Page 99 - Photoreactive Organic Thin Films

Jg ZOUHBR SEKKAT

36 AB . /H . * 1 + 3 20
f = ° ' ' '
The solution of Equation 3.20 must be of the form:

(3.21,

Because Equation 3.20 is valid for any irradiation intensity, x = -13/2, and
an
2& 2/5 + 36^4/35 = -k. Rigorously, & 2 d &4 are proportional to k, and & 2 = ~&
is a physically reasonable solution.

JL_ 13 _L_ J_ j 1 1 / M __1_ J
B
4? - ~ T ~ 4&A F' S " P 2 (cos <O B) \ 2 <£&A F
No truncation above any order has been made for the determination of Af
B
and S , and the solution given by Equation 3.21 is certainly physical, because
it corresponds to actually observed behavior (vide infra}. Equation 3.22 is
useful when isomer B is spectrally distinguishable from isomer A. For
spectrally overlapping isomers, Equation 3.23 gives the order parameters, i.e.,
the geometrical A 2, and spectral, S, that characterize the orientational
distribution of the whole — trans and cis — molecular distribution.

i-JL - _M__*L_1- /323) ]
(
S ~ A 2 ~ 2 4#A F'
Equation 3.23 is derived without truncation above any order by assuming
that the geometrical order parameters, A 2, of the orientational distribution of
the A and B isomers are equal at the photostationary state of irradiation.
Although this assumption physically mirrors a uniform molecular
orientational distribution, it does simplify considerably the expression of the
photostationary-state orientational order and provides a simple law for
steady-state photo-orientation characterization. Equation 3.23 holds when
analysis is performed at the irradiation wavelength, and fits by Equations
3,22 and 3.23 allow for the measurement of <j^ A and P 2 (cos o> B) (vide infra),
Inasmuch as measured values of P 2 (cos W B) can be rigorous because the value
of -13/2 was derived without compromise, measured values of <f% A depend on
the assumption of k 2 = -k.
When the analysis of photo-orientation is performed at a wavelength
different from the irradiation wavelength, the symmetry of the molecular
transitions in both A and B isomers can be found. Indeed, setting n=0 in
Equation 3.9, yields the following relation for the photostationary state of
irradiation:

2A 2A) = _- (1 + 2A 2B) + - r (3.24)

In this equation, the trans and cis photostationary-state order parameters,
A 2A and A 2B respectively, are given by Equation 3.23, and when the
irradiation intensity, F', is extrapolated to infinity, A 2A = A 2B = A 2 = -2/13,