Explanation of Ionic Sequences in Various Phenomena. I. Salting-Out of Uncharged Molecules

Abstract

Theoretical models for hydrated ions and their calculated effective dielectric constants obtained previously were used to explain the salting-in or salting-out of nonionic molecules. Three types of salting-out sequences were obtained: nonpolar (Na⁺ > K⁺ > Li⁺ Rb⁺ > Cs⁺), basic (K⁺ > Na⁺ > Rb⁺ > Cs⁺ > Li⁺), and acidic (Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺). The nonpolar sequence is not influenced by the A region of a cation, and therefore the ability to salt-out is great if the effective dielectric constant of the ion is small. The A region on hydrated Li⁺ ions (the tightly bound water) salts-in basic compounds because of the interaction of its positively charged hydrogen atoms with the negative dipolar charge of the base. Conversely, the A region of a cation salts-out acidic compounds because the hydroxyl group on carboxylic acids behaves as a similar cationic A region. A sulfonic polymer will cause the salting-in of the base p-nitroaniline because the addition of salts to an aqueous solution of the base and polymer destroys hydrogen bonds in the polymer and in so doing releases hydronium ions from the polymer. This release of H⁺, in turn, produces a positive charge on part of the p-nitroaniline molecules, which produces a salting-in effect.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

KCl/NaCl DMSO aqueous solutions dielectric spectra and cooperative interactions

The complex permittivity spectra of KCl/NaCl DMSO aqueous solutions were measured using microwave dielectric spectroscopy. Ion–water and dipole–water cooperative interactions are investigated by using a fractional relaxation process. Only about one cooperative relaxation was found during the cut-off relaxation time interval and the relaxation time increases with concentration increasing. Ions’ concentration dependent on effective number of water molecules in the shell around ions was calculated to reveal the interactions between K⁺, Cl^?, Na⁺ ions and DMSO molecules.     

Density Functional Theory Study of Selectivity of Crown Ethers to Li+ in Spent Lithium-Ion Batteries Leaching Solutions

It is a challenge to recover lithium from the leaching solution of spent lithium-ion batteries, and crown ethers are potential extractants due to their selectivity to alkali metal ions. The theoretical calculations for the selectivity of crown ethers with different structures to Li ions in aqueous solutions were carried out based on the density functional theory. The calculated results of geometries, binding energies, and thermodynamic parameters show that 15C5 has the strongest selectivity to Li ions in the three crown ethers of 12C4, 15C5, and 18C6. B15C5 has a smaller binding energy but more negative free energy than 15C5 when combined with Li⁺, leading to that the lithium ions in aqueous solutions will combine with B15C5 rather than 15C5. The exchange reactions between B15C5 and hydrated Li⁺, Co²⁺, and Ni²⁺ were analyzed and the results show that B15C5 is more likely to capture Li⁺ from the hydrated ions in an aqueous solution containing Li⁺, Co²⁺, and Ni²⁺. This study indicates that it is feasible to extract Li ions selectively using B15C5 as an extractant from the leaching solution of spent lithium-ion batteries.     

Thermodynamische Untersuchungen zur Chelatbildung zwischen Aminoterephthalsäure-N,N-diessigsäure und 3 d- bzw. Erdalkalimetallionen. Eine Betrachtung zum Einfluß einer koordinativ inaktiven Carboxylgruppe auf die komplexe Bindung von Metallionen durch Aminopolycarbonsäuren

