Liquid crystalline and nonlinear optical properties of bent-shaped compounds derived from 3,4′-biphenylene

Article abstract of DOI:10.1039/b700636e

The synthesis of different bent-core molecules derived from 3,4′-biphenylene bearing azo, azoxy, imine or ester linkages in their lateral structures is reported. Structure-activity relationships for their liquid crystalline behaviour are discussed. SmCP, USmCP and Col_ob mesophases are found depending on the type and number of these connecting units. The sequence ester ≈ azoxy > imine > azo can be proposed for the mesophase range, with significant differences observed in terms of mesopahase stabilization. SHG studies on these compounds give nonlinear coefficients in the range of 1-8 pm V^-1. The molecular origin for these values is analyzed semi-quantitatively. It was concluded that the SHG performance of bent-core mesogens in general can still be increased substantially. An approach to improve the properties of these materials is briefly outlined. The Royal Society of Chemistry 2007.

Full text of DOI:10.1039/b700636e

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PAPER
www.rsc.org/materials | Journal of Materials Chemistry
Liquid crystalline and nonlinear optical properties of bent-shaped
compounds derived from 3,49-biphenylene{
Inmaculada C. Pintre,a Ne´lida Gimeno,a Jose´ Lu´ıs Serrano,a M. Blanca Ros,*a Ibon Alonso,b Ce´sar L. Folcia,b
Josu Ortegac and Jesu´s Etxebarriab
Received 15th January 2007, Accepted 14th February 2007
First published as an Advance Article on the web 8th March 2007
DOI: 10.1039/b700636e
The synthesis of different bent-core molecules derived from 3,49-biphenylene bearing azo, azoxy,
imine or ester linkages in their lateral structures is reported. Structure–activity relationships for
their liquid crystalline behaviour are discussed. SmCP, USmCP and Colob mesophases are found
depending on the type and number of these connecting units. The sequence ester # azoxy . imine
. azo can be proposed for the mesophase range, with significant differences observed in terms of
mesopahase stabilization. SHG studies on these compounds give nonlinear coefficients in the
range of 1–8 pm V21. The molecular origin for these values is analyzed semi-quantitatively. It was
concluded that the SHG performance of bent-core mesogens in general can still be increased
substantially. An approach to improve the properties of these materials is briefly outlined.
both the mesomorphic properties of this type of material and
Introduction
to optimize NLO responses such as second harmonic genera-
Since the proposal by Watanabe et al.1 that chiral mesophases
tion (SHG).
could be obtained by using achiral molecules with a bent core,
With this aim in mind, materials showing the SmCP
this type of liquid crystal has attracted a great deal of
mesophase were mainly considered. Structures derived from
attention. Many different liquid crystal phases, generally
3,49-biphenylene as the angular core, in conjunction with long
denoted as B-type mesophases, have already been described
terminal tails (n-tetradecyloxy), were chosen because of their
and reviewed in the literature.2–5 Together with the B1
mesophase, which is characterized by a columnar disposition
of the molecules, the B2 arrangement, also called the SmCP
(smectic C polar) mesophase, is the most commonly observed
for bent-shaped molecules. It has been stated that this meso-
phase can exhibit either ferro- or antiferroelectric properties.
Furthermore, due to the non-centrosymmetric nature of the
SmCP phase in the ferroelectric variant (SmCPF), this
mesophase has been used to provide second-order nonlinear
optical (NLO) responses. In fact, the bent shape of the
molecules allows a significant component of the hyperpolariz-
ability along the polarization direction, thus increasing and
opening different technological possibilities for this type of
material.5
proven ability to promote SmCP mesophases.4 In order to
modulate not only the liquid crystalline, but also the optical
properties of the new materials, different connecting units such
as azo (–NLN–), azoxy [–N(O)LN–], imine (–CHLN–) and
ester (–COO–) have been studied and their effects compared
(see Scheme 1).
