Natural gas permeation in polyimide membranes

Polyimide membranes derived from 6FDA-DAM:DABA and 6FDA-6FpDA:DABA copolymers have been used to separate 50/50 CO₂/CH₄ mixtures and multicomponent synthetic natural gas mixtures at 35 °C and feed pressures up to 55 atm. For 6FDA-DAM:DABA 2:1 membranes the effects of thermal annealing and covalent crosslinking are decoupled with respect to effects on permeabilities and selectivity. Crosslinking at 295 °C with 1,4-butylene glycol and 1,4-cyclohexanedimethanol increases CO₂ permeabilities by factors of 4.1 and 2.4, respectively, at 20 atm feed pressure, without a loss in selectivity, relative to crosslinking at 220 °C. Thermal annealing and crosslinking also reduce CO₂ plasticization effects. Crosslinking of DABA-containing copolymers, therefore, can produce membranes with tunable transport properties that offer significantly higher performance with better plasticization-resistance than that reported in the literature for the commercial polymers Matrimid^® and cellulose acetate for CO₂ removal from natural gas mixtures. Separation of complex mixtures containing CO₂, CH₄, C₂H₆, C₃H₈, and C₄H₁₀ or toluene results in a significant decrease of the CO₂ permeability, but only a moderate decrease in the CO₂/CH₄ selectivity.     

Pervaporation separation of aromatic/aliphatic hydrocarbons by crosslinked poly(methyl acrylate-co-acrylic acid) membranes

Copolymers of methyl acrylate and acrylic acid were synthesized to fabricate membranes ionically crosslinked using aluminum acetylacetonate for the separation of toluene/i-octane mixtures by pervaporation at high temperatures. The formation of the ionic crosslinking via bare aluminum cations was characterized by UV–VIS spectroscopy and solubility tests. Reproducibility and the reliability of the methodology for membrane formation and crosslinking were confirmed. The effects of acrylic acid content, crosslinking conditions, pervaporation temperature, and feed composition on the normalized flux and the selectivity for toluene/i-octane mixtures were determined. A typical crosslinked membrane showed a normalized flux of 26 kg μm m⁻² h⁻¹ and a selectivity of 13 for a 50/50 wt.% feed mixture at 100°C. The pervaporation properties including solubility selectivity and diffusivity selectivity are discussed in terms of swelling behavior. The performance of the current membranes were benchmarked against other membrane materials reported in the literature.     

FT-IR study on interactions between solutes and entrainers in supercritical carbon dioxide

Fourier transform infrared (FT-IR) spectroscopy has been used to measure the molarities of hydrogen bonding species between carboxylic acids (acetic acid and palmitic acid) and water in supercritical CO₂. The equilibrium constants of dimerization for the carboxylic acids were determined in supercritical CO₂ with octane. Further, the interactions of propanol-d (1- and 2-propanol-d) or xylenol (2,5-, 2,6- and 3,4-xylenol) isomers with acetone in supercritical CO₂ were studied. Experiments were carried out at 308.2–313.2 K and 7.0–20.0 MPa. The molarities of hydrogen bonding species between the carboxylic acids and water in supercritical CO₂ increase with the increasing molarity of water. The carboxylic acids interact more easily with ethanol than water in supercritical CO₂. For supercritical CO₂+carboxylic acid+octane systems, the equilibrium constants between the carboxylic acid monomer and dimer increase with the increasing molarity of octane. The equilibrium constants of the carboxylic acids seem to approach to those in liquid paraffin according to addition of octane in supercritical CO₂. The amount of the interaction species between 1-propanol-d and acetone is larger than that between 2-propanol-d and acetone. The amount of acetone interacting with OH group for 3,4-xylenol is the largest among those for xylenol isomers. These differences among the isomers may be caused by the screen effects of methyl groups around hydroxyl group for the isomers.     

Nickel-catalyzed decarboxylative coupling of an alkynyl carboxylic acid with aryl iodides

A decarboxylative coupling reaction with an alkynyl carboxylic acid and aryl iodides in the presence of a nickel catalyst was developed. When the reaction was conducted with NiCl₂ (10 mol%), Xantphos (15 mol%), Mn (1.0 equiv), and Cs₂CO₃ (1.5 equiv), the desired diaryl alkynes were formed in moderated to good yields. Furthermore, this method does not produce the diyne, which is formed in the homocoupling of alkynyl carboxylic acids.     