N-(2-Carboxyphenyl)iminodiacetic acid (H₃A) and N-(2,5-dicarboxyphenyl)iminodiacetic acid (H₄B) are tetradentate ligands and form complexes of the composition MA- and MB^2? with M^II ions. These compounds differ by the additional charge of the second carboxylic group only, which is fixed to the benzene nucleus and which is unable for coordination for steric reasons. Using an anisothermal calorimeter ΔH values for the formation of the complexes MA- and MB^2? in aqueous solution have been measured at an ionic strength 0.1 m KNO₃. From these data, and from the stability constants of the complexes, entropy changes ΔS have been calculated. In all cases investigated (M^m+ = H⁺, Mg²⁺, Ca²⁺, Sr²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺) the ΔH values are more negative for the complexes MA^m-3 than for complexes MB^m-4, whereas the ΔS values are greater for complexes MB^m-4. Using a simple model for the molecules of the complexes MB^m-4 and empirically determined dielectric constants of the medium between the central ions and the noncoordinated ionized carboxylic group, the electrostatic attraction between these charges was calculated. Basing on these results the influence of the noncoordinated carboxylic group on the central atom by the mesomeric and inductive effect is discussed.     

The Arrangement of First- and Second-shell Water Molecules Around Metal Ions: Effects of Charge and Size

Structural features of clusters involving a metal ion (Li⁺, Na⁺, Be²⁺, Mg²⁺, Zn²⁺, Al³⁺, or Ti⁴⁺) surrounded by a total of 18 water molecules arranged in two or more shells have been studied using density functional theory. Effects of the size and charge of each metal ion on the organization of the surrounding water molecules are compared to those found for a Mg[H₂O]₆²⁺• [H₂O]₁₂ cluster that has the lowest known energy on the Mg²⁺• [H₂O]₁₈ potential energy surface (Markham et al. in J Phys Chem B 106:5118–5134, 2002). The corresponding clusters with Zn²⁺ or Al³⁺ have similar structures. In contrast to this, clusters with a monovalent Li⁺ or Na⁺ ion, or with a very small Be²⁺ ion, differ in their hydrogen-bonding patterns and the coordination number can decrease to four. The tetravalent Ti⁴⁺ ionizes one inner-shell water molecule to a hydroxyl group leaving a Ti⁴⁺(H₂O)₅ (OH⁻) core, and an H₃O⁺• • • H₂O moiety dissociates from the second shell of water molecules. These observations highlight the influence of cation size and charge on the local structure of hydrated ions, the high-charge cations causing chemical changes and the low-charge cations being less efficient in maintaining the local order of water molecules. Electronic Supplementary Material: Supplementary material is available for this article at http://dx.doi.org/10.1007/S00214-005-0056-2.     

Dielectric Shielding of Ionic Charges in Aqueous Solutions of Different Ionic Strength

The thermodynamic functions of the proton transfer H₂tn²⁺+tn → 2 Htn⁺ (tn = 1,3-diaminopropane) have been determined in aqueous solutions containing different amounts of KCl (0.05 ? μ ? 3.01). The free energy (?ΔG) of the process decreases, whereas the enthalpy (-ΔH) increases with μ. There is reason to believe that the reaction is entirely controlled by the Coulomb forces between the two protonic charges. The electrostatic energy involved can be described in terms of a model incorporating an effective dielectric constant εe, such that δε_e/δμ and δ²ε_e/δμδT are both positive. The polarisation of pure water is produced by orientation of hydrogen-bonded dipole molecules H₂O, whereas the electrolyte solution is polarised in addition by dislocation of the ions K⁺ and Cl^?. Our results demonstrate that the former type of polarisation is much more temperature dependent than the latter.     

On the SCF theory of continuum solvent effects representation: Introduction of local dielectric effects

The introduction of local dielectric effects within the SCF theory of continuum solvent effects representation is examined at a semiempirical level. The formalism is developed in the frame of the reaction field theory within the effective charge approximation. The solvation free energies of Li⁺, Na⁺, F^?, and Cl^? ions in water were calculated in order to illustrate the reliability of the proposed model. The extension to molecules and molecular ions was performed including a desolvation corrective term related to the specific neighborhood of each atomic center. The results show a qualitative agreement with experimental data. A comment on the solvatonlike models for incorporating the solvent effect into the Hamiltonian is also given.     

