Dipolar liquids

Gil-Villegas A, McGrother S C and Jackson G 1997 Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals Mol. Phys. 92 723-34... 

TABLE 3 Interfacial Widths, Bulk Composition, and Interfacial Tension in erg cm at the Interface Between Two Dipolar Liquids [5]. x Denotes the Mole Fraction of Solvent Si in Phase i... 

If water is considered a homogeneous dipolar liquid, (V)0 = 0 and the expression for the free energy change further simplifies to... 

In the original treatment of Debye and Hiickel these constants were determined under the assumption that the ion had a point charge at r = 0 and that the interior of the ion had the same dielectric constant D as the solvent. In the On-sager (5) theory of dipolar liquids it is assumed that the molecule is represented by a spherical cavity in the liquid with a singularity at its center. The characteristics of the molecule are its electric moment in vacuum po and its polarizability a. This is to be related to an internal refractive index n by... 

B. Mode Coupling Theory of Dielectric and Orientation Relaxation in Dipolar Liquids... 

Note that the MCT treatment presented above is quite general and can be extended to describe relaxation in many different systems, such as orientational relaxation in dipolar liquids [54]. This approach can also be extended to multicomponent systems, in particular to describe transport properties of electrolyte solutions [55]. The usefulness and the simplicity of the expressions lies in the separation between the single particle and collective dynamics (as in Eq. 98). Actually this sepration allows one to make connections with hydrodynamic (or continuum frameowrk) models where only the collective dynamics is included but the single particle motion is ignored. However, the same separation is also the reason for the failure... 

The mode coupling theory of molecular liquids could be a rich area of research because there are a large number of experimental results that are still unexplained. For example, there is still no fully self-consistent theory of orientational relaxation in dense dipolar liquids. Preliminary work in this area indicated that the long-time dynamics of the orientational time correlation functions can show highly non-exponential dynamics as a result of strong in-termolecular correlations [189, 190]. The formulation of this problem, however, poses formidable difficulties. First, we need to derive an expression for the wavevector-dependent orientational correlation functions C >m(k, t), which are defined as... 

Dipole-dipole interactions are responsible for the cohesion of dipolar liquids. For example, methyl ether,... 

B. Bagchi, Dynamics of solvation and charge-transfer reactions in dipolar liquids, Annu. Rev. Phys. Chem., 40 (1989) 115-141. 

B. Bagchi and A. Chandra, Polarization relaxation, dielectric-dispersion, and solvation dynamics in dense dipolar liquid, J. Chem. Phys., 90 (1989) 7338 -5 A. Chandra and B. Bagchi, Effects of molecular size in solvation dynamics, J. Phys. Chem., 94 (1990) 1874—6. 

It follows that an equation of Bom type, but based on different physical principles (Eq. 56) is a good approximation for the continuum energy in dipolar liquids up to the onset of dielectric saturation at x = 3, provided it is integrated from an appropriate distance somewhat less than that of the superdipole center of the innermost solvation shell from the central ion. This corrected radius will differ from the distance from the ion to the dipole centers of the solvation shell under consideration by about 50% more than the radius of a water molecule. 

In the case of a static field, the macroscopic relative permittivity e° has to be used in (82) for the cavity field factor, while the optical relative permittivity extrapolated to infinite wavelength e can be applied to estimate the static polarizability a(0 0) in (84). In this way the Onsager-Lorentz factor for a pure dipolar liquid is obtained (87). 

For a pure dipolar liquid the prefactors m (101) reduce to the Onsager-Lorentz factor (87). We use a double bar ( ) for the effective dipole moment in the energy expression (100). Note that the dipole moment (101) is different from the effective solute dipole moment (102) which results from (84), (88) and (90)... 

Analogous results have been obtained for the Lewis acid/base equilibrium between ionic tropylium azide and covalent 7-azidocycloheptatriene [178]. Again, in less polar solvents such as deuterio-trichloromethane and even [Dgjacetone, no ionization to give the tropylium and azide ions could be detected. Dipolar liquid sulfur dioxide, however, induces complete ionization at low temperature (—70 °C). 

Were water a simple unassociated dipolar liquid, the effect of an applied field would be simply to orient it, to inhibit its random libration and bend the average... 

Freezing of a dipolar liquid is accompanied by a rapid decrease in its electric permittivity [8-10]. Following solidification, dipole rotation ceases and the electric permittivity is almost equal to n, where n is refractive index, as it arises from deformation polarisation only. Investigation of the dynamics of a confined liquid is possible from the frequency dependences of dielectric properties, which allows both the determination of the phase transition temperature of the adsorbed substance and characteristic relaxation frequencies related to molecular motion in particular phases. 

In order that the constant Km of the solution be a strictly additive quantity, it is necessary that the constants and of the components shall not depend on the concentration. In reality, however, earlier and newer experimental results yield beyond doubt deviations from the additivity rule (208) even in dilute solutions. Particularly large deviations from (208) in the entire range of concentrations are observed in solutions of dipolar liquids in non-dipolar solvents, whereas in systems containing only non-dipolar liquids these deviations are much smaller. 

Solution of a dipolar liquid in a quadrupolar solvent. Let us assume the solvent (component 1) to be non-dipolar, and the solute (component 2) as consisting of dipolar molecules. Moreover, for the sake of simplicity, let the molecides of both components be axially symmetric. Equation (227) now yields, on ne ecting fluctuations and non-linear polarizability ... 

Hence, once the correlation parameter /g of the pure solvent is available, equation (228) permits the determination of the parameter of cross-angular correlations A . Recently, Stiles determined the value of A for several dipolar liquids by measuring the Kerr constant in dilute solutions in benzene. However, the A values thus obtained, e.g. for the benzene-nitrobenzene correlation, J ii, differ in sign from the value... 

With regard to dipolar liquids and thdr solutions in non-dipolar solvents, Piekara developed a complete theory of dipolar couplings calculating all three correlation factors Rcn, Pk, and Rs- These studies revealed that nitrobenzene molecules coalesce momentarily into antiparalld aggregates, which then tend to couple mutually into almost parallel pairs. Feterlin and Stuart performed a detailed study of the influence on Ae not orjly of Debye dipole couplings but moreover of anisotropy of the local Lorentz field. 

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