Carbon dioxide solubility in aqueous potassium salt solutions of l-proline and dl-α-aminobutyric acid at high pressures

In the present work, the solubility of CO₂ in aqueous solutions of potassium prolinate (KPr) and potassium α-aminobutyrate (KAABA) was measured at temperatures (313.2, 333.2, and 353.2) K and CO₂ partial pressures up to 1000 kPa for amino acid salt concentrations: KPr, w = (7.5, 14.5, and 27.4 wt%) and KAABA, w = (6.9, 13.4, and 25.6 wt%). It was found that the CO₂ absorption capacities of the studied amino acid salt systems were considerably high and comparable with that of industrially important alkanolamines including monoethanolamine. The CO₂ loadings in aqueous potassium α-aminobutyrate at high pressures were also found to be generally higher than the loadings in aqueous potassium prolinate. A modified Kent–Eisenberg model was applied to correlate the CO₂ solubility in the amino acid salt solution as function of CO₂ partial pressure, temperature, and concentration. The model gave good representation of the (vapour + liquid) equilibrium data obtained for the amino acid salt systems studied, and provided accurate predictions of the solubility.     

Synthesis and characterization of photocrosslinkable poly(l-lactide)s with a pendent cinnamate group

In this report, we describe the synthesis and characterization of photosensitive poly(l-lactide) with a pendent cinnamate group. α,ω-Dihydoxy terminated poly(l-lactide) (PLLA-diol) [molecular weights (MW); 2000, 4000 and 9000 g/mol ] was chain-extended with a diacyl chloride of 5-cinnamoyloxyisophthalic acid (ICA) to obtain high-molecular-weight photocrosslinkable poly(l-lactide)s (ICA/PLLA). The resulting polyesters were characterized by proton nuclear magnetic resonance spectroscopy, gel permeation chromatography, ultraviolet–visible spectroscopy, differential scanning calorimetry, thermomechanical analysis and thermogravimetry. The glass transition temperature (T_g), the melting temperature (T_m) and the degree of relative crystallinity (X_c) of ICA/PLLAs increased with the increasing MW of the PLLA-diols. The photosensitive ICA/PLLAs were irradiated with a 400 W high-pressure mercury lamp (λ > 280 nm) for various times to produce the PLLA gel films without a photoinitiator. The crosslinking rate monitored by a UV–vis spectrum decreased with the increasing MW of the PLLA-diols. The crosslinking of the ICA/PLLA ?4000 film enhanced the T_g slightly and the tensile strength and Young’s modulus significantly, while reduced the T_m and X_c. The enzymatic degradation was measured by the weight loss of the films in a phosphate buffer solution with proteinaze-k. The crosslinking of the films decreased markedly the degradation rate.     

Synthesis and properties of aromatic block copolyimides

Anhydride terminated polyamic acid prepolymer was prepared from pyromellitic dianhydride and a diamine (para-phenylene diamine/benzidine) in dimethyl formamide. The prepolymer was reacted with the other diamine to obtain (A_nB)_m block copolymic acid. The polyamic acid was converted to the polyimide by thermal cyclodehydration. The properties of block copolyimides were compared with those of random copolyimides prepared by conventional routes.     

The dimeric unit [La(H2O)4(m-PO3C6H4COOH)(m-PO2(OH)C6H4COOH)(m-PO(OH)2C6H4COOH)]2 as building block of layered hybrid material

A new hybrid organic–inorganic material with the structural formula unit [La(H₂O)₄(m-PO₃C₆H₄COOH)(m-PO₂(OH)C₆H₄COOH)(m-PO(OH)₂C₆H₄COOH)]₂ (or [La(H₂O)₄C₂₁H₁₈O₁₅P₃]₂) has been synthesized under hydrothermal condition from La(NO₃)₃·6H₂O and 3-phosphonobenzoic acid (m-PO(OH)₂–C₆H₄–COOH) which is a rigid organic precursor possessing two types of functional groups: phosphonic acid and carboxylic acid. The two units of the produced hybrid are linked together by hydrogen bonds leading to a layered framework composing of by a repetition of inorganic and organic slices. The organic layers consist of dimeric units made of two meta-phosphono-benzoic acid linked together by hydrogen bonds involving their COOH groups. Two kinds of dimeric units are observed: PO₃C₆H₄COOH?HOOCC₆H₄PO(OH)₂, present 2 times in the structure, and PO₂(OH)C6H4COOH?HOOCC₆H₄PO₂(OH). The material crystallises in a monoclinic cell (C2/c (15) space group) with the following parameters: a = 42.515(4) Å, b = 7.4378(6) Å, c = 20.307(2) Å, β = 118.031(6)°, V = 5668.2(9) Å³, Z = 4, density = 1.908 g/cm³.     

