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Experimental adsorption isotherms of hydrogen in CNT samples (CNT-A, activated CNT-A CNT-B and activated CNT-B) at T = 77, 87 and 90 K have been fitted using some theoretical model expressions treated by statistical physics through the grand canonical ensemble. The monolayer model with single energy is selected to fit and interpret the experimental data obtained with CNTs. The physico-chemical parameters, interfering in the adsorption process and implicated in the model expressions, could be directly determined from the experimental data through numerical simulation. Three parameters of the model are fitted, namely the number of hydrogen molecule per site n, the interstitial site density Nm and the energetic parameter P1/2. The evolution of these parameters as function of temperature is plotted and interpreted in relation to adsorption process. Finally, the thermo-dynamic potential functions, which involve in the adsorption mechanism like free enthalpy of Gibbs Ga, internal energy Eint and entropy Sa, are derived by statistical physics calculations from the selected model. [ABSTRACT FROM AUTHOR]

Abstract 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 N m and the energetic parameter P 1/2 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 E int , free enthalpy of Gibbs G a and entropy S a are derived by statistical physics derivation from the adopted model. Graphical abstract Image 108 Highlights • 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. [ABSTRACT FROM AUTHOR]

In this paper, three adsorption isotherms of natural yellow Gardenia dye, at three different temperatures and at three pH values, were fitted by models established through statistical physics treatment. A double-layer model with two energies is able to give good fitting of these experimental data. Four physicochemical parameters are involved in the fitting of the experimental adsorption isotherms such as the number of adsorbed dye molecules per site n, the density of receptor sites Nm and the two energetic parameters C 1 and C 2 . From the numerical simulation, the number of molecules per site showed that the adsorbate molecules have two anchorage positions parallel and nonparallel respectively when pH and temperature vary. The variation of the adsorbed quantity at saturation with temperature shows the exothermic nature of aggregation process of the natural Gardenia yellow dye. In the case of variation of pH, the acidic conditions are more favorable for the adsorption process. The numerical values of the calculated adsorption energies have revealed that the Gardenia yellow dye is physisorbed onto TiO 2 mesoporous. A new method based on Kelvin equation in liquid phase has been developed to determine the pore size distribution (PSD) of TiO 2 mesoporous in comparison with other experimental measurements. The result of PSD shows a significant effect of the variation with temperature and with pH values on the morphology of pore size structure. Finally, the calculated thermodynamic functions such as entropy, free enthalpy and internal energy exhibited that the system evolved spontaneously. [ABSTRACT FROM AUTHOR]

The increased use of antibiotics worldwide turned into a serious preoccupation due to their environmental and health impacts. Since the majority of antibiotic residuals are hardly eliminated from wastewater, based on usual methods, other treatments receive considerable attention. Adsorption is known as the most effective method of the treatment of antibiotics. In this paper, the adsorption isotherms of doripenem, ampicillin, and amoxicillin on bentonite-chitosan composite are determined at three temperatures, T = 303.15, 313.15 and 323.15 K, which are used to achieve a theoretical investigation of the removal phenomenon, based on a statistical physics theory. Three analytical models are utilized to describe the AMO, AMP, and DOR adsorption phenomena at the molecular level. From the fitting results, all antibiotic adsorption on a BC adsorbent is associated with the monolayer formation with one type of site. Concerning the number of adsorbed molecules per site (n), it is concluded that multi-docking (n < 1) and multi-molecular (n > 1) phenomena are feasible for AMO, AMP, and DOR adsorption on BC. The adsorption amounts at saturation of the BC adsorbent, deduced by the monolayer model, are found to be 70.4–88.0 mg/g for doripenem, 57.8–79.2 mg/g for ampicillin and 38.6–67.5 mg/g for amoxicillin indicating that the antibiotics adsorption performance of BC was greatly depended on temperature where the adsorption capacities increased with the increment of this operating variable. All adsorption systems are demonstrated by a calculation of the energy of adsorption, considering that the extrication of these pollutants implies physical interactions. The thermodynamic interpretation confirms the spontaneous and feasible nature of the adsorption of the three antibiotics on BC adsorbent. In brief, BC sample is regarded as a promising adsorbent to extract antibiotics from water and presents important potentials to be effected in wastewater handling at industrial level. [ABSTRACT FROM AUTHOR]

