A new class of star-shaped cholesteric liquid crystal containing a 1,3,5-trihydroxybenzene unit as a core

Article abstract of DOI:10.1016/j.molstruc.2007.08.041

A new class of star-shaped cholesteric liquid crystals were designed and synthesized, which used 1,3,5-trihydroxybenzene unit as a core and ω-cholesteric alkyl diacid monoester as mesogenic arm. Their chemical structures were confirmed by element analyses, FT-IR, and ¹H NMR. The mesomorphic properties and thermal stability were investigated by differential scanning calorimetry, thermogravimetric analysis, polarizing optical microscopy, and X-ray diffraction measurements. The experimental results demonstrated that the mesogenic arm structures strongly affected the phase behavior. 4a did not show any liquid crystallinity, while 4b, 4c and 4d revealed reversible cholesteric phase transition. As the intermedius alkyl chain of the star-shaped compounds lengthened (from n = 2 to n = 8), their melting points decreased but mesomorphic temperature ranges increased. Focal conic texture, one of cholesteric phase can be observed in the liquid crystalline state.

Full text of DOI:10.1016/j.molstruc.2007.08.041

Available online at www.sciencedirect.com
Journal of Molecular Structure 881 (2008) 83–89
www.elsevier.com/locate/molstruc
A new class of star-shaped cholesteric liquid crystal containing
a 1,3,5-trihydroxybenzene unit as a core
*
Dan-Shu Yao, Bao-Yan Zhang , Wei-Wei Zhang, Mei Tian
Center for Molecular Science and Engineering, Northeastern University, Shenyang 110004, People’s Republic of China
Received 16 April 2007; received in revised form 28 August 2007; accepted 29 August 2007
Available online 18 September 2007
Abstract
A new class of star-shaped cholesteric liquid crystals were designed and synthesized, which used 1,3,5-trihydroxybenzene unit as a core
and x-cholesteric alkyl diacid monoester as mesogenic arm. Their chemical structures were confirmed by element analyses, FT-IR, and
1
H NMR. The mesomorphic properties and thermal stability were investigated by differential scanning calorimetry, thermogravimetric
analysis, polarizing optical microscopy, and X-ray diffraction measurements. The experimental results demonstrated that the mesogenic
arm structures strongly affected the phase behavior. 4a did not show any liquid crystallinity, while 4b, 4c and 4d revealed reversible cho-
lesteric phase transition. As the intermedius alkyl chain of the star-shaped compounds lengthened (from n = 2 to n = 8), their melting
points decreased but mesomorphic temperature ranges increased. Focal conic texture, one of cholesteric phase can be observed in the
liquid crystalline state.
ꢀ
2007 Elsevier B.V. All rights reserved.
Keywords: Star-shaped compounds; Liquid crystals; Cholesteric phase; Synthesize
1
. Introduction
cholesteric liquid-crystalline polymers have been reported.
The influence of mesogenic unit structures, chiral unit
properties and flexible spacer length on cholesteric LCs
were discussed [14–20]. However, to the best of our knowl-
edge, star-shaped cholesteric LCs has been few synthesized.
As one kind of unconventional LCs, star-shaped LC usu-
ally has a small core and a few extended rigid mesogenic
units as the side-chain liquid crystal arms, and show nema-
tic phase of rod-like LCs, as well as columnar phase of dis-
cotic LCs [21–26]. The numerous applications of star-
shaped LCs include non-linear optical filters, flat-panel dis-
plays and fast switching materials, etc. [27–30].
Cholesteric liquid crystals (LCs) have attracted consid-
erable attention owing to their unique optical properties,
such as selective reflection of circularly polarized light, high
optical rotatory power, circular dichroism and electro-
optic effect [1–8]. All these outstanding optical properties
of cholesteric LCs result from their unusual helical supra-
molecular structure with the well-defined pitch. When the
wavelength of visible light in the medium is equal to the
pitch of the cholesteric helix, Bragg reflection takes place,
the cholesteric phase selectively reflects visible light and
exhibits brilliant colors [9,10]. As is well known, cholesteric
LCs can be obtained by the combination of a chiral com-
ponent and a mesogenic unit, or by polymerization of chi-
ral mesogenic units and the chirality plays an important
role in this field [11–13]. In recent years, more and more
rod-like, discotic cholesteric LCs and comblike side-chain
In this paper, we used 1,3,5-trihydroxybenzene as a core
and x-cholesteric alkyl diacid monoester as chiral meso-
genic units to synthesize a new kind of compounds. It is
a star-shaped system functionalized with cholesteric group
in its periphery. Their chemical structures were confirmed
1
by FTIR and H NMR spectra. The thermal properties
and specific rotation of chiral mesogenic units and chiral
star-shaped compounds were evaluated by differential
scanning calorimetry (DSC) and polarimetry. Liquid
*
Corresponding author.
