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Two equilibrium models based on statistical physics, i.e., monolayer model with single energy and multilayer model with saturation , were developed and employed to access the steric and energetic aspects in the adsorption of reactive violet 5 dye (RV-5) on cocoa shell activated carbon (AC) and commercial activated carbon (CAC), at different temperatures (from 298 to 323 K). The results showed that the multilayer model with saturation was able to represent the adsorption system. This model assumes that the adsorption occurs by a formation of certain number of layers. The n values ranged from 1.10 to 2.98, indicating that the adsorbate molecules interacted in an inclined position on the adsorbent surface and aggregate in solution. The study of the total number of the formed layers (1 + L 2 ) showed that the steric hindrance is the dominant factor. The description of the adsorbate–adsorbent interactions by calculation of the adsorption energy indicated that the process occurred by physisorption in nature, since the values were lower than 40 kJ mol −1 . [ABSTRACT FROM AUTHOR]

In this paper, the adsorption isotherms of the carbon dioxide onto highly porous activated carbon have been fitted by advanced statistical physics models to give reasonable interpretations of this process. Fitted physico-chemical parameters values have been deducted by means of the best fitting model. To describe the adsorption process, the fitting results showed that the CO 2 molecules formed only one layer on the modified activated carbon. These molecules have been mainly docked with a parallel position on adsorbent receptor sites with adsorption energies varying from 7.16 kJ/mol to 8.24 kJ/mol. These values reflected a physisorption process. The calculated internal energy values suggested the spontaneity and the exothermicity of the CO 2 adsorption process onto the modified activated carbon (MAC). As application, the enthalpy function is utilized and calculated to perform the thermodynamic evaluation of an adsorption cycle for a CO 2 adsorption cooling system and to calculate the coefficient of performance (COP) as a function of regeneration temperature. This parameter was found to be in the interval [0.09–0.19] corresponding to regeneration temperature varying from 303 K to 343 K. ga1 • Fitted physico-chemical parameters values have been interpreted. • The internal energy values are calculated. • The enthalpy function is calculated to perform the CO 2 adsorption cycle thermodynamics. • The coefficient of performance COP is calculated by statistical physic treatment. [ABSTRACT FROM AUTHOR]

Based on statistical physics elements, the equilibrium adsorption of diclofenac (DFC) and nimesulide (NM) on activated carbon was analyzed by a multilayer model with saturation. The paper aimed to describe experimentally and theoretically the adsorption process and study the effect of adsorbate size using the model parameters. From numerical simulation, the number of molecules per site showed that the adsorbate molecules (DFC and NM) were mostly anchored in both sides of the pore walls. The receptor sites density increase suggested that additional sites appeared during the process, to participate in DFC and NM adsorption. The description of the adsorption energy behavior indicated that the process was physisorption. Finally, by a model parameters correlation, the size effect of the adsorbate was deduced indicating that the molecule dimension has a negligible effect on the DFC and NM adsorption. [ABSTRACT FROM AUTHOR]

A modeling study has been effectuated on the adsorption kinetics of ethanol onto parent Maxsorb III and the two chemically modified activated carbons (H 2 –Maxsorb III and KOH–H 2 –Maxsorb III). In this work, a mathematical model of diffusion-adsorption is used to describe a nonlinear sorption equilibrium coupled with the diffusion of adsorbate in porous media. The new model equation is deduced from kinetic Boltzmann equation by using a term of diffusion and a term of trapping or adsorption of ethanol at the surface of activated carbon. The term of trapping is expressed by means of Henry model of adsorption, which is in turn deduced from the Hill model developed by using statistics physics treatment. In this study, we propose a new simulation model of a gas kinetic adsorption in a microporous solid in order to find a better correlation with the experimental data. Then, we determine the effect of diffusion term and source term or more exactly trapping term, which is depending on the physicochemical parameters like the number n of molecules per site, the density of receptor sites N m per unit mass, the half-saturation concentration N 1/2 , and the residence time τ ν on the dynamic development of ethanol adsorption on the three types of activated carbon. [ABSTRACT FROM AUTHOR]

