Study of the ferroelectric liquid crystal 11EB1M7 by means of 2NMR

Article abstract of DOI:10.1021/jp034301h

In this work, a new procedure for the synthesis of the selectivity deuterium-labeled chiral liquid crystal (+)-(S)-4-[4′-(1-methylheptyloxy)] biphenyl 4(10-undecenylox)benzoate (11EB1M7) has been developed, aimed to the study of its structure, orientational ordering, and dynamic behavior by means of ²H NMR. 11EB1M7 was investigated throughout its mesophasic range, formed by a very rich variety of chiral liquid crystalline phases including blue, cholesteric, TGBA*, and smectic C*. Two isotopomers were synthesized by labeling 11EB1M7 on either the phenyl or the biphenyl moiety of the mesogenic core. This allowed structural information (such as the tilt angle of the rigid fragments of the molecule and the angle between their para axes), orientational order parameters, and individual diffusional coefficients for the various overall and internal motions to be obtained from ²H NMR spectra and relaxation measurements by applying suitable data analyses based on several theoretical models.

Full text of DOI:10.1021/jp034301h

10104
J. Phys. Chem. B 2003, 107, 10104-10113
2
Study of the Ferroelectric Liquid Crystal 11EB1M7 by Means of H NMR†
Donata Catalano,‡ Leonardo Chiezzi,§ Valentina Domenici,§ Marco Geppi,§ and
Carlo Alberto Veracini*
Dipartimento di Chimica e Chimica Industriale, UniVersita` degli Studi di Pisa,
Via Risorgimento 35, 56126 Pisa, Italy
ReceiVed: February 5, 2003; In Final Form: July 1, 2003
In this work, a new procedure for the synthesis of the selectively deuterium-labeled chiral liquid crystal
(+)-(S)-4-[4′-(1-methylheptyloxy)] biphenyl 4-(10-undecenyloxy)benzoate (11EB1M7) has been developed,
2
aimed to the study of its structure, orientational ordering, and dynamic behavior by means of H NMR.
11EB1M7 was investigated throughout its mesophasic range, formed by a very rich variety of chiral liquid
crystalline phases including blue, cholesteric, TGBA*, and smectic C*. Two isotopomers were synthesized
by labeling 11EB1M7 on either the phenyl or the biphenyl moiety of the mesogenic core. This allowed
structural information (such as the tilt angle of the rigid fragments of the molecule and the angle between
their para axes), orientational order parameters, and individual diffusional coefficients for the various overall
and internal motions to be obtained from 2H NMR spectra and relaxation measurements by applying suitable
data analyses based on several theoretical models.
Introduction
Chiral smectogens originating ferroelectric (FLC) and anti-
ferroelectric (AFLC) phases represent a very interesting class
of compounds because of their possible technological applica-
tions. In this context, the rationalization of the links between
their macroscopic behavior and their compositional, structural,
and dynamic properties at a molecular level is fundamental.1
NMR has been largely applied to the investigation of
structure, orientational ordering,2 and dynamics3,4 of low-
molecular-weight achiral liquid crystals and, more recently, has
Figure 1. Molecular structure of the isotopomers 11EB1M7-d2 (top)
been revealed to be very effective for similar studies on chiral
liquid crystals.5 2H techniques are particularly powerful because
of the intramolecular nature of the dominant quadrupolar
interaction bringing about a quite straightforward interpretation
of both static spectra and relaxation measurements and allowing
structural and dynamic site-specific information to be obtained.
However, the use of deuterium NMR is strongly limited by the
requirement of purposely and selectively 2H-labeled molecules.
Following previous works6-10 based on the synthesis of
selectively deuterium-labeled FLCs and the investigation of their
structural, ordering, and dynamic properties, we report here an
extension of such studies to 4-[4′-(1-methyl heptyloxy)] biphenyl
4-(10-undecenyloxy) benzoate (11EB1M7), for which two
optically pure isotopomers, partially deuterated in either the
phenyl or the biphenyl moieties (11EB1M7-d2 and 11EB1M7-
d8, respectively), were prepared (see Figure 1). This FLC is
particularly interesting because it exhibits a very rich variety
of mesophases: blue phase, N*, TGBA*, SmA, SmC*, and
SmI*. Moreover in this mesogen, contrary to those previously
and 11EB1M7-d8 (bottom).
investigated, the achiral alkylic chain ends with a double bond,
therefore allowing its use for the synthesis of corresponding
side-chain liquid crystalline polymers, based on polysiloxane
main chains, which have been shown to retain ferroelectric
properties.11
In the first part of the paper, a 2H NMR investigation of phase
transitions, structural properties (tilt angle in the chiral smectic
C* phase and angle between the para axes of the phenyl and
biphenyl moieties in the untilted smectic phases), and ordering
behavior (order parameter SZZ and biaxiality of the phenyl and
biphenyl moieties) of 11EB1M7 are reported. In the second part,
the molecular dynamics of 11EB1M7 was studied by means of
2H NMR relaxation measurements. In the SmA phase, diffu-
sional coefficients for individual internal (rotations of the
aromatic fragments around their para axes) and overall (spinning
and tumbling) molecular motions could be determined applying
suitable theoretical models.
Experimental Section
† Dedicated to the memory of Prof. S. Castellano.
Synthesis. The schemes of the reactions carried out to
synthesize 11EB1M7-d2 and 11EB1M7-d8 are reported in
Figures 2 and 3, respectively.
