Multilayer adsorption equilibrium model for gas adsorption on solids

Adaptation of the ENSIC model to physisorption of nitrogen or argon on a solid surface first led to a 3 parameters model called multilayer adsorption equilibrium model (MAE model). One of these parameters is related to the formation of a multilayer of adsorbate on the solid surface. Exploitation of data from the literature pointed out that this parameter does not depend on the nature of the solid surface and an average value was calculated in the case of N₂ and Ar. As a consequence, the MAE model can be considered as a 2 parameters model. Linearization of the model was established allowing an easy determination of surface areas of macroporous and some mesoporous solids. Fitting of isotherms of meso and macroporous solids has led to promising results compared to the ones obtained with the BET model. Moreover, adaptation of this model to microporous solids can also be used for an uncomplicated determination of porous volume and external surface. Results obtained from data of the literature were close to those obtained with the t-plot model.     

Application of the vacancy solution theory to describe the enthalpic effects accompanying mixed-gas adsorption

The possibility of utilizing vacancy solution theory (VST) to study the enthalpic effects accompanying mixed-gas adsorption equilibria is presented. Besides heterogeneity, the interaction effects by using the regular adsorbed solution, Flory-Huggins, and Wilson models of nonideality in the adsorbed phase are taken into account. To predict adsorption phase diagrams and calorimetric effects in the mixed-gas adsorption system, only a knowledge of the single-gas adsorption isotherms and accompanying calorimetric effects is required. The possibility of simplification of the obtained theoretical expressions is shown. The obtained agreement between theory and experiment is very satisfactory.     

Gas hydrate equilibrium dissociation conditions in porous media using two thermodynamic approaches

We employ two thermodynamic approaches, based on the equal fugacities and the equal activities, to predict the gas hydrate equilibrium dissociation conditions in the porous media. The predictions are made for the hydrate systems, CH₄/H₂O, C₂H₆/H₂O, C₃H₈/H₂O, CO₂/H₂O, CH₄/CO₂/H₂O, C₃H₈/CH₄/C₂H₆/H₂O, and CH₄/CH₃OH/H₂O. For the non-hydrate phase, we used the Trebble–Bishnoi equation in the fugacity approach and the Soave–Redlich–Kwong equation in the activity approach. For the hydrate phase, the van der Waals–Platteeuw model incorporated with the capillary model of Llamedo et al. [M. Llamedo, R. Anderson, B. Tohidi, Am. Mineral. 89 (2004) 1264–1270] was used in the two approaches. The predictions are found to be in satisfactory to good agreement with the experimental data. The predictive ability of the fugacity approach is better than that of the activity approach.     

Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids

The thermodynamic treatment of adsorption phenomena is based on the Gibbs dividing surface, which is conceptually clear for a flat surface. On a flat surface, the primary extensive property is the area of the solid. As applications became more significant, necessitating microporous solids, early researchers such as McBain and Coolidge implemented the Gibbs definition by invoking a reference state for microporous solids. The mass of solid is used as a primary extensive property because surface area loses its physical meaning for microporous solids. A reference state is used to fix the hypothetical hyperdividing surface typically using helium as a probe molecule, resulting in the commonly used excess adsorption; experimentalists measure this reference state for each new sample. Molecular simulations, however, provide absolute adsorption. Theoreticians perform helium simulations to convert absolute to excess adsorption, mimicking experiments for comparison. This current structure of adsorption thermodynamics is rigorous (if the conditions for reference state helium measurements are completely disclosed) but laborious. In addition, many studies show that helium, or any other probe molecule for that matter, does adsorb, albeit to a small extent. We propose a novel thermodynamic framework, net adsorption, which completely circumvents the use of probe molecules to fix the reference state for each microporous sample. Using net adsorption, experimentalists calibrate their apparatus only once without any sample in the system. Theoreticians can directly calculate net adsorption; no additional simulations with a probe gas are necessary. Net adsorption also provides a direct indication of the density enhancement achieved (by using an adsorbent) over simple compression for gas (e.g., hydrogen) storage applications.     