The appearance of a particular B mesophase is determined
by the chemical structure of the compounds in question. An
appropriate molecular design would therefore allow control of
the supramolecular order, the transition temperature and/or
the optical properties of these materials. In this respect, the
main objective of our research is to prepare new bent-core
molecules in an effort to gain further knowledge concerning
aInstituto de Ciencia de Materiales de Arago´n, Qu´ımica Orga´nica,
Facultad de Ciencias, Universidad de Zaragoza-CSIC, 50009 Zaragoza,
Spain. E-mail: bros@unizar.es
bDepartamento de F´ısica de la Materia Condensada, Facultad de Ciencia
y Tecnolog´ıa, Universidad del Pa´ıs Vasco, 48080 Bilbao, Spain
cDepartamento de F´ısica Aplicada II, Facultad de Ciencia y Tecnolog´ıa,
Universidad del Pa´ıs Vasco, 48080 Bilbao, Spain
{ Electronic supplementary information (ESI) available: Details of
synthetic procedures, analytical data for the compounds and
techniques. See DOI: 10.1039/b700636e
Scheme 1 Chemical structures of the bent-core compounds studied.
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The ester linkage is one of the most widely used in the design
of bent-core liquid crystals due to its thermal stability.
However, there are only a few examples in the literature in
which azo or azoxy groups are incorporated,6–11 despite their
attractive possibilities for optical materials (e.g. NLO activity
and cis–trans photoisomerization)12–15 as well as for liquid
crystals.16,17 Curiously, the pioneering bent-core mesogens,
prepared a long time ago by Vorla¨nder and Apel18,19 and
further revised by Pelzl et al.,6 were azoxy compounds. Given
this background the materials discussed here are both new and
previously reported20 azo and azoxy compounds. Finally,
Schiff bases have a well known ability to afford B1 and SmCP
mesophases with outstanding characteristics.4 However,
very few examples exist of bent-core liquid crystals based on
biphenylene-imine derivatives.21
main drawbacks of the compounds under investigation are
pointed out and new alternatives to increase the SHG activity
are discussed.
The physical properties of the tetra-ester homologue
(compound IX), first reported by Tschierske’s group22 and
extensively studied by our group,23,24 have been included in
this work for comparison. With the same aim we have also
included a thioalkyl analogue named compound X.
Experimental
Synthesis of the compounds
The synthetic procedures for the new bent-core compounds are
shown in Schemes 2, 3 and 4. In all cases, synthetic methods
reported in the literature for similar intermediates or methods
adapted to our own purposes were followed. Schiff bases III
and VIII were obtained by the condensation of the corre-
sponding biphenyl-aldehyde and p-tetradecyloxyaniline. The
synthesis of the final products IV and V was carried out by
esterification of 3,49-dihydroxybiphenyl with the correspond-
ing carboxylic acid (12, 14) using DCC/DMAP. However,
compound VII was prepared via the acid chloride (15) using
the phenol and the acid previously reported by us.20 The
synthetic method used to obtain the azoxy compound gave rise
to a mixture of isomers in equilibrium, in which the oxygen
As far as the NLO properties are concerned, SHG
measurements on bent-shaped materials are scarce and some
significant discrepancies exist, even in the order of magnitude
of the second-order susceptibility tensor. In this study we
carried out an analysis of the SHG performance of the most
representative materials from this series of compounds. The
activity is discussed in terms of their molecular structures. The
Scheme 2 Synthetic scheme for compounds III and VIII.
2220 | J. Mater. Chem., 2007, 17, 2219–2227
Scheme 3 Synthetic scheme for compounds IV and V.
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Scheme 4 Synthetic scheme for compound VII.
atom can be on either of the two nitrogen atoms. The most
stable isomer is depicted in the schemes. Details of synthetic
procedures and characterization of the compounds are
included in the ESI{.
