1 3
Topics in Current Chemistry (2019) 377:22
Table 3
Common photocatalytic kinetic expressions in gas-phase photocatalytic reactions involving hydroxyl radical attack
Case
Photocatalytic reaction rate
Equations
References
Complete expression
r
X =
1 C
X C
H
2 O
⎛
⎜
⎜
⎜
⎜
⎝
1−
�
�
�
�
�
1+
2 ∫
e
a,s
d
�
1+K
X C
X +
∑
i
K
Y
i
C
Y
i
+K
H
2 O C
H
2 O
�
C
H
2 O
⎞
⎟
⎟
⎟
⎟
⎠
�
1+
3 C
X +
∑
i
i C
Y
i
+K
H
2 O C
H
2 O
��
1+K
X C
X +
∑
i
K
Y
i
C
Y
i
+K
H
2 O C
H
2 O
�
(14)
[19]
Low contaminant concentration
r
X =
1 C
X C
H
2 O
⎛
⎜
⎜
⎜
⎝
1−
�
�
�
�
1+
2 ∫
e
a,s
d
( 1+K
H
2 O C
H
2 O
)
C
H
2 O
⎞
⎟
⎟
⎟
⎠
�
1+K
H
2 O C
H
2 O
� 2
(15)
[2, 19, 20]
Low irradiation level and low contaminant concentration
r
X = −
C
X
∫
e
a,s
d
1+K
H
2 O C
H
2 O
(16)
[2, 20]
Linear adsorption isotherms
r
X =
1 C
X C
H
2 O
⎛
⎜
⎜
⎝
1−
�
1+
2 ∫
e a,s
d
C
H
2 O
⎞
⎟
⎟
⎠
1+
3 C
X +
∑
i
i C
Y
i
(17)
[21] without radical termination
reaction
Hole trapping by OH
−
r
X =
1 C
X
1−
√
1+
2
∫
e
a,s
d
1+K
X C
X +K
H
2 O C
H
2 O
(18)
[22]
Hole trapping by OH
−
and low irradiation level
r
X = −
C
X
∫
e
a,s
d
1+K
X C
X +K
H
2 O C
H
2 O
(19)
[22–24]
C
e −
= C
h +
, fast recombination rate and low contaminant concentration
r
X = −
1 C
X C
H
2 O
√
∫
e
a,s
d
1+
2 C
X +K
H
2 O C
H
2 O
1+K
H
2 O C
H
2 O
(20)
[25, 26]
271
Reprinted from the journal