Page 93 - Photoreactive Organic Thin Films

72 ZOUHEIR SEKKAT

AB
BA
F (O' -» O), P (& -> O) and Q(Q' -» O) are the probabilities that the
electric transition dipole moment of the chromophore will rotate in the A— >B
and B~-»A photoisomerizations, and B— >A thermal isomerization, respectively.
The orientational hole burning is represented by a probability proportional to
2
cos 0, and the last term in each of the equations in Equaton 3.3 describes the
rotational diffusion due to Brownian motion. The latter is a Smolucbowski
equation for the rotational diffusion characterized by a constant of diffusion
D A and D B for the A and B isomers, respectively, where 31 is the rotational
operator, k is the Boltzmann constant, T is the absolute temperature, and
U^B is an interaction energy to which the isomers can be subjected.
Depending on the type of interaction, U A>B can be polar or nonpotar. It is
polar when the chromophores are isomerized in the presence of an electric
25
field (the so called photo-assisted poling, discussed in detail elsewhere ); it is
nonpolar when intermolecular interactions, such as liquid crystalline-type
interactions, are present. I will not discuss these two cases. I will consider the
case of UAJS - 0> where friction is the only constraint in addition to
isomerization. F is a factor that takes into account that only some part of the
27
totally absorbed amount of light induces photoreaction; it is defined in
Appendix 3A. The notations and units used in photochemistry are adopted,
because the final theoretical expressions need to be compared to linear
dichroism, i.e., polarized absorbance, measurements. In Equation 3.3, as well
as in all the equations used in the rest of the chapter, the primed quantities,
except for tf and Q', refer to an analysis at the irradiation wavelength,
and the unprimed ones refer to an arbitrary analysis wavelength. The
normalizations are:

CA + Qs = C
AB BA
JP ' (O' -» Q) dQ.' = 1 }Q(O' -» Q)dO' = 1 (3.4)

where C is the total concentration of the chromophores. With bulk azimuthal
symmetry, the symmetry axis is the Z axis, i.e., the direction of the
polarization of the irradiation light. The statistical molecular orientation for
each of the photo-oriented A and B isomers is described by an orientational
distribution function, G AjB(0), that depends only on the polar angle; it can be
expressed using the standard basis of Legendre polynomials, P w(cos 0), with
B
A^ as expansion coefficients (order parameters) of order n (integer). C 4 B(O)
is given by:

1
B
with Q A>B(0) = -J- Z ^f A^' P M(cos 0}
Zn M=o 2
•7T
B
and A ;f' = } G A B(0) P H(cos 0) sin B dO
o
B
and A^' = 1 (3.5)