(-)(R)-2-Octyl-p-toluensulfonate (2). (-)(R)-2-octanol (1) (7
mL, 44.2 mmol) and p-toluensulfonyl chloride (8.8 g, 46.3
* To whom correspondence should be addressed. Phone number: +39-
050918266. Fax number: +39-050918260. E-mail address: verax@
dcci.unipi.it.
‡ Phone number: +39-050918266. E-mail address: donata@dcci.unipi.it.
§ Phone number: +39-050918289. E-mail addresses: leonardo@
dcci.unipi.it (L.C.); valentin@dcci.unipi.it (V.D.); mg@dcci.unipi.it (M.G.).
10.1021/jp034301h CCC: $25.00 © 2003 American Chemical Society
Published on Web 08/23/2003

Study of the Ferroelectric Liquid Crystal 11EB1M7
J. Phys. Chem. B, Vol. 107, No. 37, 2003 10105
Figure 2. Reaction scheme for the synthesis of 11EB1M7-d2.
Figure 3. Reaction scheme for the synthesis of 11EB1M7-d8.
mmol) were dissolved in 27 mL of anhydrous pyridine under
nitrogen atmosphere at 0 °C. The solution was stirred at room
temperature for 18 h, and then 120 mL of water was added,
and the aqueous phase was extracted with chloroform. The
organic layers were washed with a solution of HCl 3 N and
dried over magnesium sulfate and then evaporated. A yellow
(+)(S)-4-hydroxy-4′-(1-methyleptyl)biphenol (4). 4,4′-Dihy-
droxybiphenol (3) (5.7 g, 30.8 mmol) and sodium hydroxide
(1.3 g, 33.1 mmol) were dissolved in 70 mL of methanol. The
solution was refluxed for 30 min, and then a solution of 8.7 g
(30.7 mmol) of (-)(R)-2-octyl-p-toluensulfonate (2) in 20 mL
of methanol was added drop by drop. The solution was refluxed
for 12 h, and then 110 mL of water was added, and the organic
phases were extracted with chloroform, dried over magnesium
sulfate, and evaporated. The resulting solid material was purified
1
oil was obtained (8.9 g, yield 71%). H NMR (CDCl3): δ )
7.78 (2H, d), 7.32 (2H, d), 4.55 (1H, m), 2.45 (3H, s),1.7-1.0
(13H, m), 0.92 (3H, t).

10106 J. Phys. Chem. B, Vol. 107, No. 37, 2003
Catalano et al.
by chromatography on a Kieselgel 60 (0.063-0.02 mm) column
and eluted with petroleum ether and ethyl acetate (4:1) to give
2.6 g of a white solid (yield 28%). [R]20589 (deg‚dm-1‚g-1‚cm3)
(3 g, 23.2 mmol) in 20 mL of anhydrous THF was added drop
by drop to the mixture. The solution obtained was stirred at
room temperature for 5 days; then the THF was evaporated,
diethyl ether was added, and the white precipitate obtained was
filtered off. The organic phases were evaporated, and the product
was purified by chromatography on Kieselgel 60 (0.063-0.02
mm) column and eluted with petroleum ether and ethyl acetate
1
) 5 (c ) 1% CHCl3). H NMR (CDCl3): δ ) 7.43 (4H, m),
6.90 (4H, m), 4.32 (1H, m), 2.0-1.1 (13H, m), 0.88 (3H, t).
4-Hydroxy Benzoic Acid-d2 (6). 4-Hydroxy benzoic acid (5)
(4.0 g, 29.1 mmol) was dissolved in 50 g of a solution at 8% of
deuterium chloride. The solution was refluxed for 24 h, and
then the mixture was cooled at 0 °C, and the white solid formed
was filtered and dried. A total of 3.4 g (yield 84%) of 6 was
(4:1) to give 3.4 g of a white solid (yield 56%). [R]20
589
(deg‚dm-1‚g-1‚cm3) ) -5 (c ) 1% CHCl3). 1H NMR
(CDCl3): δ ) 7.44 (3.28H, m), 6.90 (0.72H, m), 4.37 (1H, m),
2.0-1.1 (13H, m), 0.88 (3H, t).
1
obtained. H NMR (DMSO-d6): δ ) 12.4 (1H, broad s), 10.2
(1H, broad s), 7.77 (2H, s + very weak d), 6.80 (0.1H, d). From
4-n-Undecenyloxy Benzoic Acid (12). 4-Hydroxy benzoic acid
(5, 2.0 g, 15 mmol) and potassium hydroxide (2 g, 36 mmol)
were dissolved in 40 mL of a mixture of water and ethanol,
9:1. The solution was refluxed for 20 min; then 4 mL (19 mmol)
of undecenyl bromide (7) was added drop by drop. The solution
was refluxed for additional 4 h; then HCl 1 N was added until
pH ) 5. The white solid precipitate obtained was filtered and
washed with water. The solid was further purificated by
recrystallization from ethanol; 2.5 g (yield 58%) of (12) were
1
the H NMR spectrum, 95% deuteration was estimated.
4-n-Undecenyloxy Benzoic Acid-d2 (8). 4-Hydroxy benzoic
acid-d2 (6, 3.4 g, 24 mmol) and potassium hydroxide (3.7 g, 66
mmol) were dissolved in 40 mL of a mixture of water and
ethanol, 9:1. The solution was refluxed for 20 min; then 7.0
mL (33.3 mmol) of undecenyl bromide (7) was added drop by
drop. The solution was refluxed for an additional 4 h; then HCl
1 N was added until pH ) 5. The white solid that precipitated
was filtered and washed with water. The solid was further
purified by recrystallization from ethanol. A total of 3.9 g (yield
56%) of 8 was obtained. 1H NMR (DMSO-d6): δ ) 12.4 (1H,
broad s), 7.85 (2H, s + very weak d), 6.97 (0.1H, d), 5.76 (1H,
m), 4.95 (2H, m), 4.00 (2H, t), 2.1-1.0 (16H, m).
