S ¼ 1=2 3 < cos
2
θ > À1
À
Á
ð1Þ
where θ represents the angle of orientation between the mesogen of the polymer
chain and the director “n.” The bracket around the cos
2
θ indicates the thermal
average over all the unit molecules. When the value of “S” becomes zero, it indicates
total isotropy in the material, whereas when S becomes 1, it indicates perfect
ordering among the molecules, where all the molecules are parallel to each other
(Ten Bosch et al. 1983). This ideal ordering of the molecules is only possible near
absolute zero temperature if the material does not freeze. Hence, the order parameter
of the material is inversely proportional to the kinetic motion of the molecules. The
exact value of S remains a compromise between the ordering effect of the mesogens
and the contribution of temperature to the disordering as well (Klein et al. 1996).
In general, S decreases with an increase in temperature and varies from
0.43 at T c , clearing temperature, to about 0.8–0.9 at lower temperatures (Nyden
and Gilman 1998). For LCP having a combination of main- and side-chain macromolecules, the order parameter is a combined contribution from both main and side
chains. The order parameter is also known as the anisotropy factor that determines
the properties of the material depending on its direction of measurement.
Liquid crystals and LCPs both exhibit different mesophases such as nematic,
smectic, columnar, cholesteric, etc., due to different degrees of molecular ordering in
O
C
O
O
C
O
Vectra LCP
O
C
O
O
O
C
O
C
O
Xydar LCP
O
C
O
O
H 2
C
H 2
C
O
C
O
C
O
Rodrun LCP
Fig. 12 Chemical structures of industrial-grade LCPs
14
S. Banerjee and K. K. Kar