Correlation of CO2 solubility in N-methyldiethanolamine + piperazine aqueous solutions using extended Debye–Hückel model

Solubility data of CO₂ in aqueous N-methyldiethanolamine (MDEA) solutions of concentration (2.52, 3.36, and 4.28) kmol/m³ were obtained at temperatures (313, 323, and 343) K and partial pressures ranging from about (30 to 5000) kPa. A thermodynamic model based on extended Debye–Hückel theory was applied to predict and correlate of CO₂ solubility in various aqueous amine solutions. The effect of piperazine (PZ) concentration on CO₂ loading in MDEA solutions was determined at PZ concentration (0.36, 0.86, and 1.36) kmol/m³. Using experimental data in various temperatures the interaction parameters of activity coefficient model for these systems were determined. The results show the model consistency with experimental and literature data and PZ is beneficial to the CO₂ loading. The comparison of results of this study with previous data work shows the wide range of CO₂ loading considered in this work and the better agreement of model with experimental data. The average absolute relative deviation percent (δ_AAD) for all data points were 8.11%.     

Excellent electrocatalytic activity of benzil for direct reduction of CO_2 as well as indirect reduction of pyridine:A kinetic view of the electrocarboxylation process

Benzil,1,2-diphenylethane-1,2-dione, was used as an excellent electrocatalyst for reduction of carbon dioxide, CO_2. The reduction overpotential of CO_2 was reduced about 900 m V in the presence of a benzil mediator. The chemical reaction of the product of the electrocatalytic reduction of CO_2,(activated CO_2,CO_2~(·-)) with pyridine at a glassy carbon electrode, GCE, surface and in an acetonitrile-But_4NClO_4 solution was investigated by cyclic voltammetry, chronoamperometry and controlled potential coulometry.By chronoamperometry, the catalytic rate constant, k, for the electron transfer between benzil and CO_2 was obtained as 8.1 ± 0.4 M~(-1)s~(-1). The results indicate that pyridine has a strong interaction with the activated CO_2. The coulometry method was used to obtain the product of the pyridine chemical reaction with CO_2~(·-). The spectral characterizations of FTIR,~1H and ~(13)C NMR of the coulometry experiment product proved that the pyridine anion radical, Py~(·-), was carboxylated by CO_2~(·-), and isonicotinic acid is the final major product.     

Water-swollen cation-exchange membranes prepared using poly(vinyl alcohol) (PVA)/poly(styrene sulfonic acid-co-maleic acid) (PSSA-MA)

A water-swollen type of poly(vinyl alcohol) (PVA)/poly(styrene sulfonic acid-co-maleic acid) (PSSA-MA) cation-exchange membrane was prepared and characterized in terms of its electrochemical properties including ion-exchange capacity (IEC), electrical resistance, and transport number, etc. PVA/PSSA-MA membranes exhibited low electrical resistance and highly swelling property. In spite of 2–4 times higher water swelling ratio (WSR) than that of CMX (Tokuyama Corp., Japan), the transport number of the prepared membrane was comparable to that of the commercial membrane (t_n>0.93). Moreover, the electric resistance of PVA/PSSA-MA membrane was measured as low as 1.0–1.5 Ω cm². Further, in this study, interrelation between the membrane characteristics and crosslinking was investigated, and the result exhibited that the crosslinking degree is one of major factors affecting the ion transport through a water-swollen ion-exchange membrane (IEM).     