1
obtained. H NMR (DMSO-d6): δ ) 12.4 (1H, broad s), 7.85
(2H, d), 6.97 (2H, d), 5.76 (1H, m), 4.95 (2H, m), 4.00 (2H, t),
2.1-1.0 (16H, m).
(-)(R)-4-[4′-(1-Methyl Heptyloxy)] Biphenyl 4-(10-Undece-
nyloxy)benzoate-d8 (13). (-)(R)-4-Hydroxy-4′-(1-methyleptyl)-
biphenol-d8 (11, 2 g, 6.5 mmol), 4-n-undecenyloxy benzoic acid
(12, 1.9 g, 6.5 mmol), and a catalytic amount of 4-dimethy-
lamino pyridine (DMAP) were dissolved in 45 mL of anhydrous
dichloromethane under nitrogen atmosphere. A solution of 1.4
g (6.5 mmol) of dicyclohexyl carbodimmyde (DCC) in 15 mL
of anhydrous dichloromethane was added drop by drop to the
mixture. The solution obtained was stirred at room temperature
for 3 days; then the precipitated was filtered off, and the organic
phases were washed with HCl 1 N and with a 5% solution of
NaHCO3, dried over magnesium sulfate, and evaporated. A total
of 1.5 g (yield 40%) of 13 was obtained after two recrystalli-
(+)(S)-4-[4′-(1-Methyl Heptyloxy)] Biphenyl 4-(10-Undece-
nyloxy)benzoate-d2 (9). (+)(S)-4-Hydroxy-4′-(1-methyleptyl)-
biphenol (4, 2.0 g, 6.7 mmol), 4-n-undecenyloxy benzoic acid-
d2 (8, 2.0 g, 6.7 mmol), and a catalytic amount of 4-dimethyl-
amino pyridine (DMAP) were dissolved in 90 mL of anhydrous
dichloromethane under nitrogen atmosphere. A solution of 1.4
g (6.7 mmol) of dicyclohexyl carbodimmyde (DCC) in 20 mL
of anhydrous dichloromethane was added drop by drop to the
mixture. The solution obtained was stirred at room temperature
for 3 days; then the precipitate was filtered off, and the organic
phases were washed with HCl 1 N and with a 5% solution of
NaHCO3, dried over magnesium sulfate, and evaporated. A total
of 3.28 g (yield 86%) of 9 was obtained after two recrystalli-
zations in ethanol. [R]20589 (deg‚dm-1‚g-1‚cm3) ) 4.8 (c ) 1%
zations in ethanol. [R]20 (deg‚dm-1‚g-1‚cm3) ) -4.8 (c )
589
1% CHCl3). 1H NMR (CDCl3): δ ) 8.18 (2H, d), 7.57 (3.28H,
m), 7.24 (0.36H, m), 6.98 (2.36H, m), 5.81 (1H, m), 4.95 (2H,
m), 4.40 (1H, m), 4.04 (2H, t), 2.2-1.0 (29H, m), 0.90 (3H, t)
(The attribution of the aromatic signals is the following: 8.18
ppm (phenyl protons in position C′), 7.57 ppm (residual protons
in positions B and B′), 7.24 ppm (residual protons in position
A), and 6.98 ppm (residual protons in position A′ and phenyl
protons in position C)).
1
CHCl3). H NMR (CDCl3): δ ) 8.18 (2H, s + very weak d),
7.57 (4H, m), 7.24 (2H, d), 6.98 (2H, d), 5.81 (1H, m), 4.95
(2H, m), 4.40 (1H, m), 4.04 (2H, t), 2.2-1.0 (29H, m), 0.90
(3H, t).
4,4′-Dihydroxybiphenol-d8 (10). Sodium (4.9 g, 213 mmol)
was dissolved in small portions in 200 mL of ethanol under
cooling, and then 4,4′-dihydroxybiphenol (20.0 g, 107.4 mmol)
was added under nitrogen atmosphere. This solution was
evaporated, and the solid material obtained was dissolved in
100 mL of D2O (5 mol) and put in an autoclave with 1 g of
Pt/C. The autoclave was heated to 200 °C (7 bar) for 3 days.
The cooled reaction mixture was evaporated and treated with
diethyl ether, and the catalyst was filtered off. The organic layers
were washed with HCl 1 N, dried over magnesium sulfate, and
evaporated. A total of 9.1 g (yield 45%) of 4,4′-dihydroxybi-
Instrumentation. The calorimetric measurements were car-
ried out on a Mettler TA4000 calorimeter. Optical textures were
obtained by a Reichert-Jung Polyvar polarizing microscope
equipped with a Mettler FP52 hot stage and Mettler FP5
1
temperature controller. H NMR spectra were performed on a
Varian VXR 300 spectrometer operating at 299.96 MHz on
proton.
Phase Transitions. The following phase behavior has been
found for the isotropomers 11EB1M7-d2 and 11EB1M7-d8,
respectively, by optical microscopy and differential scanning
calorimetry: I 115.9 °C, BPI 113.2 °C, N* 108.0 °C, TGBA*
102.0 °C, SmA 91.0 °C, SmC* 76.9 °C, SmI* 72.2°C Cr; I
111.4 °C, BPI 109.8 °C, N* 107.4 °C, TGBA* 103.1 °C, SmA
90.3 °C, SmC* 68.7 °C, SmI* 63.5 °C Cr. The following phase
transitions were previously reported for the nondeuterated
analogue:12 I 115.2 °C, BPI 114.8 °C, N* 112.8 °C, TGBA*
107.0 °C, SmA 100.0 °C, SmC* 78.0 °C, SmI* 73.8 °C Cr.