An Ab Initio MO Study on Orbital Interaction and Charge Distribution in Alkali Metal Aqueous Solution: Li+, Na+, and K+

The analysis of the orbital interaction between an alkali metal ion and the surrounding solvent molecules is performed for aqueous solutions of Li⁺, Na⁺, and K⁺, by means of the ab initio MO method with the aid of the quantum mechanical (QM)/molecular mechanics (MM) method. A total of 171 water molecules are included for each system. The effect of Li⁺ orbitals reaches as far as 6 Å 7 Å for Na⁺; and 9 Å for K⁺. This effect is caused by the orbital interactions between the valence orbitals of an alkali metal ion and of the surrounding water molecules. The electrostatic interaction and the orbital interaction must not be neglected. The difference in the effect between the alkali metal ions originates from the difference in the valence orbital extensions of the alkali metal ions.     

Molecular dynamic study of electric potentials in water clusters containing the sodium or chlorine atom

Molecular dynamics with design is used to calculate the electric potentials of isolated water clusters containing Na⁺ or Cl⁻. The number of water molecules in the clusters is from 4 to 14. It is noted that electrostatic interaction plays a dominant role in the clusters; the dependence of the dielectric constant of the cluster on the size of the latter is determined. Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 66–73, January–February, 1998.     

Ion-transfer polarographic study of the distribution of alkali and alkaline-earth metal complexes with 3m-crown-m ether derivatives (m = 6, 8) between water and nitrobenzene phases

Stability constants ( ₁ ^NB ) of the 1:1 cationic complexes of Li⁺ Na⁺, K⁺ Ca²⁺ Sr²⁺ and Ba²⁺ with benzo-18-crown-6 (B18C6), Ca²⁺ and Sr²⁺ with 18C6 and dibenzo-18C6 and Li⁺, Na⁺, Ca²⁺, Sr²⁺ and Ba²⁺ with dibenzo-24-crown-8 in a nitrobenzene (NB) solution saturated with water (w) were determined at 25°C by ion-transfer polarography. From these values, distribution constants (K _D,ML) of the 18C6-derivative complex cations between the w- and NB-phases were evaluated using the thermodynamic relation:K _D,ML =K ₁ ^NB , whereK (mol dm^–3) is an overall equilibrium constant of the processes related to the complexation in the w-phase. The data on the distribution of the 18C6-derivative complex cations between the two phases and the complexation in the NB-phase were examined on the basis of an increase in the number of water molecules hydrated to the species relevant to these processes. The 18C6 derivatives showed higher solubilities in the NB-phase than in the w-phase by complexing with the univalent-metal ions, while, for the divalent-metal ions, the derivatives showed lower solubilities in the NB-phase.     

Theoretical and Experimental Study of Complex Ions from Reactions of Al+ (Cu+) with Amine Molecules

The gas phase reactions of metal ions (Al⁺, Cu⁺) with amine molecules [CH₃NH₂=MA, (CH₃)₂NH=DMA] were investigated using a laser ablation‐molecular beam method. The directly associated product complex ions,Al⁺‐MA and Al⁺‐DMA, and the dehydrogenation product ions, Cu⁺(CH₂NH) and Cu⁺(C₂H₅N), as well as hydrated ion Cu⁺(NC₂H₅·H₂O), have been obtained and recorded from the reactions of the metal ions and organic amine molecules, and density functional theory (B3LYP) calculations have been performed to reveal the optimized geometry, energetics, and reaction mechanism of the title reactions with basis set 6‐311+G(d,p) adopted.     

Solvated positron chemistry. The reaction of hydrated positrons with chloride ions

The reaction of hydrated positrons (c_aq⁺ with cloride ions in aqueous solutions has been studied by means of positron annihilation angular correlation measurements. A rate constant of k = (2.5 ± 0.5) × 10¹⁰ M^?1 s^?1 was found. Probably the reacting positrons annihilated from an e⁺ Cl^? bound state resulting in an angular correlation curve 8% narrower than for the hydrated positron. Carbontetrachloride in benzene seems to give similar, but smaller effect.     

