Equation Kirkwood-Frohlich

For experimental estimation of the correlation factor g the Kirkwood-Frohlich equation [7]... 

The static permittivities of mixtures of organic liquids with water may be interpreted in terms of polarization theory. We shall see that water can be used as a solvent for the determination of dipole moments of highly polar molecules, but for less polar molecules the Kirkwood-Frohlich equation has been used as a method of demonstrating molecular interactions between water and solute. 

Reis JCR, Iglesias TP (2011) Kirkwood cwrelatirm factras in liquid rrrixtures from an extended Orrsager-Kirkwood-Frohlich equation. Phys Chem Chan Phys 13 10670-10680... 

Dielectric saturation produces "irrotational bounding of the solvent molecules surroimding the ion and hence yields solvation numbers. Pottel et al.25,58 use the empirical Bruggeman relation for the estimation of the "effective" volume fraction of the solvent. Comparision with its "analytical" value yields solvation numbeiTS Zp. Lestrade et al.30 39 use the Kirkwood Frohlich equation with the Kirkwood parameter assumed independent of electrolyte concentration, to calculate solvation numbers Zl Ly means of the number of molecules per unit volume required to explain the limiting slope of the permittivity depression. A siu vey of solvation numbers Zp and obtained from these methods and their critical discussion is given in Ref. 14. 

The Kirkwood-Frohlich equation incorporates this factor, and enables the mean square effective dipole moment to be deduced from measurements of the electric permittivity, refractive index and number density of a fluid ... 

The distortion polarizability contributes only to the refractive index, and the dielectric constant can be related to the molecular dipole moment through the Kirkwood-Frohlich equation, which in isotropic liquids reads as ... 

The static dielectric permittivity for an ensemble of dipolar chain molecules is given by the generalized form of the Kirkwood-Frohlich equation... 

However, the most recent discussions favour these high values of g although values of the order of 20% lower had ori nally been favoured. This is because the Frohlich equation [equation (1)] differs from the earlier version of Kirkwood, and treats the inner field in a more nearly correct manner. It is no longer necessary to make a calculation of the HjO dipole moment in its surroundings in the liquid, as had been necessary in the application of the Kirkwood equation. The dipole moment of the free molecule, /i = 1.84D, is used in equation (1), together with = 1.80 at 293 K. This leads to a value of = 2.82, which is sufficiently close to that calculated from the computer dynamics model to warrant optimism for future calculations. The exact choice of will continue to present difficulties until the far-i.r. data are complete over a wide range of temperature. 

However, recalculating the value of y using the method described in the paper for the field factors, gives the value in brackets. The unbracketed value, for the overall microscopic nonlinearity, converts to 2859 au. In the case of associating liquids the authors argue that equation (7) can be used in modified form with the inclusion of a factor, g, which they deduce from the Kirkwood-Frohlich modification of the Onsager theory,... 

More recently, Harris and Alder, keeping the general principles of Kirkwood s theory, have tried to calculate the polarization effects more rigorously. Unfortunately their final equation does not coincide as it should, with Onsager s equation when it is assumed that there are no short-range interactions cosy> = 0). This is because some of Kirkwood s equations are only valid when the assumptions of the author are justified, and cannot be used as was done by Harris and Alder, when a deformation polarization is superimposed on the orientation polarization. For instance, in presence of deformation effects boundary conditions cannot be introduced in the same manner as in Kirkwood s model (cf. Frohlich i). 

Equations (7) and (10) generalize the Kirkwood-Frohlich equilibrium theory to the dynamic situation. The correlation function approach to dielectric relaxation was first made by Glarum (37) and was extended by Cole (38) and by Steele (39). 

Onsager s equation has been used for slightly polar solvents such as toluene. With strongly polar solvents, chloroform for instance, Kirkwood s or Frohlich s theories must be resorted to, and no value of the dipole moment can be obtained unless the correlation factor g is known by independent data concerning the structure of the solution. 

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