1
phenol-d8 (10) was obtained. H NMR (DMSO-d6): δ ) 9.15
(2H, s), 7.33 (3.28H, m), 6.81 (0.72H, m). From 1H NMR, the
following percentages of deuteration were obtained: 82% for
the ortho positions marked A and A′ in Figure 1 and 18% for
the meta positions B and B′.
(-)(R)-4-Hydroxy-4′-(1-methyleptyl)biphenol-d8 (11). 4,4′-
Dihydroxybiphenol-d8 (10, 4.5 g, 23.2 mmol), triphenyl phos-
phine (6 g, 23.2 mmol), and diethyl azodicarboxylate (D.E.A.D.,
4 g, 23.2 mmol) were dissolved in 80 mL of anhydrous THF
under nitrogen atmosphere. A solution of (-)(R)-2-octanol (1)
2
2H NMR. The H NMR experiments were carried out on a
7.05 T Varian VXR-300 spectrometer working at 46.04 MHz

Study of the Ferroelectric Liquid Crystal 11EB1M7
J. Phys. Chem. B, Vol. 107, No. 37, 2003 10107
Figure 4. 2H spectra of 11EB1M7-d2 recorded, from bottom to top, in the blue phase at 109.5 °C, in the N* phase at 107.5 °C, and in the TGBA*
phase at 105.5 °C.
2
for deuterium. The 90° pulse was 16 µs. The H spectra were
recorded either with or without 1H continuous-wave decoupling.
The samples were microscopically aligned within the magnet
by slow cooling from the isotropic phase; the spectra were
recorded every 2 °C allowing 10 min for thermal equilibration.
The temperature was stable within 0.2 °C. In the interval
between the isotropic and the smectic A phase, where blue,
TGBA*, and N* phases could be observed, the spectra were
recorded every 0.5 °C by both heating and cooling the sample:
a difference in transition temperatures up to 2 °C was observed
in the two cases.
For the compound under study, a qualitative line shape analysis
has been carried out, as previously done in a recent work for a
similar chiral compound forming blue and cholesteric meso-
phases.7 There are no significant differences between the line
shapes of the two smectogens 11EB1M7-d2 and 11EB1M7-d8,
except for a greater complexity in the case of the latter due to
the superimposition of slightly different signals from the various
deuteria; therefore, we only report the analysis of the 1H-
decoupled spectra of 11EB1M7-d2.
The line shape of the blue phase is similar to that of the
isotropic phase, but the line width is remarkably higher in the
first case, around 1500 Hz instead of tens of hertz (see Figure
4). This can be explained by considering the nature of the blue
phase, presumably an isotropic distribution of nematic do-
mains.17,18
To explain the line shape typical of the cholesteric phase,
the helicoidal path described by the local nematic director must
be considered. For a thermotropic mesogen with magnetic
susceptibility anisotropy greater than zero (∆ø > 0), which is
the case of our compound, the helix axis arranges perpendicular
to the magnetic field. Consequently, the line shape first
originates from a distribution of different molecular orientations
with respect to the magnetic field. Moreover, it can be deeply
influenced by the diffusion of the molecules along the helix
axis, depending on the ratio between the quadrupolar splitting
and the exchange rate among sites with different orientations.17
In the case of 11EB1M7-d2, the experimental spectrum of the
cholesteric mesophase at 107.5 °C (Figure 4) suggests that the
sample experiences an intermediate exchange rate regime.17
The line shape characterizing the TGBA* mesophase (Figure
4) is very similar to that of the cholesteric one. The main
difference is found comparing the overall line widths, which
are, for instance, about 12 kHz for the TGBA* phase at 105.5
°C and about 5 kHz for the cholesteric phase at 107.5 °C. In
fact, the TGBA* structure consists of a helicoidal distribution
2H Zeeman (T1Z) and quadrupolar (T1Q) spin-lattice relax-
ation times were measured at 46.04 MHz at different temper-
atures within the mesophasic range through a broadband
version13 of the Jeener-Broekaert14 pulse sequence (900-2τ1-
67.5270-2τ1-4590-τ1-4590-τ2-450) under proton decoupling. The
best value of the delay τ1 was experimentally found to be 13
µs. The variable delay τ2 ranged from 100 µs to 1 s; a relaxation
delay of 1 s and a number of scans of 1000 were used.
T1Z and T1Q were obtained by fitting the sum and difference
of the integrals of each component of a quadrupolar doublet as
a function of τ2 through the following equations:15
M+(τ2) ) A[1 - B exp(-τ2/T1Z)]
M-(τ2) ) C + D exp(-τ2/T1Q)
(1)
(2)
which differ from those theoretically predicted16 because they
take into account possible experimental imperfections.
Line Shape for the Blue, Cholesteric, and TGBA* Phases
The line shapes for the blue, cholesteric, and TGBA* phases
are quite peculiar and even diagnostic of the type of mesophase
itself, as evident from several studies present in the literature.17-22

10108 J. Phys. Chem. B, Vol. 107, No. 37, 2003
Catalano et al.
