Enlarged Tetrasubstituted Alkenes With Enhanced Thermal ... · Enlarged Tetrasubstituted Alkenes...
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Enlarged Tetrasubstituted Alkenes With Enhanced Thermal
and Optoelectronic Properties
Yang Liu, Yun Lv, He Xi, Xiying Zhang,
Shuming Chen, Jacky W. Y. Lam, Ryan T. K.
Kwok, Faisal Mahtab, Hoi Sing Kwok, Xutang Tao, and Ben Zhong Tang
Contents
Experimental Section
Figure S1. 1H NMR spectra of 2ADFE in CD2Cl2.
Figure S2. 13
C NMR spectra of 2ADFE in CD2Cl2.
Figure S3. 1H NMR spectra of 2TDFE in CDCl3.
Figure S4. 13
C NMR spectra of 2TDFE in CDCl3.
Figure S5. High resolution mass spectrum of 2ADFE.
Figure S6. High resolution mass spectrum of 2TDFE.
Figure S7. The TEM images and electron diffraction patterns of (A) 2ADFE and (B)
2TDFE formed in THF/water mixtures with 95% water fractions.
Figure S8. Excitation spectra of 2ADFE (left) and 2TDFE (right) in pure THF
solution, in aqueous suspensions and in the solid state, respectively.
Figure S9. UV-vis absorption spectra of 2ADFE in THF/water mixtures with
different water fractions.
Figure S10. Decay lifetime curves of 2ADFE (left) and 2TDFE (right) in pure THF
solution, aqueous suspensions and the solid state.
Figure S11. TGA thermograms of (A) 2ADFE and (B) 2TDFE.
Figure. S12. DSC thermograms of 2ADFE (A) and 2TDFE (B) recorded at a heating
rate of 10 oC/min. (the second heating and cooling cycle).
Figure S13. Optimized geometries and molecular orbital amplitude plots of HOMO
and LUMO energy levels of 2ADFE and 2TDFE.
Figure S14. Cyclic voltammogram of 2ADFE in 0.1 M Bu4NPF6/CH3CN.
Figure S15. Energy level diagrams and device configurations of multilayer EL
devices of 2ADFE with and without hole-transporting layers.
Figure S16. (A) Cyclic voltammogram of 2ADFE in 0.1 M Bu4NPF6/CH3CN; (B)
Energy level diagram and device configuration of multilayer EL device of 2TDFE.
Table S1 EL performances of devices based on 2ADFE and 2TDFE.
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Experimental Section
Materials and Instrumentations
THF was distilled from sodium benzophenone ketyl under nitrogen immediately
prior to use. All the chemicals and other regents were purchased from Aldrich and
used as received without further purification.
1H and
13C NMR spectra were measured on a Bruker AV 400 spectrometer in
CDCl3 or CD2Cl2 using tetramethylsilane (TMS; δ = 0) as internal reference.
Photoluminescence spectra were recorded on a Perkin-Elmer LS 55
spectrofluorometer. The fluorescence lifetime measurement was performed on the
Edinburgh FLS920 spectrofluorimeter with a hydrogen flash lamp as the excitation
source on the same spectrofluorometer. High resolution mass spectrum (HRMS) was
recorded on a GCT premier CAB048 mass spectrometer operating in MALDI-TOF
mode. Thermogravimetric analysis (TGA) was carried on a TA TGA Q5500 under
dry nitrogen at a heating rate of 20 oC/min. Thermal transitions were investigated by
differential scanning calorimetry (DSC) using a TA DSC Q1000 under dry nitrogen at
a heating rate of 10 oC/min.
Cyclic voltammogram was recorded on a Princeton Applied Research (model 273A)
at room temperature. The working and reference electrodes were glassy carbon and
Ag/AgNO3 (0.1 M in acetonitrile), respectively. All the solutions were deactivated by
bubbling nitrogen gas for a few minutes prior to electrochemical measurements. The
oxidation potential of ferrocene was measured to be 0.05 eV, and the onset oxidation
potential of 2ADFE was found at 0.52 eV (Figure S14). The formula used to estimate
the HOMO level is as follows:
HOMO = −e(Eonset-ox + 4.8 - Eferrocene)
For 2ADFEE, the HOMO = -e (0.52 + 4.8–0.05)V ≈ -5.3 eV.
