterize the interaction between the methane molecules and the adsorption sites of shales . The adsorption energy can be estimated on the basis of parameter half-saturation pressure p 1/2 , and the expression is given as the following: ,, where Δ E is the adsorption energy, R is the ideal gas constant, and p 0 is the saturated vapor pressure, which are calculated by the Clausius–Clapeyron equation . The calculate p 0 values of CH 4 are 36.25 MPa at 318 K, 43.11 MPa at 338 K, and 50.72 MPa at 358 K, respectively.…”

“…The microscopic states of the adsorption system can be described by using the grand canonical partition, which has the following expression: ,, where z gc represents the grand canonical partition function of one receptor site, T is the temperature, μ is the chemical potential of the adsorbed molecule, ε is the adsorption energy of the receptor site, N i is the occupation state of a site i , and β is the Boltzmann factor, which is determined as 1/ k B T , where k B is the Boltzmann constant.…”

“…In order to understand the adsorption process of methane on shale well and deeply, it is necessary to choose a suitable analytical model for describing adsorption isotherms. Previous studies have shown that the analytical models developed from the statistical physics theory can be used to characterize the adsorption data, and some new theoretical interpretations of the adsorption isotherms can also be simultaneously provided by these analytical models. , A number of statistical physics models have been applied to simulate the adsorption of gases or liquids, such as hydrogen adsorption on MOF-5s, hydrogen adsorption on zeolites, ethanol adsorption on activated carbon, and heavy metal ions adsorption on bone char . The application of statistical physics models can be extended to describe the adsorption process of methane on shales, which are characterized by complex composition and structure.…”

Adsorption of CO2 on ZSM-5 Zeolite: Analytical Investigation via a Multilayer Statistical Physics Model

“…Based on the adsorption energy (ε), which is related to the pressures at half saturation (P1) and (P2) of the substance, we determined the site energy distribution using the formalism of Polanyi potential [38,39]. The tested isotherms Qa(P) can be described versus ɛ and becomes Qa(ε) by incorporating Equation (7) in Equation(3).…”