J. Phys. Chem. 1992,96, 2505-2509
absorption cross section coefficients of the P and N species. a = IpN, which is the rate of light absorption, where I, is the excitation fluence. w is the rate of sample renewal within the irradiated volume by circulation of the solution. k and k'are the rate constants of the Po No and No Po processes, and T N and rp are the lifetimes of excited states for the normal and photoisomeric species. @"p and @ p are ~ the quantum yields of N 1 Po and PI No isomerization processes. Under steady-state irradiation conditions and low absorption, the following expression can be obtained:
the results of section 11.3. dN0 - , dt
--
dNI -- aNo _ dt
-
(2 + (i +
-dPl- - BaPo dt
2505
w)NI
-
w)PI O= -P N
In eq A l , No, NI and Po, PI are the ground- and excited-state populations of the normal and photoisomer species, respectively, and N No N1 + Po + PI. B = u P / u N , with u p and UN as the
+
-
-
+ k' (@Np + B @ ~ N )+ u k + k'+ @Npa
w
('42)
where excited-state populations are taken negligibly small because the pump intensity, 11,is small compared to the saturation intensity for the excited-state populations, I = hv/u which are in the MW/cm2 region and the depopulation of N, and PI by circulation (w