For 2TDFE, as shown in Figure S16 the CV spectrum, the HOMO level derived
from the onset oxidation potential is of -5.5 eV.
The absolute fluorescence quantum yields were measured by an integrating
sphere mounted in an Edinburgh FPLS 920 fluorescence spectrophotometer. The
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fluorescence quantum yield is the percentage of photons emitted by a bulk sample
when a given number of photons are absorbed by the sample, i.e. the number of
photons emitted divided by the number of photons absorbed by a sample. The number
of photons absorbed by a bulk sample is equal to the number of photons incident on
the sample minus the photons passing through and not being absorbed by it. Thus the
quantum yield can be represented simply in the equation below:
reflectorreflectorreflector
Where η is the quantum yield;
ε is the number of photons emitted by the sample; α is the number of photons
absorbed by the sample;
Lemission is the luminescence emission spectrum of the sample, collected using the
sphere;
Ereflector is the spectrum of the light used for excitation with only the standard
reference reflector in the sphere, collected using the sphere;
Esample is the spectrum of the light used to excite the sample, collected using the
sphere.
During a typical measurement procedure, the complete emission spectrum of the
sample (Sample Emission, Lemission), the spectra of the excitation light recorded with
the sample in place (Sample Scatter, Esample) and the spectra of the excitation light
recorded with the standard reference reflector in place (Reference Scatter, Ereflector) are
measured one by one. After combination of these individual spectra, the software will
calculate the fluorescence quantum yield. The instrument is calibrated by using
standard Alq3 (Tris(8-hydroxyquinolinato)aluminium) film before formal
measurement.
Device fabrication and characterization
EL devices were fabricated on 80 nm-ITO coated glass with a sheet resistance of
25Ω/. Prior to load into the pretreatment chamber, the ITO coated glasses were
soaked in ultrasonic detergent for 30 min, followed by spraying with de-ionized water
for 10 min, soaking in ultrasonic deionized water for 30 min and ovenbake for 1 h.
The cleaned samples were treated by CF4 plasma with a power of 100 W, gas flow of
50 sccm and pressure of 0.2 Torr for 10 s in the pretreatment chamber. The materials
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are purified before device fabrication by train sublimation. Then the samples were
transferred to the organic chamber with a base pressure of 7 × 10-7
Torr without
breaking vacuum for depositing a 60 nm 4,4-bis(1-naphthylphenylamino)biphenyl
(NPB), a 20 nm emitter, a 10 nm
2,2’,2’’-(1,3,5-benzinetriyl)tris(1-phenyl-1-H-benzimidazole) (TPBi), and a 30 nm
tris(8-hydroxyquinoline)aluminum (Alq3), which serve as hole-transporting,
hole-blocking, and electron-transporting layers, respectively. The samples were
transferred to the metal chamber for cathode deposition which composed of 1 nm LiF
capped with 100 nm Al. The light-emitting area was 4 mm2
defined by the overlap of
cathode and anode. The current density-voltage characteristics of the devices were
measured by the HP4145B semiconductor parameter analyzer. The forward direction
photons emitted from the devices were detected by a calibrated UDT PIN-25D silicon
photodiode. The luminance and external quantum efficiencies of the devices were
inferred from the photocurrent of the photodiode. The electroluminescence (EL)
spectra were obtained with the PR650 spectrophotometer. All the measurements were
carried out under air at room temperature without device encapsulation.
Synthesis
TiCl4/Zn
O
THF
2BrDFEBr
Br
Br
2ADFE
THF/
2MNa 2
CO 3
/Pd(
PPh 3
) 4
THF/2M
Na
2 CO
3 /Pd(P
Ph
3 )4
B
HO
OH
N
B OH
HO
2TDFE
Yield: 85%
Yield: 87%
Yield: 90%
Scheme 1 Synthetic routes to 2ADFE and 2TDFE.
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2-bromo-7-benzoylfluorene was synthesized by AlCl3 catalyzed Friedel-Crafts
acylation of 2-bromo-fluorene.