Figure 5. 2H spectra of 11EB1M7-d2 recorded at different temperatures in the SmA, SmC*, and SmI* phases.
of SmA blocks with a high local orientational order. The
observed difference between line widths can be explained by
an increase of the local order parameter by a factor of about
1.5 (comparable with typical values of the order parameter
usually observed in the SmA (0.7-0.9) and nematic (0.4-0.6)
mesophases23,24) together with an appreciable slowing of the
molecular diffusion at low temperature.
Line Shapes, Order Parameters, and Tilt Angles in SmA,
SmC*, and SmI* Phases
Different from the spectra discussed in the previous para-
graph, those recorded in the SmA, SmC*, and SmI* phases show
that the smectic planes are macroscopically ordered perpen-
dicularly to the magnetic field. Moreover, the molecular director
in the SmC* and SmI* phases is tilted with respect to the field.
The line shape simulations presented in this section were
performed using a modified version of the “Lequor” software.25
Figure 5 shows the 2H NMR spectra of 11EB1M7-d2 recorded
in the temperature range 50-98 °C, in which three smectic
phases are present. We can always observe a quadrupolar
doublet, the components of which, in the SmA and SmI* phases,
Figure 6. 2H experimental (top) and simulated (bottom) spectra of
11EB1M7-d2 at 98 °C in the SmA phase without proton decoupling.
the spectra at other temperatures in the smectic A and I* phases
1
were also obtained, confirming that the Haromatic-2H dipolar
1
are further shaped and split by H-2H dipolar couplings. The
splitting, ∆νd, which will appear in eq 3, could be directly
determined from the splitting between the two maxima of each
quadrupolar peak. In the SmC* phase, where the average
observed interactions are substantially reduced by the tilt
between the local directors and the magnetic field and this
splitting is no longer resolved, the 1Haromatic-2H dipolar coupling
could be estimated by the simulation procedure.
most important dipolar interaction is between each deuterium
nucleus and the nearest aromatic proton. Such interaction
produces a doubling of the signals in the SmA and SmI* phases
and just a broadening in the SmC* phase. The dipolar coupling
between the deuterons and the protons of the nearest methylenic
group in the alkoxylic chain also contributes to the signal shape.
The simulation of the 1H-coupled experimental spectrum at 98
°C (see Figure 6) in the SmA phase was performed by using
the quadrupolar splitting and the line width determined from
As far as 11EB1M7-d8 is concerned (see, for example, the
case T ) 98 °C, reported in Figure 7), the 1H-decoupled
spectrum could be easily explained. Four quadrupolar doublets
are expected because of the deuterons in the A, A′, B, and B′
positions (see Figure 1). The most intense signals are ascribed
to the more abundant ortho deuterons A and A′, while two much
weaker doublets, due to meta deuterons B and B′, are partially
the 1H-decoupled spectrum of 11EB1M7-d2 and the 1Haromatic
2H dipolar coupling estimated from the splitting of each peak
-
1
1
in the H-coupled spectrum. A value for the Hmethylenic-2H
dipolar coupling was taken from the corresponding 1H-1H
dipolar coupling found for a similar compound in a nematic
phase,26 suitably scaled taking into account the different nuclei
involved in the interaction and the different degree of orienta-
tional order. A satisfactory agreement between the experimental
and simulated line shapes could be obtained by slightly adjusting
the 1Hmethylenic-2H dipolar coupling and keeping all of the other
parameters fixed at their original values. Good simulations of
1
superimposed on them. To explain the H-coupled spectrum,
we must consider that the compound 11EB1M7-d8 is, in effect,
a mixture of 11EB1M7 molecules variously deuterated on the
biphenyl fragment. The most abundant species is that deuterated
1
only on the ortho positions. It contributes to the H-coupled
spectrum with the two intense quadrupolar doublets, the signals
of which are split by the dipolar interaction between the deuteron

Study of the Ferroelectric Liquid Crystal 11EB1M7
J. Phys. Chem. B, Vol. 107, No. 37, 2003 10109
Figure 7. 2H experimental (top) and simulated (bottom) spectra of 11EB1M7-d8 at 98 °C in the SmA phase with proton decoupling (left) and
without proton decoupling (right).
the mean value of the two quadrupolar splittings of the ortho
deuteria corresponds to the difference between the two maxima
of the experimental quadrupolar doublet of the 1H-coupled
spectra.
The quadrupolar splitting of 11EB1M7-d2 and the mean value
of the two quadrupolar splittings of the ortho deuteria of
11EB1M7-d8 are shown in Figure 8 as a function of temperature.
In the SmA phase, the splittings regularly increase with
decreasing temperature for both mesogens. Below the SmA-
SmC* transition, a gradual decrease of the quadrupolar splittings
takes place indicating a progressive tilt of the local directors
with respect to the magnetic field. A jump to higher values is
observed on entering the SmI* phase, followed by an almost
1
constant trend within this phase. The Haromatic-2H dipolar
splitting trend vs temperature for the isotopomer 11EB1M7-d2
is also reported in Figure 8. This splitting increases up to about
1700 Hz in the SmA phase, while in the SmC* one, it decreases
Figure 8. Quadrupolar (O and 9 for d2 and d8 isotopomers,
to a minimum of 1440 Hz and then increases again up to about
respectively) and 1H-2H dipolar (b for d2 isotopomer) splittings (Hz)
1750 Hz, remaining constant within the experimental error limits
vs temperature (°C) measured for 11EB1M7 in the various smectic
in the SmI* phase.
phases.
