János Liszi

Calculations on ionic solvation—V The calculation of partition coefficients of ions

Abstract The solvation free energy of an ion in an organic solvent is calculated using our new electrostatic method, and is combined with the hydration free energy to yield the free energy of transfer of the ion from water to the organic solvent. It is shown that for the solvent systems water/1,2-dichloroethane, dichloromethane, chloroform, o -dichlorobenzene, chlorobenzene, and nitrobenzene there is good agreement between the calculated ΔG t o values and the free energies for partition of ions, ΔG p o = -RTlnP. For organic phases in which water is quite soluble, for example 1-octanol, 1-pentanol, isopentanol, ethyl acetate, and methylisobutylketone, the calculated ΔG t o values are always more positive than the observed partition values, ΔG p o . It is shown that this effect is due to hydration of the ions in the wet organic phase and by calculations on a solvation model in which an ion in the wet organic phase is surrounded by a layer of water of thickness 3.1 A (the diameter of a water molecule) it is concluded that in the first group of solvents most ions are unhydrated in the wet organic phase; Cl − is an exception and is partially hydrated. In the second group of wet solvents, all ions are at least partially hydrated, and Cl − is hydrated by a layer of water that must be even thicker than the diameter of a water molecule.

Calculations on ionic solvation. III. The electrostatic free energy of solvation of ions, using a multilayered continuum model

For the calculation of the electrostatic free energy (and also the entropy) of solvation of an ion, a model is set up in which an ion of given crystallographic radius is surrounded by a series of concentric spherical layers, each with a different relative permittivity, immersed in the bulk liquid. A complete general solution is given for any number of such layers, both for the electrostatic free energy of solvation and the corresponding entropy term. The dielectric saturation effect is taken into account through the different relative permittivities of the layers. The first layer, next to the ion, is considered to have a special role and to have a relative permittivity e=n2, independent of the dielectric saturation effect of the ion.

Calculations on ionic solvation. Part 6.—Structure-making and structure-breaking effects of alkali halide ions from electrostatic entropies of solvation. Correlation with viscosity B-coefficients, nuclear magnetic resonance B′-coefficients and partial molal volumes

The electrostatic entropy of solvation of an ion, ΔS°e, or the contribution to ΔS°e from the co-ordination sphere of the ion, ΔSI, II, have been shown to be quantitative measures of the structure-making and structure-breaking effects of ions of the alkali halide series in water and in non-aqueous solvents. Both entropy criteria indicate that in water the ions Li+, Na+, Ag+ and F– are net structure-makers, the ions Rb+, Cs+, Cl–, Br–, I– and ClO–4 are structure-breakers, and K+ is a borderline case. In the non-aqueous solvents formamide, methanol, N-methylformamide, dimethylformamide, dimethylsulphoxide and acetonitrile, all the above ions are structure-makers with the exceptions of the weak structure-breaking ion ClO–4 in formamide and the borderline cases of ClO–4 in methanol and I– in formamide.It is shown that the ΔS°e or ΔS°I, II values may be used to assign single-ion B- or B′-coefficients and that for water and several non-aqueous solvents there are good linear correlations between the entropy values and the single-ion coefficients. There are also good linear correlations between the entropy values and single-ion text-decoration:overlineV° values when the latter are based on text-decoration:overlineV°(H+, aq, 1 mol dm–3)=–5.4 cm3 mol–1 and when values of text-decoration:overlineV° in non-aqueous solvents are assigned by the correspondence method. It is further shown that the general conclusions reached do not depend on any particular choice of ionic radii, although the Goldschmidt–Pauling set is preferred, and it is suggested that the derived ΔS°e and ΔS°I, II values are close to ‘absolute’ values and hence provide an ‘absolute’ measure of ion–solvent interactions.

A study of orientational ordering in a fluid of dipolar Gay-Berne molecules using density-functional theory

We present a density-functional approach to describe the orientational ordering of nonpolar and dipolar Gay–Berne fluids. The first-order perturbation theory developed by Velasco et al. [J. Chem. Phys. 102, 8107 (1995)] for a Gay–Berne fluid is simplified and tested for molecules with a length to breath ratio of κ=3 and energy anisotropies of κ′=1,u20091.25,u20092.5, and 5. The theory is found to be in fair agreement with existing simulation data for the location of the isotopic–nematic phase transition, but it overestimates the vapor–liquid critical point of the fluid due to a description of the free energy at the mean-field level. The effect on the phase behavior of including a central longitudinal point dipole within the Gay–Berne molecule is studied using a correct treatment of the long-range dipolar contribution at the level of a second-order virial theory [B. Groh and S. Dietrich, Phys. Rev. E 50, 3814 (1994)]. For a given energy anisotropy of κ′=5 and reduced dipole moment μ*=0.5 we search for a stable fer...

The field dependence of the Kirkwood factor and the nonlinear dielectric behavior of some liquids

An equation is deduced for the field dependence of relative permittivity of liquids making allowance for the field dependence of the Kirkwood g factor too. The equation gives predictions on both normal and anomalous dielectric saturation as well as on the structure‐breaking or structure‐making effect of the field. Comparison with experimental data indicates that the field dependence of the g factor can alter significantly the nonlinear coefficient Δe/E2 calculated for some alcohols, water, and nitrobenzene. Comparison is also made with approximations, published previously. It is indirectly confirmed that the dielectric behavior of liquids can be described by the same equation even in the vicinity of ions in electrolyte solutions, provided that the average field strength, calculated on the basis of the lattice model of electrolytes, does not exceed the value of about 104 esu. This is about 100 times stronger than the maximum field applied in macroscopic measurements of the nonlinear coefficient.