1,2-bis(2-fluorenyl-7-bromo)-1,2-diphenylethene (2BrDFE): In a two-necked
flask equipped with a magnetic stirrer were added 0.52 g (8 mmol) of zinc powder,
0.698 g (2 mmol) of 1,2-bis(2-fluorenyl-7-bromo)-1,2-diphenylethene and 60 mL of
THF. TiCl4 (0.44 mL, 4 mmol) was slowly added by a syringe at 0 oC under nitrogen.
The mixture was then heated to reflux overnight. After cooled to room temperature,
the reaction was quenched with 10% K2CO3 aqueous solution and extracted with
CH2Cl2. The organic layer was collected and concentrated. The crude product was
purified by silica-gel chromatography to give a colorless solid in 85% yield (1.133 g).
1H NMR (400 MHz, CD2Cl2), δ (TMS, ppm): 7.61–7.41 (m, 8H), 7.31–7.19 (m, 3H),
7.14-7.05 (m, 9H), 3.75-3.68 (m, 4H). HRMS (MALDI-TOF): m/z 666.0363 [M+,
calcd 666.0381].
1,2-Bis[4'-(diphenylamino)phenyl-4-yl-(2-fluoren-7-yl)]-1,2-diphenylethene
(2ADFE): Into a stirred mixture of 0.667 g (1 mmol) of 2BrDFE, 1.012 g (3.5 mmol)
of (4-(diphenylamino)phenyl)boronic acid, and 10 mL of 2 M Na2CO3 solution in 30
mL THF was added 0.02 g of Pd(PPh3)4 under nitrogen. The mixture was heated to 80
°C for 12 h. After cooled to room temperature, the solution was extracted with 80 mL
of CH2Cl2 twice, washed with water, and dried over Na2SO4. After filtration and
solvent evaporation under reduced pressure, the product was purified by silica-gel
column chromatography using hexane/dichloromethane as eluent. A pale yellow solid
was obtained in 87% yield (0.866 g). 1H NMR (400 MHz, CD2Cl2), δ (TMS, ppm):
7.73–7.66 (m, 4H), 7.57–7.48 (m, 8H), 7.29–7.22 (m, 10H), 7.12–6.99 (m, 28H), 3.75
(d, 4H); 13
C NMR (100 MHz, CD2Cl2), δ (TMS, ppm): 148.28, 147.69, 144.98,
144.75, 143.70, 143.66, 143.22, 141.87, 140.83, 140.25, 139.57, 139.53, 135.83,
131.95, 130.87, 129.94, 128.21, 126.93, 125.90, 124.95, 124.49, 123.51, 120.56,
119.49, 37.39; MS (MALDI-TOF): m/z 994.3856 [(M)+, calcd 994.4287]. Anal.
Calcd. For C44H33N: C, 91.72; H, 5.47; N, 2.81. Found: C, 91.39; H, 5.69; N, 2.86.
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1,2-diphenyl-1,2-bis(7-(4-(1,2,2-triphenylvinyl)phenyl)-fluoren-2-yl)ethene
(2TDFE): The compound was prepared from 0.667 g (1 mmol) of 2BrDFE, 1.317 g
(3.5 mmol) of (4-(1,2,2-triphenylvinyl)phenyl)boronic acid, and 0.02 g of Pd(PPh3)4
using the same procedure described above. Yellow solid; yield 90% (1.052 g).
1H NMR (400 MHz, CDCl3), δ (TMS, ppm): 7.71-7.63 (m, 4H), 7.55-7.46 (m, 4H),
7.40-7.35 (m, 4H), 7.22 (d, 2H, J = 8.4 Hz), 7.15-7.01 (m, 46H), 3.73 (d, 4H); 13
C
NMR (100 MHz, CDCl3), δ (TMS, ppm): 144.161, 144.102, 143.798, 143.748,
142.922, 142.897, 142.627, 142.560, 142.535, 141.187, 141.052, 140.698, 140.648,
140.555, 139.670, 139.645, 139.106, 131.802, 131.726, 131.423, 131.364, 130.521,
130.521, 130.471, 130.378, 128.053, 127.952, 127.699, 126.427, 126.183, 126.115,
125.660, 123.436, 123.335, 119.982, 119.940, 119.156, 119.123, 119.097, 119.030,
119.005, 36.806. HRMS (MALDI-TOF): m/z 1169.6068 (M+, calcd 1169.5042). Anal.
