Page 120 - Photoreactive Organic Thin Films

3 PHOTO-ORIENTATION BY PHOTOISOMERIZATION 99

extinction coefficient of the trans (respectively cis) isomer, <f> t' c (respectively
<f>ct) the quantum yield of the trans-»cis (respectively cis— >trans) photo-
isomerization, and c t the concentration of the trans isomers. IQ, is the
intensity of the irradiating light (flux of photons per square centimeter), and
2
the factor 1000 occurs when / 0' is expressed in mol of photon/cm . The
extinction coefficients (proportional to the cross section) and the concen-
1
1
1
trations are expressed in L.mol~ .cm~ and mol.LT , respectively. Equation
3 A.I can be rewritten as:
dyldt = F'(t)e' t<f> t' c - (F'(t)Q' + k)y (3A.2)
We denote by c 0 the total concentration of the isomers (CQ = c t - c c), y the
molar fraction of cis form (y - c cl c 0), F'(t] the following dependent time
A f
function (F'(t) = 1000/ 0'(1 - W~ ')/A'), and Q' the following factor (Q = s t& c
+ Sc<f>c t). For the photostationary state, denoted by the index °°, dyldt is
equal to zero and:
f
e't&c = (F'M + k)yj F: (3A.3)
The total absorbance A(i) can be expressed as a function of y:
A(t) = e tc tL + s cc cL = [(e c - e t)y + e t]c QL (3A.4)

In this equation, L is the thickness of the sample along the analysis beam.
From Equations 3A.3 and 3A.4 written for the photostationary state, the
equation is as follows:
= F'^fa = A,-qcoL = A^-A t A
/c
* FLQ' + k (e c-s t}c QL (s c-e t}c QL (e c~e t)c QL
In this equation, both A«, and F'l depend on the irradiation intensity IQ. A t
stands for the optical density of a similar sample containing only the trans
isomer. A is the optical density's variation when a sample (initially containing
only the trans isomer) is irradiated to the photostationary state. The second
and the last terms of this equation can be arranged to give:
i F:' + k F;' + k
A FLe'tfa c,Le - e F' (e - e
Q'
s c-e tt< e c -e tt c e c- e tt<
(3A.6)
A
where X = A'J(l - 10- ')/o- By plotting the left-hand side of Equation 3A.6
f
versus X at different irradiation intensities I 0', we may obtain <j> tc from the
slope and dj>' ct from the intercept, provided that the extinction coefficients are
known. s t and s' t can be experimentally measured, whereas Fischer's method
is needed to determine each e c and e' c.

3A.2 FISCHER'S METHOD

This method is valid for systems without thermal relaxation. Therefore, all
data concerning the photostationary state were extrapolated to infinite flux.