In this work, the performances of a commercial activated carbon (Filtrasorb 400, provided by Calgon) were experimentally tested for the adsorption of different aromatic compounds, i.e., toluene and benzene from synthetic groundwater. Batch adsorption tests were carried out at constant pH (8) and four different temperatures (10–50 °C). The experimental equilibrium adsorption data were fitted with a new statistical physics model named as ‘multilayer model with saturation’ and established through the grand canonical ensemble in statistical physics. The characteristic model parameters of the adsorption isotherm such as the number of benzene or toluene molecule(s) per site, n, the receptor site densities, N M , the number of adsorbed layers (N L ) and the energetic parameter, (-ε 1 ) and (-ε 2 ), were estimated for the studied systems by a non-linear least square regression. These parameters were discussed and interpreted for their temperature dependence. The calculated thermodynamic parameters such as entropy, Gibbs free energy and internal energy from experimental data showed that the adsorption of benzene and toluene onto activated carbon Filtrasorb 400 was feasible, spontaneous and exothermic in nature. [ABSTRACT FROM AUTHOR]

• Modeling of the Resorcinol adsorption isotherms on activated carbon by the double layer model with two energies. • Steric and energetic interpretations of Resorcinol adsorption process were provided. • AED and PSD were computed with our statistical physics model. The adsorption isotherms of Resorcinol (RES) on activated carbon from avocado seeds (ASAC) at different temperatures were interpreted using a double layer model with two energies. The formulation of this model was established by a statistical physics treatment. Steric and energetic parameters related to the adsorption process have been considered. In addition, PSD and AED are determined from the expression of the adsorbed quantity Q. According to our detailed study the double layer model with two energies is the best fitting model. The estimated values of the adsorption energies indicated that the Resorcinol is physiosorbed. The theoretical expressions provide a good understanding and interpretation of the adsorption isotherms at the microscopic level. ASAC is macroporous since the size of the activated pores is between 60 nm and 80 nm. Moreover, we underline the fact that an increase in temperature implies a considerable increase in AED and a slight translation towards the lowest energies. Our results indicated that for working at high temperature represents the best efficiency of wastewater depollution. This work contributed to new theoretical insights on the resorcinol adsorption. [ABSTRACT FROM AUTHOR]

New statistical physicochemical interpretations of an adsorption process at molecular level were developed to explain the binary adsorption isotherms of lead and zinc ions on activated carbon derived from Styrax officinalis seeds (Balikesir, Turkey) and a commercial activated carbon at different temperatures, 298, 308 and 318 K. The extended Hill model was developed to explain heterogeneous model in terms of the grand canonical ensemble in statistical physics. Steric and energetic parameters, like the numbers of ions per site n 1 and n 2 , the densities of receptor sites N M1 and N M2 and the adsorption energies (− ε 1 ) and (− ε 2 ) were directly obtained from the fitting of the experimental adsorption isotherms by numerical simulation to describe the process. The simulation results suggested that two adsorbates per site were anchored on activated carbon surface. The magnitudes of the calculated adsorption energies indicated that Zn 2 + and Pb 2 + were physically adsorbed by the activated carbon. Thermodynamic potential functions, namely entropy, enthalpy and internal energy were calculated to explain the order and disorder of the adsorbate at the adsorbent surface during the binary adsorption process. The values of the free enthalpy and the internal energy indicated spontaneous adsorption process. [ABSTRACT FROM AUTHOR]

The adsorption isotherms network at three temperatures of ibuprofen on a raw activated carbon and two chemically modified samples of the same carbon were simulated using models established through statistical physics formalism. Among the different tested models, a multilayer model with saturation was found to be the best to reproduce the experimental data. In this model, five parameters affecting the adsorption process were adjusted, namely the number of molecules per site, the density of receptor sites, the two energetic parameters and the number of layers. These parameters deduced from the fitting of the experimental adsorption isotherms by numerical simulation were discussed and interpreted for their temperature dependence. [ABSTRACT FROM AUTHOR]