Relation of the Gibbs free energy of transfer of ions from water to polar solvents to the properties of the solvents and the ions

A statistical treatment of data for the standard molar Gibbs free energies of transfer of monovalent ions from water to polar solvents has been made in terms of properties of the solvents and the ions. A common multiple regression equation with seven fitting constants, for almost 200 data points, has been found to describe the data in terms of four solvent properties: their electron donor and acceptor abilities, dielectric constant, and cohesive energy density, and three ionic properties: charge, size, and softness. For the ions Na⁺, K⁺, Rb⁺, Cs⁺, Tl⁺, (Ph)₄As⁺, Cl^?, Br^? and N ₃ ^? the predictions of the equation are within acceptable error limits of the data, and encourage its application to solvents beyond the thirteen used for the data base. For other ions, e.g. H⁺, Ag⁺, and the larger anions, further interactions must be taken into account.     

OH stretching force constants in complexes of water with F−, Cl−, Li+ ions and LiF,LiCl ion pairs by 6-31G ab initio MO calculations

Ab initio MO calculations using 6-31G and 6-31 + G (for complexes with F⁻ and LiF) basis sets have been carried out for complexes of H₂O (monomer and dimer) with F⁻, Cl⁻, Li⁺ ions as well as with LiF and LiCl ion pairs for the evaluation of the OH stretching force constants. The changes in force constants are discussed in terms of molecular interactions, cooperativity effect and interionic electrostatic interactions. It is noticed that the cooperativity effect also operates through ionic bonds in symmetrically hydrated ion pairs and that OH stretching force constants are found to increase in the case of solvent bound ion pairs and symmetrically hydrated halide ions showing anticooperativity effect.     

Marked variations of proton release energy of the G–M (M = Li, Na) in the water circumstance

The variations of N1–H proton release energy of G–M (M = Li, Na) cation have been investigated employing density functional theory using B3LYP/6-31++G^**//B3LYP/6-31+G^* method. There are three modes (NO mode, N mode and O mode) when the hydrated-M⁺ bonds to guanine. The bonding energy of the hydrated M⁺ to the guanine reduces following the increase in the number of water molecules. The proton release energies of the G–M⁺ complexes are calculated at the condition of the different numbers of water molecules and the different modes of water molecules bonded on the G–M⁺. The results show that the difference of proton release energy on three modes is very small, and the proton release energies of the Na⁺ complexes are slightly larger than those of the Li⁺ complexes. The effect on the N1–H proton release is very small when the water molecules bond on the M⁺ cation, but the effect is very large when the water molecule bonds on the N1–H proton and the proton releases as the hydrated proton. The IR vibrational frequencies of the hydrated G–M⁺ complexes are calculated using analytic second derivative methods at the B3LYP/6-31+G^* level. The vibrational frequency analyses show that the changes of the vibrational frequency are consistent with the changes of geometry and the changes of the N1–H proton release energy. The N1–H proton release (N1–H proton release energy: 45–60 kcal/mol) of the guanine occurs easily under the biological environment.     

Proton-bound cluster ions in ion mobility spectrometry

Gaseous oxygen and nitrogen bases, both singly and as binary mixtures, have been introduced into ion mobility spectrometers to study the appearance of protonated molecules, and proton-bound dimers and trimers. At ambient temperature it was possible to simultaneously observe, following the introduction of molecule A, comparable intensities of peaks ascribable to the reactant ion (H₂O)_nH⁺, the protonated molecule AH⁺ and AH⁺ · H₂O, and the symmetrical proton bound dimer A₂H⁺. Mass spectral identification confirmed the identifications and also showed that the majority of the protonated molecules were hydrated and that the proton-bound dimers were hydrated to a much lesser extent. No significant peaks ascribable to proton-bound trimers were obtained no matter how high the sample concentration. Binary mixtures containing molecules A and B, in some cases gave not only the peaks unique to the individual compounds but also peaks due to asymmetrical proton bound dimers AHB⁺. Such ions were always present in the spectra of mixtures of oxygen bases but were not observed for several mixtures of oxygen and nitrogen bases. The dimers, which were not observable, notable for their low hydrogen bond strengths, must have decomposed in their passage from the ion source to the detector, i.e. in a time less than ∼5 ms. When the temperature was lowered to −20 °C, trimers, both homogeneous and mixed, were observed with mixtures of alcohols. The importance of hydrogen bond energy, and hence operating temperature, in determining the degree of solvation of the ions that will be observed in an ion mobility spectrometer is stressed. The possibility is discussed that a displacement reaction involving ambient water plays a role in the dissociation.     