Immobilized glycerol-based liquid membranes in hollow fibers for selective CO2 separation from CO2–N2 mixtures

Glycerol-based liquid membranes immobilized in the pores of hydrophilic microporous hollow fibers have been studied for selective separation of CO₂ from a mixed gas (CO₂, N₂) feed having low concentrations of CO₂ characteristic of gases encountered in space walk and space cabin atmosphere. The immobilized liquid membranes (ILMs) investigated consist of sodium carbonate–glycerol or glycine-Na–glycerol solution. Based on the performances of such liquid membranes in flat hydrophilic porous substrates [Chen et al., Ind. Eng. Chem. Res. 38 (1999) 3489; Chen et al., Ind. Eng. Chem. Res. 39 (2000) 2447], hollow fiber-based ILMs were studied at selected CO₂ partial pressure differentials (Δp_CO2 range 0.36–0.50 cmHg), relative humidities (RH range 45–100%), as well as carrier concentrations. The sodium carbonate concentration was primarily 1.0 mol/dm³; the glycine-Na concentration was 3.0 mol/dm³. The sweep gas was always dry helium and it flowed on the shell side. Very high CO₂/N₂ selectivities were observed with porous polysulfone microfiltration membranes as substrate. As in the case of flat film-based ILMs (see references above), feed side RH is an important factor determining the ILM performances. Generally, lower permeances and greater CO₂/N₂ selectivity values were observed at lower feed stream RHs. When the feed side average RH=60%, p_CO2,f=0.005 atm and glycine-Na concentration was 3.0 M, the CO₂/N₂ separation factor observed was over 5000. Prolonged runs lasting for 300 h showed that the hollow fiber-based ILM permeation performances were stable.     

Influence of the alkyl group on thermophysical properties of carboxylic acids in 1-butyl-3-methylimidazolium thiocyanate ionic liquid at various temperatures

In the present study, influence of the alkyl group and temperature on the interactions between the carboxylic acid and ionic liquid (IL) mixtures were discussed in term of density and sound velocity measurements. The IL used in this study was 1-butyl-3-methylimidazolium thiocyanate ([BMIM]⁺[SCN]⁻). The density (ρ), and sound velocity (u), of the IL, acetic acid, propionic acid, and their corresponding binary systems {[BMIM]⁺[SCN]⁻ (x₁) + acetic or propionic acid (x₂)} have been measured at T = (293.15, 298.15, 303.15, 308.15 and 313.15) K and at p = 0.1 MPa. The excess molar volumes, $V_{\text{m}}^{\text{E}}$, isentropic compressibility, κ_s, and deviation in isentropic compressibility, Δκ_s, were calculated using experimental density and sound velocity data, respectively. The Redlich–Kister polynomial equation was used to fit the excess/deviation properties. These results are useful for describing the intermolecular interactions that exist between the IL and carboxylic acid mixtures.     

CO2 adsorption on granular and monolith carbonaceous materials

We evaluated the CO₂ adsorption capacity on granular and monolith carbonaceous materials, obtained by chemical activation of African palm stones with H₃PO₄, ZnCl₂ and CaCl₂ solutions at different concentrations. Textural properties of the synthesized materials were analyzed using N₂ adsorption measurements at 77 K, the isotherms showed obtaining of materials microporous and moderately mesoporous, with surface areas between 161 and 1700 m²/g and pore volume between 0.09 and 0.64 cm³ g⁻¹. Were observed different behaviors for textural parameters in each series, associated with the activating agent used in the preparation. The materials obtained have a CO₂ adsorption capacity between ∼114 and 254 mg CO₂/g, at atmospheric pressure and 273 K. It was established that the total amount of CO₂ adsorbed under these experimental conditions is defined by the narrow micropore volume (V_n) and increased the total basicity of the materials.     

Simultaneous acquisition of differential electrochemical mass spectrometry and infrared spectroscopy data for in situ characterization of gas evolution reactions in lithium-ion batteries

Gassing in batteries is a major issue contributing to capacity fading upon cycling, and thus far, differential electrochemical mass spectrometry (DEMS) has been a suitable analytical tool to investigate such gas evolution reactions. However, the identity of molecules is ambiguous knowing only the m/z value(s) and quantification is complicated. Therefore, the setup of a novel technique for in situ gas analysis of operating lithium-ion batteries is introduced, namely, DEMS combined with infrared spectroscopy. In a “long-term” study of a Li_1 + xNi_0.5Co_0.2Mn_0.3O₂ (NCM 523)/graphite cell being close to technical conditions, we monitor the CO₂ evolution over more than twenty cycles and show the dependence of the amount of generated CO₂ on the charge cut-off potential. Furthermore, we deconvolute the MS channel m/z = 28 and show, for the first time, the direct observation of its constituent gases. Other gaseous decomposition products (like CO₂ here) can be determined unambiguously as well through both their m/z values and their characteristic IR absorptions, but are not discussed here.     

