A synthesized MIL-101-NH2 has been used as an adsorbent to analyze Congo red (CR), methyl orange (MO), and acid chrome blue K (AC) dye adsorption phenomena. This investigation, based on statistical ...physics treatment, applied the double layer model with two energies to understand dye adsorption on three samples, namely, MIL-101-NH2-1, MIL-101-NH2-2, and MIL-101-NH2-3, at T = 298 K. Modeling results indicated that dye adsorption occurred via a mixed adsorption orientation for CR and MO dyes and a non-parallel orientation for AC dye on the MIL-101-NH2 surface. Dye uptake quantities varied from 2534.4 to 3440 mg/g for CR dye, 240.4 to 490.8 mg/g for MO dye, and 277 to 293 mg/g for AC dye. Thus, the highest adsorption amount appeared in the case of CR dye. Interpretation of the calculated energies showed that adsorption of the dyes on MIL-101-NH2 is a physisorption phenomenon, which could be controlled through energetic parameters obtained via numerical findings using the statistical double layer model. Moreover, the expression of the model is exploited to investigate the thermodynamic functions, such as internal energy.
In this paper, a synthesized zeolite (ZSM-5) is used as an adsorbent to analyze the adsorption phenomenon of carbon dioxide. This investigation, based on the statistical physics treatment, applied ...the multilayer model with saturation to understand the CO2 adsorption on four samples, namely M-ZSM-5 (M = Na+, Mg2+, Zn2+, La3+), at various temperatures T = 0 °C, 30 °C and 60 °C. The modeling results indicated that CO2 adsorption occurred via a non-parallel orientation on the ZSM-5 surface. The CO2 adsorption capacities varied from 26.14 to 28.65 cm3/g for Na-ZSM-5, from 25.82 to 27.97 cm3/g for Mg-ZSM-5, from 54.82 to 68.63 cm3/g for La-ZSM-5 and from 56.53 to 74.72 cm3/g for Zn-ZSM-5. Thus, Zn-ZSM-5 exhibits the highest adsorption amount. The analysis of the adsorption energies shows that the adsorption of CO2 on ZSM-5 zeolite is a physisorption phenomenon that could be controlled thanks to the energy parameters obtained via the numerical findings using the multilayer statistical model. Finally, the distribution of site energy was determined to confirm the physical character of the interactions between adsorbate/adsorbent and the heterogeneity of the zeolite surface.
Molecularly imprinted polymers (MIPs), as magnetic extraction adsorbents, are used for the selective, rapid determination and extraction of dexamethasone and hydrocortisone in skincare products. ...Therefore, in this paper, magnetic molecularly imprinted polymers (MMIPs) and magnetic non-molecularly imprinted polymers (MNIPs) were utilized as adsorbents to describe the adsorption phenomena of dexamethasone and hydrocortisone. This interpretation, based on a statistical physics theory, applies the multilayer model with saturation to comprehend the adsorption of the drugs. Results obtained via numerical simulation revealed that dexamethasone and hydrocortisone adsorption happens via a non-parallel orientation on the surfaces of MMIPs and MNIPs, and they also showed that the adsorption amount of the MMIPs for the template molecule was notably greater than that of the MNIPs at the same initial concentration. The adsorption energy values retrieved from the data analysis ranged between 7.65 and 15.77 kJ/mol, indicating that the extraction and determination of dexamethasone and hydrocortisone is a physisorption process. Moreover, the distribution of a site’s energy was calculated to confirm the physical nature of the interactions between adsorbate/adsorbent and the heterogeneity of the surfaces of the MMIPs and MNIPs. Finally, the thermodynamic interpretation confirmed the exothermicity and spontaneous nature of the adsorption of these drugs on the tested adsorbents.
•Application of a statistical physics model to adjust hydrogen absorption and desorption isotherms on LaNi3.8Al1.0Mn0.2.•Steric and energetic interpretations of hydrogen absorption/desorption process ...are given.•A dynamic of the absorption/desorption phenomena is proposed.•A thermodynamic study is applied to calculate internal energy, free enthalpy and entropy.
In the present work, experimental absorption and desorption isotherms of hydrogen in LaNi3.8Al1.0Mn0.2 metal at two temperatures (T = 433 K, 453 K) have been fitted using a monolayer model with two energies treated by statistical physics formalism by means of the grand canonical ensemble. Six parameters of the model are adjusted, namely the numbers of hydrogen atoms per site nα and nβ, the receptor site densities Nmα and Nmβ, and the energetic parameters Pα and Pβ. The behaviors of these parameters are discussed in relationship with temperature of absorption/desorption process. Then, a dynamic investigation of the simultaneous evolution with pressure of the two α and β phases in the absorption and desorption phenomena using the adjustment parameters. Thanks to the energetic parameters, we calculated the sorption energies which are typically ranged between 276.107 and 310.711 kJ/mol for absorption process and between 277.01 and 310.9 kJ/mol for desorption process comparable to usual chemical bond energies. The calculated thermodynamic parameters such as entropy, Gibbs free energy and internal energy from experimental data showed that the absorption/desorption of hydrogen in LaNi3.8Al1.0Mn0.2 alloy was feasible, spontaneous and exothermic in nature.