Calcd. For C92H64: C, 94.48; H, 5.52. Found: C, 94.19; H, 5.78.
Figure S1. 1H NMR spectra of 2ADFE in CD2Cl2.
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Figure S2. 13
C NMR spectra of 2ADFE in CD2Cl2.
7 .8 7 .3 6 .8 6 .3 5 .8 5 .3 4 .8 4 .3 3 .8
C h e m ic a l s h if t (p p m )
Figure S3. 1H NMR spectra of 2TDFE in CDCl3.
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140 120 100 80 60 40 20
Figure S4. 13
C NMR spectra of 2TDFE in CDCl3.
ly-2TPADFE, MW=995; DHB, LP200
m/z100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
%
0
100
tan090723_7 10 (0.333) Cn (Cen,5, 50.00, Ht); Sb (99,40.00 ); Sm (SG, 5x3.00); Cm (9:20) TOF LD+ 2.22e4992.3739
498.2481
299.1393
243.0223
409.1988
321.1353
322.1400
488.2480
410.2026
500.2525
916.3318501.2519
825.2963
994.3856
995.3884
996.3911
997.3942
1050.4673
ly-2TPADFE, MW=995; DHB, LP200
m/z100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
%
0
100
tan090723_7 10 (0.333) Cn (Cen,5, 50.00, Ht); Sb (99,40.00 ); Sm (SG, 5x3.00); Cm (9:20) TOF LD+ 2.22e4992.3739
498.2481
299.1393
243.0223
409.1988
321.1353
322.1400
488.2480
410.2026
500.2525
916.3318501.2519
825.2963
994.3856
995.3884
996.3911
997.3942
1050.4673
Figure S5. High resolution mass spectrum of 2ADFE.
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ly-2TDFE; MW=1169, DHB, LP200;
m/z400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
%
0
100
tan090922_8 8 (0.266) Cn (Cen,5, 50.00, Ht); Sb (99,40.00 ); Sm (SG, 5x3.00); Cm (6:22) TOF LD+ 1.24e41169.6068
1168.6049
1167.6022
585.3566
583.3375438.9678
517.3117
673.3811
595.3581
1165.5991
1090.5867709.3676 1003.5107
752.1403
1170.6085
1171.5922
1172.0990
1172.5696
1174.2181
1665.62661261.3760 1344.2321
1737.2244
Chemical Formula: C92H64
Exact Mass: 1168.5008
ly-2TDFE; MW=1169, DHB, LP200;
m/z400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
%
0
100
tan090922_8 8 (0.266) Cn (Cen,5, 50.00, Ht); Sb (99,40.00 ); Sm (SG, 5x3.00); Cm (6:22) TOF LD+ 1.24e41169.6068
1168.6049
1167.6022
585.3566
583.3375438.9678
517.3117
673.3811
595.3581
1165.5991
1090.5867709.3676 1003.5107
752.1403
1170.6085
1171.5922
1172.0990
1172.5696
1174.2181
1665.62661261.3760 1344.2321
1737.2244
Chemical Formula: C92H64
Exact Mass: 1168.5008
Figure S6. High resolution mass spectrum of 2TDFE.
100 nm 100 nm
(A) (B)
100 nm 100 nm100 nm100 nm 100 nm
(A) (B)
Figure S7. The TEM images and electron diffraction patterns of (A) 2ADFE and (B)
2TDFE formed in THF/water mixtures with 95% water fractions.
250 300 350 400 450 500
0
1000
2000
3000
4000
5000
Inte
ns
ity
(a
u)
Wavelength (nm)
in THF
in water/THF(90/10)
in solid state
X 20
2ADFE
250 300 350 400 450 500
0
1000
2000
3000
4000
2TDFE
X 20
Inte
ns
ity
(a
u)
Wavelength (nm)
in THF
in water/THF(90/10)
in solid state
250 300 350 400 450 500
0
1000
2000
3000
4000
5000
Inte
ns
ity
(a
u)
Wavelength (nm)
in THF
in water/THF(90/10)
in solid state
X 20
2ADFE
250 300 350 400 450 500
0
1000
2000
3000
4000
2TDFE
X 20
Inte
ns
ity
(a
u)
Wavelength (nm)
in THF
in water/THF(90/10)
in solid state
Figure S8. Excitation spectra of 2ADFE (left) and 2TDFE (right) in pure THF
solution, in aqueous suspensions and in the solid state, respectively.