Equilibrium solubility of carbon dioxide in the amine solvent system of (triethanolamine + piperazine + water)

In this study, a new set of data for the equilibrium solubility of carbon dioxide in the amine solvent system that consists of triethanolamine (TEA), piperazine (PZ), and water is presented. Equilibrium solubility values were obtained at T = (313.2, 333.2, and 353.2) K and pressures up to 153 kPa using the vapour-recirculation equilibrium cell. The TEA concentrations in the considered ternary (solvent) mixture were (2 and 3) kmol · m^?3 and those of PZ’s were (0.5, 1.0, and 1.5) kmol · m^?3. The solubility data (CO₂ loading in the amine solution) obtained were correlated as a function of CO₂ partial pressure, system temperature, and amine composition via the modified Kent–Eisenberg model. Results showed that the model applied is generally satisfactory in representing the CO₂ absorption into mixed aqueous solutions of TEA and PZ.     

High pressure measurement and CPA equation of state for solubility of carbon dioxide and hydrogen sulfide in 1-butyl-3-methylimidazolium acetate

Removal of acid gases such as CO₂ and H₂S from natural gas is essential for commercial, safety and environmental protection that demonstrate the importance of gas sweetening process. Ionic liquids (IL) have been highly demanded as a green solvent to remove acid gases from sour natural gas and capturing of CO₂ from flue gases. In this work, the solubility of CO₂ in 1-butyl-3-methylimidazolium acetate ([bmim][Ac]) is measured at temperatures (303.15, 328.15, 343.15) K and pressure range of (0.1 to 3.9) MPa. Moreover, the experiments are carried out for simultaneous measurements of (CO₂ + H₂S) (70% + 30% on a mole basis) solubility in the same ionic liquid at T = (303.15, 323.15, 343.15) K and a pressure range of (0.1 to 2.2) MPa. To model the solubility of acid gases in IL, both physical and chemical equilibria are applied so that the (vapour + liquid) equilibrium calculation is carried out through Cubic-Plus-Association (CPA) EoS. The reaction equilibrium thermodynamic model is used in liquid phase so that the chemical reaction is taking place between IL and acid gasses. The Henry’s and reaction equilibrium constants are obtained though optimization of the solubility data. Using CPA EOS, the pure parameters of [bmim][acetate] are optimised and consequently using these parameters, gas partial pressure calculation is performed for the (CO₂ + IL) and (CO₂ + H₂S + IL) systems. For the (CO₂ + IL) system, the percent average absolute deviation (AAD%) of 4.83 is resulted and for the (H₂S + CO₂ + IL) system the values of 18.8 and 13.7 are obtained for H₂S and CO₂, respectively.     

Adsorption of CO2 and CH4 on a magnesium-based metal organic framework

A magnesium-based metal organic framework (MOF), also known as Mg-MOF-74, was successfully synthesized, characterized, and evaluated for adsorption equilibria and kinetics of CO₂ and CH₄. The Mg-MOF-74 crystals were characterized with scanning electron microscopy for crystal structure, powder X-ray diffraction for phase structure, and nitrogen adsorption for pore textural properties. Adsorption equilibrium and kinetics of CO₂ and CH₄ on the Mg-MOF-74 adsorbent were measured in a volumetric adsorption unit at 278, 298, and 318 K and pressures up to 1 bar. It was found that the Mg-MOF-74 adsorbent prepared in this work has a median pore width of 10.2 Å, a BET specific surface area of 1174 m²/g, CO₂ and CH₄ adsorption capacities of 8.61 mmol g^?1 (37.8 wt.%) and 1.05 mmol g^?1 (1.7 wt.%), respectively, at 298 K and 1 bar. Both CO₂ and CH₄ adsorption capacities are significantly higher than those of zeolite 13X under similar conditions. The pressure-dependent equilibrium selectivity of CO₂ over CH₄ (q_CO2/q_CH4) in the Mg-MOF-74 adsorbent showed a trend similar to that of zeolite 13X and the intrinsic selectivity of Mg-MOF-74 at zero adsorption loading is 283 at 298 K. The initial heats of adsorption of CO₂ and CH₄ on the Mg-MOF-74 adsorbent were found to be 73.0 and 18.5 kJ mol^?1, respectively. The adsorption kinetic measurements suggest that the diffusivities of CO₂ and CH₄ on Mg-MOF-74 were comparable to those on zeolite 13X. CH₄ showed relatively faster adsorption kinetics than CO₂ in both adsorbents. The diffusion time constants of CO₂ and CH₄ in the Mg-MOF-74 adsorbent at 298 K were estimated to be 8.11 × 10^?3 and 4.05 × 10^?2 s^?1, respectively, showing a modest kinetic selectivity of about 5 for the separation CH₄ from CO₂.     