A critique of a thermodynamic description of hydrophobic aggregation in aqueous solution

The conclusions recently summarised by A. Marmur [J. Am. Chem. Soc. 122 (2000) 2120] concerning hydrophobic aggregation of solutes in aqueous solution are examined. The thermodynamic analysis is critically reviewed and the impact of implicit extrathermodynamic assumptions discussed. These assumptions are questioned and shown to lead to a model for hydrophobic aggregation which is flawed.     

Modeling of gas adsorption equilibrium over a wide range of pressure: a thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV. The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R1 in the temperature range from 25 to 70 degrees C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems.     

Thermal vacancy effects on the thermodynamic properties and stability of fullerites

We study the influence of thermal vacancies on equilibrium thermodynamic properties of the high-temperature phase of fullerites taking into account the strong anharmonicity of the lattice vibrations. Treating a crystal with point defects as a quasi-multicomponent system and using the correlative method of the unsymmetrized self-consistent field and the Girifalco interaction potential for the molecular subsystem, we have obtained the vacancy formation parameters for the C(60) fullerite. We also take into account the divacancies. The influence of the lattice defects on the specific heats of fullerites is negligible, since a dominant contribution to them is given by intramolecular degrees of freedom. We have calculated the contributions of vacancies to various thermodynamic properties, the volume thermal expansion coefficient, the isothermal bulk modulus, and the components of the isothermal elastic tensor, depending on the temperature and pressure. Near the estimated triple point, these contributions run to more than 10% and increase still further at a metastable region. We also discuss the influence of defects on the thermodynamic stability of fullerites.     

Discussion of thermodynamic data obtained by adsorption gas chromatography on carbograph 6

Summary Carbograph 6, a new graphitized carbon black with a specific surface area of 203 m² g⁻¹, as measured by BET, both uncoated and coated with up to 12% (w/w) of squalane, a non-polar stationary phase, has been studied by gas chromatographic determination of the enthalpy, entropy, and free energy of adsorption of a series of alkanes (C₂−C₆) and benzene. The data obtained are discussed and compared with those available in the literature for other graphitized carbon blacks. An example of a separation obtaned with Carbograph 6 is reported.     

Kinetic, equilibrium and thermodynamic studies of cadmium (II) adsorption by modified agricultural wastes

Agricultural wastes have great potential for the removal of heavy metal ions from aqueous solution. The contamination of water by toxic heavy metals is a worldwide environmental problem. Unlike organic pollutants, the majority of which are susceptible to biological degradation, heavy metals do not degrade into harmless end products. Discharges containing cadmium, in particular, are strictly controlled because of the highly toxic nature of this element and its tendency to accumulate in the tissues of living organisms. This work aims to develop inexpensive, highly available, effective metal ion adsorbents from natural wastes as alternatives to existing commercial adsorbents. In particular, Tamrix articulata wastes were modified chemically by esterification with maleic acid to yield a carboxyl-rich adsorbent. The adsorption behavior of treated Tamrix articulata wastes toward cadmium ions in aqueous solutions in a batch system has been studied as a function of equilibration time, adsorbent dose, temperature and pH. Results showed that the maximum adsorption capacity was 195.5 mg/g in a pH 4 solution at 30 °C with a contact time of 120 min, an initial concentration of 400 mg/L and an adsorbent dose of 0.3 g/L. The kinetic data were analyzed using pseudo-first-order and pseudo-second-order kinetic models. It was shown that the adsorption of cadmium could be described by a pseudo-second-order equation. The experimental data were also analyzed using the Langmuir and Freundlich models of adsorption. Thermodynamic parameters such as ΔG°, ΔH° and ΔS° have been evaluated and it has been found that the sorption process was spontaneous and exothermic in nature. From all of our data, we conclude that the treated Tamrix articulata wastes investigated in this study showed good potential for cadmium removal from aqueous solutions.     

Kinetics and thermodynamic study of aniline adsorption by multi-walled carbon nanotubes from aqueous solution

Multi-walled carbon nanotubes (MWCNTs) were used in the adsorptive removal of aniline, an organic pollutant, from an aqueous solution. It was found that carbon nanotubes with a higher specific surface area adsorbed and removed more aniline from an aqueous solution. The adsorption was dependent on factors, such as MWCNTs dosage, contact time, aniline concentration, solution pH and temperature. The adsorption study was analyzed kinetically, and the results revealed that the adsorption followed pseudo-second order kinetics with good correlation coefficients. In addition, it was found that the adsorption of aniline occurred in two consecutive steps, including the slow intra-particle diffusion of aniline molecules through the nanotubes. Various thermodynamic parameters, including the Gibbs free energy change (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°), were calculated. The results indicated that the spontaneity of the adsorption, exothermic nature of the adsorption and the decrease in the randomness reported as ΔG°, ΔH° and ΔS°, respectively, were all negative.     

