Page 95 - Photoreactive Organic Thin Films

74 ZOUHEIR SEKK.AI

2) = (« + !)(« + 2) , = *(«-!)
' " J w "
This system of equations shows, through even orders, that polarized light
irradiation creates anisotropy and photo-orientation by photoisomerization.
A solution to the time evolution of the cis and trans expansion parameters
cannot be found without approximations; this is when physics comes into
play. Approximate numerical simulations are possible. I will show that for
detailed and precise comparison of experimental data with the photo-
orientation theory, it is not necessary to have a solution for the dynamics,
even in the most general case where there is not enough room for
approximations, i.e., that of push-pull azo dyes, such as DR1, because of the
strong overlap of the linear absorption spectra of the cis and trans isomers of
such chromophores. Rigorous analytical expressions of the steady-state
behavior and the early time evolution provide the necessary tool for a full
characterization of photo-orientation by photoisomerization.
3.3.2.3 Dynamical Behavior of Photo-Orientation
3.3.2.3. / Onset of Photo-Orientation
The purpose of this section is to give an approximate analytical
expression that reproduces the dynamics of anisotropy during photo-
orientation. The experimentally observed evolution of photo-orientation
when only one isomer is photoisomerized as well as when the two isomers
are simultaneously photoisomerized presents a characteristic behavior that
can be approximated by a double-exponential function. To solve analytically
the system of Equation 3.9, I shall introduce approximations that are
physically valid for at least the azobenzene molecule in a polymeric environ-
ment, and I shall neglect the expansion parameters above the third order. The
fourth Legendre polynomial moment is a small correction to the second
Legendre polynomial moment, which gives the anisotropy. I have assumed
that only the trans isomer significantly absorbs the irradiation light, i.e., the
pump light, and that the rates of both the cis— »trans thermal isomerization
and the diffusion in the cis and trans forms are small. Analytical solutions are
found (see Equation 3.10) for the cis and trans populations (aC and (1 - a)C
respectively) and the even-order parameters (Af and Af respectively) that
characterize the orientation. If the irradiating light is turned on at the time
t = 0, the solution is given by:

a = 1 - |{0.78exp(-fc 2f) + 1.22exp(-M},

A
1
A 2 = 5(1 _ a)(exp(-M - exp(-V)}, (3.10)
A$ = LL°LP}-+*A},

A
where k 2 = 2.23*1000/0 (1 - lO^o)^**, and k 0 = 0.35*10001^ (1 - lQr 'o)
For photo-orientation analysis of actual data, Equation 3.10 must be
combined with Equations 3.1 and 3.2. The time-evolution simulation (see