Studies on the equilibrium among poly(sodium 4‐styrenesulfonate), Cu2+, and iminodiacetic acid by ultrafiltration at constant ionic strength

The ultrafiltration technique evaluates the interactions of water‐soluble polymers with metal ions. Aqueous solutions containing poly(sodium 4‐styrenesulfonate) (PSS), Cu(NO₃)₂, NaNO₃, and iminodiacetic acid (IDAA) are examined by this technique. Cu²⁺ undergoes complex formation with IDAA and intreracts electrostatically with PSS. On the other hand, Na⁺ ions are in competition with Cu²⁺ for the electrostatic binding to PSS. The solutions are ultrafiltered keeping the ionic strength constant, so their compositions are allowed to change continuously. The concentration of Cu²⁺ bound to the polymer showed an exponential decay during filtration. The concentration of Cu²⁺ bound to the polymer before ultrafiltration is calculated by extrapolation. The concentration of the different species in solution is proposed as a function of the filtration factor. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2587–2593, 2002     

A theoretical study of cation--π interactions: Li+, Na+, K+, Be2+, Mg2+ and Ca2+ complexation with mono- and bicyclic ring-fused benzene derivatives

DFT (B3LYP functional) and MP2 methods using 6-311+G(2d,2p) basis set have been employed to examine the effect of ring fusion to benzene on the cation--π interactions involving alkali metal ions (Li⁺, Na⁺, and K⁺) and alkaline earth metal ions (Be²⁺, Mg²⁺ and Ca²⁺). Our present study indicates that modification of benzene (π-electron source) by fusion of monocyclic or bicyclic (or mixture of these two kinds of rings) strengthens the binding affinity of both alkali and alkaline earth metal cations. The strength of interaction decreases in the following order: Be²⁺ > Mg²⁺ > Ca²⁺ > Li⁺ > Na⁺ > K⁺ for any considered aromatic ligand. The interaction energies for the complexes formed by divalent cations are 4–6 times larger than those for the complexes involving monovalent cations. The structural changes in the ring wherein metal ion binds are examined. The distance between ring centroid and the metal ion is calculated for all of the complexes. Strained bicyclo[2.1.1]hexene ring fusion has substantially larger effect on the strength of cation--π interactions than the monocyclic ring fusion for all of the cations due to the π-electron localization at the central benzene ring.     

Microwave dielectric properties of aqueous potassium iodide solutions as a function of temperature

The complex dielectric permittivity of aqueous KI solutions was studied for molalities of 0.50–4.01 m and temperatures of 288–323 K in the region of water dielectric permittivity dispersion. The values of high-frequency of dielectric permittivity (ε) and dielectric losses (ε″) were obtained at seven frequencies ranging between 7.5 and 25 GHz. The low-frequency electrical conductivity of the aforementioned solutions was measured for calculating ionic losses. A single relaxation process is observed in these solutions, fitted by the Debye or Cole-Cole equation with small distribution parameters. The static dielectric constant and dielectric relaxation time were studied as functions of temperature and concentration; the activation enthalpy of dielectric relaxation was calculated. The temperature dependence of the static dielectric constant was found to disappear in highly concentrated solutions. The structure-breaking effect on water caused by K⁺ and I⁻ ions was affirmed, this effect disappearing in going to elevated temperatures.