Effective adsorption of U(VI) from aqueous solution using magnetic chitosan nanoparticles grafted with maleic anhydride: equilibrium,kinetic and thermodynamic studies

The in situ formed magnetite nanoparticles was encapsulated by maleated chitosan to synthesize a novel magnetic chitosan nano-sorbent (MCN-MA) for the effective sorption of uranium. The sorption kinetics could be described by the pseudo-second-order model, whereas the sorption isotherms could be fitted to the Langmuir model (q _m = 187.9 mg/g). The MCN-MA showed higher U(VI) sorption capacities (compared to MCN) due to high affinity of carboxylate groups introduced from grafting maleic anhydride. Thermodynamic parameters indicate that U(VI) sorption is endothermic and feasible. The nano-size and magnetic property of the MCN-MA allow its efficient U(VI) sorption and facile magnetic separation from wastewaters.     

Investigation of equilibrium, kinetic, thermodynamic and mechanism of Basic Blue 16 adsorption by montmorillonitic clay

The adsorption of a cationic dye, Basic Blue 16 (BB16), by montmorillonitic clay was studied in detail. Changes in the molecular structure during adsorption were analyzed by FTIR spectroscopy. BB16 adsorption onto the clay mainly results from hydrogen bonding between OH and NH₂ groups of dye molecules and OH groups of clay and electrostatic interaction between the negatively charged clay surface and cationic dye. The montmorillonitic clay dose had an inverse effect on the adsorption performance, while the highest dye removal was 305 mg/g at pH 3.6. An increase in temperature and dye concentration positively enhanced the adsorption capacity of the montmorillonitic clay. Temperature had no effect on the adsorption at a dye concentration less than 500 mg/L, while dye adsorption was positively enhanced at elevated dye concentrations. Three-parameter equations provided higher better fitting than two-parameter equations while the Freundlich model had the highest correlation coefficient and the lowest error values with experimental data. The BB16 adsorption was well followed by pseudo-second order model and the rate of adsorption process was controlled by surface and intraparticle diffusion. Thermodynamic evaluations revealed that the adsorption process was spontaneous and endothermic, while the randomness increased during adsorption. Experimental results indicate that montmorillonitic clay from Eskisehir is a promising adsorbent for the removal of cationic dye molecules from aqueous solutions.     

Beta-casein bilayer adsorption at the solution/air interface: experimental evidences and theoretical description

Ellipsometric and surface pressure studies of beta-casein adsorption layers at the water/air interface support the idea of a model that assumes the formation of a second layer adjacent to the primary adsorption layer. A thermodynamic model describes the concentration behavior of the surface pressure and the adsorbed amount with one and the same set of model parameters over the entire concentration range studied.     

Axial-base equilibrium and thermodynamic studies of ribosylcobalamins

Thermodynamic and equilibria properties of two vitamin B12 coenzyme analogues, i.e. 1-methyl-5-deoxy--d-(–)ribofuranosylcobalamin (RibCbl) and 1-methyl-5-deoxy-2,3-isopropylidene--d-(–)ribofuranosylcobal- amin (Rib*Cbl) were studied by u.v.-vis. spectroscopy. Their temperature-dependent equilibria between 6-coordinate base-on species and 5-coordinate unprotonated base-off species, and pH-dependent equilibria for the protonation and displacement of 5,6-dimethylbenzimidazole at 25°C have been examined. Values of H and S in neutral solution and at pH 4.00, and the axial base pKa were determined. Comparing the results with those for coenzyme B12 and other cobalamins, it has been found that H and S values for two ribosylcobalamins fall in the range of organocobalamins, but for RibCbl*, a ca. 1 unit difference in pKa values exists. The effect of the ribofuranose structure on the Co-N(dbzm) strength is considered.