Free Energy Of Sorption Research Articles

Determination of Thermodynamic Interactions of the Pvc-Pmma Blend System by Inverse gas Chromatography

In this study, the sorption enthalpy (δHS1), sorption free energy (δG1), sorption entropy (δS1), enthalpy, and free energy at infinite dilution (δH1 and δG1) values were calculated for selected probes such as alcohols, ketones, acetates, cyclic ethers, aromatics, and alkanes in the temperature range 403-433 K for poly(methyl methacrylate) (PMMA), poly(vinyl chloride) (PVC) homopolymers, and the PVC-PMMA blend system. The values of the Flory-Huggins interaction parameters χ1(23) have been calculated in this temperature range and show the importance of specific interactions between the polymers and the solvents. The values of the polymer-polymer interaction parameters χ23(for the temperature range 403–433 K) were found to change from +3.57 to +1.16 for alcohols, from +2.99 to +0.52 for ketones, from + 1.60 to −0.48 for acetates, from +0.96 to −1.46 for cyclic ethers, from +2.66 to +0.12 for aromatics, and from +8.73 to +1.06 for alkanes.

Determination of Thermodynamic Properties of Poly(4-tert-Butylstyrene) by Inverse Gas Chromatography

Abstract Some thermodynamic quantities were obtained for the interactions of poly (4-tert-butylstyrene) with alcohols, ketones, acetates, aromatics and alkanes by the inverse gas chromatography method in the temperature range of 343-463 K. The specific retention volumes (Vg°), the adsorption enthalpy of probes (ΔH2), the partial molar free energy of sorption (ΔG1 S), the enthalpy of sorption (ΔH1 S), the entropy of sorption (ΔS1 S), the weight fraction activity coefficients of solute probes at infinite dilution (Ω1 ∞), and the Flory- Huggins thermodynamic interaction parameters (χ∞ 12) between polymer and solvents are given. The partial molar free energy (ΔG1 ∞, the partial molar heat of mixing (ΔH1 ∞ at infinite dilution and the solubility parameters of the polymer (δ2) were calculated. The solubility parameter of poly (4-tert-butyl- styrene) was determined from either the slope or intercept as 7.25 (cal/cm3)0,5 and 7.00 (cal/cm3)0,5 at 180°C, respectively.

Thermodynamics of Cationic Surfactant Sorption onto Natural Clinoptilolite

Sorption enthalpies of hexadecyltrimethylammonium bromide (HDTMA) as monomers and micelles and tetraethylammonium bromide (TEA) were used with surfactant, counterion, and co-ion sorption isotherms to infer the conformation, sorption mechanism, and relative stability of the sorbed surfactants on natural clinoptilolite. The average value of the sorption enthalpy was −10.38 kJ/mol for monomers, −11.98 kJ/mol for micelles, and +3.03 kJ/mol for TEA. Sorption of monomers produced a lower sorption plateau than equivalent micelle sorption (maxima 145 mmol/kg, 225 mmol/kg). Analysis of the sorption data demonstrated a change in the sorption mechanism at the external cation exchange capacity (ECEC) of clinoptilolite. Sorption data from below and above the ECEC were fit to a simple polynomial model and the Gibbs free energy of sorption (ΔG0m) and sorption entropies were calculated. Resultant values of ΔG0mwere −9.27 and −14.38 kJ/mol for HDTMA monomers and micelles, respectively, for sorption below the ECEC, and −16.11 and −23.10 kJ/mol, respectively, for sorption above the ECEC. The value for TEA was −1.04 kJ/mol, indicating weaker sorption than for HDTMA. Monomer sorption to clinoptilolite exceeded the ECEC, even when the solution concentration was below the critical micelle concentration. Hydrophobic (tail–tail) components of ΔG0mwere the driving force for sorption of HDTMA, both below and above the ECEC. A significant kinetic effect was observed in the sorption isotherms with a period of rapid sorption followed by slow equilibration requiring 7 days to achieve steady state for HDTMA; TEA equilibration occurred within 24 h.

