Page 123 - Photoreactive Organic Thin Films
P. 123
102 ZOUHEIR SEKKAT
APPENDIX 3B
DEMONSTRATION OF EQUATIONS 3.12
THROUGH 3.15
In this appendix, I show how Equation 3.12 and 3.13 were derived. At the
early time evolution, the cis concentration is negligible. If we introduce the
extent, a, of the concentration of isomer B, i.e., C B = aC and C A = (1 - a)C,
with C the total concentration, and C A and C B the concentrations of the A
and B isomers, respectively, we obtain the following equation by setting n = 0
in Equation 3.9:
A 2A must be determined to find the expression of a. The following two
equations, derived from Equation 3.9 for the early time evolution, i.e., a « 1,
allow us to do that.
= - 3F<^V; [C A] - n(n (3B.2)
tin. 3\
(3B.3)
Setting n = 2 in Equation 3B.2 yields the second- and fourth-order parameter
of the trans distribution. These are given by:
A 2A = - F'eMn-t and A 4A = (P^^ B + D A).t (3B.4)
where t represents the time. Now, substituting A 2A into Equation 3B.1, and
2
noting that at the early time evolution t « t, Equation 3B.1 yields:
a = F'e A<f> AB.t (3B.5)
At a given analysis wavelength, the absorption change, A = A - A A, is given
by:
