Optical properties of triphenylamine decorated with naphthalimide

Article abstract of DOI:10.1080/15421406.2016.1277892

A propeller conformed triphenylamine molecule was decorated with naphthalimide. The two fluorophores were bonded with alkynyl bridge unit, which conjugates the two fragments. The resulting compound was fully characterized. Several solvents were used to investigate its absorption and emission behavior with the solvent polarity variation from weak to strong. The quantum yield increased with the increasing of solvent polarity. It is also highly emissive in film and in a solid with significant emission shift toward longer wavelength, reaching to 544 and 593?nm, respectively. The underlying signal mechanism was interpreted by the HOMO/LUMO potentials based on TDDFT calculations.

Full text of DOI:10.1080/15421406.2016.1277892

Molecular Crystals and Liquid Crystals
ISSN: 1542-1406 (Print) 1563-5287 (Online) Journal homepage: http://www.tandfonline.com/loi/gmcl20
Optical properties of triphenylamine decorated
with naphthalimide
Xiaochuan Li, Anqi Li, Wenjuan Jiang & Young-A Son
To cite this article: Xiaochuan Li, Anqi Li, Wenjuan Jiang & Young-A Son (2017) Optical properties
of triphenylamine decorated with naphthalimide, Molecular Crystals and Liquid Crystals, 645:1, 1-9,
DOI: 10.1080/15421406.2016.1277892
To link to this article: http://dx.doi.org/10.1080/15421406.2016.1277892
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Date: 14 May 2017, At: 20:00

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
, VOL. , –
http://dx.doi.org/./..
Optical properties of triphenylamine decorated
with naphthalimide
Xiaochuan Lia,b, Anqi Lia, Wenjuan Jianga, and Young-A Sonc
aCollaborative Innovation Center of Henan Province for Green Manufacturing of Fine Chemicals, Key Laboratory
of Green Chemical Media and Reactions, Ministry of Education, Henan Normal University, Xinxiang, Henan,
P. R. China; bHenan Key Laboratory of Green Chemical Media and Reactions, School of Chemistry and Chemical
Engineering, Henan Normal University, Xinxiang, Henan, P. R. China; cBK, Department of Advanced Organic
Materials Engineering, Chungnam National University, South Korea
ABSTRACT
KEYWORDS
Triphenylamine;
naphthalimide; highly
emissive; shift
A propeller conformed triphenylamine molecule was decorated with
naphthalimide. The two fluorophores were bonded with alkynyl bridge
unit, which conjugates the two fragments. The resulting compound was
fully characterized. Several solvents were used to investigate its absorp-
tionandemissionbehaviorwiththesolventpolarityvariationfromweak
to strong. The quantum yield increased with the increasing of solvent
polarity. It is also highly emissive in film and in a solid with significant
emission shift toward longer wavelength, reaching to 544 and 593 nm,
respectively. The underlying signal mechanism was interpreted by the
HOMO/LUMO potentials based on TDDFT calculations.
Introduction
The organic fluorescence emitters are brighter than that of the inorganic ones and have more
intense color, while inorganic fluorescence emitters exhibit better stability than that of the
organic fluorescence emitters. Organic fluorescent dyes are generally more soluble in most of
the organic solvents as the molecular lattices of organic dyes hold the molecules loosen and
can be separated by the solvent molecules. Their unusual strong light emission in solution,
film, and solid state has prompted extensive efforts in designing /synthesizing new photo-
luminescent compounds and exploring their application as smart materials. Certain dyes
has also demonstrated enhanced fluorescence upon selective sensing of biomolecules and
aggregation-induced emission in diagnose specific health conditions. Up to now, several typ-
ical frameworks have been widely accepted in configuring organic fluorescence emitter, such
as coumarins, naphthalimide, bisindolylmalimide, perylemediimides, rhodamine, and BOD-
IPY [1–14]. The application for material science and biotechnology is based on the logic in-
/out- put and translation of optical signal, which are desired by the chemists, physicists, and
biochemists [15–18]. Naphthalimide derivatives are one of the dyes attracted the attention of
scientists over the past decade [2–4]. 1,8-Naphthalimide could be conveniently synthesized
from 1,8-naphthalic anhydride, which is available as the product of petroleum processing. In
CONTACT Prof. Young-A Son
National University,  Gung-dong, Daejeon, -, South Korea; Prof. Xiaochuan Li
yason@cnu.ac.kr
Department of Advanced Organic Materials Engineering, Chungnam
lixiaochuan@htu.cn School of
Chemistry and Chemical Engineering, Henan Normal University, East Jianshe Rd. , Xinxiang, Henan, , China.
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gmcl.
©  Taylor & Francis Group, LLC

