Design of liquid crystals with de Vries-like properties: Frustration between SmA- and SmC-promoting elements

Article abstract of DOI:10.1021/ja9087727

According to a new design strategy for de Vries-like liquid crystal materials, which are characterized by a maximum layer contraction of ≤1% upon transition from the SmA phase to the SmC phase, we report the synthesis and characterization of two homologous series of organosiloxane mesogens. The design of these new materials is based on a frustration between one structural element that promotes the formation of a SmC phase (a trisiloxane-terminated side-chain) and one that promotes the formation of a SmA phase (either a chloro-terminated side-chain or a 5-phenylpyrimidine core). Measurements of smectic layer spacing d as a function of temperature by small-angle X-ray scattering (SAXS) combined with optical tilt angle measurements revealed that the mesogens 5-(4-(11-(1,1,1,3,3,5,5- heptamethyltrisiloxanyl)-undecyloxy)phenyl)-2-(1-alkyloxy)pyrimidine (3(n)) undergo SmA-SmC phase transitions with maximum layer contractions ranging from 0.5% to 1.4%. A comparison of reduction factors R and f suggests that this behavior is due in part to a pronounced negative thermal expansion in the SmC phase that counterbalances the layer contraction caused by increasing tilt. SAXS measurements also revealed that compounds 3(n) are characterized by low orientational and high translational order, which is consistent with theoretical predictions that such materials should exhibit de Vries-like properties. The R values for series 3(n) are comparable to, and even lower than, those reported for established de Vries-like materials such as the perfluorinated 2-phenylpyrimidine material 3M 8422.

Full text of DOI:10.1021/ja9087727

Published on Web 12/08/2009
Design of Liquid Crystals with “de Vries-like” Properties:
Frustration between SmA- and SmC-Promoting Elements
Jeffrey C. Roberts,† Nadia Kapernaum,‡ Qingxiang Song,†
Dorothee Nonnenmacher,‡ Khurshid Ayub,† Frank Giesselmann,‡ and
Robert P. Lemieux*,†
Chemistry Department, Queen’s UniVersity, Kingston, Ontario K7L 3N6, Canada, and Institute
of Physical Chemistry, UniVersita¨t Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
Received October 14, 2009; E-mail: lemieux@chem.queensu.ca
Abstract: According to a new design strategy for “de Vries-like” liquid crystal materials, which are
characterized by a maximum layer contraction of e1% upon transition from the SmA phase to the SmC
phase, we report the synthesis and characterization of two homologous series of organosiloxane mesogens.
The design of these new materials is based on a frustration between one structural element that promotes
the formation of a SmC phase (a trisiloxane-terminated side-chain) and one that promotes the formation
of a SmA phase (either a chloro-terminated side-chain or a 5-phenylpyrimidine core). Measurements of
smectic layer spacing d as a function of temperature by small-angle X-ray scattering (SAXS) combined
with optical tilt angle measurements revealed that the mesogens 5-(4-(11-(1,1,1,3,3,5,5-heptamethyltri-
siloxanyl)-undecyloxy)phenyl)-2-(1-alkyloxy)pyrimidine (3(n)) undergo SmA-SmC phase transitions with
maximum layer contractions ranging from 0.5% to 1.4%. A comparison of reduction factors R and f suggests
that this behavior is due in part to a pronounced negative thermal expansion in the SmC phase that
counterbalances the layer contraction caused by increasing tilt. SAXS measurements also revealed that
compounds 3(n) are characterized by low orientational and high translational order, which is consistent
with theoretical predictions that such materials should exhibit de Vries-like properties. The R values for
series 3(n) are comparable to, and even lower than, those reported for established de Vries-like materials
such as the perfluorinated 2-phenylpyrimidine material 3M 8422.
Introduction
The self-organization of amphiphilic molecules forming liquid
crystal phases is generally described as the nanosegregation of
two or more incompatible segments into distinct domains with
topographies dictated by molecular shape and amphiphilic
interfacial curvature.1 The formation of lamellar smectic phases
by calamitic (rod-shaped) mesogens is driven by the nanoseg-
regation of rigid aromatic cores from flexible aliphatic side-
chains and may be further promoted by the introduction of
incompatible segments such as perfluorinated side-chains or
oligomeric siloxane end-groups. The fluid smectic A (SmA) and
smectic C (SmC) phases have diffuse lamellar structures
described by a density wave with a period d corresponding to
the smectic layer spacing.2 In the uniaxial SmA phase, the axes
of orientational and translational order are coincident, with the
director n parallel to the smectic layer normal z; in the biaxial
SmC phase, n is tilted relative to z by a tilt angle θ that varies
with temperature. According to the classic rigid-rod model
shown in Figure 1a, the SmA-SmC phase transition is
Figure 1. Schematic representations of the SmA-SmC phase transition
according to (a) a classic rigid-rod model and (b) the diffuse cone model
proposed by de Vries.4
accompanied by a contraction of the layer spacing d that scales
with the cosine of the tilt angle θ and is typically on the order
of 7-10% in conventional calamitic materials.3 This layer
contraction has been a problem in the formulation of chiral
SmC* mixtures for ferroelectric liquid crystal (FLC) display
devices, which may be solved by a design strategy focused on
balancing nanosegregation and low orientational order (vide
infra).