An integral equation derived using a statistical physics treatment by considering the adsorption energy distribution (AED) was used to model the adsorption of ethylene and ethane on ...resorcinol–formaldehyde-based activated carbon xerogels. Hill's model was taken as a local adsorption isotherm. This model was based on a grand canonical ensemble. Then a relationship between the energetic and the structural heterogeneities is used to determine the pore-size distribution (PSD) function. The AED and PSD obtained illustrate the greater affinity of activated carbon for adsorption of ethylene compared to ethane. In addition, this method was applied to determine the PSD of the British Drug House (BDH) activated carbon. The behaviour of the obtained PSDs at different temperatures was examined and related to the adsorption capacity of BDH activated carbon towards ethane, methane and nitrogen.
Experimental absorption and desorption isotherms of hydrogen in Ti1-xZrx Mn1.4 (x = 0, 0.1, 0.2, 0.3, 0.4) alloys at T = 293 K have been fitted using some theoretical model expressions treated by ...statistical physics through the grand canonical ensemble. The monolayer model with two types of sites is used to fit and interpret the experimental data. The physicochemical parameters governing the absorption-desorption processes and included into the model expressions could be numerically deduced from the relevant experimental isotherms. Six parameters of the model are fitted, namely the numbers of hydrogen atoms per site n1 and n2, the receptor site densities N1m and N2m, and the energetic parameters P1 and P2. The evolution of these parameters as function of composition x is plotted and explained in correlation with absorption-desorption processes. Finally, the thermo-dynamic potential functions which govern the sorption mechanisms such as internal energy Eint, free enthalpy of Gibbs Ga and entropy Sa were derived from statistical physics calculations based on the model adopted.
•A proposed statistical physics model was developed in this work.•Steric and energetic interpretations of hydrogen absorption and desorption process are given.•A thermodynamic study is applied to calculate internal energy, free enthalpy and entropy.
By means of the grand canonical ensemble and using statistical physics, experimental adsorption isotherms of hydrogen on three adsorbents (zeolite A, X and Y) at T = 77 K have been best fitted with a ...developed monolayer model with one type of sites. Exploiting some simplifying hypotheses, the model analytical expression of this model was established involving three physicochemical parameters with which we can describe the adsorption process at a microscopic level. These characteristic parameters are: the number of hydrogen molecules per site n, the receptor site density Nm and the energetic parameter P1/2 which are all deduced from the experimental data by numerical simulation. The evolution of these parameters was investigated of different types of zeolite and different type of exchanged cations. Our fitting results revealed that the hydrogen adsorption surface for each zeolite is homogeneous with physical bond energies. Finally, the thermo-dynamical potential functions which govern the adsorption process such as internal energy Eint, free enthalpy of Gibbs Ga and entropy Sa are derived by statistical physics derivation from the adopted model.
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•Application of statistical physics models to desribe the adsorption of hydrogen in zeolites A, X and Y.•Steric and energetic interpretations of hydrogen adsorption process are given.•a thermodynamic study is applied to calculate internal energy, free enthalpy and entropy.
•Measurement of hydrogen absorption and desorption isotherms of the LaNi4Co0.5Mn0.5 alloy.•A proposed statistical physics model was developed in this work.•Steric and energetic interpretations of ...hydrogen absorption process are given.•A thermodynamic study is applied to calculate internal energy, free enthalpy and entropy.
The microstructure and hydrogen storage properties of LaNi4Co0.5Mn0.5 alloy were studied by X-ray diffraction, scanning electron microscopy and pressure-composition-temperature isotherm measurements. The effect of the partial substitution of Ni by Mn and Coon the long-term hydrogen absorption/desorption properties are revealed. The alloy have single LaNi5 phase structure. The equilibrium data expressing the absorbed quantity of hydrogen per unit of absorbent mass gave interesting information to describe the absorption mechanism. Indeed, statistical physics formalism has been applied to ascribe new interpretations to the complexation process. The physicochemical parameters included in the analytical model are numerically deduced from the fitting of the relevant experimental isotherms such as the host sites densities (N1m and N2m), the numbers of atoms per site (n1 and n2) and the energetic parameters, (P1 and P2). The behavior of each parameter is examined in relationship with absorption temperature. The energetic interpretation reveals that the absorption of H-gas in LaNi4Co0.5Mn0.5 alloy is characterized by chemical interactions. The expression of the appropriate model is used to determine the thermodynamic potential functions which govern the absorption process such as entropy, internal energy, and Gibbs free enthalpy.
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