Isosteric study of sorption thermodynamics of single gases and multi-component mixtures on microporous materials

Abstract The isosteric sorption technique with minimum dead volume is a useful and effective tool to obtain highly accurate sorption thermodynamic data for microporous sorption systems, i.e. enthalpy, entropy and Gibbs free energy of sorption, as functions of sorption phase concentration up to its saturation value. The latter parameter is available without presupposing a sorption isotherm model. The present study shows by relevant examples, i.e. sorption of carbon dioxide and nitrogen–oxygen mixtures into faujasite-type zeolites and a micro-(meso)-porous carbonaceous sorbent, that from isosteric measurements those thermodynamic data as functions of sorbate concentration were obtained with high accuracy, and isotherms were calculated therefrom over any physically meaningful regions of temperature and pressure. The energetic heterogeneity of sorbents due to specific interactions between molecules of carbon dioxide and zeolitic cations is quantified by characteristic concentration dependences of the thermodynamic functions. The isosteric method can be utilized for measurement of sorption equilibria/thermodynamics of multi-component gas mixtures.

Relevance of Elastic Energies during Sorption of CO2 Molecules in Glassy Polymers Demonstrated for Two Very Similar Polyimides

Data on CO2-sorption in and corresponding volume changes of three polyimides are evaluated in the framework of a recent model where elastic distortion of glassy polymers during dissolution of small molecules is taken into account. Due to the chemical identity and structural similarity of the polymers, differences in the behavior of CO2 can be attributed solely to differences in the distribution of the intermolecular space (holes). Thus the polyimide with the lowest volume change has the smallest elastic energy and, therefore, the largest solubility of CO2. The evaluation yields values of the average free energy of sorption and the width and average volume of the distribution of holes.

Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO2 in Kapton and various substituted polycarbonates and for H2O, Ar, N2, CH4, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998

Sorption of n-pentane, 2-methylbutane and cyclopentane in microporous AlPO 4-5

Sorption isotherms for n-pentane, 2-methylbutane and cyclopentane in the aluminophosphate molecular sieve AlPO 4-5 are reported at 303, 313, 323 and 333 K. The sorption data were fitted into Langmuir, Sips and Dubinin–Radushkevich isotherms. The heats of sorption at zero coverage determined from the data in the Henry region are in the order 2-methylbutane>cyclopentane>n-pentane. Free energy and entropy changes and heats of sorption for these sorbates at various sorption coverages were also determined from the sorption data. The heat of sorption for n-pentane varies only marginally with sorption coverage. However, the heats of sorption for 2-methylbutane and cyclopentane increase significantly with the coverage indicating an increase in sorbate–sorbate interactions. The dependence of thermodynamic properties like the free energy of sorption (Δ G) and the entropy change (Δ S) for 2-methylbutane and cyclopentane on coverage show a sharp decrease and increase at sorption coverages 0.1–0.2 mmol g −1 suggesting the rearrangement of molecular packing in the sorbed phase. These observations have been explained in terms of molecular interactions between the AlPO 4-5 channels and sorbate molecules.

Sorption of selenium at micromolar levels onto hydrous titanium oxide from aqueous solutions using radiotracer technique

Titanium oxide (TiO 2·2H 2O) has been prepared and characterized by surface area, pore size and porosity measurements, thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC). The sorption of selenium(IV) at micromolar levels (7 × 10 −8 − 7.09 × 10 −6 M) onto titanium oxide has been studied in detail. The sorption is dependent upon the nature and concentration of electrolyte, sorbent and sorbate and on the equilibration time between the two. Maximum sorption of selenium is achieved from 0.01 M nitric acid solution at a w/v ratio of 22.2 mg cm 3 at 1.77 × 10 −8 M selenium concentration. Only thiosulphate ions inhibit the sorption significantly whereas acetate, citrate, oidide, sodium and zinc ions cause relative enhancement in the sorption. Ag(I), Mn(II) and Co(II) have shown low sorption under optimal conditions chosen for selenium sorption. Titanium oxide can be used for the preconcentration of selenium and other elements having large R d values and their separation from Ag(I), Mn(II), and Co(II). Sorption capacity (86.7 ± 7.3 mmol g −1), sorption free energy (9.41 ± 0.67 kJ mol −1) and B(− 0.00564 ± 0.00082 mol 2 kJ −2) are evaluated for this system using linear regression analysis and D-R parameters.

