Orientation polarisation

Pq the dipole or orientation polarisation P itself is defined by the Clausius-Mosotti Equation... 

Electric polarisation (P ef deformation, Por orientation polarisation) Momentum coordinate Spatial coordinate... 

Fig. 14. Orientation polarisation of dipole moments in an electric field Eot, (1), (2) possible orientation angles 8 and rr — 8 and (3), (4) stochastic orientation (angles 6j and 82)...

In conformity with the mechanical losses we can calculate the orientation polarisation using Eq. (28). It will btA= - Ho or exp/cof. If there are three possible confor-... 

In the case of two possible positions distributed stochastically for the orientation polarisation we find... 

Besides the orientation polarisation we observe a deformation polarisation, identical to that of an induced dipole moment. In a spatial unit the polarisation caused by deformation (due to a shift of the electrical charges) will be... 

As in the solid state the share rate a of dipoles taking part in dipole orientation is much more smaller than in the liquid state, where orientation polarisation Eqs. (78) and (79) is also low. The dielectric constant even in polar polymers is not higher than 6. 

Molecular polarisability is the result of two mechanisms (a) distortional polarisation and (b) orientation polarisation. Distortional polarisation is the result of the change of electric charge distribution in a molecule due to an applied electric field, thereby inducing an electric dipole. This distortional polarisation is coined ad. Permanent dipoles are also present in the absence of an electric field. At the application of an electric field they will orient more or less in the direction of the electric field, resulting in orientation polarisation. However, the permanent dipoles will not completely align with the electric field due to thermal agitation. It appears that the contribution of molecular polarisability from rotation is approximately equal to p2/(3kT). Accordingly, the total molecular polarisability is... 

The polarisation itself is, just as the molecular polarisability is, the result of deformation polarisation Pd and the orientation polarisation Ps. Accordingly, the total polarisation is equal to P = Pd + Pa. Because of the resistance to motion of the atom groups in the dielectric, there is a delay between changes in the electric field and changes in the polarisation. The deformation polarisation takes place instantaneously (more precisely in a time of the order of 10-14 s) on the application of an electric field. There are two limiting values of e Erxi at short times or high frequencies and es at long times or low frequencies. This means that we have for the deformation polarisation... 

Consequently, polarisation due to dipolar orientation is directly proportional to the local field strength and inversely proportional to temperature. We can think of the quantity ifikT as an orientational polarisability and simply add... 

Its lower limit is of the order of E-ll s. for small molecules and, often, of the order of E-2 to E+4 s. for polymers at room temperature. Since this orientation polarisability, aro, involves physical movement of parts of the macromolecules it is not surprising that, apart from the temperature, other factors which determine the molecular mobility affect it. 

Next to electronic, atomic and orientation polarisation (see 5.1.2), two other polarisation types can occur during TSD experiments ... 

A number of common molecules, including water, carry a permanent dipole. If such molecules are exposed to an electric field they will try to orient the dipole along the field (Figure 11.4c). As the movement of molecules in solids is restricted, orientational polarisability is more often noticed in gases and liquids. 

At optical frequencies a = 0 , because the molecules cannot reorient sufficiently quickly in the oscillatory electric field of the light wave for the orientational polarisability to contribute, as discussed further in section 9.2.4. Setting a = a in equation (9.9) gives in terms of the optical refractive index and, if this expression for is inserted, equation (9.16) can then be rearranged as follows ... 

In considering dielectric relaxation it is, however, necessary to remember that there are two dilferent types of contribution to the polarisation of the dielectric, the deformational polarisation and the orientational polarisation so that P = + P. For the sudden application of a... 

Molecular polarisability is discussed in detail in chapter 9. Orientational polarisation involves the rotation, under the influence of an electric field, of molecules, or parts of molecules, that have permanent electric dipoles. This effect clearly leads to a possible mechanism for orienting molecules and, in particular, for reorienting the domains of liquid crystals or LCPs that have permanent dipoles. It is less obvious that deformational polarisation can lead to orientation. If, however, the polarisability of a molecule is anisotropic, as is usually the case, the polarisability and hence the induced electric dipole will differ for different orientations of the molecule in the field. The interaction energy with the field is therefore reduced if the molecule rotates so that its direction of maximum polarisability coincides with the field direction. Electric-field orientation is largely of importance in device applications. 

In principle in a dielectric experiment [la,b] an electric field is applied to a material under study and the resulting polarisation current is measured (Fig. 21.1). It is composed out of two contributions, the induced (time constant = 10 s) and the orientational polarisation (time constant > 10 s). Modem broadband dielectric measurements are carried out in the frequency domain. The sample geometry has to be adapted to the spectral range in which the measurements are carried out (Fig. 21.2). 

I Introduction to molecular motion in polymers 12.4 Dipole orientation polarisation... 

Reference solvent 1,4-dioxane Monte-Carlo method from PCM surface from PCM volume mean of b and c induction polarisation orientation polarisation... 

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. 

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