into the dynamical equations describing the field‐induced effects in nematic liquid crystals.
On the other hand, if the molecules are not strongly anchored to the boundary, that is, the so‐called soft‐boundary condition (Figure 3.3), an applied field will perturb the orientation of the molecules at the cell boundaries. In this case, a quantitative description of the dynamics of the field‐induced effects must account for these surface energy terms. A good account of surface energy interaction may be found in the work of Barbero and Simoni [4], which treats the case of optical‐field‐induced effects in a hybrid aligned nematic liquid crystal cell.
Figure 3.2. A homeotropic nematic liquid crystal with strong surface anchoring: (a) external field off; (b) external field on – only the bulk director axis is deformed.
Figure 3.3. Soft‐boundary condition. The applied field will reorient both the surface and bulk director axis.
From Eq. (3.6) for the free energy, one can obtain the corresponding so‐called molecular fields
where
(3.10)
More explicitly, Eq. (3.9) gives, for the total molecular field associated with splay, twist, and bend deformations,
and torque
(3.12)
(3.14)
with
3.3. DIELECTRIC CONSTANTS AND REFRACTIVE INDICES
Dielectric constants and refractive indices, as well as electrical conductivities of liquid crystals, are physical parameters that characterize the electronic responses of liquid crystals to externally applied fields (electric, magnetic, or optical). Because of the molecular and energy level structures of nematic molecules, these responses are highly dependent on the direction and the frequencies of the field. Accordingly, we shall classify our studies of dielectric permittivity and other electro‐optical parameters into two distinctive frequency regimes: (1) dc and low frequency and (2) optical frequency. Where the transition from the regime (1) to (2) occurs, of course, is governed by the dielectric relaxation processes and the dynamical time constant; typically, the Debye relaxation frequencies in nematics are on the order of 1010 Hz.
3.3.1. DC and Low‐frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility
The dielectric constant ε is defined by the Maxwell equation [5]:
where