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300 400 500 600
Water fraction
(vol %)
Ab
so
rban
ce
(a
u)
Wavelength (nm)
0
10
30
50
60
70
80
90
Figure S9. UV-vis absorption spectra of 2ADFE in THF/water mixtures with different
water fractions.
2ADFE in THF
2ADFE in water/THF(90/10)
2ADFE in solid state
2TDFE in THF
2TDFE in water/THF(90/10)
2TDFE in solid state
2ADFE in THF
2ADFE in water/THF(90/10)
2ADFE in solid state
2ADFE in THF
2ADFE in water/THF(90/10)
2ADFE in solid state
2TDFE in THF
2TDFE in water/THF(90/10)
2TDFE in solid state
2TDFE in THF
2TDFE in water/THF(90/10)
2TDFE in solid state
Figure S10. Decay lifetime curves of 2ADFE (left) and 2TDFE (right) in pure THF
solution, aqueous suspensions and the solid state.
From the time-resolved fluorescence at 500 nm of the dye molecules in different
state, we can see for both AIE compounds, in pure THF the decay lifetimes are very
short (the lifetime τ for 2ADFE is only 0.37 ns and for 2TDFE is 0.35 ns, where the
values represent the major decay component and similarly hereinafter). Because the
dyes in aqueous mixtures with large water fractions form actually small solid particles,
the decay lifetimes in 90 % water mixtures and in solid state are quite similar. (for
2ADFE the lifetime τ in 90 % water mixture is 3.7 ns, in solid state is 3.4 ns; for
2TDFE the lifetime τ in 90 % water mixture is 3.3 ns, in solid state is 4.1 ns) The
experimental results are consistent with previous studies of the time-resolved
photoluminescence on aggregation-induced emissive chromophores (Y. Ren, et.al., J.
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Phys. Chem. B 2005, 109, 1135-1140; M. H. Lee, et.al., J. Korean Phys. Soc., 2004,
45, 329-332).
The fluorescence quantum yield ΦF =τ/τr, where the PL lifetime τ is related to
radiative (τr) and nonradiative (τnr) lifetimes by the expression of 1/τ=1/τr + 1/τnr. τr is
the intrinsic property of the molecule. Comparison of the fluorescence decay lifetimes
and the fluorescence quantum yields in different state, we can deduce the decay
pathways of the excited state of AIE molecule: in well dissolved solutions, it relaxes
mainly via a very fast nonradiative intramolecular rotations; while in the aggregate
particles and the solid state, the excited molecule decays radiatively with a lifetime of
several nanoseconds.
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 458
oC
We
igh
t (%
)
Temperature (oC)
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 484
oC
Weig
ht
(%)
Temperature (oC)
(A) (B)
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 458
oC
We
igh
t (%
)
Temperature (oC)
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 484
oC
Weig
ht
(%)
Temperature (oC)
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 458
oC
We
igh
t (%
)
Temperature (oC)
100 200 300 400 500 600 700 80020
30
40
50
60
70
80
90
100
Td = 484
oC
Weig
ht
(%)
Temperature (oC)
(A) (B)
Figure S11. TGA thermograms of (A) 2ADFE and (B) 2TDFE.
50 100 150 200 250
Tg = 163
oC
Cooling
Heating
<e
nd
o H
ea
t fl
ow
e
xo
>
Temperature (oC)
50 100 150 200 250
Tg = 220
oC
Cooling
Heating
Temperature (oC)
(A) (B)
50 100 150 200 250
Tg = 163
oC
Cooling
Heating
<e
nd
o H
ea
t fl
ow
e
xo
>
Temperature (oC)
50 100 150 200 250
Tg = 220
oC
Cooling
Heating
Temperature (oC)
(A) (B)
Figure. S12 DSC thermograms of 2ADFE (A) and 2TDFE (B) recorded at a heating
rate of 10 oC/min. (the second heating and cooling cycle)
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Figure S13. Optimized geometry and molecular orbital amplitude plots of HOMO
and LUMO energy levels of 2ADFE and 2TDFE.