2/[268]
X. LI ET AL.
addition, the post function of 1,8-naphthalimide could be proceeded at the 3- or 4-position,
which derives various functional molecules. Altering the electron substitution of electron
donating/withdrawing power could effectively modify the emission behavior of the naphthal-
imide derivatives and span the emission spectrum from the green to red part [2]. The door
was opened up for rational design of multifunctional smart molecules and put into practical
application.
Based on the character of naphthalimide mentioned above, triphenylamine was config-
ured as the core and naphthalimide was decorated as peripheral unit with acetylene bond
linked together. The propeller like of triphenylamine twists the conformation of the molecule
structure and inhibits the regular π-π packing, which facilitates the solid emission. An elec-
tron push-pull model was constructed with the electron-donated N atom of triphenylamine
and the electron-withdrawing imide of naphthalimide attached. Any influence, for example
the solvent polarity, towards the electron push-pull will alter the electronic properties. The
remarkable photo-physical properties induced by the electronic interaction is deserved to be
investigated.
Experimental
General procedures and materials
The solvents used in the reaction were carefully dried according to the standard procedure
˚
and stored over 4A molecular sieve. All the reagent-grade chemicals were purchased from
Sigma-Aldrich CO. LLC./Alfa Aesar-A Johnson Matthey Company (South Korea) and used
without further purification. Melting points were determined on a Mel-Temp IA9200 digital
®
melting point apparatus in a glass capillary and were uncorrected. All synthesized compounds
were routinely characterized by TLC and 1H NMR. TLC was performed on aluminum-backed
silica gel plates (Merck DC. Alufolien Kieselgel 60 F254).
1H/13C NMR, IR, and high resolution mass spectroscopy
1H and 13C nuclear magnetic resonance (NMR) spectra were recorded on a Bruker AM-400
spectrometer operating at frequencies of 400 MHz for proton 100 MHz for carbon in CDCl3.
Proton chemical shifts (δ) are relative to tetramethylsilane (TMS, δ = 0) as internal standard
and expressed in parts per million. Spin multiplicities are given as s (singlet), d (doublet),
t (triplet), and m (multiplet) as well as b (broad). Coupling constants (J) are given in Hertz.
Infrared (IR) spectra were run in KBr on an FTS-175C IR spectrometer (υmax in cm−1). High
resolution mass spectra (HRMS) were measured on a Bruker autoflex X III instrument.
UV-Vis and emission spectra
The absorption spectra were measured with a PERSEE TU-1900 and an Agilent 8453 spec-
trophotometer. Emission spectra were measured with Shimadzu RF-5301PC fluorescence
spectrophotometer. The solvents used in photochemical measurement were spectroscopic
grade and were purified by distillation. The stock solution of compounds (2×10−3 M) was
prepared in CH3CN, and a fixed amount of these concentrated solutions were added to each
experimental solution. All the experiments were done repeatedly, and reproducible results
were obtained. Prior to the spectroscopic measurements, solutions were deoxygenated by bub-
bling nitrogen through them.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
[269]/3
Scheme . Synthetic routes toward the triphenylamine-naphthalimide derivative (TN).
Synthesis
The synthesis of 4,4ꢀ,4ꢀꢀ-tri(N-butyl-4-ethynyl)-1,8-napthalimide-triphenyl amine (TN) is
depicted in Scheme 1. The synthesis of TN started from commercial available triphenylamine.
Iodination of triphenylamine proceeded conveniently when treated with KI/KIO3/HOAc
with 80% yield [19, 20]. 3 was prepared by Songashira coupling of tris(4-iodophenyl)amine
(2) with trimethylsilylacetylene. Subsequently, deprotection of the TMS group of 3 using
anhydrous K2CO3/MeOH yielded tris(4-ethynylphenyl)amine (4). Imidization of commer-
cial available 4-bromo-1,8-naphthalic anhydride (5) with n-butylamine produced N-butyl-
4-bromo-1,8-napthalimide (6) [4, 21]. Finally, the target compound TN was successfully
obtained by Sonogashira coupling between tris(4-ethynylphenyl)amine (4) and N-butyl-4-
bromo-1,8-napthalimide (6) using Pd(PPh3)4 (5 mol %) as catalyst, CuI (1.8 mol %) as co-
catalyst, and Et3N as base in THF.
,ꢀ,ꢀꢀ-tri(N-butyl--ethynyl)-,-napthalimide-triphenyl amine (TN)
In flame dried Schlenk flask (100 mL), tris(4-ethynylphenyl)amine (105.8 mg, 0.33 mmol),
Pd(PPh3)4 (62.4 mg, 0.054 mol), CuI (3.4 mg, 0.018 mmol), and anhydrous THF (10 mL) were
charged under N2 atmosphere. After 30 min stirring, 4-bromo-1,8-napthalimide (328.9 mg,
0.99 mmol) in anhydrous THF (20 mL) and Et3N (6 mL) were added. The mixture was
stirred at room temperature overnight. After the starting materials were full reacted, as con-
firmed by TLC, the mixture was poured to distilled water 50mL. Then, it was extracted by
dichloromethane (25 mL × 3). The organic phase dried over Mg2SO4 and evaporated in vac-
uum. The residue was loaded to the column. Column separation (silica gel 200-300 mesh,
eluent: dichloromethane/petroleum = 2/1) produced 286 mg yellow powder (80%).
Mp: 281–284°C; IR (KBr, υ, cm−1): 780, 1085, 1235, 1274, 1319, 1353, 1503, 1511, 1587,
1660, 1697, 2196, 2960. 1H NMR(400 MHz, CDCl3): δ (ppm): 8.73 (3H, d, J = 8.0 Hz), 8.65
(3H, d, J = 8.0 Hz), 8.56 (3H, d, J = 8.0 Hz), 7.95 (3H, d, J = 8.0 Hz), 7.84 (3H, t, J = 8.0
Hz), 7.64 (6H, d, J = 8.0 Hz), 7.23 (6H, d, J = 8.0 Hz), 4.20 (6H, t, J = 8.0 Hz), 1.73 (6H, m),

