Onsager induced moment

According to Onsager the induced moment term M( ) is determined by the internal or local field whereas the permanent dipole term is related to the directing field E<,ij orienting the permanent dipoles p. The combination of Eqs. (3.10) and (3.2) requires that the two different field vectors must be expressed in terms of the measured Maxwell field. The calculations of the terms and M p as functions of Ej , and E jj usually are approximations. The final expressions may be written in terms of conversion factors (g factors ) which are a function of particle anisotropies as well as of the properties of the medium in which the particles are embedded (polar, nonpolar, gas phase, or fluid phase). 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

By analogy with the the Onsager s theory, it is assumed that the response of the molecule to an external probing field can be expressed in terms of an external dipole moment fit, sum of the molecular dipole moment and the dipole moment arising from the molecule-induced dielectric polarization. Following ref. [8] and ref. [47],... 

The experimental data reported in the Table for gas phase have been extracted from measurements in dioxane solution by applying the Onsager reaction field model to eliminate the solvent effect [37], By contrast, the cyclohexane experimental dipole moments have been obtained from those reported in Ref. [37] re-including the proper reaction field factors. Once recalled these facts, we note that the observed solvent-induced changes on both ground and excited state dipole moments are quantitatively reproduced by the calculations. 

In contrast to diamagnetism where the magnetic interactions between molecules can be neglected, the polarization field in the medium becomes important when discussing dielectric anisotropy (see, e.g., Bottcher< >). Maier and Meier > took this into account by applying the Onsager theory.The effective induced dipole moments per molecule along and... 

Note that the induced part is formally separated from the permanent dipole moment contribution in a particular manner. In Frohlich s version of the Onsager model the spherical dipoles have effective dipole moments... 

The external static electric field applied to a dielectric material induces fire polarisation P, that is the dipole moment per unit volume. For low fields P is prt rtional to the electric field E [1>3], P = 8o(8s - 1) E, where 8s is the relative dielectric permittivity or dielectric constant and 8o is the dielectric permittivity of free space. All these quantities concom the macroscopic volume of the dielectric medium. In order to relate them to the relevant microscopic param ers (for example dipole moment and polarisability) the local electric field Eioc acting on a molecule must be known. The relation between Eioc and E is the crucial problem of the physics of dielectrics and has not been solved in general. For isotropic fluids the Onsager theory is commonly used [4]. 

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