7 Plasmon-Associated Control of Chemical Reaction at Nanometer …
129
this photochromic reaction of fDAE also localized at nanometer scale. To our best
knowledge, this is the first experimental demonstration of nanometer-scale control
of photochromic reaction without the influence of far-field light.
Miyasaka and co-workers have reported similar one-color reversible multiphoton
photochromic reactions in amorphous film of a DAE derivative [22]. In their report,
the ratio of the number of open and closed-form molecules, N O and N C , respectively
was discussed as follows. Time dependencies of the open and closed-form at the PSS
are represented by the following equations.
−
∂ N O
∂t
= N O I
n
δ
(n)
O→C − N C I
m
δ
(m)
C→O = 0
( 7 . 2 )
−
∂ N C
∂t
= N C I
m
δ
(m)
C→O − N O I
n
δ
(n)
O→C = 0
(7.3)
Here, I is the intensity of the laser pulse. δ
(n) and δ
(m) are the n- and m-photon
absorption cross-sections for the open and the closed-form, respectively. O→C and
C→O are the cyclization and cycloreversion quantum yields. From Eqs. (7.2) and
(7.3) and the relation N O + N C = N total , Eq. 7.4 can be obtained.
N C
N O
=
N C
N total − N C
=
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
(7.4)
By considering that n and m would be 3 and 2, respectively, the relation between
N C /N O and I would be linear dependence on excitation intensity as the following.
N C
N O
∝ I
(7.5)
They experimentally confirmed the relation using absorbance of the open and
closed-form. In our study, we measured fluorescence intensity instead of absorbance,
and open form is non-fluorescent. Therefore, measured fluorescence intensity, F(I) is
directly related to the number of closed-form. From Eqs. (7.3), F(I) can be represented
as the following.
F(I ) ∝ N C = (N total − N C ) ×
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
(7.6)
By assumption that N total is extremely large to N C , N total –N C = N total , F(I) can be
also represented as linear equation to I.
F(I ) ∝ N total ×
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
∝ I
(7.7)
129
this photochromic reaction of fDAE also localized at nanometer scale. To our best
knowledge, this is the first experimental demonstration of nanometer-scale control
of photochromic reaction without the influence of far-field light.
Miyasaka and co-workers have reported similar one-color reversible multiphoton
photochromic reactions in amorphous film of a DAE derivative [22]. In their report,
the ratio of the number of open and closed-form molecules, N O and N C , respectively
was discussed as follows. Time dependencies of the open and closed-form at the PSS
are represented by the following equations.
−
∂ N O
∂t
= N O I
n
δ
(n)
O→C − N C I
m
δ
(m)
C→O = 0
( 7 . 2 )
−
∂ N C
∂t
= N C I
m
δ
(m)
C→O − N O I
n
δ
(n)
O→C = 0
(7.3)
Here, I is the intensity of the laser pulse. δ
(n) and δ
(m) are the n- and m-photon
absorption cross-sections for the open and the closed-form, respectively. O→C and
C→O are the cyclization and cycloreversion quantum yields. From Eqs. (7.2) and
(7.3) and the relation N O + N C = N total , Eq. 7.4 can be obtained.
N C
N O
=
N C
N total − N C
=
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
(7.4)
By considering that n and m would be 3 and 2, respectively, the relation between
N C /N O and I would be linear dependence on excitation intensity as the following.
N C
N O
∝ I
(7.5)
They experimentally confirmed the relation using absorbance of the open and
closed-form. In our study, we measured fluorescence intensity instead of absorbance,
and open form is non-fluorescent. Therefore, measured fluorescence intensity, F(I) is
directly related to the number of closed-form. From Eqs. (7.3), F(I) can be represented
as the following.
F(I ) ∝ N C = (N total − N C ) ×
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
(7.6)
By assumption that N total is extremely large to N C , N total –N C = N total , F(I) can be
also represented as linear equation to I.
F(I ) ∝ N total ×
O→C
C→O
×
δ
(n)
δ (m) × I
(n−m)
∝ I
(7.7)