4/[270]
X. LI ET AL.
Table . Optical data of TN in several solvents.
UV-Vis
Fluorescence
Solvent
THF
λabs (nm)
log εmax
λem (nm)
ꢀF
FWHM (cm−
)
Stokes shift (cm−
)










.
.
.
.
.
.
.
.
.
.



.
.
.
.






Chloroform
Ethyl acetate
Ethanol









Hexane
.
.
Acetronitrile
a Full width at half maximum is abbreviated as FWHM.
1.53-1.44 (6H, m), 0.99 (9H, t, J = 8.0 Hz). 13C NMR (100 MHz, CDCl3): δ (ppm): 164.1,
163.9, 147.4, 133.5, 132.4, 131.73, 131.67, 130.7, 130.5, 128.2, 127.7, 127.6, 124.5, 123.2, 122.2,
118.1, 117.5, 99.1, 86.8, 40.5, 30.4, 29.8, 20.6, 14.0. Maldi-Tof: [M+H]+ C72H56N4O5 requires
1071.412; found [M+H]+ 1071.501; and [M+2H]+ C72H57N4O5 requires 1072.420; found
1072.508 (Base).
Result and discussion
The spectral property of TN was investigated in several solvents, such as hexane, chloroform,
THF, ethyl acetate, acetonitrile, ethanol, and DMF. TN exhibited medium to excellent solu-
bility in organic media, which may contribute to the alkyl attachment to the naphthalimide
moiety. No color fading was observed even after several days of exposure to the room light.
Additionally, the solvent polarity does not induce significant solvatochromism. The funda-
mental absorption/emission peaks, absorption coefficient, quantum yields, and Stokes shifts
are collected in Table 1. Figure 1 shows the absorption spectra of TN in various solvents. The
absorption spectra are of similar shape with each other. Strong absorption band was observed
around 390 nm and a shoulder at the shorter wavelength side. The molar absorption coeffi-
cients for TN are relatively high and lie in the 4.72-5.02 (log ε) range. The absorption spectra
Figure . Absorption spectra of TN in several solvents (. × − M).