E-mail address: baoyanzhang@hotmail.com (B.-Y. Zhang).
0
022-2860/$ - see front matter ꢀ 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2007.08.041

84
D.-S. Yao et al. / Journal of Molecular Structure 881 (2008) 83–89
crystal phases were studied through polarized optical
microscopy (POM) and were conformed by using X-ray
diffraction method. The influence of the length of the mes-
ogenic units on phase behavior of the star-shaped com-
pounds were discussed.
decanedioic acid monocholesterol ester 2d, the same
method was adopted. The synthesis of 2b was given as an
example. Adipyl chloride (18.2 g, 0.10 mol) obtained from
hexanedioic acid reacting with excess thionyl chloride was
dissolved in 50 ml THF, cholesterol (7.6 g, 0.02 mol) in
50 ml THF with the presence of 5 ml pyridine was added
2
. Experimental procedures
dropwise with stirring, the reaction mixture was refluxed
for 10 h in a dry atmosphere. After cooling to room tem-
perature, the mixture was poured into 200 ml cold water
and acidified with 6 N hydrochloric acid. The precipitate
was isolated by filtration and dried in a vacuum oven.
Recrystallization from ethanol gave white crystals of 2b.
Yield 58%.
2
.1. Materials
Cholesterol was purchased from Henan Xiayi Medical
Co. 1,3,5-trihydroxybenzene, succinic anhydride, hexa-
nedioic acid, octanedioic acid and decanedioic acid were
purchased from Beijing Chemical Company (China) and
used without any further purification. All solvents and
reagents were purified by standard methods.
2.3.2. Tri[x-alkyl diacid monocholesterol ester]
phloroglucinol ester (4a–4d)
All star-shaped liquid crystals (4a–4d) were prepared by
the same synthetic method. First, x-alkyl diacid monocho-
lesterol ester 2a–2d (0.033 mol) was reacted at 65 ꢁC with
50 ml thionyl chloride containing a few drops of N,N-dim-
ethylfomamide (DMF) for 3 h, and then the excess thionyl
chloride was removed under reduced pressure to give the
corresponding acid chloride 3. The acid chloride obtained
was dissolved in 20 ml dry THF, followed by adding
1,3,5-trihydroxybenzene (0.01 mol) in 20 ml pyridine. The
reaction mixture was refluxed for 12 h in a dry atmosphere.
After cooling to room temperature, the mixture was
poured into 150 ml cold water and acidified with 6 N
hydrochloric acid. The crude product obtained was col-
lected by filtration, and was purified by recrystallization
from acetone to yield white crystals 4a–4d (65–76%).
4a Yield 65%. m.p. 150–151 ꢁC. Anal. calcd for
C H O : C, 77.65; H, 9.80%. Found: C, 77.47; H,
2
.2. Measurements
The element analyses were carried out by using a Ele-
mentar Vario EL III (Elementar, Germany). FT-IR spectra
were measured on a Perkin-Elmer spectrum One (B) spec-
trometer (Perkin-Elmer, Foster City, CA). H NMR spec-
tra (300 MHz) were obtained with a Varian Gemini 300
spectrometer (Varian Associates, Palo Alto, CA). Optical
rotations were obtained on a Perkin-Elmer 341 polarime-
ter. Phase transition temperatures and thermodynamic
parameters were determined by using a Netzsch DSC 204
1
(
Netzsch, Germany) equipped with a liquid nitrogen cool-
ing system. The heating and cooling rates were 10 ꢁC/min.
A Leica DMRX (Leica, Germany) POM equipped with a
Linkam THMSE-600 (Linkam, England) hot stage was
used to observe phase transition temperatures and analyze
LC properties for the mesogenic units and star-shaped
liquid crystals through observation of optical textures.