† Queen’s University.
‡ Universita¨t Stuttgart.
(1) (a) Tschierske, C. J. Mater. Chem. 1998, 8, 1485–1508. (b) Goodby,
J. W.; Mehl, G. H.; Saez, I. M.; Tuffin, R. P.; Mackenzie, G.; Auze´ly-
Velty, R.; Benvegnu, T.; Plusquellec, D. Chem. Commun. 1998, 2057–
2070. (c) Tschierske, C. J. Mater. Chem. 2001, 11, 2647–2671.
(2) (a) McMillan, W. L. Phys. ReV. A 1971, 4, 1238–1246. (b) McMillan,
W. L. Phys. ReV. A 1972, 6, 936–947.
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9
364 J. AM. CHEM. SOC. 2010, 132, 364–370
10.1021/ja9087727  2010 American Chemical Society

Design of Liquid Crystals with “de Vries-like” Properties
A R T I C L E S
In a surface-stabilized planar alignment, the chiral SmC*
phase has ferroelectric properties: it exhibits a spontaneous
electric polarization PS perpendicular to the tilt plane that can
be coupled to an electric field to produce an ON-OFF light
shutter switching between opposite tilt orientations on a
microsecond time scale.5,6 Materials used in FLC display
applications are normally composed of an achiral liquid crystal
mixture and a chiral dopant that induces a spontaneous
polarization in the SmC phase. To produce a uniform alignment
between parallel rubbed polyimide-coated ITO glass slides, the
liquid crystal material is cooled from the isotropic phase to the
SmC* phase via the SmA* phase, which normally results in a
buckling of the smectic layers into a chevron geometry due to
the combined effect of surface anchoring and the layer contrac-
tion depicted in Figure 1a. Chevrons of opposite fold directions
are separated by zigzag line defects, which severely degrade
the optical quality of the FLC film.7
One solution to this problem is to develop materials with
minimal layer contraction at the SmA-SmC phase transition.
Over the past 20 years, several groups have focused on a
class of liquid crystal materials referred to as “de Vries-like”,
which are characterized by maximum layer contractions of
e1% upon transition from the SmA phase to the SmC
phase.3,8-14 This reference stems from the diffuse cone model
proposed by de Vries that describes the SmA phase as a
lamellar structure in which mesogens have a tilted molecular
orientation and random azimuthal distribution.4 According
to this idealized model, the SmA-SmC transition is described
as an ordering of the azimuthal distribution that results in
zero layer contraction, as shown in Figure 1b. In fact, the
structure of the SmA phase formed by de Vries-like materials
has yet to be fully elucidated, but recent theoretical studies
do suggest that calamitic materials combining low orienta-
tional order and high lamellar order are likely to exhibit this
behavior.15,16 This is consistent with the fact that most de
Vries-like materials feature nanosegregating structural ele-
ments such as siloxane end-groups or perfluorinated side-
chains that strongly promote lamellar ordering.3 Examples
of such materials include 3M 8422 and TSiKN65, which
show maximum layer contractions of 0.4% and 0.65%,
respectively.10,11
Although there are now several examples of liquid crystals
with de Vries-like properties, there is still no strategy for the
rational design of these unusual materials. In an effort to develop
de Vries-like liquid crystal hosts that are structurally similar to
components of FLC mixtures, we have shown that one can
increase the “de Vries character” of PhP1 by integrating one
structural element that promotes the formation of a SmC phase
(trisiloxane end-group) with one that promotes the formation
of a SmA phase (chloro-terminated side-chain).17 The “de Vries
character” of a liquid crystal material can be expressed by the
reduction factors R and f according to eqs 1 and 2:
(4) de Vries, A. J. Chem. Phys. 1979, 71, 25–31.