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
[271]/5
Figure . Emission spectra of TN in several solvents (. × − M). Emission and excitation slit widths were
set to be  nm.
are only barely affected by solvent polarity with the maximum absorption value being slightly
shifted hypsochromically (∼5 nm) when the solvent is changed from hexane (388 nm) to chlo-
roform (393 nm), which is consistent with the general behavior of triphenylamine derivatives
[22]. This shift reflects the polarizability of the solvent and has also been observed for cyanine
dyes and aromatic amines [23]. The maximum absorption at longer wavelength side could be
attributed to S0→S1 transition with the bands on the high- and low-energy side corresponding
to 0-1 and 0-0 vibration transition, respectively. In addition, a considerably medium absorp-
tion bands are found around 280 nm with TN in THF, ethanol, DMF, hexane and acetonitrile.
We attribute this absorption bands to the S0→S2 transition. While in chloroform and ethyl
acetate, the S0→S2 transition red shifted and overlapped with the vibronic progression of the
S0→S1 transition. It is characterized by a relatively wide and structureless band.
Notably, TN exhibited intense fluorescence in most of the studied organic media, in
films, and in solid state, indicating their potential application in materials science and bio-
technology. Their detailed emission properties are listed in Table 1. Figure 2 presented the
emission profile in several solvents. TN shows the typical emission features of triphenylamine
derivatives, that is, strong blue emission and high fluorescence quantum yield (ꢀF) which
increases (from 0.50 in hexane to 0.73 in acetonitrile) with increasing the solvent polarity.
In addition, the fluorescence bands are bathochromically shifted (from 448 nm in hexane
to 490 nm in acetonitrile) with increasing solvent polarity. The Stokes shift (ꢁν), calculated
from the wavelengths of maximum intensity, also increase with increasing solvent polarity.
The slightly variation of the Stokes shift upon the solvents (except for acetonitrile) indi-
cates that the permanent dipole moments (if any) do not differ between the ground state
and the excited state [24]. It confirms that the van der Walls interactions with a polariz-
able solvent can rationalize the solvent dependence of the excitation energy. In acetonitrile,
the longer wavelength emission points to an excited state with a large dipole. For aromatic
compounds, the dipole moment in the excited electronic state (μe) was enlarged and larger
than that of the ground state (μg). With the polarity of solvent increasing, the stabilization by
polar solvent cage toward excited is stronger than that of ground state. Thus, emission red-
shift was observed in polar environment. Obviously, this stabilization mechanism is weaker
in non-polar solvent, while enhanced in polar solvent. In polar environment, the excited
state of TN interacted with the polar solvent and was stabilized. Due to the rigidity of the

6/[272]
X. LI ET AL.
Figure . Emission spectra of TN in film at  wt.% in polycarbonate and in a solid. Emission and excitation
slit widths were set to be  nm.
molecular framework and stability enhancement of excited state, nonradiation transition in
polar solvents would be less than that in non-polar solvent, thus lead to higher quantum yield.
The FWHM also expanded more in more polar solvent, which is similar to the trend observed
in Stokes shift. With the solvent varied from hexane to acetonitrile, the FWHM varied from
narrow (2297 cm−1) to broad (3107 cm−1).
TN is also emissive in film and in the slid state and their emission spectra are shown in
Figure 3. Compared to it in solution, the emission maxima in the film exhibited an obvious
bathochromic shift (544 nm) due to its tighter packing than in solution. The most intense
band around 544 nm contributed by monomers with the FWHM 2230 cm−1. In the solid
state, the propeller conformation of triphenylamine hindered the π-π stacking of naphthal-
imide, which is likely responsible for the quenching of the emission in the solid state for most
aromatic fluorphores [25-27]. The emission maximum was observed around 593 nm with
a shoulder at the higher energy band. In contrast to the emission behavior in solution (in
acetonitrile), the solid emission shifts 130 nm toward longer wavelength. It is obvious that
packing in solid is tighter than that in film. Therefore, the interaction between molecules in
solid would be stronger than that in film due to more closely adjacent between dye molecules.
This intensified interaction in solid enhanced the non-radiation transition from the excited
state to the ground state and significantly red-shifted the solid emission maximum. The solid
emission spectrum of TN shows similar bandwidth to that in film (FWHM: 2210 cm−1). It
suggests that the aggregate emission contributes mainly due to the most steric hindrance for
tighter packing. The monomers only contribute slightly to the solid emission as confirmed by
the blue shoulder emission around 544nm.
The emission color changes in solution/film/solid were characterized by CIE coordinates
(Figure 4). In solution, the emission color of TN varied from blue to sky blue with the sol-
vent polarity increasing (from hexane to acetonitrile). The CIE coordinates of TN in hexane,
chloroform, THF, ethyl acetate, and ethanol are adjacent, which is in agreement with their
emission profile in solution. However, the CIE coordinates of TN shifts to the sky blue region
in acetonitrile, where the largest Stokes shift was induced. Notable change in the CIE coor-
dinates of TN was observed due to the tight molecular packing in film and in solid state. In

