Читать книгу Liquid Crystals - Iam-Choon Khoo - Страница 47

In this section, we consider the interactions of nematic liquid crystals with applied fields (electric or magnetic); we will limit our discussion to only dielectric and diamagnetic interactions.

For a generally applied (dc, low frequency, or optical) electric field , the displacement may be written in the form

(3.23)

The electric interaction energy density is therefore

(3.24)

Note that the first term on the right‐hand side of Eq. (3.24) is independent of the orientation of the director axis. It can therefore be neglected in the director axis deformation energy. Accordingly, the free‐energy density term associated with the application of an electric field is given by

(3.25)

in SI units (in cgs units, ). The molecular torque produced by the electric field is given by

(3.26)

Similar considerations for the magnetic field yield a magnetic energy density term U_m given by

(3.27)

a magnetic free‐energy density (associated with director axis reorientation) F_m given by

(3.28)

and a magnetic torque density

(3.29)

These electric and magnetic torques play a central role in various field‐induced effects in liquid crystals.