Calculations on ionic solvation. Part 4.—Further calculations in solvation of gaseous univalent ions using one-layer and two-layer continuum models

The equation for the electrostatic free energy of solvation of a gaseous ion, based on a one-layer model, contains two disposable parameters, the dielectric constant of the layer Iµ1 and the thickness of the layer. If Iµ1 is taken as 1.05n2, where n is the solvent refractive index, results are no better than our previous calculations when Iµ1 was set equal to 2.0. However, if Iµ1= 1.05n2 and if (b–a) is used as an adjustable parameter, excellent agreement with observational values is obtained for both aprotic and hydroxylic solvents; the required values of (b—a) are quite close to the solvent radii used previously. In order to calculate the corresponding entropy of solvation, a value of δIµ/δT is required. For aprotic solvents the necessary δIµ/δT values to obtain agreement with experiment are close to values of δn2/δT and close to the value of –1.6 – 10–3 K–1 used before. However, for hydrogen bonded solvents rather unrealistic values of δIµ/δT are needed to reproduce the observed entropies of solvation and it is concluded that for these solvents an extra positive entropic contribution is necessary. It is shown also that using the one-layer model, the variations of ΔGos with solvent, for a given ion, arise both from effects within the layer and effects in the bulk solvent, but that the corresponding variation of ΔGos is almost entirely due to effects beyond the layer. The observations of Criss and Abraham that the entropy of transfer of alkali metal cations and halide anions between solvents depends only on the solvents and not on the ion transferred is interpreted satisfactorily using the one-layer model.Calculations have also been carried out using a model in which an ion is surrounded by two concentric solvent layers and then the bulk solvent. Although this model contains extra disposable parameters, it is shown that results using the two-layer model are not significantly better than the latest results using the one-layer model. In particular, it is demonstrated that the extra entropic effects in hydrogen bonded solvents are still necessary even using the two-layer model to calculate the electrostatic entropies of solvation.

Calculations on Ionic Solvation. VII* The Free Energy of Solvation of Ions Calculated from Various Local Solvent Dielectric Constant-Distance Functions

Calculations on the electrostatic free energy of solvation of Rb+ (and also Br-) in acetonitrile have been carried out by using various functions that relate the local solvent dielectric constant to distance from the centre of an ion immersed in the solvent. A simple one-step dielectric constant-distance function yields a calculated value in good agreement with the experimentally observed value; this agreement does not depend on any arbitrary single-ion convention. The new dielectric constant profile suggested by Stiles leads generally to too negative a calculated value, as does the Born equation, but an amended profile of similar mathematical form to the function used by Stiles also leads to good agreement between calculated and observed values. It is suggested that although mathematical functions of dielectric constant-distance may be selected on the basis of agreement between calculation and experiment and of convenience of use, not too much physical significance should necessarily be attributed to these functions.

Calculation of the thermodynamics of solvation of gaseous univalent ions in water from 273 to 573 K

Values of ΔG⊖s, ΔS⊖s, and ΔC⊖ps for solution of gaseous univalent ions in water from 273 to 573 K have been calculated using Abraham and Liszis method, in which a neutral term is obtained from data on rare gases and an electrostatic term is obtained using a solvation model in which an ion of radius a is surrounded by a solvent layer of thickness (b – a) and dielectric constant Iµ1. It is shown that when (b – a) is held constant for a given ion and when Iµ1 is obtained from Iµ1= 1.87 at 298 K and ∂Iµ1/∂T=–1.6 × 10–3 K–1 there is good agreement between calculated quantities and those from Tremaine and Goldman at temperatures > ca. 423 K. There is similarly good agreement between ΔC⊖ps(calc.) and values from Cobble et al. for solution of (Na++ Cl–) above 423 K. It is suggested that below this temperature there are effects due to the structure of water that cannot be calculated on an electrostatic theory. It is shown that whereas at 298 K ions may be structure making (Na+) or structure breaking (Cs+, Cl–, Br– and I–), at temperatures > ca. 400 K all the ions studied (Na+, K+, Rb+, Cs+, Cl–, Br– and I–) are structure making. The structure-making and -breaking effects of ions in water as deduced from entropies of solvation may quantitatively be connected with ionic viscosity B coefficients at all temperatures studied (273–423 K).

Field-dependent Kirkwood factor in the non-linear dielectric behaviour of binary liquid mixtures

Literature data on the non-linear dielectric behaviour of binary liquid mixtures have been recalculated with respect to the field dependence of the Kirkwood factor of the associating component. Thus the concentration-dependence of the first non-linear coefficient of the Kirkwood factor has been obtained. The dilution of the polar component by the apolar one alters the association equilibria, as is reflected in the first non-linear coefficient for both normal and anomalous dielectric saturation.

Influence of static electric field on the vapour–liquid coexistence of dipolar soft-sphere fluids

The influence of a static homogeneous electric field on the vapour–liquid equilibrium of dipolar soft-sphere fluids has been studied by the Gubbins–Pople–Stell perturbation theory. The thermodynamic properties of the fluid as functions of the field strength were derived from the Helmholtz energy containing the field-dependent relative permittivity. The dielectric saturation was studied by a perturbation theoretical treatment of the Kirk-wood equation. Our calculations can yield a weak negative saturation. It was found that the critical quantities increase, while the temperature range of the phase coexistence narrows with the field strength. A comparison between our electrostriction results and simulation data shows reasonable agreement at low field strengths.