29 Femtosecond Pump-Probe Microspectroscopy …
509
Here, ε, ρ, and N p represent the molar absorption coefficient, 1.0 × 10
3 (M
−1
cm
−1 ) at the excitation wavelength, the molecular density, 2.21 (M) and the number
of photons at the excitation area (cm
−2 ), respectively. At the fluence of 18 mJ cm
−2
pulse
−1 , the M ex was calculated to be 8.0 × 10
19 . Considering the concentration
of the ground-state molecules (molecules cm
−3 ) (M gr = ρ × N A × 10
−3 ), N A is
Avogadro constant), 6% of the ground-state molecules are excited simultaneously
by single shot of the femtosecond excitation laser pulse. This value, which showed
three times higher as compared to the reported one by Ma et al. [29], could be enough
to consider singlet–singlet annihilation process. When the annihilation process takes
place together with the singlet fission, the yield of T 1 state formation should tend
to decrease, resulting in the saturation tendency of the transient absorbance of the
T 1 state at 510 nm against the laser fluence. The singlet–singlet annihilation process
leads to the formation of a higher excited-state molecule and a ground-state one; S 1
+ S 1 → S N + S 0 , and the S N state molecule could generate two T 1 state molecules
through the singlet fission. Consequently, two S 1 state molecules are converted to
two T 1 state molecules. Through the annihilation process , the amount of the T 1 state
molecules decreases when S 1 -S 1 annihilation takes places with the normal singlet
fission. However, the experimental result in Fig. 29.10d presents a linear relationship
between the excitation intensity and the amount of the T 1 state. Here, because both
singlet fissions finished in 100 ps, transient absorbance at 100 ps was used as the
amount of the T 1 state. From this result, we concluded that the effect of the singlet–
singlet annihilation on the singlet fission processes could be negligible in the present
experiments, and it is no important to consider the mechanism of the excitation
intensity-dependent time constant of the T 1 state formation.
As another possible mechanism to explain the excitation laser fluence dependence
of the TAF, the influence of transient local heating in a ps time scale is considered in
Fig. 29.11a, b. As stated above, rubrene molecules are excited to the higher vibrational
levels of the S 1 state by the 397-nm femtosecond excitation and relax quickly to lower
levels of the S 1 state through the vibrational relaxation process. This indicates that the
photothermal conversion will induce temperature elevation at the excitation volume
of the rubrene microcrystal in a few ps after excitation, leading to the acceleration
of the triplet state formation through the TAF. So, we assume that the excess energy
of the photoexcitation (397 nm) from E(S 1 ) converts into heat in a few ps and that
the heat dissipation is ignored, and estimated the local temperature elevation (T )
at focal spot of the excitation laser by using Eq. (29.2).
T = κ/(ρ × C) × F × (hν 397 nm − E(S 1 ))/(hν ex )
(29.5)
Here, F, ρ, and C are the laser fluence (J cm
−2 ), the molecular density (M), and the
heat capacity, 609 (J K
−1 mol
−1 ), respectively. κ is the absorption coefficient, which
is the inverse of skin depth of the excitation light. The skin depth is determined
to be approximately 1.9 μm from the ε and the thickness. hν 397 nm is the photon
energy of the excitation laser and set to be 3.12 eV and E(S 1 ) is the 0–0 transition
energy of rubrene crystal (2.23 eV). The value of T was estimated to be 19 K at the
laser fluence of 18 mJ cm
−2 pulse
−1 . The temperature elevation will be enough to
509
Here, ε, ρ, and N p represent the molar absorption coefficient, 1.0 × 10
3 (M
−1
cm
−1 ) at the excitation wavelength, the molecular density, 2.21 (M) and the number
of photons at the excitation area (cm
−2 ), respectively. At the fluence of 18 mJ cm
−2
pulse
−1 , the M ex was calculated to be 8.0 × 10
19 . Considering the concentration
of the ground-state molecules (molecules cm
−3 ) (M gr = ρ × N A × 10
−3 ), N A is
Avogadro constant), 6% of the ground-state molecules are excited simultaneously
by single shot of the femtosecond excitation laser pulse. This value, which showed
three times higher as compared to the reported one by Ma et al. [29], could be enough
to consider singlet–singlet annihilation process. When the annihilation process takes
place together with the singlet fission, the yield of T 1 state formation should tend
to decrease, resulting in the saturation tendency of the transient absorbance of the
T 1 state at 510 nm against the laser fluence. The singlet–singlet annihilation process
leads to the formation of a higher excited-state molecule and a ground-state one; S 1
+ S 1 → S N + S 0 , and the S N state molecule could generate two T 1 state molecules
through the singlet fission. Consequently, two S 1 state molecules are converted to
two T 1 state molecules. Through the annihilation process , the amount of the T 1 state
molecules decreases when S 1 -S 1 annihilation takes places with the normal singlet
fission. However, the experimental result in Fig. 29.10d presents a linear relationship
between the excitation intensity and the amount of the T 1 state. Here, because both
singlet fissions finished in 100 ps, transient absorbance at 100 ps was used as the
amount of the T 1 state. From this result, we concluded that the effect of the singlet–
singlet annihilation on the singlet fission processes could be negligible in the present
experiments, and it is no important to consider the mechanism of the excitation
intensity-dependent time constant of the T 1 state formation.
As another possible mechanism to explain the excitation laser fluence dependence
of the TAF, the influence of transient local heating in a ps time scale is considered in
Fig. 29.11a, b. As stated above, rubrene molecules are excited to the higher vibrational
levels of the S 1 state by the 397-nm femtosecond excitation and relax quickly to lower
levels of the S 1 state through the vibrational relaxation process. This indicates that the
photothermal conversion will induce temperature elevation at the excitation volume
of the rubrene microcrystal in a few ps after excitation, leading to the acceleration
of the triplet state formation through the TAF. So, we assume that the excess energy
of the photoexcitation (397 nm) from E(S 1 ) converts into heat in a few ps and that
the heat dissipation is ignored, and estimated the local temperature elevation (T )
at focal spot of the excitation laser by using Eq. (29.2).
T = κ/(ρ × C) × F × (hν 397 nm − E(S 1 ))/(hν ex )
(29.5)
Here, F, ρ, and C are the laser fluence (J cm
−2 ), the molecular density (M), and the
heat capacity, 609 (J K
−1 mol
−1 ), respectively. κ is the absorption coefficient, which
is the inverse of skin depth of the excitation light. The skin depth is determined
to be approximately 1.9 μm from the ε and the thickness. hν 397 nm is the photon
energy of the excitation laser and set to be 3.12 eV and E(S 1 ) is the 0–0 transition
energy of rubrene crystal (2.23 eV). The value of T was estimated to be 19 K at the
laser fluence of 18 mJ cm
−2 pulse
−1 . The temperature elevation will be enough to