Near critical measurements of HmEandVmE for { xCO2 + (1 − x)SF6} and measurements made over the pressure range 2.5 to 10.0 MPa at the temperature T = 301.95 K

A flow mixing calorimeter, followed by a vibrating tube densimeter, has been used to measure excess molar enthalpies H_m^Eand excess molar volumesV_m^E of {xCO₂ +  (1  − x)SF₆}. Measurements over a range of mole fraction x have been made at the temperatures T =  302.15 K and T =  305.65 K at the pressures (3.76, 5.20, 6.20, and 7.38) MPa. The lowest pressure 3.76 MPa is close to thecritical pressure of SF₆ and the highest pressure 7.38 MPa is close to the critical pressure of CO ₂. Measurements atx =  0.5 have been made over the pressure range (2.5 to 10.0) MPa at the temperature 301.95 K. Some of the measurements are very close to the critical locus of the mixture. The measurements are compared with the Patel–Teja equation of state which reproduces the main features of the excess function curves as well as it does for similar measurements on {xCO₂ +  (1  − x)C₂H₆} and{xCO₂ +  (1  − x)C₂H₄} . The equation was used to calculate residual enthalpies and residual volumes for the pure components and for the mixture, and inspection of the way these combine to give excess enthalpies and volumes assisted the interpretation of the pressure scan measurements.     

(Solid + solute) phase equilibria in aqueous solution. XIII. Thermodynamic properties of hydrozincite and predominance diagrams for (Zn2 + + H2O + CO2)

The thermodynamic properties ofZn₅(OH)₆(CO₃)₂ , hydrozincite, have been determined by performing solubility and d.s.c. measurements. The solubility constant in aqueous NaClO₄media has been measured at temperatures ranging from 288.15 K to 338.15 K at constant ionic strength (I =  1.00 mol · kg ^− 1). Additionally, the dependence of the solubility constant on the ionic strength has been investigated up to I =  3.00 mol · kg ^− 1NaClO₄at T =  298.15 K. The standard molar heat capacity C_{p, m}^ofunction fromT =  318.15 K to T =  418.15 K, as well as the heat of decomposition of hydrozincite, have been obtained from d.s.c. measurements. All experimental results have been simultaneously evaluated by means of the optimization routine of ChemSage yielding an internally consistent set of thermodynamic data (T =  298.15 K): solubility constant log ^* K_{ps 0}⁰ =  (9.0  ±  0.1), standard molar Gibbs energy of formationΔ_fG_m^o {Zn₅(OH)₆(CO₃)₂ }  =  ( − 3164.6  ±  3.0)kJ · mol ^− 1, standard molar enthalpy of formation Δ_fH_m^o{Zn₅(OH)₆(CO₃)₂ }  =  ( − 3584  ±  15)kJ · mol ^− 1, standard molar entropy S_m^o{Zn₅(OH)₆(CO₃)₂ }  =  (436  ±  50)J · mol ^− 1· K ^− 1and C_p,m^o / (J · mol ^− 1· K ^− 1)  =  (119  ±  11)  +  (0.834  ±  0.033)T / K. A three-dimensional predominance diagram is introduced which allows a comprehensive thermodynamic interpretation of phase relations in(Zn^2 +  +  H₂O  +  CO₂) . The axes of this phase diagram correspond to the potential quantities: temperature, partial pressure of carbon dioxide and pH of the aqueous solution. Moreover, it is shown how the stoichiometric composition{n(CO₃) / n(Zn)} of the solid compoundsZnCO₃ and Zn₅(OH)₆(CO₃)₂can be checked by thermodynamically analysing the measured solubility data.