Temperature changes of sorption parameters of di-n-alkylketones and methylcyclohexanones in capillary gas chromatography

The gas chromatographic behavior of di-n-alkylketones and isomeric methylcyclohexanones at variable temperatures in the isothermal runs has been studied using three capillary columns coated with SE-30, OV-225, and PEG-40M/KF stationary phases. The retention indices and their temperature increments were determined, and the partial molar free energies of the compounds under study were calculated. A linear dependence of the values of the partial molar free energy of sorption on the homologue number in di-n-alkylketones is not observed for the first member on the nonpolar SE-30 phase and for the third member on the polar OV-225 and PEG-40M/KF phases.

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.

Sorption of cobalt on bentonite

Sorption of Co on bentonite has been studied by using a batch technique. Distribution coefficients (Kd) were determined for the bentonite-cobalt solution system as a function of contact time, pH, sorbent and sorbate concentration and temperature. Sorption data have been interpreted in terms of Freundlich, Langmuir and Dubinin-Radushkevich equations. Thermodynamic parameters for the sorption system have been determined at three different temperatures. The positive value of the heat of sorption, AH 0 = = 22.08 kJ/mol at 298 K shows that the sorption of cobalt on bentonite is endothermic, where as the negative value of the free energy of sorption, AG O = -10.75 kJ/mol at 298 K shows the spontaneity of the process. AG O becomes more negative with an increase in temperature which shows that the sorption process is more favourable at higher temperatures. The mean free energy E ~ 7.7 kJ/mol for sorption of cobalt on bentonite shows that ion-exchange is the predominant mode of sorption in the concentration 3 range of the metal studied i.e. 0.01 to 0.3 tool/din . The presence of some complementary cations depress the sorption of cobalt on bentonite in the orderof K + > Ca 2+ > Mg 2+ > Na +. Some organic complexing agents and natural ligands also affect the sorption of cobalt. The deso~tion studies with ground water at low cobalt loadings on bentonite show that about 97% metal is irreversibly sorbed. Cobalt-60 (5.26 y) is formed in a nuclear fission process during the operation of a nuclear power reactor by activation of S9Co present as an impurity in the metal from which the structural parts of the fuel assemblies are made. The decay energies of 6~ are E~ = 0.32, Er= 1.173 and 1.333 MeV. Because of higher energies of T-radiation and long-half life, large quantities of cobalt-60 are used as T-ray sources for various applications in research, industry and medicine. Therefore, cobalt is an important element from the fuel processing and waste disposal point of view. Cheap natural clays may be useful as barrier materials to surround radioactive waste repository because of their ion-exchange and low permeability properties. The sorption behaviour of cobalt from aqueous solutions on a variety of materials including clay minerals is therefore been a subject of interest. The sorption behaviour of cobalt on clay minerals and soils has been investigated by TILLER et al.,1 HODGSON,2 CHESTER,3 ROUTSON et al.4 and AL-SUHYBANI. 5 Fixation and mobility was studied by MAHARA and KUDO 6 and migration by

Unexpected diffusion behavior of gas molecules in crystalline poly(4-methyl-1-pentene)

