Available online at www.sciencedirect.com
Journal of Photochemistry and Photobiology A: Chemistry 197 (2008) 359–363
Photochemical reaction kinetics in optically dense media:
The influence of thermal reactions
Andrey Kh. Vorobiev
∗
, Denis Menshykau
1
Moscow State University, Department of Chemistry, Leninskie Gory 1/3, GSP-2, 119991 Moscow, Russian Federation
Received 30 November 2007; received in revised form 14 January 2008; accepted 22 January 2008
Available online 6 February 2008
Abstract
The kinetics of photochemical reactions in optically dense media essentially free from diffusion was considered. The photochromic isomerization
A ↔ B was studied as an example. If thermal isomerization is possible, a stationary state is achieved in time determined by rate constants for the
thermal reactions. The concentration wave profile is changed during the photochemical reaction propagation. Low values of thermal reaction
constants and decrease in sample optical density during photochemical isomerization were found to be essential for maximal wave penetration into
the sample. Sharp concentration gradients of A and B can be observed when both the optical density is increased during photochemical isomerization
and the quantum yield of the direct photochemical reaction A → B is higher than that of the reverse photochemical reaction B → A.
© 2008 Elsevier B.V. All rights reserved.
Keywords: Optically dense media; Kinetics of photochemical reaction; Photochromic isomerization; Wave propagation; Thermal reactions
1. Introduction
Photochemical reactions in optically dense media are of inter-
est in a wide variety of applications. Examples range from optical
data recording to polymer degradation, solar energy capture and
biological systems (photosynthesis and photodynamic therapy).
The kinetics of photochemical reactions in optically dense
media essentially free from diffusion has been examined in
several papers [1–14]. A decrease of light intensity within the
sample has been found to constitute a significant feature of
such systems. The outermost layers absorb light significantly,
therefore the light intensity and the photochemical reaction rate
depend on the distance from the irradiated surface. As a result,
the reagent and reaction product concentrations are described
by a wave-like distribution along the irradiation direction.
Evolution of the wave-like distribution shall be described by
a system of partial differential equations (PDE) (1). The first
equation is a differential form of the Beer–Lambert law. The
∗
Corresponding author. Tel.: +7 495 9394900; fax: +7 495 9328846.
E-mail addresses: vorobiev@excite.chem.msu.ru (A.Kh. Vorobiev),
dzianis.menshykau@sjc.ox.ac.uk (D. Menshykau).
1
Moved to University of Oxford, Department of Chemistry, Physical and
Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK.
Tel.: +44 1865 275400; fax: +44 1865 275410.
next equations are kinetic:
∂I (l, t )
∂l
=-I (l, t )
i
ε
i
c
i
(l, t )
∂c
i
(l, t )
∂l
= I (l, t )F (φ
1
,ε
1
,c
1
,...,φ
n
,ε
n
,c
n
) + k(c
1
,...,c
n
)
(1)
where I(l, t): light intensity; c
i
(l, t): concentration of ith sub-
stance; ε
i
: absorption coefficient for ith substance; ϕ
i
: quantum
yield of ith reaction. Function F describes the photochemical
reaction, and function k describes thermal reactions, which take
part in the system.
Thermal reactions have normally been neglected in study of
the kinetics of photochemical reactions in optically dense media
[1–8,12–14]. To this approximation, the method of complete
primitive determination has been applied [4,12–14]. In some
special cases, the primitive has been integrated analytically. The
reverse thermal reaction has been taken into account in some
papers [9–11]. An analytical solution for the distribution of A
and B in the stationary state, in presence of both the photochem-
ical reaction A → B and the reverse thermal reaction B → A, has
been found in [11]. In general, a kinetic description of photo-
chemical reactions in the presence of thermal reactions has not
been thoroughly developed at this time. Therefore, the aim of
1010-6030/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.jphotochem.2008.01.014