Crystallization 239 Electric charge relaxation

In this section we wish to consider all the possible contributions to the electric permittivity of liquid crystals, regardless of the time-scale of the observation. Conventionally this permittivity is the static dielectric constant (i.e. it measures the response of a system to a d.c. electric field) in practice experiments are usually conducted with low frequency a.c. fields to avoid conduction and space charge effects. For isotropic dipolar fluids of small molecules, the permittivity is effectively independent of frequency below 100 MHz, but for liquid crystals it may be necessary to go below 1 kHz to measure the static permittivity polymer liquid crystals can have relaxation processes at very low frequencies. 

Orientational polarization is not a resonant process since the molecular dipoles have inertia. The response of the orientational polarization to a charge of the electric field is, therefore, always retarded. This process is called dielectric relaxation. The characteristic time constant of such a relaxation process—this is the time for reaching new equilibrium after changing the excitation—is called relaxation time (r). It is strongly temperature dependent, since it is closely related to the viscosity of the material. At room temperature, the relaxation times of the orientational polarization in crystals are of 10 -10 s. In amorphous solids and polymers, however, they can reach a few seconds or even hours, days, and years, depending on the temperature. 

In a homopolar crystal, such as Ge, the strong electric dipoles created in a displacement of bare core-charges +4]ej are completely cancelled by the electronic charge density, which readily relaxes, l.e. adapts its distribution to the displacement. In a polar crystal, however, this cancellation is not complete, and we are interested in the resulting electric moment, which the phenomenological theories traditionally represent as a displaced effective charge. 

The relaxation of the quadrupolar Xe nucleus is predominantly due to the interaction between the nuclear electric quadrupole moment and the fluctuating EFG at the nuclear site. The origin of the EFG contributing in a solution is, however, still partly an open question. Various models, both electrostatic and electronic, have been developed. The electrostatic models assume the EFG to be due to solvent molecules represented by point charges, point dipoles or quadrupoles, or a dielectric continuum. In the electronic approach, EFG is considered to be a consequence of the deformation of the spherical electron distribution of Xe. The deformation arises from the collisions between xenon and solvent molecules. It is obvious (evidence is provided, for example, by i Xe NMR experiments in liquid-crystal solutions, and by first principles calculations) that neither of these approaches alone is sufficient. In typical isotropic solvents, the Xe ranges from 4 ms to -40 ms. 

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