A set of 61 ion polarizabilities has been derived from the dielectric constants of 129 oxides and 25 fluorides using a least squares refinement technique in conjunction with the Clausius–Mosotti equation. These polarizabilities can be used to estimate mean dielectric constants of ‘‘well‐behaved’’ compounds. They should be particularly useful in calculation of mean dielectric constants of compounds whose dielectric constants have not been determined. They can also be used as a framework for distinguishing unusual dielectric behavior from normal dielectric behavior where deviations can frequently be attributed to piezo‐ or ferroelectricity, conductivity (ionic or electronic), ‘‘rattling’’ or ‘‘compressed’’ cations with correspondingly high or low polarizabilities, or the presence of dipolar impurities. Deviations observed from calculated dielectric constants can be used to search for unusual physical behavior.

Dielectric polarizabilities of ions in oxides and fluorides

Starting from known properties of non-specific salt effects on the surface tension at an air–water interface, we propose the first general, detailed qualitative molecular mechanism for the origins of ion-specific (Hofmeister) effects on the surface potential difference at an air–water interface; this mechanism suggests a simple model for the behaviour of water at all interfaces (including water–solute interfaces), regardless of whether the non-aqueous component is neutral or charged, polar or non-polar Specifically, water near an isolated interface is conceptually divided into three layers, each layer being 1 water-molecule thick We propose that the solute determines the behaviour of the adjacent first interfacial water layer ( I 1 ); that the bulk solution determines the behaviour of the third interfacial water layer ( I 3 ), and that both I 1 and I 3 compete for hydrogen-bonding interactions with the intervening water layer ( I 2 ), which can be thought of as a transition layer The model requires that a polar kosmotrope (polar water-structure maker) interact with I 1 more strongly than would bulk water in its place; that a chaotrope (water-structure breaker) interact with I 1 somewhat less strongly than would bulk water in its place; and that a non-polar kosmotrope (non-polar water-structure maker) interact with I 1 much less strongly than would bulk water in its place We introduce two simple new postulates to describe the behaviour of I 1 water molecules in aqueous solution The first, the ‘relative competition’ postulate, states that an I 1 water molecule, in maximizing its free energy (—δG), will favour those of its highly directional polar (hydrogen-bonding) interactions with its immediate neighbours for which the maximum pairwise enthalpy of interaction (—δ H ) is greatest; that is, it will favour the strongest interactions We describe such behaviour as ‘compliant’, since an I 1 water molecule will continually adjust its position to maximize these strong interactions Its behaviour towards its remaining immediate neighbours, with whom it interacts relatively weakly (but still favourably), we describe as ‘recalcitrant’, since it will be unable to adjust its position to maximize simultaneously these interactions The second, the ‘charge transfer’ postulate, states that the strong polar kosmotrope–water interaction has at least a small amount of covalent character, resulting in significant transfer of charge from polar kosmotropes to water–especially of negative charge from Lewis bases (both neutral and anionic); and that the water-structuring effect of polar kosmotropes is caused not only by the tight binding (partial immobilization) of the immediately adjacent ( I 1 ) water molecules, but also by an attempt to distribute among several water molecules the charge transferred from the solute When extensive, cumulative charge transfer to solvent occurs, as with macromolecular polyphosphates, the solvation layer (the layer of solvent whose behaviour is determined by the solute) can become up to 5- or 6-water-molecules thick We then use the ‘relative competition’ postulate, which lends itself to simple diagramming, in conjunction with the ‘charge transfer’ postulate to provide a new, startlingly simple and direct qualitative explanation for the heat of dilution of neutral polar solutes and the temperature dependence of relative viscosity of neutral polar solutes in aqueous solution This explanation also requires the new and intriguing general conclusion that as the temperature of aqueous solutions is lowered towards o °C, solutes tend to acquire a non-uniform distribution in the solution, becoming increasingly likely to cluster 2 water molecules away from other solutes and surfaces (the driving force for this process being the conversion of transition layer water to bulk water) The implications of these conclusions for understanding the mechanism of action of general (gaseous) anaesthetics and other important interfacial phenomena are then addressed

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500005369

The Hofmeister effect and the behaviour of water at interfaces.

Publisher Summary In an idealized picture, an ionic crystal is regarded as composed of spherical, nonoverlapping ions, bearing net charges of integral amount. The electrostatic interactions of these pointlike charges give rise to a net binding (Madelung energy), as each ion is preferentially surrounded by ions of opposite charge. In typical ionic crystals, the Madelung energy is in fact quite close to the observed cohesive energy. The Born model was originally proposed for the purpose of evaluating the lattice energy of crystals, which approach this idealized picture, and because of its success and simplicity it has subsequently been applied to the description of a variety of physical properties of ionic crystals, with varying degrees of success. In the framework of the Born model, it is convenient to describe the lattice energy of an ionic crystal as composed of energy terms arising from interactions between the ions. In addition to the net binding provided by the electrostatic interactions of point-like ionic charges, the binding arising from a synchronization of the electronic motions in the ions is considered explicitly in some versions of the model. The contribution of this so-called “van der Waals interaction” to the lattice energy is small, of the order of a few per cent. The ratio between the polarization energy that is connected with the mutually induced electronic dipoles on a pair of ions and the Coulomb interaction energy of the net charges of the ions is definitely less than the ionic polarizability per unit volume. The attractive forces in the crystal are balanced by the so-called overlap repulsive forces, which oppose the interpenetration of the ions.