We have studied the behavior of carbon dioxide and methane in crystalline poly(4-methyl-1-pentene) (PMP) by means of molecular simulation. Gas diffusion coefficients in the direction of the crystal axes have been determined by equilibrium and nonequilibrium molecular dynamics techniques. We find that both gases diffuse along the channels of free volume between the PMP helices as well as perpendicular to these channels. The diffusion of CH4 is more isotropic than that of CO2: It diffuses perpendicular to the helices with almost the same rate as parallel. This is attributed to the fact that CH4 dissolves better in the outer perimeters of the PMP helices which are not dissimilar to fluid alkanes. A map of the local relative free energy of sorption within the unit cell is calculated both by test-particle insertion and from the residence periods of gas molecules at certain positions. It also shows that the barriers to perpendicular diffusion are lower for CH4 than for CO2.

Adsorption of Cs(I), Sr(II) and Co(II) on Al2O3

The sorption of Cs(I), Sr(II) and Co(II) from aqueous solutions on alumina under various experimental conditions has been studied by batch techniques. Freundlich, Langmuir and Dubnin-Raduskevich equations have been used to interpret the sorption data. The values of various thermodynamic parameters have been determined. The sorption of Cs(I) and Sr(II) on alumina is exothermic in nature while that of Co(II) is an endothermic process. The ΔHo values for Cs(I), Sr(II) and Co(II) were−23.29 KJ/mol at 298K,−35.3 KJ/mol at 293 K and 13.49 KJ/mol at 293 K, respectively. Negative values of ΔGo show the spontaneity of the sorption processes; ΔGo values of Cs(I) and Sr(II) becomes less negative at higher temperatures while the ΔGo values of Co(II) become more negative with increasing temperature. At higher temperatures, less amounts of Cs(I) and Sr(II) and greater amounts of Co(II) are sorbed on alumina. The values of the mean free energies of sorption,E, for Sr(II) and Co(II) at various temperatures were within the range of 7–10 KJ/mol which show that these metals are sorbed on alumina predominantly by an ion-exchange process.

Adsorption of chromium (III), chromium (VI) and silver (I) on bentonite

The sorption of Cr(III), Cr(VI) and Ag(I) from aqueous solutions on bentonite has been studied by a batch technique. Distribution coefficients ( K d) were determined for sorption systems as a function of contact time, pH, sorbent and sorbate concentration and temperature. Sorption data have been interpreted in terms of Freundlich, Langmuir and Dubinin-Raduskevich (D-R) equations. Thermodynamic parameters for the sorption systems have been determined at different temperatures. The sorption of Cr(III) and Ag(I) on bentonite is exothermic in nature while that of Cr(VI) is an endothermic process. The ΔH° values for Cr(III), Cr(VI) and Ag(I) were −51.94 kJ/mol at 298 K, 5.619 kJ/mol at 293 K and −7.64 kJ/mol at 303 K respectively. The mean free energy of sorption, E, for Cr(VI) is 10 kJ/mol which shows that chromate ions from aqueous solutions at 10 −5 to 10 −3 M are predominantly sorbed on bentonite by an ion-exchange process. The sorption data for Cr(III) and Ag(I) do not fit in the D-R equation. Negative values of ΔG° show the spontaneity of the sorption processes; ΔG° values for Cr(III) and Ag(I) become less negative at higher temperatures which shows that sorption is less favoured at higher temperatures, while the increase in the negative values of ΔG° for Cr(VI) with the increase in temperature indicates that sorption is favoured at higher temperatures.