We could eventually determine the order parameter SZZ(T)
and the biaxiality (∆biax ) SXX - SYY, assumed to be independent
of temperature within each phase) for the two deuterated
molecular fragments by fitting the experimental values of the
1Haromatic-2H dipolar and quadrupolar splittings by eqs 3 and
42:
and the nearest proton. Therefore, the experimental line shape,
roughly resembling an unresolved triplet, must be mostly
ascribed to the partial superimposition of two dipolar doublets.
An excellent agreement between the experimental and simulated
line shape was then reached taking into account the composition
of the mixture and building up a weighted superimposition of
the spectra of the differently deuterated species. Relevant dipolar
couplings are those between ortho-meta protons and deuterons
and between the A′ deuteron and the near methinic proton. From
simulations of spectra at various temperatures, we observed that
Szz[T]
∆νd[T] ) -2KDH
(3)
3
rDH

10110 J. Phys. Chem. B, Vol. 107, No. 37, 2003
Catalano et al.
3
2
1
2
η
6
η
6
η
6
∆νq[T] ) qaa Szz[T] cos2 φ - sin2 φ - cos2 φ +
+
{
(
η
1
η
6
sin2 φ + ∆biax sin2 φ + cos2 φ +
(4)
)
(
)}
3
2
where KDH ) 18 434.4 Hz‚Å3, rDH ) 2.5 Å, η ) 0.04, and qaa
) 185 kHz. The angle φ between the C-D bond and the para
axis of the rigid fragment has been assumed equal to 60° in all
cases. For the phenyl fragment of 11EB1M7-d2, the best-fitting
parameters for ∆biax are 0.047, 0.039, and 0.019 in the SmA,
SmC*, and SmI* phases, respectively, while those for SZZ at
the different temperatures are reported in Figure 9.
For the isotopomer 11EB1M7-d8, the dipolar splittings could
not be directly measured from the spectra; their values,
determined by the line shape simulation, allowed us to verify
that the biaxiality is about zero, in agreement with the results
obtained for a very similar compound.6 The trend of the order
parameter SZZ of the biphenyl fragment, which could be therefore
calculated from the quadrupolar splittings measured for
11EB1M7-d8 by eq 4, is also reported in Figure 9.
In both smectogens, the SmA-SmC* transition is evident
from the sudden decrease of the order parameters. The tilt angle
θ in the tilted SmC* phase could be estimated by assuming
that the deviation from a regular order parameter trend is fully
ascribable to the tilt of the molecules with respect to the
magnetic field. To this aim, the order parameter trend in the
untilted SmA phase has been extrapolated in the tilted smectic
phase for the two isotopomers, and the tilt angles have been
determined by the ratios of the so-calculated and experimental
SZZ values as described by eq 5:
Figure 9. Order parameter Szz of the phenyl (O) and biphenyl (9)
fragments as a function of temperature (°C).
densities of motion, Ji(iω0) (which are the Fourier transforms
of the autocorrelation functions), at the Larmor frequency and
at twice this frequency through the following relationships:
1
T1Z
) J1(ω0) + 4J2(2ω0)
(7)
(8)
1
) 3J1(ω0)
T1Q
calcd3 cos2 θ - 1
SeZxZptl ) S
(5)
where ω0 is the Larmor frequency. Several motional processes
contribute to these spectral densities, which can be classified
in three distinct types: overall reorientations of the whole
molecule, internal motions of molecular fragments, and collec-
tive motions. However, the information on these motions is
contained in a quite implicit form within the spectral densities,
and therefore, its extraction requires the use of suitable
theoretical models.
Several models have been proposed to describe the overall
molecular reorientations, going from the simplest diffusion in
a cone27 to those proposed by Nordio et al.28,29 and by Freed et
al.30,31 (anisotropic Viscosity model), which consider these
motions as small step diffusional rotation in a Maier-Saupe
mean field potential, up to the extensions of Vold and Vold32
(third rate anisotropic Viscosity model), of Tarroni and Zan-
noni,33 and of Berggren et al.,34 the last two models taking into
account either molecular or phase biaxiality.
ZZ
2
The tilt angles obtained independently for the two sets of data
(phenyl and biphenyl order parameters) show a good agreement,
and their average value increases by decreasing the temperature
within the SmC* phase assuming a limiting value of 18°.
At the SmC*-SmI* transition, a dramatic change in the order
parameter trends can be observed: on one side, the SZZ of both
fragments experiences a jump to higher values; on the other
side, within the SmI* phase, the SZZ of the biphenyl fragment
is higher than that of the phenyl fragment, contrary to what is
observed within the SmA and SmC* phases. The SZZ jump
indicates a sudden decrease of the tilt angle on entering the
SmI* phase. Moreover, the biphenyl fragment becomes so
ordered in the SmI* phase (SZZ ≈ 0.9) that its para axis can be
substantially assumed to be aligned to the magnetic field.
On the other hand, when the para axis of one aromatic moiety
is aligned to the magnetic field, the angle æ between the para
axes of the phenyl and biphenyl fragments can be evaluated on
the basis of eq 6.
