Polarisable ions

P and Q are also called as Neumann s constants and in turn they are related to Pockel s coefficients, which can be similarly defined. Stress optic coefficients are thus related to differences in refractive indices of e-and o- rays. Glasses containing PbO and such highly polarisable ions have been known to exhibit very low values of stress-optic coefficients. The stress optic coefficients have the units of inverse pressure and are of the order of lO Pa" (known as Brewster) or 10 cm dyne" and generally vary between 2.5 - 4.0 Brewsters in glasses. 

It is well known that large polarisable ions bind strongly to interfaces. The ion effect is particularly pronounced for systemsbased on cationic surfactants. The choice of counterion for anionic surfactants seems to be of less importance. The fact that anions interact more strongly than cations with oil-water interfaces is well known and the magnitude of the interaction of different anions follows the so-called Hofmeister series [30]. 

Structure breaker ions bind water molecules around them sufficiently to cause a mismatch between the structure of the bound water and that of unmodified water typical of the pure solvent. But the order induced is not great enough to outweigh the disorder created in the misfit region, and this will occur with the less strongly polarising ions such as Rb, ... 

Fig. 1.1 The Faber-Ziman Sap k) a, /3 = M, X) and Bhatia-Thornton Su k) (/, / = N, C) partial structure factors for liquid and glassy ZnCl2. The points with vertical (black) error bars are the measured functions in (a) and (c) for the liquid at 332(5) °C [ 16] and in (b) and (d) for the glass at 25(1) °C [15, 16]. The solid (red) curves are the Fourier backtransforms of the corresponding partial pair-distribution functions after the unphysical oscillations at r-values smaller than the distance of closest approach between the centres of two atoms are set to the calculated Unlit at r = 0. The broken (green) curves in (a) are from the polarisable ion model of Sharma and Wilson [63] for the Uquid at 327 °C...

Fig. 1.2 The Faber-Ziman partial structure factors Sap(k) and partial pair-distribution functions gafi (r) (a, /S = M, X) as calculated for models using two different values for the anion polarisability ax [61]. The curves in (a) and (b) correspond to a rigid ion model (RIM) with ax = 0, while the curves in (c) and (d) correspond to a polarisable ion model (PIM) with ax = 20 au. The introduction of anion polarisability leads to the appearance of an FSDP in S mm (k) at kpsop 1.2 A and to an alignment of the principal peaks in aU three Safi(k) functions atkpp 2 A. The alignment of the principal peaks in (c) arises from in-phase large-r oscillations in the ga r) functions shown in (d)...

Fig. 1.3 The Bhatia-Thornton pair-correlation functions rhu(r) (I, J = N, C) [solid dark (black) curves] where the upper, middle and lower pairs of panels show the NN, CC and NC functions, respectively. For each pair, the upper panel gives the function obtained for a polarisable ion model (PIM) with ax = 20 au [20] and the lower panel gives the measured function for glassy ZnCh [15, 16], Each function is broken down into its contributions from rhxx(r) [broken (n 4) curves], rhuxir) [light solid (green) curves] and rhuMO") [solid (blue) curves]. The abscissa for the simulated functions are scaled by 1.98/2.09 to reflect the relative positions of the principal peak in the simulated and measured (k) partial structure factors...

In Chap. 8, a more comprehensive data set including salt mixtures in water will be presented. Nevertheless, Fig. 8 shows the main features. Salts with soft, polarisable ions increase the surface tension of water less than salts composed of hard ions. However, the effect is small, which makes it difficult not only for precise measurements, but also for quantitative predictions with simulations and theories. Anions seem to change the surface tension more than cations. Whereas it is intuitively comprehensible that hard ions tend to stay away ftom the surface, more than only weakly hydrated soft or hydrophobic ions, it was for a long time a mystery, why acids lower the surface tension. This means that protons should go to the surface, which is counter-intuitive, at least for a chemist. A plausible explanation is given by Jungwirth and co-workers, based on their molecular dynamics (MD) simulations. It seems that for geometrical reasons, HsO" fits better into the surface layer than into the bulk. 

The theoretical approach based on the HNC integral equation is described in the context of ionic specificity. Two levels of description of the water medium are considered. Within the Primitive Model (continuous solvent), ionic specificity is introduced via effective, solvent-averaged, dispersion forces. The agreement with experimental data in bulk or at air-water interfaces is only partial and illustrates the limits of that approach. Within the Born-Oppenheimer model, the molecular HNC equation is solved with an explicit description of the solvent molecules (SPC water). Ionic and solvent profiles in bulk and at interfaces are enriched by short-range osdUated structures. The ionic polaris-ability is introduced via the self-consistent mean-field theory, the polarisable ions carrying an effective, fixed dipole moment. The study of the air-water interface reveals the limits of the conventional HNC approach and the needs for improved integral equations. 

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