Читать книгу Liquid Crystals - Iam-Choon Khoo - Страница 57

Field‐induced director axis reorientation, accompanied by fluid flow, is quite complicated as it involves much more physical parameters. Consider the interaction geometry shown in Figure 3.13. A homeotropically aligned nematic liquid crystal film is acted on by an electric or a magnetic field in the x‐direction. Let ϕ denote the director axis reorientation angle from the original alignment direction z. Assume hard‐boundary conditions at the two cell walls at z = 0 and at z = d. The flow is in the x‐direction, with a z dependence.

The following are the pertinent parameters involved:

(3.83a)

Figure 3.13. Director axis reorientation causing flows.

(3.83b)

(3.83c)

(3.83d)

(3.83e)

(3.83f)

(3.83g)

Using Eq. (3.65), the equation of motion taking into account these torques, as well as the moment of inertia I of molecules involved, is given by

(3.84)

This equation may be solved for various experimental conditions. Optically induced director axis reorientation and flow effects have been studied by two groups [21, 22] using picosecond laser pulses. A solution to the previous equation is also presented in [22].