• Activated carbons and MOF-based composite are prepared to study the adsorption of methylene blue. • Adsorption isotherms of the dye were carried out at different temperatures. • Advanced and classical models are applied to explain the adsorption mechanism. • Dye adsorption with activated carbons was endothermic, while exothermic with the MOF. Activated carbons and MOF-based composite were prepared from the ashitaba biomass and they were applied and compared in the adsorption of methylene blue from aqueous solution. Surface chemistry of these adsorbents was characterized with different analytical techniques and results were used to analyze the corresponding adsorption interactions. Statistical physics calculations were performed to interpret the physicochemical parameters involved in the dye adsorption mechanism. Results showed that the dye adsorption with activated carbons was endothermic, while an exothermic dye removal was observed with the MOF-activated carbon composite. Dye adsorption mechanism was a multimolecular process mainly for ashitaba-based activated carbons where electrostatic interactions, van der Waals forces and hydrogen bonding were present. In particular, the activated carbon functionalized with a surfactant outperformed other adsorbents prepared with the ashitaba biomass thus showing adsorption capacities higher than 400 mg/g. This adsorbent is promising for its application in the treatment of wastewaters polluted by this and other dye molecules. [ABSTRACT FROM AUTHOR]

Abstract: The adsorption energy distribution (AED) function of a commercial activated carbon (BDH-activated carbon) was investigated. For this purpose, the integral equation is derived by using a purely analytical statistical physics treatment. The description of the heterogeneity of the adsorbent is significantly clarified by defining the parameter . This parameter represents the energetic density of the spatial density of the effectively occupied sites. To solve the integral equation, a numerical method was used based on an adequate algorithm. The Langmuir model was adopted as a local adsorption isotherm. This model is developed by using the grand canonical ensemble, which allows defining the physico-chemical parameters involved in the adsorption process. The AED function is estimated by a normal Gaussian function. This method is applied to the adsorption isotherms of nitrogen, methane and ethane at different temperatures. The development of the AED using a statistical physics treatment provides an explanation of the gas molecules behaviour during the adsorption process and gives new physical interpretations at microscopic levels. [Copyright &y& Elsevier]

• Single and binary adsorption of antibiotics on activated carbon was investigated. • Statistical physics modeling of antibiotics adsorption was performed. • Monolayer and competitive monolayer models explained the adsorption mechanism. • Antibiotic antagonistic adsorption was associated to statistical physics parameters. The adsorption mechanism of two antibiotics, namely amoxicillin (AMX) and tetracycline (TCN), on durian shell activated carbon (AC) was investigated in single and binary systems. Adsorption isotherms were determined under the same experimental conditions and they showed that the adsorption capacities of AMX were higher than those of TCN at all tested temperatures suggesting that this adsorbent preferred to remove AMX from the aqueous solution. It was also observed that all adsorption capacities decreased from single to binary systems, which was reasonably explained by an antagonistic adsorption between AMX and TCN on the active sites of AC creating an inhibition effect between these adsorbates. Monolayer and competitive monolayer models were developed via statistical physics theory and they were applied to explain and understand the adsorption mechanism of AMX and TCN via steric and energetic parameters. Results suggested that the parallel and non-parallel orientations of both antibiotics on the adsorbent surface of AC could be possible at tested experimental conditions. Modeling results demonstrated that the numbers of accepted antibiotic molecules per active site of AC varied with linear and inverse trends in single and binary systems, respectively, at all tested temperatures thus corroborating the adsorption inhibition effect caused by both adsorbates. An estimation of adsorption energies was also performed to describe and characterize the interactions between both antibiotics and AC surface. The assessment of the parameters of statistical physics models contributed to the explanation of the single and binary adsorption mechanisms of these water pollutants. [ABSTRACT FROM AUTHOR]