Internal motions are usually considered decoupled from the
overall molecular ones. In particular, aromatic ring rotations
have been described in an isotropic potential by means of either
small step diffusion35,36 or strong collision models37 or in a
2-fold symmetric intramolecular potential considering coupled
rotational isomerization and libration processes.38
II 3 cos2 æ - 1
SIZZ ) SZZ
(6)
2
Collective motions essentially consist of order director
fluctuations (ODF), which are usually considered not coupled
to the faster overall and internal molecular motions; their
contribution to the spectral densities can be expressed on the
basis of the theories proposed by Pincus39 and Blinc et al.40
Other slower collective dynamic processes can be present in
tilted smectic phases, such as the Goldstone and soft modes,1
but their contribution to the spectral densities in the megahertz
range is usually negligible.
where I and II correspond to the less- and more-ordered
fragments, respectively. The values of æ so calculated in the
SmA and SmI* phases are substantially constant within each
phase, and the average value of æ is 11.6° ( 1.5° in the SmA
phase and 18.2° ( 0.5° in the SmI* phase, in good agreement
with values previously obtained for a similar compound.6
Dynamics: Theory
The Redfield theory directly relates the quadrupolar (T1Q) and
Zeeman (T1Z) spin-lattice relaxation times to the spectral
The analysis of the relaxation data has been here carried out
using the Nordio model for the overall dynamics, using both

Study of the Ferroelectric Liquid Crystal 11EB1M7
J. Phys. Chem. B, Vol. 107, No. 37, 2003 10111
small step diffusion and strong collision for the internal rotation
of either phenyl or biphenyl fragments about their para axes,
and neglecting the contribution of ODF. This assumption is
based on the theoretical prediction of a null contribution to J2-
(2ω0) and of a contribution to J1(ω0) that is directly proportional
and to the geometrical term (3 cos2 â - 1), â being
-1/2
to ω0
the angle between the C-D bond and the axis of the fragment
under examination. Indeed, in our case, the Larmor frequency
and â are, respectively, high enough (46.04 MHz) and close
enough to the magic angle (60°) to safely allow the ODF
contribution to be neglected.
The autocorrelation functions, gm m (t), relative to the overall
L
M
molecular motions, can be expressed, following Vold and
Vold,32 as a sum of decreasing exponential functions:
t
gm m (t) ) cm m
a(j) exp -
(9)
∑
mLmM
L
M
L
M
(j)
mLmM
j
(
)
τ
Figure 10. Experimental spectral densities (s-1), J1(ω0) (O and 4 for
d2 and d8 isotopomers, respectively) and J2(2ω0) (9 and [ for d2 and
d8 isotopomers, respectively), of 11EB1M7 in the SmA, SmC*, and
SmI* phases vs 1000/T (1/K).
(j)
The correlation times, τ
, can be expressed in terms of the
diffusional coefficients on the basis of Nordio model through
the following relationship:
mLmM
the relaxation trend, however, did not allow any difference to
be revealed among the different components of the line shape.
From the measured relaxation times, which are on the order
of tens of milliseconds, the corresponding spectral densities have
been calculated by eqs 7 and 8 (see Figure 10). The spectral
densities decrease with increasing temperature, indicating a
motional narrowing regime (ω0τc , 1) for the motions mainly
contributing to the relaxation, in agreement with what is usually
found for low-molecular-weight liquid crystals.9,41,42 The trends
of the various relaxation times and corresponding spectral
densities do not show any particular discontinuity throughout
the temperature range investigated, as already observed for both
2H9 and 13C43 spin-lattice relaxation times of other ferroelectric
liquid crystals. This is a clear indication of the absence of
dramatic changes in the motional processes occurring in the
megahertz range over the different mesophases and, in particular,
at the transition between untilted (smectic A) and tilted (smectic
C*) phases.
A more detailed, quantitative analysis of the spectral densities
could be performed on the basis of existing diffusional models
only in the untilted smectic A phase because of the lack of
specific models for tilted smectic phases. However, a procedure
that allows the analysis of the spectral densities in terms of
diffusional coefficients to be extended to tilted phases has been
recently developed in our group,44 and the data analysis for
11EBM7 and other ferroelectric liquid crystals is currently in
progress.
6D
1
)
+ mM2(D| - D )
(10)
(j)
(j)
mLmM
τ
b
mLmM
where D| and D are the principal components of the diffusion
tensor, diagonalized in a molecular frame, describing the
molecular spinning and tumbling motions, respectively, and the
(j)
(j)
coefficients a
, b
, and cm m have been calculated in
L
M
mLmM
mLmM
ref 32 as a function of the principal order parameter for a
Maier-Saupe potential.
The internal motions can be “superimposed” to the overall
molecular motions by taking the products of the respective
autocorrelation functions, which can be Fourier-transformed to
give eventually the following expression for J3:
Jm (mLω0) )
L
3π2
2
2
(νq)2
c
[d 2(â )]2[d
2(âM,i)]2
mMmR
∑ ∑
mLmM mR0
i,Qi
2
mM)- 2mR)-2
(j)
mLmM
(τ
)
-1 + ê(mR)Di
a(j)
(11)
∑
mLmM
(mLω0)2 + [(τ(j)
)
-1 + ê(mR)Di]2
j
mLmM
2
where νq is the quadrupolar coupling constant, drs are the
reduced Wigner matrices, âi,Q is the angle between the C-D
bond and the axis about which the internal rotation takes place,
i
The relaxation data in the smectic A phase were analyzed
using a global target approach by assuming an Arrhenius
behavior for the four diffusional coefficients (D| and D for
molecular spinning and tumbling, and DR(phe) and DR(biphe) for
the rotation of the phenyl and biphenyl fragments about their
para axes). Moreover, the ratio D|/D was fixed to the value of
11, arising from the application of the model proposed by
Perrin,45 which gives an estimate of this value on the basis of
the ratio between the semiaxes of the ellipsoid to which the
molecule is approximated. In fact, it has been recently shown9,42
that when relaxation data at a single Larmor frequency or of
only few different deuterons or both are available, the diffusional
coefficient for the tumbling motion exhibits a high indetermi-
nacy and constraints must be applied to obtain physically
meaningful results. The values of the order parameter relative
â
M,i is the angle between this axis and the molecular long axis,
Di is the diffusion coefficient relative to the internal rotation of
the fragment considered, and ê(mR) is (1 - δm ) or mR if the
strong collision or small step diffusion models are used,
respectively, for this motion.
