Kirkwood-Frohlich theory

In order to apply the Kirkwood-Frohlich theory to the calculation of the static permittirity co of water at temperature T, the approximation b sometimes made that the liquid contains a number of different molecular species. It is necessary to know ... 

Schroer, W. Generalization of the Kirkwood-Frohlich theory of dielectric polarization for ionic fluids. J. Mol. Liquids, 2001, 92, p. 67-76. 

Booth" calculated the deviation of As from quadratidty by OnsagCT s model. Calculations of non-linear As-variations of higher order have also been poformed by Kielich in the Kirkwood-Frohlich semi-macroscopic approach taking into consideration statistical molecular correlations. Results such as these can be derived with the non-linear polarization (282). This treatment, however, is not directly applicable to the description of complete electric saturation, and we shall not develop it furtho- here. It appears preferable, for simplicity, to proceed within the framework of classical Langevin-Debye theory, which yidds results wdl adapted to numerical computations. ... 

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. 

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). 

Kirkwood took a more rigorous statistical-mechanical approach in an attempt to incorporate the effect of local ordering. His theory is only valid for rigid dipoles, and it was left to Frohlich to extend the treatment properly to a system of polarisable dipolar molecules. The work is well described in Frohlich s classic text (1949). The final outcome was the following formula,... 

To show the influence of various microscopic and structural factors on linear and non-linear effects in dense dielectrics, it is convenient to apply first a semi-macroscopic treatment of the theory, and then to proceed to its molecular-statistical interpretation, assuming appropriate microscopic models. The semi-macroscopic method was initially applied by Kirkwood and modified by Frohlich in the theory of linear dielectrics, and has beat successfully used in theories of non-linear tUelectrics. "... 

Further developments in the theory of the structure of polar liquids included estimates of the correlation of a given dipole to its neighbors. Important contributions were made in this direction by Kirkwood [22] and Frohlich [23]. In Kirkwood s model, the field Ej is calculated by considering all possible orientations of surrounding dipoles in a spherical cavity for a fixed orientation of the central dipole. By averaging over these orientations, Kirkwood obtained an improved estimate of the polarization of the medium. For the case of non-polarizable dipoles the result is... 

Theoretical calculations of dielectric properties according to Kirkwood s or Frohlich s theories can only be carried out if the correlation factor g is known from independent investigations on the structure of the dielectric. Conversely, as was shown by Frohlich, experimental determinations of the dielectric properties may give us precious information as to the structure of condensed, and particularly of liquid phases. In particular data concerning the influence of temperature on the function... 

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. 

Molecular theories for the static permittivity bq of dipolar liquids developed originally by Onsager, Kirkwood, and Frohlich were adapted for linear bulk... 

---