Internal field correction

It was pointed out by Cunningham et al.4) that it is strictly necessary to take into account the internal field correction, and define quantities cps instead of A, where... 

A more rigorous theory [40, 41] accounting for an internal field correction yields the following ratio of two field complex amplitudes ... 

The relationship (139), of course, is not rigorous, but it is based on an elementary macroscopic consideration [41] of the internal-field correction. Being widely used (GT, VIG), such a relationship is sufficient for an accurate description of the low-frequency dielectric response of strongly polar fluids. We return to this problem later in this section. 

Finally, we remark that our microscopic approach is mainly aimed at the study of the resonance-interaction mechanisms, which are revealed in the FIR range. In this range, where 3> x 1 and x > 0.1, inclusion of the internal field correction, which is accounted for in Eqs. (139) and (141), gives only a small effect. 

A theory, accounting for an internal field correction [40, 41], gives the relationship % ( ), Eq. (139), between the complex susceptibility and permittivity. For calculation of the wideband spectra it is more convenient to employ the reverse dependence (% ), Eq. (141). 

Taking into account the internal-field correction, replacing % and s by x r and E r, we use the same relationships connecting the complex susceptibility and permittivity as were employed in Sections IV-VI ... 

Equation (5.10) shows that if we take into account the internal field correction, that is, the fact that A 1, the oscillator strength for the transition is not changed and only the resonance frequency is shifted - the e(w) resonance is shifted by Au lower frequencies from the frequency of the transition in the isolated molecule ... 

Indeed, the dipole moment appearing in eqn (5.45) is not the dipole moment in vacuum but an effective dipole moment found by taking into account the internal field correction. In the isotropic medium this is pa = [(e + 2)/3 p°J which yields precisely eqn (5.69) if we take into account eqn (5.68). This conclusion is valid for the local centers of any nature in the nonconducting medium. We mean here media in which the intermolecular interaction does not violate the neutrality of molecules. The specific effects found in ionic crystals are discussed by Smith and Dexter (27). 

A general connection between the static susceptibility xs and permittivity es, which accounts for the internal field correction is given by... 

Simplifying assumptions a highly oriented polymer has the simplest form of uniaxial distribution and is fully oriented, there is no correction for reflection at the surface of the sample, no internal field corrections and no scattering of radiation. 

Appendix 5B. Lorentz Calculation, Internal Field Correction... 

As far as spontaneous fluctuations of orientation are concerned, that is within the frame of linear response, this function can be expressed in terms of measured susceptibilities respective to any external field coupled with the orientational degrees of freedom. Such is the case for hertzian electromagnetic radiation that couples with the molecular electric moments. Suitable expressions in terms of the susceptibilities have been proposed, duly incorporating a convenient internal field correction. One among them reads ... 

This point has been made particularly clear by Fulton (29), who demonstrated both qualitative and quantitative changes that take place when the correlation functions are calculated by taking the refractive index to be constant instead of including the actual variation of refractive index with frequency in the calculation. Furthermore, some statistical functions such as the rotational velocities memory functions alluded below (IV.3.3), have analytical expressions that depend critically on terms like (e -e ) which enter the internal field corrections. These terms are very sensitive to the variations of real permittivity since. 

In Eq. (5.7) we have substituted S for the principal value of the order tensor Su. It should be clear from the results of Eq. (5.7) in conjunction with the relationship between the polarizability and the refractive index (Eq. (5.5), leaving aside complications associated with anisotropic internal-field corrections), that n w 7 In short, a nematic liquid may be readily distinguished from an ordinary liquid because... 

As noted earlier, Qa/9 may be equally well-defined in terms of other macroscopic properties such as the refractive index or dielectric tensor. However, the simple relation [Eq. (3.6)] cannot be expected to hold for the dielectric anisotropy Ae and electric polarizability aij. This is due to complicated depolarization effects caused by the relatively large near-neighbor electrostatic interaction. The internal field corrections [3.3] are necessary in the electric case. It has been shown that Qa can be used to describe orientational order both in uniaxial and biaxial phases. Furthermore, measurement of Qa/3 is particularly useful when description of flexible molecules using microscopic order parameters becomes problematic. Experimentally, both magnetic resonance and Raman scattering techniques [3.3] may be employed to monitor the orientational order of individual molecules and to determine microscopic order parameters. 

Appendix Internal Field Correction for Ionic Dielectric Function... 

Some solid-state physics texts (e.g., Kittel) include the correction for internal fields in calculating the electronic dielectric function but ignore it when calculating the ionic dielectric function and obtain the same result as Equation 23.17. Instead of computing the internal field corrections for ionic and electronic contributions to the dielectric function separately and then adding them, Ashcroft and Mermin combine the polarizabilities of the ions and the electrons and then apply the Clausius-Mossotti equation to the sum ... 

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