2
R
Dynamics: Results and Discussion
The deuterium relaxation times T1Z and T1Q have been
measured in the two isotopomers by means of the broadband
Jeener-Broekaert pulse sequence throughout the mesophasic
range. A single relaxation time has been determined in the case
of the isotopomer d8 for all of the deuterium nuclei, because of
the difficulty of extracting individual contributions of different
biphenyl deuteria to the whole spectrum; a close inspection of

10112 J. Phys. Chem. B, Vol. 107, No. 37, 2003
Catalano et al.
diffusional coefficients for the spinning motion, which is
intermediate between them, being slightly higher than those of
the reorientational motion of the phenyl ring.
The values of both diffusional constant and activation energies
(40 kJ/mol for D| and D , and 32 kJ/mol for DR(phe) and DR(biphe)
)
are in general agreement with those previously found for similar
smectogens.9,41,46 The errors of the Arrhenius preexponential
coefficients are 5% for D| and 10% for DR(phe) and DR(biphe)
,
while those of the activation energies are 0.5% and 1% for the
spinning and internal motions, respectively.
A satisfactory reproduction of the experimental data could
not be obtained by using the small step rotational diffusion
model in place of the strong collision one for the internal
reorientation of either the phenyl or the biphenyl group. This is
a quite unusual behavior, because usually the two models are
equally suitable to describe the internal dynamics of aromatic
fragments in achiral low-molecular-weight liquid crystal. How-
ever, the same discrimination between the two models was
previously observed by us in the SmA phase of the ferroelectric
liquid crystal 8BEF5.10 The results here shown thus further
support the hypothesis that internal motions of aromatic
fragments may have a peculiar behavior in the SmA phases of
FLCs.
Figure 11. Calculated (lines) and experimental (symbols) spectral
densities (s-1), J1(ω0) (O and 4 for d2 and d8 isotopomers, respectively)
and J2(2ω0) (9 and [ for d2 and d8 isotopomers, respectively), of
11EB1M7 in the SmA phase vs T (K).
Conclusions
2H NMR was employed to investigate the orientational order
and the dynamic properties of the liquid crystalline phases of
the smectogen 11EB1M7 by using two different selectively 2H-
2
labeled isotopomers. The line shape behavior of the H NMR
spectra has been used to follow the phase transitions. From the
quadrupolar and dipolar splittings, the orientational order
parameters of the rigid phenyl and biphenyl fragments were
obtained as a function of the temperature. The tilt angle within
the SmC* phase, as well as the angle between the para axes of
the phenyl and biphenyl aromatic fragments within the SmA
and SmI* phases, could be estimated from the SZZ ratios. The
change in the relative orientation of the two aromatic fragments
with respect to the magnetic field occurring at the SmC*-SmI*
transition, allowed by the noncollinearity of their para axes, is
in agreement with the more solidlike structure of the SmI*
phase, where the more bulky biphenyl fragment becomes the
more ordered one, perhaps because of more constrained packing
interactions. This behavior is possibly related to the different
angle between the para axes of the two fragments estimated in
the SmI* phase with respect to the SmA one.
Figure 12. Logarithm of the diffusional constants D|, D , DR(phe), and
D
superimposed Nordio and strong collision models (see text).
R(biphe) (s-1) vs 1000/T (1/K) derived by a global target procedure using
The dynamic behavior of 11EB1M7 was investigated in its
smectic A and C* phases. The spectral density data of the phenyl
and biphenyl deuterons could be quantitatively analyzed in terms
of diffusional models only in the smectic A phase by superim-
posing internal rotations of each fragment onto the overall
molecular reorientations. The diffusional coefficients of the
internal rotations of both the phenyl and biphenyl rings have
been found to be of the same order of magnitude of those of
the molecular spinning and approximately 1 order of magnitude
higher than those of the molecular tumbling. Contrary to what
has been observed for achiral low-molecular-weight liquid
crystals, only the strong collision model could suitably describe
the internal motions of the aromatic fragments around their para
axes, confirming previous results and suggesting a peculiar
dynamic behavior of FLCs.
to the phenyl moiety (the para axis of which is assumed to be
aligned to the magnetic field) reported in the Line Shapes, Order
Parameters, and Tilt Angles in SmA, SmC*, and SmI* Phases
section were used. In agreement with the orientational order
data analysis, the angle âi,Q was taken as 60° for all of the
i
deuterons, the molecular long axis was assumed to be parallel
to the para axis of the phenyl fragment, and the angle between
the molecular long axis and the para axis of the biphenyl
fragment was taken from the results obtained by the ratio of
the order parameters of the two aromatic fragments. The analysis
performed using the strong collision model for the internal
motions gave a very good agreement between calculated and
experimental spectral densities for all of the deuterons over the
whole SmA range, as shown in Figure 11.
The diffusional coefficients obtained for the spinning and
tumbling molecular motions, as well as for the internal motions
of both the phenyl and the biphenyl moieties, are reported in
Figure 12. It can be noticed that diffusional coefficients for the
two internal motions are of the same order of magnitude of the
Acknowledgment. We thank the Italian MIUR for partial
financial support. Special thanks to Prof. G. Galli and Prof. K.
Fodor-Csorba for their collaboration.

Study of the Ferroelectric Liquid Crystal 11EB1M7
J. Phys. Chem. B, Vol. 107, No. 37, 2003 10113
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