0.0 0.4 0.8 1.2 1.6 2.0 2.4
-4
-2
0
2
Cu
rre
nt
( µµ µµA
)
Potential (V)
Figure S14. Cyclic voltammogram of 2ADFE in 0.1 M Bu4NPF6/CH3CN.
NPB
2.3
5.3
2.5
5.3
2.7
6.2
3.1
5.7
2ADFE
TPBi Alq34.7
ITO
LiF/Al
3.1
with HTL
2.5
5.3
2.7
6.2
3.1
5.7
2ADFE
TPBi Alq34.7
ITO
LiF/Al
3.1
without HTL
NPB
2.3
5.3
2.5
5.3
2.7
6.2
3.1
5.7
2ADFE
TPBi Alq34.7
ITO
LiF/Al
3.1
with HTL
2.5
5.3
2.7
6.2
3.1
5.7
2ADFE
TPBi Alq34.7
ITO
LiF/Al
3.1
without HTL
Figure S15. Energy level diagrams and device configurations of multilayer EL
devices of 2ADFE with and without hole-transporting layers. Abbreviations: NPB =
4,4-bis(1-naphthylphenylamino)biphenyl, TPBi = 2,2’,2’’-(1,3,5-benzinetriyl)tris(1
-phenyl-1-H-benzimidazole).
HOMO
LUMO
2ADFE 2TDFE
HOMO
LUMO
2ADFE 2TDFE
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4.7
ITO
NPB
2.3
5.3
2.5
5.5
2.7
6.2
3.1
5.7
2TDF
E TPBi Alq3
LiF/Al
3.1
(A)
0.0 0.5 1.0 1.5 2.0
-40
-30
-20
-10
0
10
20
Cu
rren
t ( υυ υυ
A)
Potential (V)
(B)
4.7
ITO
NPB
2.3
5.3
2.5
5.5
2.7
6.2
3.1
5.7
2TDF
E TPBi Alq3
LiF/Al
3.1
4.7
ITO
NPB
2.3
5.3
2.5
5.5
2.7
6.2
3.1
5.7
2TDF
E TPBi Alq3
LiF/Al
3.1
(A)
0.0 0.5 1.0 1.5 2.0
-40
-30
-20
-10
0
10
20
Cu
rren
t ( υυ υυ
A)
Potential (V)
(B)
Figure S16. (A) Cyclic voltammogram of 2ADFE in 0.1 M Bu4NPF6/CH3CN; (B)
Energy level diagram and device configuration of multilayer EL device of 2TDFE.
Table S1 EL performances of devices based on 2ADFE and 2TDFE.a
Emitter HTL
V
[V]
L
[cd/m2]
ηC
[cd/A]
ηP
[lm/W] ηext
[%]
CIE
[x,y]
√
3.4b
6.2
8.0
25550c
100
1000
13.2c
10.4
8.9
11.0c
5.3
3.5
4.3c
3.4
2.9
(0.26, 0.45)
2ADFE
×
3.4b
6.6
8.2
19100c
100
1000
13.7c
10.6
9.2
11.3c
5.3
3.5
4.4c
3.4
2.9
(0.26 ,0.44)
2TDFE √
3.6b
5.8
7.5
35160c
100
1000
15.9c
14.6
14.6
9.6c
8.0
6.3
4.9c
4.7
4.7
(0.25, 0.45)
a Device configurations, with HTL: ITO/NPB (60 nm)/2ADFE(20 nm)/TPBi (10 nm)/Alq3 (30
nm)/LiF/Al (200 nm); without HTL: ITO/ 2ADFE(80 nm)/TPBi(10 nm)/Alq3(30 nm)/LiF/Al(200
nm) ; Device configuration for 2TDFE: ITO/NPB(60 nm)/2TDFE(20 nm)/TPBi(10 nm)/Alq3(30
nm)/LiF/Al(200 nm); b
turn-on voltage; c maximum value.
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