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
[273]/7
Figure . CIE  chromaticity diagram of the emissions of TN in solutions, film, and solid state.
film, CIE coordinates of TN scattered in green region with largely shift. While in solid, nearly
orange emission was observed due to the significant aggregated emission.
To better understand the geometric, electronic, and optical properties of TN, a compre-
hensive computational investigation was undertaken using Materials Studio software pack-
age. To reduce the initial run times, the ground state energy-minimized structures were cal-
culated using DFT and the LDA/DN basis set. Further refinement and optimization of the
structure were achieved using time-dependent DFT (TDDFT) with B3LYP/DND basis set,
as implemented in the Dmol3 package [28, 29]. Only the highest occupied molecular orbitals
(HOMO) and lowest unoccupied molecular orbitals (LUMO) were calculated because the
strong absorption bands in the visible region are generally dominated by HOMO-LUMO tran-
sition. Figure 5 shows the electron density map of HOMO/LUMO with distinct contribution
of each atomic orbital. In HOMO, most of the electron density crowded on the triphenylamine
Figure . HOMO/LUMO diagrams of TN obtained from Dmol calculations.

8/[274]
X. LI ET AL.
moiety. Only a small amount of electron density distributed on the alkynyl bridge. It reflects
that the electron-donating nature of triphenylamine. The LUMO of TN is π∗-type molecule
orbital with the electron density distributing on naphthalimide moiety mostly. It presumably
is the bridging alkynyl facilitate the charge transfer (CT) process. In weak polarity solvent
(hexane), the dipole moment difference between the CT state and the ground state is similar
to the calculation in vacuum, with which the electron photon coupling with solvent pho-
ton will become increasingly important (for example: internal conversion), leading to a lower
quantum yield. Upon excitation, the CT state will be stabilized by more polar solvents than
that in hexane, leading to red-shift and stronger emission. The HOMO/LUMO distribution
character is in agreement with the emission behavior of TN in solvents variation from weak
(hexane) to strong (acetonitrile).
Conclusions
In summary, a newly designed triphenylamine-naphthalimide based molecules was synthe-
sized and fully characterized. The highly emissive behaviors in solution, in the solid state, and
in polycarbonate film were demonstrated. In solutions, bright blue emissions were observed
with the quantum yield varying from 0.5 to 0.73. In acetonitrile, the largest Stokes shift, 5365
cm−1, was found and the emission peak shifted to 490 nm. In film, the propeller conforma-
tion hindered the molecules to packing regular in polymer matrix, which leads to its highly
emissive character. In addition, intermolecular interactions induced significant emission shift
to green region. While in solid state, this trend was further amplified and shifted the emission
wavelength to 593 nm. Such emission properties from structurally control are remarkable and
hold promise for potential implementation in future applications. The unique fluorophore
packing make them potential candidates for both organic emitters and for solid/film-state
device fabrication. Further investigation of their application in optoelectronic devices is cur-
rent underway in our laboratory.
Funding
This work was supported by the National Natural Science Foundation of China (21272060), PCSIRT
(Grant no. IRT1061), and the Program for Innovative Research Team in Science and Technology in
University of Henan Province (15IRTSTHN003). This study was supported by the National Research
Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No.
2016901050).
References
[1] Sethan, S. M., & Shah, N. M. (1945). Chem. Rev., 36, 1.
[2] Banerjee, S., Veale, E. B., Phelan, C. M., Murphy, S. A., Tocci, G. M., Gillespie, L. J., Frimannsson,
D. O., Kelly, J. M., & Gunnlaugsson, T. (2013). Chem. Soc. Rev., 42, 1601.
[3] Li, X., & Son, Y.-A. (2015). J. Nanosci. Nanotechnol., 15, 5370.
[4] Li, X., & Son, Y. A. (2015). Mol. Cryst. Liq. Cryst., 604, 184.
[5] Chen, C.-T. (2004). Chem. Mater., 16, 4389.
[6] Li, X., Zhao, N., Yu, L., & Son, Y.-A. (2015). Mol. Cryst. Liq. Cryst., 608, 273.
[7] Li, X., & Son, Y.-A. (2014). Mol. Cryst. Liq. Cryst., 601, 182.
[8] Würthner, F, Saha-Möller, C. R., Fimmel, B., Ogi, S., Leowanawat, P., & Schmidt D. (2016). Chem.
Rev., 115, 962.
[9] Beija, M., Afonso, C. A. M., & Martinho, J. M. G. (2009). Chem. Soc. Rev., 38, 2410.
[10] Loudet, A., & Burgess, K. (2007). Chem. Rev., 107, 4891.