Fig. 1 Experimental geometry for the SHG measurements. Two
different polarizations for the input beam were used, p and s. An in-
plane electric field E is applied to the sample to obtain homeotropic
alignment. A SmCSPF phase is depicted in the figure, although in some
compounds measurements were carried out in the SmCAPF phase. In
both cases the corresponding deff are deff = Dsin2h and deff = d for the
s–p and p–p configurations, respectively.
Techniques
The mesomorphic properties of the materials were studied by
optical microscopy using an Olympus BH2 microscope
with crossed polarizers. The microscope was connected to a
Linkam THMS 600 hot stage. Transition temperatures were
determined by differential scanning calorimetry (DSC) using a
TA2910 differential calorimeter calibrated with indium
where deff = d for p–p and deff = D sin2h for s–p configurations,
respectively. Here h is the tilt angle in the SmCPF phase, L is
the sample thickness and Dn = n(2v) 2 n(v) is the refractive
index mismatch between the second harmonic and funda-
mental lights. Dn is first obtained in each configuration by
measuring the SHG signals of two samples of different thick-
nesses. Finally, d and D are deduced by comparing each SHG
signal with that of a y-cut quartz crystal (d11 = 0.4 pm V21).
(156.6 uC, 28.44 J g21) at a scanning rate of 10 uC min21
.
X-Ray measurements of non-oriented samples were per-
formed using both a Pinhole (Anton–Paar) diffractometer and
a small-angle goniometer, with samples heated using a
variable-temperature attachment. The diffraction patterns
were collected either on flat photographic films or on a
position-sensitive detector (PSD) with an angular range of 4u.
The samples were held in Lindemann glass capillaries of
W = 1 mm or 0.5 mm, respectively. Monochromatic Ni-filtered
Cu-Ka radiation was used in both sets of equipment.
Results and discussion
Liquid crystalline properties and electro-optic responses of the
materials
Cells for SHG measurements were fabricated in our
laboratories and had in-plane ITO electrodes and gaps of
about 100 mm. Materials were subjected to a square-wave field
(amplitude 15 V mm21, frequency 5 Hz) to achieve home-
otropic alignment after a few minutes of field application. In
all cases a uniform area with clear extinction directions was
obtained inside the gap. The fundamental light source came
from a Nd:YAG laser and had a wavelength l = 1.064 nm.
Measurements were carried out under square-wave electric
fields in the SmCPF phases, by synchronizing the fields to the
laser pulses.25 According to ref. 26 only two parameters (d and
D) are needed to fully characterize the d tensor of the materials
with a good degree of approximation. This tensor was then
obtained by means of SHG measurements at normal incidence.
Two different input–output light polarization geometries
were used (see Fig. 1): p–p (input and output polarizations
parallel to the applied electric field) and s–p (perpendicular
input polarization and parallel output polarization). In these
geometries the SHG power P(2v) is given by
(a) Mesomorphic characterization. All of the new 3,49-biphe-
nyl derivatives reported here were studied by polarizing optical
microscopy (POM), differential scanning calorimetry (DSC)
and X-ray diffraction (XRD) in order to characterize their
liquid crystalline behaviour. Furthermore, the electro-optic
responses of the different materials were also investigated by
POM in order to obtain additional information about the
liquid crystalline phases formed by these molecules.
The results obtained using the different techniques led us to
assign the liquid crystalline properties gathered in Table 1 for
these compounds. For the sake of completeness, the properties
of the related materials I, II, VI and IX are also included in
this table.
