Chemistry Reference
In-Depth Information
k
M;Ln
et
M
0
ð
Þ
t
e
k
M;Ln
k
M
e
k
Ln
Ln½ ¼
þ
t
ð
6
:
19
Þ
et
k
Ln
k
M;Ln
et
k
M
þ
As expected, Equation 6.19 reveals that the decay rate of the excited state of the donor
M
increases when energy is transferred onto the acceptor. The experimental decay of the
donor metal ion thus corresponds to the sum of the two deactivation rate constants
k
obs
¼
k
M
k
M;Ln
et
M
(Equation 6.20):
þ
, which translates into a reduced lifetime
t
k
obs
1
1
M
k
M
k
M;Ln
et
t
¼
¼
þ
ð
6
:
20
Þ
Interpretation of Equation 6.19 depends on the magnitude of
k
M;Ln
et
which controls the
population rate of the Ln
excited state. In fact, the decay profile of Ln
after initial excita-
tion of the donor depends on the relative magnitudes of the rate constants
k
obs
¼
k
M
þ
k
M;Ln
et
and
k
Ln
.
Two limiting cases can be described. The first refers to a situation for which
k
obs
k
Ln
, that is the Ln
level is almost completely populated before any significant
lanthanoid-centred deactivation starts. As a consequence, the experimental deactivation
rate
k
Ln
app
is identical to the one found in the absence of intermetallic communication,
k
Ln
.
Introducing
k
obs
k
Ln
into Equation 6.19 gives Equation 6.21, in which the time depen-
dence of the luminescence decay corresponds to an apparent rate constant
k
Ln
k
Ln
:
app
¼
M
0
k
M;Ln
et
k
M;Ln
et
e
k
Ln
Ln½ ¼
t
for
k
obs
k
Ln
k
M
ð
6
:
21
Þ
þ
This situation occurs for several d-f pairs, because the intrinsic deactivation rates of the
d-block donors
k
M
are often considerably larger than the deactivation of the NIR-emitting
Ln-centred excited states. This holds for instance for the Ru
Yb transfer in [YbRu
(L25)
3
]
5þ
(Figure 6.17, top). As expected, the experimental decay rate of the donor
k
Ru
!
obs
10
5
s
1
(measured for [RuGd(L25)
3
]
5þ
), which
is diagnostic for the existence of an axial Ru
10
5
s
1
is larger than
k
Ru
¼
1.2
¼
1.0
Yb energy transfer. Since
k
Ru
10
5
!
obs
¼
1.2
10
4
s
1
(measured for [ZnYb(L25)
3
]
5þ
), Equation 6.21 predicts that
the experimental Yb-centred decay rate recorded for [RuYb(L25)
3
]
5þ
should be equal to
k
Yb
, which is the case, within experimental error:
k
Yb
s
1
k
Yb
>
¼
5.0
10
4
s
1
.
app
¼
4.4
k
Ln
, that is when the Ln-centred excited
state relaxes almost instantaneously after being populated by the slow-decaying d-block
chromophore. Therefore, de-excitation of the donor M ion (
k
obs
¼
The second limiting case arises when
k
obs
k
M
k
M;Ln
et
) controls
the overall deactivation process, and the apparent Ln-centred deactivation rate
k
Ln
þ
app
should
be equal to
k
obs
. Introducing the condition
k
obs
k
Ln
into Equation 6.19 provides a sim-
plified Equation 6.22, which points to the time dependence of the Ln
luminescence
decay corresponding to
k
Ln
app
k
obs
:
¼
M
0
k
M;Ln
et
M
0
k
M;Ln
et
e
k
M;Ln
ð
Þ
t
et
þ
k
M
e
k
obs
t
Ln½ ¼
for
k
obs
k
Ln
k
Ln
¼
k
Ln
ð
6
:
22
Þ
This situation is illustrated when Ru
II
is replaced with Cr
III
as the donor in [CrYb
(L25)
3
]
6þ
. The combination of the intrinsic deactivation rate of the Cr-centred donor
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