XRD measurements were performed with a nickel-filtered
9
9
150 12
ꢀ
1
9.71%. IR (KBr, cm ): 2950, 2869 (ACH , ACH A);
3
2
1768, 1735 (C@O); 1606, 1506 (ArA); 1272, 1135
1
(CAOAC). H NMR (CDCl , ppm): 0.64–2.10 (m, 129H,
3
Cu-K (k = 0.1542 nm) radiation with a DMAX-3A Riga-
cholesteryl-H), 2.55 (m, 12H, AOCCH A), 3.95–4.08 (m,
a
2
ku (Rigaku, Japan) powder diffractometer.
3H, OCH< in cholesteryl), 5.23–5.35 (m, 3H, @CHA in
cholesteryl), 7.03 (s, 3H, ArAH).
2
.3. Synthesis
4b Yield 72%. m.p. 126–128 ꢁC. Anal. calcd for
C105H162O : C, 78.07; H, 10.04%. Found: C, 78.23; H,
12
ꢀ
1
The synthetic routes of the mesogenic units containing
9.88%. IR (KBr, cm ): 2945, 2866 (ACH , ACH A);
3
2
monocholesterol ester (2a–2d) and star-shaped liquid crys-
tals (4a–4d) were shown in Scheme 1.
1762, 1731 (C@O); 1608, 1510 (ArA); 1280, 1142
1
(CAOAC). H NMR (CDCl , ppm): 0.63–2.07 (m, 141H,
3
cholesteryl-H and AOCCH (CH ) A), 2.46 (m, 12H,
2
2 2
2
.3.1. x-Alkyl diacid monocholesterol ester (2a–2d)
AOCCH A), 3.92–4.06 (m, 3H, AOCH< in cholesteryl),
2
Butanedioic acid monocholesterol ester 2a was prepared
by an esterification of cholesterol (3.8 g, 0.01 mol) with
butanedioic anhydride (1.0 g, 0.01 mol) in 20 ml THF using
5.38–5.50 (m, 3H, @CHA in cholesteryl), 6.95 (s, 3H,
ArAH).
4c Yield 76%. m.p. 108–110 ꢁC. Anal. calcd for
2
ml pyridine as catalyst. The mixture was refluxed for 18 h
C111H174O : C, 78.45; H, 10.25%. Found: C, 77.97; H,
12
ꢀ
1
in a dry atmosphere. Cooled to room temperature, the
reaction solution was poured into 100 ml cold water. The
precipitate was isolated by filtration, washed with hot
water, then recrystallized from ethanol to yield white crys-
tals (74%).
10.59%. IR (KBr, cm ): 2948, 2864 (ACH , ACH A);
3
2
1766, 1732 (C@O); 1605, 1502 (ArA); 1275, 1140
1
(CAOAC). H NMR (CDCl , ppm): 0.60–2.04 (m, 153H,
3
cholesteryl-H and AOCCH (CH ) A), 2.42 (m, 12H,
2
2 2
AOCCH A), 3.96–4.04 (m, 3H, AOCH< in cholesteryl),
2
For the synthesis of hexanedioic acid monocholesterol
ester 2b, octanedioic acid monocholesterol ester 2c and
5.36–5.46 (m, 3H, @CA in cholesteryl), 7.02 (s, 3H,
ArAH).

D.-S. Yao et al. / Journal of Molecular Structure 881 (2008) 83–89
85
SOCl2
HOOC(CH ) COOH
ClOC(CH ) COCl
2
n
2 n
1
Pyridine
Chol*OOC(CH ) COOH
2 n
1
+
HO Chol*
THF
2
2b: n=4; 2c: n=6; 2d: n=8
O
O +
O
Pyridine
THF
Chol*OOC(CH ) COOH
HO Chol*
2 2
2
2a: n=2
SOCl2
Chol*OOC(CH ) COCl
2
2 n
Chol*=
3
Chol*OOC(CH ) COO
HO
HO
Pyridine
THF
2 n
OOC(CH ) COOChol*
OH
2 n
3
+
Chol*OOC(CH ) COO
2 n
4
4a: n=2; 4b: n=4; 4c: n=6; 4d: n=8
Scheme 1. The synthetic route of star-shaped liquid crystals.
