Page 97 - Photoreactive Organic Thin Films

ZOUHE1R SEKKAT

a = a 0 exp(-&£), A% = A^o exp[-(fe + /

1-a An A { <*0 ^ Q w
AA = exp(-kgt) \1 + t A T^ (1 exp(-feH)) , (3.11)
/i Mio [ o A n 0 ^
kA-k$ J
K.£)
K.£)
1 A B
F = 1
, and J^> = n(« + 1)D
where r = 1 - : , and &n' = «(« + 'nr A B
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k
Equation was derived without approximations. It is noteworthy that these
solutions do not couple tensorial components of different orders and that
they confirm that rotational diffusion and cis-»trans thermal isomerization
are isotropic processes that do not favor any spatial direction. In Section 3.4,
I discuss, through the example of azobenzene, how Equation 3.11 can be
used to study reorientation processes during cis— »trans thermal isomerization
after the end of irradiation. The next subsection gives analytical expressions
at the early-time evolution and steady-state of photo-orientation, for the full
quantification of coupled photo-orientation and photoisomerization in A«-»B
photoisomerizable systems where B is unknown.
3.3.2.4 Early Time Evolution of Photo-Orientation
3.3.2.4. / A->B Photo-Orientation
At the early time evolution of photoselection, the cis population is
negligible compared to the trans population, and the quantification of
coupled photo-orientation and photoisomerization can be done for spectrally
overlapping isomers as well as for individualizable isomers. For spectrally
overlapping isomers, the analysis light is absorbed by both isomers, and
the slopes, p(A) and p(AA), of A (proportional to the population change) and
AA (proportional to the orientation) during irradiation, respectively, are
rigorously given by:
A
I - 10- o)^ B( % - £A) (3.12)
B
B{P^ P 2 (cos a> B} SB - P 2 (cos a> A)e A] (3.13)
For individualizable isomers, and for an analysis light that can be absorbed
only by the B isomer, p(A) and p(AA) are rigorously given by:
p(A) = lOOOfo (1 - KHo)^^ (3.14)

A A
p(AA) = |lOOOJS (1 - 10~ o)^ BP 2 (cos o» B)P 2 -*% (3.15)
I will go on to show how Equations 3.12 through 3.15 can be used to
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determine <^B and P 2 (cos wg)?^"* from A-»B photo-orientation experi-
ments. The algebra of the derivation of Equations 3.12 through 3.15 is
detailed in Appendix 3B.

3.3.2.4.2 B-^A Photo-Orientation
B— >A photo-orientation is observed only for individualizable isomers,
and its evolution is described by a double-exponential behavior in the form of