Page 92 - Photoreactive Organic Thin Films

3. PHOTO-ORIENTATION BY PHOTO1SOMER1ZATION 7 |

and
4 B
S A, B = ? 2(cosa> A)B)A2 ' (3.1)
B
where A 2' is the isomer's geometrical order parameter. It is independent of
the spectral properties of the chromophore, and P 2(cos G> AVB) is the second-
order Legendre polynomial of W A B given by:
2
F 2(cos fc> A, B) = (3cos o> A;B - l)/2 (3.2)
with <w A)B the angle that defines the orientation of a transition that
corresponds to the analysis wavelength versus the irradiation wavelength
transition. In other words, if analysis is done at the irradiation wavelength,
W an cos W B B
A,B = 0 d ^2( A,B) = 1- Absft' and Abs^ stand for absorption of light
polarized parallel and perpendicular to the polarization of the irradiation
light, respectively. We represent by C A and C B, and s\ and eg, the
concentrations and the isotropic extinction coefficients, i.e., those coefficients
that can be measured from the isotropic absorbance spectra, of the isomers A
2
and B, respectively. £ A)B is proportional to I M A B| . For all the equations, the
sub- and superscripts A and B, if any, refer to the isomers A and B,
respectively. It is noteworthy that if analysis is performed at a wavelength
that is absorbed by either isomer A or B, the case of individualizable isomers,
the observed absorbance and anisotropy are directly proportional to the
concentration and orientation of only that isomer. Photo-orientation
observation in both spectrally individualizable and overlapping isomers will
be addressed after the discussion of the phenomenological theory of photo-
orientation.

3.3.2.2 Phenomenological Theory and General Equations
The time-dependent expression of photo-orientation is derived by
considering the elementary contribution per unit time to the orientation by
the fraction of the molecules JC A;B(O), whose representative moment of
transition is present in the elementary solid angle d& near the direction
Q(0,^>) relative to the fixed laboratory axes (see Figure 3.4). This elementary
contribution results from orientational hole burning, orientational redistribu-
tion, and rotational diffusion. The transitions are assumed to be purely
polarized, and the irradiation light polarization is along the Z axis. The
elementary contribution to photo-orientation is given by:

2
= -3F<£ ABe A cos $ C A(0) + 3F> ABe B ( C B(a')cos
dt Q'

T B
2
= -3F'<£ BA4 cos B C B(«) + 3F> ABe A f C A(0')cos
dt

-f i C B(0') + D B9*.sRC B(«) + C B(&W 2 (33)
T B