Cohesion of Ionic Solids in the Born Model

Ionic sizes and born repulsive parameters in the NaCl-type alkali halides—II: The generalized Huggins-Mayer form☆

The basicity of an oxide glass can be measured experimentally from the frequency shifts in the ultra-violet (UV) (s-p) spectra of probe ions such as Pb2+ and can be expressed on the numerical scale of optical basicity Λ (ideally Λ lies between zero and unity). It is possible to relate Λ with (i) the constitution, and (ii) the electronegativity of the cations (e.g. Na+, Si4+, etc.) of the glass, and the relationship allows microscopic optical basicities λ to be assigned to individual oxides and oxy-groups in the glass. These microscopic optical basicities are used for interpreting various aspects of the physics and chemistry of glass including refractivity, network coordination number changes, chemical durability, the glass electrode, UV transparency and the host behaviour of glass towards metal ions generally. Changes in glass basicity in going from one alkali metal oxide to another are also discussed. Finally, the concept of optical basicity, both as an experimentally obtained quantity and as a number calculated from glass constitution and electronegativity, is discussed in relation to the traditional approach to acid-base behaviour in glass.

An interpretation of glass chemistry in terms of the optical basicity concept

A set of electronic polarizabilities has been obtained from a least-squares fit of experimental refraction data using simple additivity and a Lorentz factor of $\frac{4\ensuremath{\pi}}{3}$. Except for the fluorides, the electronic polarizability values of the alkali-halide crystals calculated from this set agree with the experimental data within 3 percent. Similar least-squares fits were attempted with various values of the Lorentz factor, the best fit being obtained for $\frac{4\ensuremath{\pi}}{3}$. On the basis of $\frac{4\ensuremath{\pi}}{3}$, the additivity assumption and the alkali-halide set, polarizabilities have been obtained for other ions. The best values for the sodium $D$ line in ${\mathrm{A}}^{3}$ are ${\mathrm{Li}}^{+}$ 0.03, ${\mathrm{Na}}^{+}$ 0.41, ${\mathrm{K}}^{+}$ 1.33, ${\mathrm{Rb}}^{+}$ 1.98, ${\mathrm{Cs}}^{+}$ 3.34, ${\mathrm{F}}^{\ensuremath{-}}$ 0.64, ${\mathrm{Cl}}^{\ensuremath{-}}$ 2.96, ${\mathrm{Br}}^{\ensuremath{-}}$ 4.16, ${\mathrm{I}}^{\ensuremath{-}}$ 6.43, ${\mathrm{Ca}}^{++}$ 1.1, ${\mathrm{Sr}}^{++}$ 1.6, ${\mathrm{Ba}}^{++}$ 2.5, ${\mathrm{O}}^{\ensuremath{-}\ensuremath{-}}$ 0.5-3.2, ${\mathrm{S}}^{\ensuremath{-}\ensuremath{-}}$ 4.8-5.9, ${\mathrm{Se}}^{\ensuremath{-}\ensuremath{-}}$ 6.0-7.5, ${\mathrm{Te}}^{\ensuremath{-}\ensuremath{-}}$ 8.3-10.2, ${\mathrm{Ag}}^{+}$ 2.4, ${\mathrm{Cu}}^{+}$ 1.6, ${\mathrm{Cu}}^{++}$ 0.2, ${\mathrm{Zn}}^{++}$ 0.8, ${\mathrm{Cd}}^{++}$ 1.8, ${\mathrm{Ge}}^{4+}$ 1, ${\mathrm{Sn}}^{4+}$ 3.4, ${\mathrm{Pb}}^{++}$ 4.9. Values represented by a spread indicate ions that cannot be treated additively.

Electronic Polarizabilities of Ions in Crystals

The spin wave method of Heller and Kramers is applied to a cubic antiferromagnetic crystal, oriented so that the direction of alignment of the sublattice spins is parallel to an external magnetic field. Taking into account exchange interactions and an anisotropy term, then the parallel susceptibility ${\ensuremath{\chi}}_{\mathrm{II}}$ is zero at $T=0$\ifmmode^\circ\else\textdegree\fi{}K, in agreement with the result of the molecular field treatment of the problem by Van Vleck. If nearest neighbor magnetic dipole interactions are included, ${\ensuremath{\chi}}_{\mathrm{II}}$ is nonzero but negligibly small: ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\sim}{10}^{\ensuremath{-}11}$ at $T=0$\ifmmode^\circ\else\textdegree\fi{}K. For $Tg0$ but much less than the antiferromagnetic Curie temperature, if the dipole interactions are neglected and the anisotropy is small, such that $\ensuremath{\zeta}=\frac{S{(24JK)}^{\frac{1}{2}}}{\mathrm{k}T}\ensuremath{\ll}1$, where $K$ is an anisotropy constant, then ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\propto}{T}^{2}$. If $\ensuremath{\zeta}\ensuremath{\gg}1$, then ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\propto}{T}^{\frac{1}{2}}\mathrm{exp}[\ensuremath{-}\frac{S{(24JK)}^{\frac{1}{2}}}{\mathrm{k}T}]$.

Jack R. Tessman

Papers

Electronic Polarizabilities of Ions in Crystals

The Parallel Susceptibility of an Antiferromagnet at Low Temperatures

The Lorentz Correction in Hexagonal Barium Titanate