As can be seen, all 3,49-biphenylene derivatives studied here
exhibit liquid crystalline phases characteristic of bent-core
compounds. Enthalpy values for the mesophase–isotropic
liquid transitions are in the range 20–30 kJmol21
.
sin2ð2pDnL=lÞ
(b) Optical texture characterization. POM studies were
Pð2vÞ!de2ff
(a)
2
ð2pDnL=lÞ
performed at different temperatures. For this purpose both
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Table 1 Thermal properties of the bent-core compounds studied
Compound Phase transitiona/uC (DH/kJ mol21
)
I20
C
I
C
I
C
I
C
I
C
I
C
I
C
I
C
I
139.1 (57.5) Colob
160.9 (18.5) Colob
120.3 (55.0) USmCPA 207.1
204.6 (24.8) USmCPA 102.5
165.4
127.8
(18.6)
(57.6)
(25.8)
(53.0)
(27.6)
(19.3)
(25.7)
(47.7)
(21.3)
(20.4)
(24.4)
(61.7)
(26.7)
(29.3)
(28.1)
(43.6)
(27.9)
(17.5)
I
C
I
C
I
C
I
C
I
C
I
C
I
C
I
II20
III
140.6 (19.6) SmCSPA
207.0 (27.5) SmCSPA
100.7 (42.8) SmCAPA
141.0 (25.3) SmCAPA
97.2 (28.4) SmCAPA
133.4 (20.9) SmCAPA
116.4 (62.0) SmCAPA
159.6 (24.0) SmCAPA
97.7 (31.5) SmCAPA
177.7 (26.2) SmCAPA
114.5 (45.0) SmCAPA
184.7 (27.6) SmCAPA
74.2 (21.4) SmCAPA
156.5 (27.1) SmCAPA
207.0
114.9
148.2b
75.2
134.8
42.1
163.1
101.4
179.8
73.4
187.7
89.6
IV
V
VI20
VII
VIII
IX22
a
C
I
C
C
I
156.9
67.7
C: crystal, SmCP: smectic C polar mesophase, USmCP: undulated
smectic C polar mesophase, Colob: columnar oblique mesophase,
I: isotropic liquid. Maximum of a broad peak.
b
uncoated cells (fabricated in our laboratories) and commercial
5 mm coated cells were used.
Fig. 2 (a) Texture of the I–SmCP transition shown by compound
Photomicrographs of the typical textures observed for some
of these materials between two uncoated glass plates in the
SmCAPA phase are shown in Fig. 2. On cooling from the
isotropic liquid the mesophase grows by forming concentric
defects, behaviour typical of SmCP mesophases [Fig. 2(a)].
Rather different textures were observed for compounds I
and II. When a sample of I was cooled from the isotropic
liquid phase in commercial coated cells, long shaped domains
(banana leaves) were observed together with focal conic
regions and small fan-shaped domains.20 In the case of
uncoated glass samples, large smooth focal conic domains
with extinction brushes parallel to the polarizers are
formed readily on cooling the material from the liquid phase
[Fig. 3(a)]. As the temperature is decreased, highly colored
concentric fringes start to appear in the focal conic domains
[Fig. 3(b)].
VII, during the cooling process at 179.9 uC and (b) SmCP mesophase
shown by compound VIII at 175.0 uC (both between two glass plates,
uncoated cell).
measured and indicates tilted arrangements of the molecules in
the mesophase with angles in the range 37–47u. These data are
consistent with a SmCP phase in each case.
In samples of compound II on uncoated glass, slow cooling
from the liquid phase leads to the mesophase entering by
forming telephone-wire structures [Fig. 4(a)]. On further
cooling, the material develops a texture similar to the one
described for the SmCP mesophase [Fig. 4(b)]. The appearance
of telephone-wire textures has been related to 2D periodic
structures.4,27,28 In this case a USmCP mesophase was
assigned for compound II on the basis of our XRD studies.20
(c) Structural characterization. Data from X-ray diffraction
studies are listed in Table 2. The diffraction patterns for
compounds from III to VIII in their mesophases are very
similar. In the wide angle region the presence of diffuse
scattering suggests the absence of in-plane order. In the small-
angle regions there are sharp layer reflections up to third-
order, which can be indexed as (001), (002) and (003). This
indicates well-defined layer structures for the liquid crystalline
phase in all cases. The estimated length of the molecules
Fig. 3 (a) Texture of the Colob mesophase shown by compound I
during the cooling process, at 160 uC and (b) at 146 uC (both between
two glass plates, uncoated cell).
