Modern Polymer Spect..

2.3 Theory
Throughout this chapter the general form of the order parameter S will be used
[3, 3 1 j to describe the long-range orientational order of the investigated liquidcrystalline
materials. In contrast to the theory of Maiei- and Saupe 132, 331, which
considers the uniaxial distribution of the mesogens in a nematic phase relative to the
macroscopic preferential direction (director), this formalism also allows negative
values. The relation of S to the inclination angle 0 of the inesogenic/structural-unit
axis and the reference direction (if not otherwise stated, the external field direction)
is outlined for the case of an SCLCP in Figure 2-3. Also shown are the values of
S for parallel and perpendicular orientation of the mesogens and their isotropic
distribution. The derivation of S, which corresponds to the orientation factor f in
general polynier orientation terminology [14, 17-20], is given in Figure 2-3, where
R is the dichroic ratio determined from the experimental absorbance values measured
with light polarized parallel and perpendicular, respectively, to the chosen
reference direction. Ro is the theoretical dichroic ratio for perfect aligiiinent of the
mesogen, and p is the angle between the transition moment of the absorbing group
and the local chain axis (in the present case the long axis of the mesogenic group)
[14j. The structural absorbance Ao has been chosen as parameter which represents
the intensity of an absorption band exclusive of contributions from the orientation
of the investigated polymer. It is given by [14]:
Both, order parameter S and structural absorbance A0 are based on the assumption
of a uniaxial orientation syniinetry [14, 18-20].
external field
(referencc direction)
s= I
(e =or)
parallel orientation
a
1
S=-- (0=900)
2
perpendicular orientation
s=o
isotropic distribution
Figure 2-3. Geometrical considerations for the
derivation of the order parameter S of a side-chain
liquid-crystalline polymer under the influence of an
exterilal field (ff = inclination angle of the inesogen
with the reference axis, v, = angle between the
transition moment of the absorbing group and the
local chain axis, Rn = theoretical dichroic ratio for
a perfectly aligned structural unit).