9 Photosynergetic Effects on Triplet–Triplet Annihilation …
167
that the encounter probability of the quasi-2D energy migration tends to be less than
the 1D one for this specific region.
Next, we consider the case that two excitons are generated at the different sensitizers independently (the distance of them is assumed to be the separation of two
sensitizers, L S ), and they encounter after the migration. The encounter probability
can again be approximated by the Gaussian with a different center and a (normalized)
duration time, τ duration (n duration = τ duration /τ TTET ) between two different sensitizers
to two different emitters, P(x−L S , n TTET −n duration ). Note that the duration time is
completely random compared to the lag time. In this case, the encounter probability,
R mD (m: dimension), is approximately proportional to S mD exp[−α (L S /a)
2 ], where
the exponent (α > 0) is a function of n TTET and n duration , and a is the distance between
the neighboring emitters, a << L S . This means that the encounter probability is generally smaller than the values estimated above when L S is distant enough. Thus, the
obtained results for the single-site case here seems to be an upper bound for the
encounter probability. However, it is noticed here that the quasi-two-dimensional
diffusion case might have higher probability than one-dimensional case when the
concentration of the sensitizer is high enough since the TTA in DPA occurs all
neighboring sites, while that in C7-sDPA does not always.
9.4 Conclusion
In this chapter, we mainly described experimental and theoretical studies on TTA-UC
processes, an important application of the TTA process. Usage of the TTA process is
one of the key issues of Photosynergetics to overcome the conventional limitation of
efficient usage of photoexcitation. Especially, we focused solid-state system of TTAUC because it is interesting in views of fundamental studies and device applications.
Using the rapid-drying casting method, we have achieved the TTA-UC in solid as
efficient as that in the solution for green-to-blue conversion by using PtOEP:DPA
(or its derivative). The drop casting method improved TET in solid by achieving
molecular dispersion of the sensitizer molecules. By changing the emitter molecule
from DPA to C7-sDPA, a strapped derivative, I th for the microparticles was reduced
by two or three orders of magnitudes, and UC was enhanced up to 10–20%.
To explain these experimental facts, we have established the theoretical protocol
to estimate kinetic constants (inverse of reaction times) for the elementary processes
concerning about TTA-UC in crystal. The results indicated that the TTET of exciton
migration is the time-limiting step compared to the spin conversion process of TTA.
Using random walk models of TTET, we concluded that not only the time scale of
TTET but also the difference in dimensionality of the TTET direction, the lifetime
of the triplet excitons, and the lag (recovery) time of the sensitizer after TTET to the
emitter play an important role in determining the encounter probability, i.e., quantum
yield and emission intensity of TTA-UC.
We have extended the achievement by the rapid-drying technique to NIR excitation. By using the binary solid of PdTPTAP: rubrene, NIR-to-vis TTA-UC was
167
that the encounter probability of the quasi-2D energy migration tends to be less than
the 1D one for this specific region.
Next, we consider the case that two excitons are generated at the different sensitizers independently (the distance of them is assumed to be the separation of two
sensitizers, L S ), and they encounter after the migration. The encounter probability
can again be approximated by the Gaussian with a different center and a (normalized)
duration time, τ duration (n duration = τ duration /τ TTET ) between two different sensitizers
to two different emitters, P(x−L S , n TTET −n duration ). Note that the duration time is
completely random compared to the lag time. In this case, the encounter probability,
R mD (m: dimension), is approximately proportional to S mD exp[−α (L S /a)
2 ], where
the exponent (α > 0) is a function of n TTET and n duration , and a is the distance between
the neighboring emitters, a << L S . This means that the encounter probability is generally smaller than the values estimated above when L S is distant enough. Thus, the
obtained results for the single-site case here seems to be an upper bound for the
encounter probability. However, it is noticed here that the quasi-two-dimensional
diffusion case might have higher probability than one-dimensional case when the
concentration of the sensitizer is high enough since the TTA in DPA occurs all
neighboring sites, while that in C7-sDPA does not always.
9.4 Conclusion
In this chapter, we mainly described experimental and theoretical studies on TTA-UC
processes, an important application of the TTA process. Usage of the TTA process is
one of the key issues of Photosynergetics to overcome the conventional limitation of
efficient usage of photoexcitation. Especially, we focused solid-state system of TTAUC because it is interesting in views of fundamental studies and device applications.
Using the rapid-drying casting method, we have achieved the TTA-UC in solid as
efficient as that in the solution for green-to-blue conversion by using PtOEP:DPA
(or its derivative). The drop casting method improved TET in solid by achieving
molecular dispersion of the sensitizer molecules. By changing the emitter molecule
from DPA to C7-sDPA, a strapped derivative, I th for the microparticles was reduced
by two or three orders of magnitudes, and UC was enhanced up to 10–20%.
To explain these experimental facts, we have established the theoretical protocol
to estimate kinetic constants (inverse of reaction times) for the elementary processes
concerning about TTA-UC in crystal. The results indicated that the TTET of exciton
migration is the time-limiting step compared to the spin conversion process of TTA.
Using random walk models of TTET, we concluded that not only the time scale of
TTET but also the difference in dimensionality of the TTET direction, the lifetime
of the triplet excitons, and the lag (recovery) time of the sensitizer after TTET to the
emitter play an important role in determining the encounter probability, i.e., quantum
yield and emission intensity of TTA-UC.
We have extended the achievement by the rapid-drying technique to NIR excitation. By using the binary solid of PdTPTAP: rubrene, NIR-to-vis TTA-UC was