˚
(about 64 A in all cases) is larger than the interlayer distances
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respectively. The structural models for these phases were
deduced from the analysis of the charge density distributions
using data both from the positions (Bragg angles) and
intensities of the X-ray diffraction peaks.20
(d) Polar and electro-optic behaviour of the materials. The
polar character of the materials studied in the present work
was confirmed by means of the triangular wave method. In all
cases a double peak for the polarization current was observed,
indicating that the mesophase is antiferroelectric (compound I
undergoes a transition to a ferroelectric smectic phase under
electric fields20). The polarization values obtained are in the
range 450–900 nC cm22. The applied field had an amplitude of
about 20 V mm21 and a frequency of 30 Hz. Despite the fact
that all of these measurements were carried out with unaligned
samples, as is common for bent-core compounds, it should
be noted that the lowest polarizations were determined for
compounds with two azo, azoxy or imine bonds (compounds I,
II and III). On the other hand, a significant influence of the
lateral dipole moment provided by the azoxy group was
not observed.
The synclinic or anticlinic ordering of the lamellar phase for
each compound was deduced from the electro-optic behaviour
under POM. This characterization is straightforward when the
texture exhibits circular domains with concentric fringes, as in
compounds IV to VIII. In all cases, extinction brushes were
observed in the direction of the polarizers. When an electric
field was applied, the extinction brushes rotated clockwise and
anticlockwise, following the polarity of the field, and the
textures usually changed to fan-shaped domains without
fringes. In light of these results, we have assigned a SmCAPA
mesophase to practically all of the compounds. In the case of
the di-imine (compound III), the textures observed under the
field exhibited extinction brushes along the directions of the
polarizers irrespective of the field polarity. Thus, the meso-
phase is assigned as SmCAPF under the field and SmCSPA on
removing it, a situation that is in good agreement with many
di-imine 1,3-phenyl-derivatives reported to date. Compound
IX is unique in this study because the action of an electric field
produced a dark conglomerate phase. This phenomenon has
been discussed extensively in the literature.23
Fig. 4 Texture of the I–USmCP transition shown by compound II,
(a) during the cooling process at 206.9 uC and (b) USmCP mesophase
at 202.8 uC (both between two glass plates, uncoated cell).
Table 2 X-Ray diffraction data for the compounds I–IX
Measured
˚
spacings/A
Miller
index
˚
Parameters/A
Compound
Mesophase
Colob
I20
a: 92.0
c: 48.0
b: 87.5u
47.8
46.1
43.2
41.7
33.9
26.6
49.8
48.8
24.4
51.2
25.4
47.2
23.7
15.8
45.3
22.7
15.1
44.3
22.2
14.8
47.7
24.4
16.3
44.3
22.2
14.8
42.8
21.2
14.1
(001)
(200)
(101)
(-101)
(201)
(301)
(001)
(101)
(202)
(001)
(002)
(001)
(002)
(003)
(001)
(002)
(003)
(001)
(002)
(003)
(001)
(002)
(003)
(001)
(002)
(003)
(001)
(002)
(003)
II20
USmCP
a: 255.6
c: 49.8
III
IV
SmCP
SmCP
c: 51.0
c: 47.3
(e) Structure–activity relationships. The strong ability of the
3,49-biphenylene structures to induce and stabilize B-type
mesophases can be seen from Table 1 and Fig. 5, regardless of
the connecting bonds used. The structural characteristics of
the lateral linking units do, however, tune the supramolecular
packing. When nitrogen-based bonds are used to connect
two aromatic rings, less common phases such as an oblique
columnar arrangement (di-azo compound, I), USmCP
(di-azoxy compound, II) or a smectic phase with a synclinic
arrangement (di-imine compound, III) are stabilized. Likewise,
these linking units favour the stabilization of the crystal phase
more than the ester unit.
