Page 121 - Photoreactive Organic Thin Films

ZGUHEiR SEKKAT

These extrapolated data are denoted by the exponent <*>. Under these
conditions, the ratio of the equilibrium concentrations cZ are given by;
C _______ _
s
t<*> 4>ct c $<;! Ac
A' c is the equivalent of A' t for the cis isorner. When comparing the results of
irradiation at any two wavelengths A' and A", we have two equations of type
3 A. 7. By taking the ratio between these two equations, <f>^ l$l c and tf># /<f> t"
will cancel (assuming the ratio does not depend on the irradiation wavelength),
We then get Equation 3 A. 8:

,, A8 ,

If we introduce the extent a°° of trans — » cis conversion at infinite flux, then:
<£/<£= (l-a")/a- (3A.9)
a is the equivalent of y in Rau's method. Rewriting Equation 3 A. 9 for
irradiation wavelengths A' and A" and inserting them in the left-hand side of
Equation 3 A. 8 leads to:

AX, \ / 1 //«, \ / A'\ / A"\
(3A.10)

Next, A c and a are expressed in terms of experimentally measurable data.
The optical density of a mixture of cis and trans, where the overall
concentration c c + c t is constant (c 0), is given by:

A = A t(l - a) + A ca (3A.ll)
This equation is also valid when at the infinite flux photostationary state:
00
A c = A t + A / oT (3A.12)
Recall that A was introduced in Equation 3 A. 5 and that it is measured at the
00
same wavelength as the irradiation. The infinite flux extrapolated value A is
the intercept of the curve corresponding to Equation 3A.6. Introducing
Equation 3A.12 for A' and A" into Equation 3A.10, we have:

(3A.13)
In this equation, 8°° and 5"°° denote the relative change of absorbance observed
at wavelengths A' and A", respectively, when a solution of Zraws-isomers is
photoequilibrated with an infinite-flux light at the respective wavelength.
m
Furthermore, the ratio p (p - a°°la" } of a°° at two different excitation wave-
lengths A' and A" is equal to the ratio of the A's measured at the maximum A
wavelength when irradiating with wavelengths A' and X". Finally, one gets:
a"- = (8'~- 8"-) I ([I + 5"" - p(l + S"~)] (3A.14)
All these parameters can be measured experimentally, and the numerical
value of a"°° determined by this equation can then be used to calculate the