Sorption of strontium on bentonite

Sorption of Sr on bentonite was studied using the batch technique. Distribution coefficients ( K d) were determined as a function of contact time, pH, sorbent and sorbate concentration and temperature. The data were interpreted in terms of Freundlich, Langmuir and Dubinin-Radushkevich isotherms. Thermodynamic parameters for the sorption system were determined at three different temperatures. The positive value of the heat of sorption, ΔH° = 30.62 kJ/mol at 298 K, shows that the sorption of strontium on bentonite is endothermic. The negative value of the free energy of sorption, ΔG° = −10.69 kJ/mol at 298 K, shows the spontaneity of the reaction. ΔG° becomes more negative with increasing temperature, which shows that the sorption process is more favorable at higher temperatures. The mean free energy for sorption, E ∼ 9 kJ/mol, suggests that ion exchange is the predominant mode of sorption in the Sr concentration range studied, i.e. 0.01 – 0.3 mol/dm 3. The presence of complementary cations depresses the sorption of strontium on bentonite in the order Ca 2+>Mg 2+>K +>Na +. Some organic complexing agents and natural ligands also affect the sorption of strontium. The desorption studies with ground water at low strontium loadings on bentonite show that about 90% of Sr is irreversibly sorbed on the bentonite.

Sorption characteristics of polyfluorocarboxamides

The dependence of the variations in the differential molar free energy of sorption of polyfluorocarboxamides RFC(O)NR2 (RF = CF3(CF2)i,i=0 to 5, R=H or Me) on capillary columns on the molecular structure of the amides, the temperature of analysis, and the nature of the stationary phases (OV-101, XE-60, and PEG-40M) were investigated by GLC. The peculiarities of the variation of the sorption characteristics of amides in XE-60 and PEG-40M polar phases, which cause the inversion of the order of retention of the members of pseudohomologous series, were found.

Gas chromatographic determination of the free energy of sorption of methylene units ofN-alkylsubstituted six-membered cyclic amines

The free energy of sorption of methylene units, ΔG(CH2), for the homologous series ofN-alkylsubstituted morpholines, thiomorpholines, piperidines and 2-methyl-, 3-methyl-, 4-methyl- and 2,6-dimethylpiperidines was determined. It was shown that the dependence of these values on the number of CH2 units in the carbon chain is not linear. Universal equations for calculating the values of the energy contribution depending on the number of CH2 units in the carbon chain were obtained. Abnormally high values of free energy of sorption of the first CH2 unit were found in all series studied and reasons for the anomaly are discussed.

Sorption of organic vapors at the air-water interface in a sandy aquifer material

It was hypothesized that the mineral surfaces in a sandy aquifer material would be sufficiently hydrated in a GC column fed with humidified carrier gas to provide an airwater interface for the sorption of nonpolar organic vapors. To test this, the properties of three sorbents were investigated: an aquifer material, an oxidized version of the aquifer material, and a soil then from the vadose zore overlying the aquifer. Isotherms, vapor-phase sorption constants, partial molar enthalpies of sorption, and the incremental free energy of sorption for a methylere group were measured using a variety of volatile organic compounds

The regularities of the gas-chromatographic behavior of methyl-substitutedN-alkylpiperidines

The gas-chromatographic behavior of 2-, 3-, 4-methyl- and 2,6-dimethylpiperidine bases on glass capillary columns with OV-101/KF and PEG-40M/KF at 110 °C has been studied. The contribution of a methyl group to the total molar free energy of Sorption of nonalkylated piperidine bases depends on its position in the piperidine cycle and is the least for positions 2 and 6. The variation in the retention indices of homologousN-alkylpiperidines (C1-C7) is given by a universal type of equation.

Physical surface-complexation models for sorption at the mineral–water interface

NONE of the traditional models of surface complexation of ions at oxide–water interfaces, such as the constant-capacitance, double-diffuse-layer and triple-layer models1–5, provides an explicit, quantitative treatment of ion solvation. Here I show that this process can be included quantitatively in surface-complexation theory by describing it using the Born theory of ion solvation6,7. In this way, the standard Gibbs free energy of sorption can be decomposed into three terms: the standard coulombic term, a Born solvation contribution and a term intrinsic to the ion alone. Consideration of the Born solvation term shows that the equilibrium constant for sorption depends linearly on the inverse of the dielectric constant of the solid. By this means, all three contributions to the free energy can be estimated empirically or calculated theoretically. Inclusion of this physical description of ion solvation should facilitate the application of the theory of ion sorption to complex natural oxide and silicate minerals.