Maier-Meier equations

The last equation shows that the induced polarization is proportional to S, whereas the orientation polarization is governed by S/T. The experimental temperature dependence of Ac can roughly be explained with the Maier-Meier equations. 

The ratio Ae/Ae" " =can give some information about a degree of dipole-dipole associations in the nematic phase of the substances under consideration. However, the obtained value of g <0.5 seems to be unreliable in the light of the above discussion concerning the applicability of the Maier-Meier equations to real nematic phase prop-... 

Maier function, hard-core repulsion 56 Maier-Meier equations 236 f Maier-Saupe theory 44 f, 279 f, 332... 

EQNS (1), (2) and (3) are commonly used as the basis of the molecular interpretation of the static permittivities measured as a function of temperature (e.g. [6,12-15,20,21,28-30,36,37]) and/or pressure [30,38]. Recently, quite successful predictions of anisotropic optical and dielectric constants from molecular modelling calculations were achieved with the aid of the Maier-Meier theory [39,40]. It seems worthwhile, therefore, to analyse these equations in order to point out the weak and strong points of the theory. EQN (3) is the most convenient for this purpose (both components of the permittivity are discussed by Jadzyn et al in a recent paper [41]). The parameters N, F and h in the Maier-Meier equations vary little with temperature. Therefore, the contribution from the polarisability anisotropy Aa to A8 varies with temperature in the same way as the order parameter S, whereas that connected with the orientation polarisation varies like S/T. Especially interesting seems to be the case of constant temperature discussed in [38] where As was measured as a function of pressure, p. The discussion of the measured permittivities, Sj and the anisotropy As as a function of the order parameter S obtained from the independent experiment seems to be the best way of verifying the assumptions on which the theory is based. 

These are the Maier and Meier equations [7] for the low frequency components of the permittivity extended [8] to include all orientational order parameters. They predict that the mean value of the permittivity... 

For such a comparison one has to consider the step of the density at the phase transition. All the other relations which connect molecular parameters such as the molecular dipole moment /i, the polarizability a and the angle between the molecular long axis and fj, with each other have a general problem the calculation of the internal field and its anisotropy. Therefore, all the equations given in Vol. 1, Chap. VII.2 are necessary and useful but one has to take always into account the limitations of the models. Nevertheless, the Onsager theory [27] (basis for the Maier-Meier model [28]) and Kirkwood-Frbhlich model [29] have been... 

As an example, let us consider the data presented in FIGURE 2(c) in order to check the applicability of the Maier-Meier EQN (3) for the determination of S. This equation can be rewritten as... 

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