4
d
Yield 68%. m.p. 83–85 ꢁC. Anal. calcd for
strated the existence of 1,3,5-trihydroxybenzene esters
products.
C117H186O : C, 78.79; H, 10.44%. Found: C, 78.31; H,
0.17%. IR (KBr, cm ): 2942, 2860 (ACH , ACH A);
12
ꢀ
1
1
3
2
1
754, 1729 (C@O); 1601, 1498 (ArA); 1277, 1138
3.2. Liquid crystalline behavior of mesogenic units (2a–2d)
1
(
CAOAC). H NMR (CDCl , ppm): 0.65–2.05 (m, 165H,
3
cholesteryl-H and AOCCH (CH ) A), 2.55 (m, 12H,
2
2 6
The mesomorphic properties of mesogenic units 2a–2d
were investigated by differential scanning calorimetry
DSC) and polarizing optical microscopy (POM).
The DSC results presented in Table 1 revealed only iso-
AOCCH A), 3.90–4.02 (m, 3H, OCH< in cholesteryl),
2
5
.40–5.50 (m, 3H, @CHA in cholesteryl), 7.04 (s, 3H,
(
ArH).
tropic melting for the mesogenic unit 2a with short alkyl
chain length (n = 2) during the heating scan. In contrast,
the mesogenic units 2b, 2c and 2d, with long alkyl chain
length n = 4, 6 and 8, were found to exhibit liquid crystal-
line properties in heating trace, they showed a melting tran-
sition at 135.6, 122.4 and 118.8 ꢁC, a clearing transition at
3
. Results and discussion
3
.1. Synthesis
1
7
43.0, 131.6 and 123.9 ꢁC, the mesogenic region (DT ) at
This new kind of star-shaped cholesteric liquid crystals
1
.4, 9.2 and 5.1 ꢁC, respectively. However, in cooling cycle,
were synthesized according to Scheme 1. Their structural
characterization were in agreement well with the predic-
tion. The mesogenic units (2a–2d)were obtained from the
reaction of cholesterol with corresponding anhydride or
alkyl diacids, the star-shaped liquid crystals (4a–4d) were
synthesized from corresponding cholesteryl carboxylic
acids chloride with 1,3,5-trihydroxybenzene. IR spectra of
the mesogenic units 2a–2d all displayed a mesophase. The
region of liquid crystal phase (DT ) was 23.1, 39.2, 29.9
2
and 21.6 ꢁC singly. In addition, when the mesogenic units
2a–2d were in the liquid crystal state, broken focal conic
texture, one of cholesteric phases, was observed using the
crossed polarizer. All these data indicated that 2b, 2c and
2d were enantiotropic cholesteric liquid crystals, and 2a
2
a–2d showed characteristic bands at 3290–2550; 1725
was monotropic cholesteric liquid crystal. Fig. 1 displayed
the representative textures of mesogenic units.
and 1700 nearby attributed to carboxylic acid AOH, ester
C@O and carboxylic acid C@O stretching bands. Whereas
IR spectra of 4a–4d did not show carboxylic acid AOH
stretching bands, the peaks of the carboxylic acid C@O
stretching vibration disappeared as well. Analysed with
3.3. Thermal properties of star-shaped liquid crystals (4a–4d)
1
H NMR Spectra, 4a–4d showed multiplet at 0.6ꢀ2.10,
The thermal properties of star-shaped liquid crystals 4a–
4d evaluated by DSC were summarized in Table 2 and the
representative DSC thermograms were shown in Fig. 2. All
the phase transitions were reversible and did not change on
2
.40ꢀ2.55, 3.90–4.10 and 6.95ꢀ7.05 ppm corresponding
to methyl, methylene protons, olefinic protons and aro-
matic protons, respectively. These results clearly demon-

86
D.-S. Yao et al. / Journal of Molecular Structure 881 (2008) 83–89
Table 1
Phase transition temperatures and specific rotations of mesogenic units
ꢀ1
a
b
25
c
Mesogenic units
n
Transition temperature (ꢁC) (corresponding enthalpy changes, J g ) Heating/cooling
DT
1
DT
2
½aꢁD
2
2
2
2
a
b
c
2
4
6
8
Cr176.6(52.92)I/I155.5(ꢀ3.675)Ch132.4(ꢀ21.25)Cr
–
23.1
39.2
29.9
21.6
ꢀ20.50
ꢀ28.33
ꢀ37.61
ꢀ43.25
Cr135.6(65.11)Ch143.0(3.613)I/I141.8(ꢀ4.723)Ch102.6(ꢀ28.58)Cr
Cr122.4(61.88)Ch131.6(2.992)I/I129.3(ꢀ7.289)Ch99.4(ꢀ66.01)Cr
Cr118.8(29.98)Ch123.9(1.25)I/I119.3(ꢀ5.678)Ch97.7(ꢀ41.41)Cr
7.4
9.2
5.1
d
Cr, crystal, Ch, cholesteric; I, isotropic.