MOLECULAR CRYSTALS AND LIQUID CRYSTALS
[275]/9
[11] Ulrich, G., Ziessel, R., & Harriman, A. (2008). Angew Chem. Int. Ed., 47, 1184.
[12] Frath, D., Massue, J., Ulrich, G., & Ziessel, R. (2014). Angew Chem. Int. Ed., 537, 2290.
[13] Li, X., Ji, G., & Son, Y.-A. (2016). Dyes Pigments, 124, 232.
[14] Li, X., & Son, Y.-A. (2014). Dyes Pigments, 107, 182.
[15] Li, H., & Qu, D.-H. (2015). Sci. China Chem., 58, 916.
[16] Pu, S.-Z., Sun, Q., Fan, C.-B., Wang, R.-J., & Liu, G. (2016). J. Mater. Chem. C, 4, 3075.
[17] Qu, D.-H., Wang, Q.-C., Zhang, Q.-W., Mang, X., & Tian, H. (2015). Chem. Rev., 115, 7543.
[18] Tian, H. (2010). Angew Chem. Int. Ed., 49, 4710.
[19] Majumdar, K. C., Mondal, S., De, N., Sinha, R. K., & Roy, N. P. B. (2010). Tetrahedron Lett., 51,
521.
[20] Zhang, Q., Xu, M. L., & Zhang, C. J. (2011). Fine Chemical Intermediates, 41, 57.
[21] Li, X., Zhang, Y., Zhao, N., & Son, Y.-A. (2014). Mol. Cryst. Liq. Cryst., 600, 163.
[22] Li, X., Kim, S.-H., & Son, Y.-A. (2009). Dyes Pigments, 82, 293.
[23] Noukakis, D., Van der Auweraer, M., Toppet, S., & De Schryver, F. C. (1995) J. Phys. Chem., 99,
11860.
[24] Mataga, N., Kaifu, Y., & Koizumi, M. (1955). Bull. Chem. Soc. Jpn., 28, 690.
[25] Ooyama, Y., & Yoshida, K. (2005). New J. Chem., 29, 1204.
[26] De Halleux, V., Calbert, J.-P., Brocorens, P., Cornil, J., Declercq, J.-P., Brédas, J.-L., & Geerts, Y.
(2004). Adv. Funct. Mater., 14, 649.
[27] Mizukami, S., Houjou, H., Sugaya, K., Koyama, E., Tokuhisa, H., Sasaki, T., & Kanesato, M. (2005).
Chem. Mater., 17, 50.
[28] Delley, B. (1990). J. Chem. Phys., 92, 508.
[29] Delley, B. (2000). J. Chem. Phys., 113, 7756.