giving maximum adsorption, that is,ks, and the other is the
adsorption equilibrium constant,K. The former parameter is a
product of rate constant and adsorption capacity of a
photocatalyst and this may be a photocatalytic activity. The lat-
ter parameter shows the strength of adsorption and must be
the same as that estimated from an adsorption isotherm
measured in the dark. If kinetically obtainedKis different from
that obtained in dark adsorption measurement, the L–H mecha-
nism cannot be adopted. Therefore, dark adsorption measure-
ment is always required. Finally, it should be noted also in this
case that a linear relation fitting to a Langmuir-type adsorption
isotherm and similarity of adsorption equilibrium constant
evaluated using photocatalytic reaction rate and by dark adsorp-
tion experiments are only necessary conditions; the observed
reaction rate is “consistent” with kinetics of a substrate
undergoing Langmuir-type adsorption and does not exclude the
possibility of other reaction kinetics ( 24 ).
C. ELECTRON–HOLERECOMBINATION
Recombination of e–and hþoccurs in photocatalysts in some
degree and it has been believed that this reduces quantum effi-
ciency, that is, efficiency of e––hþused in the chemical reaction
(s), and overall photocatalytic reaction rate. Since recombination
does not produce any chemicals, it is not easy to estimate the
rate of recombination directly. One possible way for estimation
of recombination rate is to subtract the overall rate of chemical
reaction by e––hþ from the rate of photoabsorption, but the
obtained data cannot give any other information.
Kinetics of e––hþrecombination may depend on its mode; if one
electron is excited and this is recombined with hþ, the recombi-
nation rate obeys the first-order rate law, while if multiple
e––hþappears at the same time within a photocatalyst particle,
the rate obeys the second-order rate law. Actually, in a femtosec-
ond pump–probe diffuse reflection spectroscopic analysis of tita-
nia samples, photoabsorption at 620 nm by trapped electrons
showed second-order decay with a component of baseline as
follows:
ðÞ¼absorption a½e 0
1 þkr½e 0 tþBL
; ð 4 Þwherea, [e 0 ],kr,t, and BL are a constant, initial concentration of
trapped electrons at time zero, second-order rate constant, time
410 B. OHTANI