R ) δ(T)/θopt(T) ) cos-1[dC(T)/dAC]/θopt(T)
f ) θXray(T)/θopt(T) ) cos-1[dC(T)/dA(T)]/θopt(T)
(1)
(2)
(5) Clark, N. A.; Lagerwall, S. T. Appl. Phys. Lett. 1980, 36, 899–901.
(6) Lagerwall, S. T. Ferroelectric and Antiferroelectric Liquid Crystals;
Wiley-VCH: Weinheim, 1999.
(7) Rieker, T. P.; Clark, N. A.; Smith, G. S.; Parmar, D. S.; Sirota, E. B.;
Safinya, C. R. Phys. ReV. Lett. 1987, 59, 2658–2661.
In eq 1, δ(T) is the tilt angle required to give the observed layer
contraction relative to the layer spacing at the SmA-SmC
transition dAC assuming a rigid-rod model;8 in eq 2, θXray(T) is
the tilt angle required to give the observed layer contraction
relative to the SmA layer spacing dA(T) extrapolated in the SmC
phase at a given reduced temperature according to a least-squares
fit of the data points in the SmA phase near the SmA-SmC
transition.10 The latter gives a reduction factor that is normalized
with respect to negative thermal expansion. In each equation,
the tilt angle derived from layer spacing measurements is divided
by the optical tilt angle θopt(T) measured by polarized optical
microscopy (POM).
(8) Takanishi, Y.; Ouchi, Y.; Takezoe, H.; Fukuda, A.; Mochizuki, A.;
Nakatsuka, M. Jpn. J. Appl. Phys. 1990, 29, L984–L986.
(9) Giesselmann, F.; Zugenmaier, P.; Dierking, I.; Lagerwall, S. T.; Stebler,
B.; Kaspar, M.; Hamplova, V.; Glogarova, M. Phys. ReV. E 1999, 60,
598–602.
(10) Radcliffe, M. D.; Brostrom, M. L.; Epstein, K. A.; Rappaport, A. G.;
Thomas, B. N.; Shao, R.; Clark, N. A. Liq. Cryst. 1999, 26, 789–794.
(11) Spector, M. S.; Heiney, P. A.; Naciri, J.; Weslowski, B. T.; Holt, D. B.;
Shashidhar, R. Phys. ReV. E 2000, 61, 1579–1584.
(12) Lagerwall, J. P. F.; Giesselmann, F.; Radcliffe, M. D. Phys. ReV. E
2002, 66, 031703.
(13) Panarina, O. E.; Panarin, Y. P.; Vij, J. K.; Spector, M. S.; Shashidhar,
R. Phys. ReV. E 2003, 67, 051709.
(14) Naciri, J.; Carboni, C.; George, A. K. Liq. Cryst. 2003, 30, 219–225.
(15) (a) Gorkunov, M. V.; Osipov, M. A.; Lagerwall, J. P. F.; Giesselmann,
F. Phys. ReV. E 2007, 76, 051706. (b) Gorkunov, M. V.; Giesselmann,
F.; Lagerwall, J. P. F.; Sluckin, T. J.; Osipov, M. A. Phys. ReV. E
2007, 75, 060701.
As shown in Figure 2, the trisiloxane derivatives 1 and 2(8)
undergo SmA-SmC phase transitions with maximum layer
contractions of 4.2% and 1.6%, respectively, which are signifi-
(16) (a) Saunders, K.; Hernandez, D.; Pearson, S.; Toner, J. Phys. ReV.
Lett. 2007, 98, 197801. (b) Saunders, K. Phys. ReV. E 2008, 77,
061708. (c) Saunders, K. Phys. ReV. E 2009, 80, 011703.
(17) Li, L.; Jones, C. D.; Magolan, J.; Lemieux, R. P. J. Mater. Chem.
2007, 17, 2313–2318.
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Roberts et al.
mesogens 2(n).23 These results, together with differential
scanning calorimetry, tilt angle, and order parameter measure-
ments, will be discussed in the context of current theoretical
models for the SmA-SmC phase transition of de Vries-like
liquid crystals.15,16
Results and Discussion
Synthesis. The mesogens 2(n) were derived from com-
mercially available 2-(4-hydroxyphenyl)-5-pyrimidinol (4) via
sequential Mitsunobu reactions with the appropriate chloro-
terminated alcohols to give 5(n), and with 11-(1,1,1,3,3,5,5-
heptamethyltrisiloxanyl)-undecanol, as shown in Scheme 1 (see
Supporting Information for details). The mesogens 3(n) were
derived from 2-chloro-5-(4-methoxyphenyl)pyrimidine (6)24 by
a nucleophilic aromatic substitution reaction with the appropriate
sodium alkoxides to give 7(n), followed by selective demethyl-
ation using NaSEt to give 8(n) and then alkylation via a Mitsunobu
reaction with 11-(1,1,1,3,3,5,5-heptamethyltrisiloxanyl)undecanol
to give 3(n).