a
Mesophase temperature ranges on heating cycle.
Mesophase temperature ranges on cooling cycle.
Specific rotation of compounds, in toluene.
b
c
of thermotropic mesophases in this star-shaped system.
As a rule, mesomorphic units which arrange in a parallel
direction are prone to generate liquid crystals [31]. To this
new kind of star-shaped compounds, lamellar cholesterol
mesomorphic units were attached to a small core with a
flexible spacer derived from alkyl diacid, the arm-to-arm
interaction between neighbouring and within molecules
existed. When the length of the flexible spacer was long
enough, cholesterol mesomorphic units were capable of
folding an anisotropic shape to give rise to the appearance
of a cholesteric liquid crystalline order. Among these star-
shaped compounds, 4d, with the longest flexible spacer,
were found to exhibit the widest mesophase temperature
range, transitions from the crystalline to the liquid crystal-
line phase at 84.4 ꢁC and from the liquid crystalline to the
isotropic phase at 121.4 ꢁC were observed. The cooling
curve also confirmed this phase behavior.
3.4. Specific rotation of star-shaped liquid crystals (4a–4d)
The Specific rotations of star-shaped liquid crystals 4a–
d were carried out in toluene using Na-lamp light at
4
k = 589 nm. As shown in Table 2, the specific rotations
of them are all negative values, and as the intermedius alkyl
chain of the star-shaped compounds lengthened (from
n = 2 to n = 8), the absolute value of the specific rotations
increased gradually (from ꢀ8.37ꢁ to ꢀ13.68ꢁ). It revealed
similar tendency as those described above for 2a–2d shown
in Table 1. The results suggest that the configuration of the
cholesteric groups must be retained for all synthesized star-
shaped liquid crystals 4a–4d, and the length of flexible alkyl
chain might affect the molecule array leading to the
increase of the specific rotations.
Fig. 1. Polarized optical micrograph of mesogenic units (200·). (a)
Broken focal conic texture of 2a at cooling to 144.9 ꢁC. (b) Broken focal
conic texture of 2d at cooling to 103.4 ꢁC.
3.5. Texture analysis of star-shaped liquid crystals (4a–4d)
repeated heating and cooling cycles. It was found that
three-armed star-shaped liquid crystal 4a (n = 2) did not
exhibit a liquid crystalline phase, showing only melting
and crystallization behavior on heating and cooling,
whereas three-armed star-shaped liquid crystals 4b
The optical textures of star-shaped liquid crystals (4a–
4d) obtained are studied by POM with hot stage. POM
results showed that 4a was a non-mesogenic compound,
while 4b–4d exhibited enantiotropic cholesteric phase.
When 4b was heated to 127 ꢁC, the sample began to melt,
the focal-conic texture and reflection color appeared grad-
ually. Texture and reflection color disappeared at 139 ꢁC.
When the isotropic state was cooled to 129 ꢁC, cholesteric
focal-conic texture appeared, and the liquid crystalline
(
n = 4), 4c (n = 6) and 4d (n = 8) displayed a mesophase.
