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Enhancement of the Exciton Coherence Size in Organic Semiconductor by Alkyl-Chain Substitution Shunsuke Tanaka, Kiyoshi Miyata, Toshiki Sugimoto, Kazuya Watanabe, Takafumi Uemura, Jun Takeya, and Yoshiyasu Matsumoto J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b12686 • Publication Date (Web): 30 Mar 2016 Downloaded from http://pubs.acs.org on April 1, 2016
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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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†
† ‡
† ‡
∗ † ‡
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∗† ∗†
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b
f
b
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The Journal of Physical Chemistry
π−π π
b
f
b 10
10
ab
c
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10
a = 618.7, b = 766.2, c = 1620
ab
10
β=
◦ c β a = 599.5, b = 761.6, c = 3805
◦
∼
10
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10 ◦ 10
2
td
Ir (ν) d
Ic (ν) = Ir (ν)
α(νe )
α(νe ) − α(ν) α(νe ){exp[−α(ν)d] − exp[−α(νe )d]}
α(ν)
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10
10
1
2
1 2
←
←
0
0 1
←
0
10
10 10
10
10
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10
10
10
r=
I∥ − I⊥ , I∥ + 2I⊥
I∥(⊥)
r r
r
±
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r = (I∥ −I⊥ )(I∥ +2I⊥ )
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10
td td
10
r
r
10
r
10
td
10
10
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10
10
10
td
10 10
10
10
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10
10
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N N
N
N
Ncoh
J
g
Γ Ncoh
Ncoh ∝
J
Γ
J . Γ
J ≈ g
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J ≪ g
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Ncoh Ncoh
N Ncoh =
Z=
! i
N , Z
"
h ¯ ωi − h ¯ ωi=0 exp − kB T
h ¯ ωi=0
#
,
h ¯ ωi
i T =0
Ncoh
N Ncoh
N
Ncoh
k
I0−0 k ̸=
Ncoh Ncoh
I0−1
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Ncoh
Ncoh =
I0−0 2 λ, I0−1
λ2
I0−0 Ncoh
I0−1
10
1
←
0
c ab
a
a
ab
c
c
b
b Ncoh b
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b
a, c
kB T h ¯ ω0 " 2#" 2# N λ µb = exp − , Z N µ2 " 2#" 2# λ µa 0−1 2 ⟨Ia ⟩T = λ exp − /(W + 1)2 , 2 N µ " 2#" 2# λ µb ⟨Ib0−1 ⟩T = λ2 exp − , N µ2 " 2#" 2# λ µc 0−1 2 ⟨Ic ⟩T = λ exp − /(W + 1)2 , 2 N µ ⟨Ib0−0 ⟩T
⟨Ib0−0 ⟩T
b
i
µi
i
⟨Ii0−1 ⟩T i = a, b, c
W
h ¯ ω0
Z
⟨Ib0−0 ⟩T
T ⟨Ia0−1 ⟩T
(W + 1)
ac
b a, b
c
0−0 Iobs = ⟨Ib0−0 ⟩T , 0−1 Iobs = ⟨Ia0−1 ⟩T + ⟨Ib0−1 ⟩T + ⟨Ic0−1 ⟩T ,
0−0 Iobs
0−1 Iobs
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⟨Ic0−1 ⟩T
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Ncoh =
0−0 2 Iobs λ {µ2a + µ2b (W + 1)2 + µ2c } . 0−1 Iobs (W + 1)2 µ2b 0−0 Iobs
10
0−1 Iobs
td
µa : µb : µc
W
1.3 : 1.0 : 2.9
10
W = 8J0 /¯hω0
J0 h ¯ ω0
W ≫ 1
W > 3
λ2
10
Ncoh 10
Ncoh
ka km ka = Ncoh km .
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10
10
10
ΦPL
Ncoh =
ktot
ka ΦPL ktot = . km km
km Ncoh (T )
Ncoh Ncoh (T ) ΦPL (T )ktot (T ) = . Ncoh (293 ) ΦPL (293 )ktot (293 ) ΦPL ΦPL (T )
ktot (T ) Ncoh
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Ncoh Ncoh
N N ′ (< N )
N Ncoh N′ Ncoh ∼ = ′, Z Z′
Ncoh
J0
J1 J0
J0
J1
10
J1 π
n
n×n
n ab
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ac
10 10
n
10
Z′ Ncoh = N ′ /Z ′ Ncoh Ncoh Ncoh
10
N ′ ∝ J/Γ Γ
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N′
10
N ′ ∝ J0 /Γ
J0
Γ
J0 ∆E = 8J0 N′
N′ ∼ N′ Z′ N′
Ncoh
10
Ncoh
c
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Ncoh
Ncoh
µ
2
10
Ncoh
2
2
10
10
10
∼
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10
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The Journal of Physical Chemistry
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The Journal of Physical Chemistry
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The Journal of Physical Chemistry
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