V
SmCP
SmCP
SmCP
SmCP
SmCP
c: 45.4
c: 44.3
c: 48.4
c: 48.4
c: 42.5
VI20
VII
VIII
IX22
On the other hand, it can be seen clearly that the presence of
azo-groups (compounds I and VI) dramatically shortens the
mesophase range for biphenylene derivatives. This is not the
case for the azoxy or the imine analogues (compounds II, III,
VII and VIII). Thus, azoxy or imine bonds stabilize the crystal
Significant differences were described for the di-azo (I) and
the di-azoxy (II) compounds. An oblique synclinic columnar
mesophase (Colob) and a USmCP mesophase are proposed,
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Scheme 5 Chemical structure of compound X.
packing within the mesophase were not detected when the
hydroxy group is either in the central or the outer phenyl ring.
These results are in good agreement with those reported for
halogen-substituted bent-core molecules. In the latter case,
slight differences in the melting and clearing points were
observed on moving the halogen substituent from an inner to
an outer position.31
(f) Second harmonic generation. The second-order suscepti-
bility tensor d of the most representative compounds in the
present work have been fully characterized. This tensor can be
described in terms of only two independent parameters (D and
d) and the tilt angle,32 assuming the approximation proposed
by Araoka et al.26 for the nonlinear molecular response.
Furthermore, for the sake of completeness, we have also
included in this study the values for a new material, compound
X (see Scheme 5) [I 160 uC B1 120 uC B2 83 uC Cryst]. This
Fig. 5 Comparative study of the liquid crystal behaviour of the
different 3,49-biphenylene bent-core molecules studied on heating.
packing but also the mesophase in comparison with the ester
analogue (compound IX) giving rise to higher clearing points.
In the case of compounds II and III this increase is
remarkable, with increases of up to 40 uC in the clearing
points, which could have an adverse effect in terms of the
thermal stability of the imine groups.
compound is
a thioalkyl analogue of compound IX.
Finally, both –N(O)LN– and –NLCH– linkages give rise to
similar mesophase ranges to the ester link (compound IX),
with little influence observed from the number of azoxy or
imine groups present in the molecule. Furthermore, the liquid
crystalline properties of the asymmetrically linked bent-core
molecules (compounds VI, VII and VIII) could be considered
to be the result of a modulated contribution of both lateral
structures, where the ester unit generally leads to a decrease in
the transition temperature.
Compound X has been extensively studied by us previously.33
In this study the nonlinear activity of this compound was
investigated and this allowed us to assess the influence of a new
structural modification on the SHG efficiency of this type of
material; namely the presence of more polarizable atoms
(sulfur vs. oxygen) in the terminal chains.
All the SHG measurements were carried out on the SmCPF
phase. The measurement procedure is detailed in the experi-
mental section. The results are gathered in Table 3.
The introduction of hydroxy groups as lateral substituents
has been used previously in the field of liquid crystals, in
calamitic liquid crystals and Schiff base derivatives in
particular,29 usually to great effect. However, this approach
has rarely been applied to bent-core compounds.30 In both
fields very attractive results in terms of stabilization of the
mesophase order have been achieved through inter- and intra-
molecular H-bonding interactions.
It can be seen that the characteristic parameters d and D
in all cases range from 1 to 8 pm V21. Although all of these
values are of the same order of magnitude, the compounds can
be divided into two groups according to their SHG perfor-
mance. Compounds I and III (D about 7 pm V21 and d
about 3 pm V21) have a larger nonlinear efficiency (D and d
about 1 pm V21) than compounds IV, IX and X. Furthermore,
neither the presence of a lateral hydroxy group nor sulfur
atoms lead to any significant change in the nonlinear activity
of the compounds whose lateral parts contain only ester
groups.