These were consistent with the POM results. On heating
trace, the mesogenic region of 4b, 4c and 4d was extended
to 11.6, 24.5 and 37.0 ꢁC. These results indicated that the
length of the flexible spacer greatly affected the formation

D.-S. Yao et al. / Journal of Molecular Structure 881 (2008) 83–89
87
Table 2
Phase transition temperatures and specific rotations of star-shaped liquid crystals
ꢀ1
a
1
b
25
c
Star-shaped liquid crystals
n
Transition temperature (ꢁC) (corresponding enthalpy changes, J g ) Heating/cooling
DT
DT
2
½aꢁD
4
4
4
4
a
b
c
2
4
6
8
Cr151.6(65.5)I/I145.0(ꢀ41.30)Cr
–
–
ꢀ8.37
ꢀ11.55
ꢀ12.34
ꢀ13.68
Cr127.1(43.30)Ch138.7(3.173)I/I129.2(ꢀ2.997)Ch89.5(ꢀ17.04)Cr
Cr108.8(39.52)Ch133.3(3.186)I/I121.4(ꢀ1.404)Ch75.8(ꢀ21.74)Cr
Cr84.4(20.64)Ch121.4(0.9102)I/I110.3(ꢀ1.519)Ch63.4(ꢀ23.11)Cr
11.6
24.5
37.0
39.7
45.6
46.9
d
Cr, crystal; Ch, cholesteric; I, isotropic.
a
Mesophase temperature ranges on heating cycle.
Mesophase temperature ranges on cooling cycle.
Specific rotation of compounds, in toluene.
b
c
cholesteric liquid crystal phase is typically composed of a
chiral center which produces intermolecular forces that
favor alignment between molecules at a slight angle to
one another. This leads to the formation of a periodic heli-
cal structure. The helical structure of cholesteric phase
selectively reflects light of wavelengths equal to the pitch
length, so that a color will be reflected when the pitch is
equal to the corresponding wavelength of light in the visi-
ble spectrum. As the helical pitch is temperature depen-
dent, the change of temperature will result in the
alteration of the pitch of the helical structure of the chole-
steric phase. Therefore the reflection color changes at dif-
ferent temperatures.
3.6. XRD analysis of star-shaped liquid crystals (4a–4d)
X-ray diffraction measurements can provide more
detailed information on the liquid crystalline phase struc-
tures. In general, a sharp and strong peak appears at low
angle (1ꢁ < 2h < 4ꢁ) in small-angle X-ray scattering (SAXS)
curves only for smectic structure, a broad peak associated
with lateral packing at 2h = 16–22ꢁ is observed in wide-
angle X-ray diffraction (WAXD) curves for nematic, smec-
tic and cholesteric phase structure. The diffraction angles of
cholesteric structure at wide angle are obvious less than
those of smectic and nematic structures, this is very impor-
tant characteristic to judge cholesteric structure [32]. The
quenched samples of star-shaped liquid crystals 4b–4d were
studied by SAXS and WAXD. Data showed amorphous
diffuse peaks at about 2h of 17ꢁ, which suggests the average
˚
distance of 5 A between two neighbor LC molecules within
the layers of the mesophase (calculating according to Bragg
equation, k = 2d sin h)and there was no sharp peak at low
angles region. Representative XRD curves were shown in
Fig. 4. This result suggested that 4a–4d exhibited only cho-
lesteric mesophases, which was consistent with their optical
textures.
Fig. 2. DSC thermograms of star-shaped liquid crystal 4b and 4d.
phase began to crystallize at 90 ꢁC. Compounds 4c and 4d
had optical properties similar to those of compound 4b.
Fig. 3 displayed the representative textures of 4b–4d. As
the extension of the flexible spacer from C H (4a) to
2
4
C H (4d) leads to a significant increase in the mesogenic
4. Conclusions
8
16
region during the heating processes. Moreover the reflec-
tion color changed from yellow, green to blue with increas-
ing temperature and it was in reverse direction as the
temperature decreased in the cooling cycle. This unique
optical property is related to the helical supermolecular
structure of cholesteric liquid crystals. As we know, the
In this study, a novel series of star-shaped cholesteric
liquid crystals 4a–4d based on 1,3,5-trihydroxybenzene as
a core, cholesteryl as chiral units and x-cholesteric alkyl
diacid monoester as mesogenic arms were synthesized
and characterized. The experimental results demonstrated

88
D.-S. Yao et al. / Journal of Molecular Structure 881 (2008) 83–89
Fig. 4. X-ray diffraction patterns of quenched samples.
optical texture was focal conic texture, one of cholesteric
phase. Along with the change of temperature, they exhib-
ited different reflection color in the liquid crystalline states.
Acknowledgements
The authors are grateful to National Natural Science
Fundamental Committee of China, HI-Tech Research
and development program (863) of China, National Basic
Research Priorities Program (973) of China, Science and
Technology Bureau of Liaoning Province for financial sup-
port of this work.
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