• Xenon adsorption isotherms on chabazite were fitted by using the integral equation. • The integral expression of local equation is based on statistical physics formalism. • Significant physico-chemical parameters were determined. • The adsorption energy and pore size distributions were derived. • The adsorption chemical potential was calculated at different pressure values. In order to investigate the toxic Xenon removal by an adsorption process on chabazite, the grand canonical formalism of statistical physics has been used. This conducted statistical physics treatment enabled us to draw information about the interactions between Xenon atoms and chabazite surface through the determined physico-chemical parameters. The adsorption energy and pore size distributions have been derived by using an integral expression based on a monolayer model as local isotherm. The fitted values of the steric coefficient showed that one chabazite active site can trap only one Xenon atom. The evaluated densities of receptor sites played an important role in the assess of the adsorption capacity. Ca−CHA sample showed the maximum adsorption capacity (2.36 mmol.g−1). By using the adsorption energy distributions (G D), the physisorbed character of the Xenon adsorption on chabazite samples was brought out. The diversification of the active sites is noticed for all chabazite samples. The highest adsorption energies are observed in the case of the Xenon adsorption on CA−CHA sample. Furthermore, by using the pore size distribution (PSD), the microporous character of all samples (Ca−CHA, Cs−CHA, Li−CHA, K−CHA and Rb−CHA) has been showed. The maximum surface area was found to be 187.23 m2. g−1 for Ca−CHA. The calculated surface tensions are in the range [10.07E-5 N.m−1-13.46E-5 N.m−1. Finally, by combining the thermodynamical and statistical physics treatments, the chemical potential describing the Xenon adsorption, is calculated at different pressures. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we have realized three adsorption isotherms of the ruthenium-based dye molecules, cisdi (thiocyanato)bis (2,2′bipyridyl-4,4′-dicarboxylate)ruthenium (II) (N3) into the mesoporous TiO 2 (anatase) at three different temperatures:298.15, 313.15 K and 333.15 K using the UV–vis spectroscopy method. These adsorption isotherms have been simulated using several models established through a statistical physics formalism in order to involve in model expressions some parameters which have physicochemical meaning and to better interpret information about the adsorption process at the molecular level. A multilayer model was determined to best reproduce and simulate the experimental data. In this model, five parameters affecting the adsorption process have been adjusted, namely the number of molecules per adsorption site n, the density of receptor sites N m , the two energetic parameters: the concentrations at half saturation C 1 and C 2 and the number of layers N L. These parameters have been deduced from the fitting of the experimental adsorption isotherms by numerical simulation. Thanks to the grand canonical ensemble in statistical physics, the energetic parameters suggest physical bonding of the N3 dye to the TiO 2 surface in the case of low concentrations through monodentate and bidentate with hydrogen bond configurations. Finally, a new method based on Kelvin equation in the liquid phase is used to determine the pore size distribution (PSD) and the adsorption energy distribution (AED) of the mesoporous TiO 2. Graphical abstract Image 1 Highlights • A statistical physics model has been developed for the considered N3 adsorption. • Three adsorption isotherms of N3 dye on TiO 2 were fitted and interpreted. • Using the energetic parameters to calculate the adsorptions energies. • New method based on Kelvin equation is used to determine the (PSD) and the (AED). [ABSTRACT FROM AUTHOR]

This work represents a contribution to understanding the taste or gustatory mechanism of sucrose by using a proposed model expression established by a statistical physics treatment. Gustative and physicochemical parts are used as constituents in this work. We start with a modeling of experimental adsorption isotherms of sucrose molecules onto β-cyclodextrin followed by a similar modeling of sweet taste dose-response curves of sucrose by a putative adsorption process of sucrose molecules onto nerve receptor sites. Numerical values of the three involved parameters in the expression of the best fitting model are derived by adjustment, namely the number of adsorbed molecules per site n, the adsorption capacity Q M and the energetic coefficient C 1/2. Steric and energetic interpretations are given. The internal energy, adsorption entropy, and Gibbs free enthalpy are studied. The pore size distribution (PSD) and the adsorption energy distribution (AED) of β-cyclodextrin and of host cavities in gerbil nerve. In the second part the same method of fitting is applied to the biological sweet taste dose-response curves of the same molecule (sucrose) on taste receptor cells in gerbil nerve (electro-physiological) and in human (psychophysical). All this information and physicochemical parameters are introduced in the model expression to fit the putative adsorption of sucrose molecule. And, all these stereographic and energetic parameters will be considered henceforward to objectively characterize the sucrose molecule sweet taste. Furthermore, all these parameters determined in the two parts are compared with other sucrose adsorption results established by other authors. • Modeling of adsorption process isotherms of sucrose on β-cyclodextrin • A putative adsorption used for of fit dose-taste response of sucrose on gerbil • Quantitative characterization of sucrose taste with fitting parameters values • Comparison of parameters of sucrose from β-CD adsorption and gerbil nerve response [ABSTRACT FROM AUTHOR]