However, similar effects were not observed for the ester
systems reported here. In the case of ester connecting bonds,
the presence of –OH groups on the ortho position does not lead
to the special interaction known from Schiff bases and this
group is a sterically disturbing lateral substituent. Thus,
compounds IV and V exhibit shorter SmCP phase ranges
than compound IX. Likewise, effects on the type of molecular
This difference can be explained because the azo and
imine groups in the lateral structures of the molecules for I
and III, respectively, allow for a delocalized electronic charge
Table 3 Refractive index mismatches for the p–p and s–p configurations and second-order susceptibilities for the different materials. The (xyz)
coordinate frame is explained in Fig. 1
Compound
Dnp-p = n2zv 2 nvz
Dns-p = n2zv 2 nvx
d/pm V21
D/pm V21
I20
III
IV
IX34
X
0.035 ¡ 0.003
0.026 ¡ 0.004
0.022 ¡ 0.007
0.021 ¡ 0.006
0.028 ¡ 0.002
0.027 ¡ 0.003
0.00 ¡ 0.02
0.02 ¡ 0.01
0.026 ¡ 0.004
0.020 ¡ 0.004
3.3 ¡ 0.2
4 ¡ 1
1.0 ¡ 0.4
1.2 ¡ 0.3
1.8 ¡ 0.3
6.1 ¡ 0.7
8 ¡ 2
1.9 ¡ 0.4
2.0 ¡ 0.3
2.0 ¡ 0.4
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distribution between the donor and acceptor groups along the
whole separation distance. This is not the case for compounds
IV, IX and X, whose lateral parts contain only ester groups,
which partially cut the electronic conjugation. Therefore, in
these compounds the distance between donor and acceptor
groups is much smaller. The high temperatures and electric
fields used with the azoxy compound II prevented full
characterization of this material and, as a result, it is
impossible to draw any conclusions concerning the effect of
this bond on the NLO response.
where N is the density of molecules in the mesophase, f a local-
field factor and Q the angle between z and the spontaneous
polarization direction. The brackets denote a thermal average.
Assuming perfect molecular order, the thermal averages are
equal to unity and eqn (3) becomes
D = Nf3bzxx, d = Nf3bzzz
(4)
In the present model the whole susceptibility tensor is fully
determined by bl. Eqn (4) will be used to obtain the upper limit
for the NLO efficiencies.
On the other hand, compounds with imine and azo groups
exhibit similar SHG performance. In this respect, the SHG
efficiency of the classical family of bent-shaped compounds
P-n-O-PIMB is expected to be similar to that of compounds I
and III in the present study, as pointed out in our previous
paper.20 This family of compounds is probably the most
widely studied from the viewpoint of NLO, but the values
obtained for their second-order susceptibility tensors by
several authors show significant discrepancies, even in the
order of magnitude.34–36 The reason for these inconsistencies
remains unclear.
For this purpose, we have taken for bl the hyperpolariz-
ability value corresponding to a chemical compound whose
nonlinear response is expected to be similar to the imine-based
group of P-n-O-PIMB, which is the main contributor to its
SHG efficiency. The candidate chosen is 49-methoxy-4-
cyanostilbene. The corresponding bl value (19 6 10230 esu
for a fundamental wavelength of 1.91 mm) was taken from
the work published by Cheng et al.,37 who reported the
hyperpolarizabilities of more than one hundred compounds
that were carefully measured in solution using the EFISH
technique. In this compound the stilbene structure works as
the conjugating spacer and the methoxy and cyano groups as
donor and acceptor entities, respectively. This compound is
expected to exhibit a higher nonlinear response than that of
the imine-based group of P-n-O-PIMB. In fact, the –HCLCH–
connection in stilbene is more efficient than the imine
connecting group,37 and the –CN group is a better acceptor
than the ester group (–COO–) in P-n-O-PIMB. The maximum
D and d parameters corresponding to a hypothetical bent-
shaped molecule with the selected 4,49-substituted stilbene
structure incorporated in the lateral parts can be calculated
using eqn (1), (2) and (4).
In order to clarify this point, we carried out a simple
estimation of an upper limit for the d and D parameters of the
compound P-8-O-PIMB and analyzed the molecular origin of
the macroscopic d tensor. The molecular structure of a typical
banana-shaped compound is represented schematically in
Fig. 6. X and Y represent the donor and acceptor groups,
respectively, and these are connected to each other by a
conjugating spacer. The SHG efficiency is expected to be
mainly driven by the longitudinal hyperpolarizability bl along
the lateral structure.26 In the reference system depicted in the
figure, this assumption gives rise to two dominant values for
the molecular hyperpolarizabilities, bzxxand bzzz, given by
In order to compare these values with our experimental
results the corresponding bl value at a wavelength of 1.064 mm
must be used. Assuming a two-level model for the hyper-
polarizability dispersion with an absorption maximum at
l0 = 340 nm,37 we obtain bl = 30 6 10230 esu for 1.064 mm.
The resulting second-order susceptibility parameters are D =
20 pm V21 and d = 6.7 pm V21. In this calculation, a Lorentz
factor was used as the local-field factor, with a refractive index
of 1.5 both for the fundamental and second harmonic waves.
Finally, N for P-8-OPIMB was evaluated by taking a density
of 1 g cm23 for the mesophase. As previously mentioned, these
estimated values suppose an upper boundary for these
parameters. When these calculated values are compared
with the experimental NLO data from the literature, those
from ref. 34 are below these limits and those from ref. 35 and
36 are clearly above it.
ꢀ ꢁ
a
b
zzz~2 cos3
bl
(1)
(2)
2
ꢀ ꢁ
ꢀ ꢁ
a
a
b
zxx~2 cos
sin2
bl
2
2
The connection between these b components and the
macroscopic D and d parameters is given approximately by
the equations
D = Nf3ScosQTbzxx, d = Nf3Scos3QTbzzz
(3)
On the other hand, recent experimental results on the
hyperpolarizability of P-8-O-PIMB using the EFISH techni-
que with a fundamental wavelength of 1.91 mm give a value
mbz = 40 6 10248 esu.38 Here, bz = bzxx + bzyy + bzzz is the
so-called vector part of the hyperpolarizability tensor along the
direction of the permanent dipole moment m. Taking a typical
value of m = 3 D39,40 we obtain, assuming a bending angle
a = 120u, bz = bl = 13 6 10230 esu. This value seems to be
consistent with the measured hyperpolarizabilities of other
materials that have donor-p-acceptor structures comparable to
Fig. 6 Schematic representation of the chemical structure of an
average bent-core molecule. X and Y represent donor and acceptor
groups, respectively, and these are connected to each other through a
conjugated spacer. bzxx and bzzz are assumed to be the dominant
hyperpolarizability coefficients, with the rest being negligible. The
whole b tensor can be considered to arise from a unique one-
dimensional hyperpolarizability bl directed longitudinally along the
wings of the molecule.
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J. Mater. Chem., 2007, 17, 2219–2227 | 2225

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the one present in P-8-O-PIMB. Among these materials we
include, for example, some 4,49-substituted stilbenes that have
moderate donor and acceptor groups, as discussed above.37
If we again assume a two-level model for the hyperpolariz-
ability dispersion, with an absorption maximum at l0 = 362 nm
(deduced from the absorption data for P-8-O-PIMB in
solution), we obtain bl = 23 6 10230 esu for l = 1.064 mm,
which in turn implies
Acknowledgements
This work was supported by projects MAT2003-07806-C02
and MAT2006-13571-C02 (CICYT-FEDER) from Spain-EU
and by the DGA (Spain) and University of the Basque
Country (Project. Nu 9/UPV 00060.310-13562/2001). I. P.
and I. A. also thank DGA and the Ministry of Education of
Spain, respectively, for grants.
D = 10 pm V21 and d = 2.5 pm V21
(5)
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