Figure 2. Relative smectic layer spacing d/dAC versus reduced temperature
T - TAC for compounds 1 (b), 2(8) (O), and PhP1 (0) measured by small-
angle X-ray scattering (SAXS).
cantly smaller than the layer contraction of 7.1% observed with
PhP1.18 If one takes into account the difference in optical tilt
angle θopt in the SmC phase at a reduced temperature of T -
TAC ) -10 K, the R values for 1 and 2(8) are 0.57 and 0.43,
respectively, again significantly smaller (i.e., more de Vries-
like as R f 0) than the R value of 0.80 measured for PhP1.
However, these are still far from the R value of 0.18 derived
from SAXS measurements reported for 3M 8422,10 which is
considered to be a benchmark in terms of de Vries character.
An interesting feature of the d/dAC versus T - TAC profile of
compound 2(8), which is also found in the profiles of 3M 8422
and other de Vries-like materials, is the pronounced negative
thermal expansion of the layer spacing in the SmA phase that
persists in the SmC phase and appears to counterbalance the
layer contraction caused by the increasing tilt. This is reflected
by a R/f ratio of 0.68 that is much smaller than that of 0.96 for
both 1 and PhP1. This negative thermal expansion is likely due
to an increase in orientational ordering together with an increase
in effective molecular length as the alkyl chains become more
extended at lower temperature.
The trisiloxane-terminated undecyloxy side-chain and the
chloro-terminated octyloxy side-chain were shown to strongly
promote the formation of SmC and SmA phases, respectively.17,19
The combination of these two elements, which resulted in the
lower R value of compound 2(8), may reflect a frustration similar
to that invoked in the formation of smectic twist-grain-boundary
phases that could form the basis of a rational design strategy
for de Vries-like materials.20 To test this hypothesis, and to
investigate the effect of broadening the temperature range of
the SmA phase on de Vries-like behavior,21 we designed a
homologous series of trisiloxane mesogens 3(n) in which the
SmA-promoting element is a nonplanar 5-phenylpyrimidine
core,22 and we compared their R and f values to those measured
for a homologous series of the chloro-terminated trisiloxane
Scheme 1a
a Reagents and conditions: (a) HO(CH2)nCl, DIAD, Ph3P, THF, 25 °C;
(b) Me3SiO(Me)2SiO(Me)2Si(CH2)11OH, DIAD, Ph3P, THF, 25 °C; (c)
CnH2n+1OH, NaH, THF, 25 °C; (d) EtSH, NaH, DMF, reflux.
Mesophase Characterization. The mesophases formed by
compounds 2(n) and 3(n) were characterized by POM and
differential scanning calorimetry (DSC). All compounds in series
2(n) and 3(n) form SmA and SmC phases on heating and
cooling (Figure 3 and Table S1 in Supporting Information), as
shown by the characteristic fan and homeotropic textures of
the SmA phase that turn into the broken fan and Schlieren
textures of the SmC phase, respectively, with a pronounced
change in interference color. The color change of the fan/broken
fan texture observed by POM for a 19 µm film of 3(8) from
just above the SmA-SmC transition point to 5 K below is
shown in Figure 4. This color change corresponds to an increase
in birefringence of ca. 20% based on a Michel-Levy chart,
which is comparable to that reported for 3M 8422 and indicates
an increase in orientational order that is expected for de Vries-
like materials.3 In addition, DSC and POM analyses suggest
that compounds 2(4) and 2(5) form an unidentified higher order
SmX phase below the SmC phase and do not crystallize at
temperatures as low as -80 °C.25 As shown in Figure 3,
increasing the length of the nonsiloxane side-chain in 2(n) and
3(n) results in a gradual decrease of the SmA temperature range
(from 36 to 3 K in 2(n) and from 22 to 1 K in 3(n)).18
(18) Hartley, C. S.; Kapernaum, N.; Roberts, J. C.; Giesselmann, F.;
Lemieux, R. P. J. Mater. Chem. 2006, 16, 2329–2337.
(19) Goodby, J. W.; Saez, I. M.; Cowling, S. J.; Go¨rtz, V.; Draper, M.;
Hall, A. W.; Sia, S.; Cosquer, G.; Lee, S.-E.; Raynes, E. P. Angew.
Chem., Int. Ed. 2008, 47, 2754–2787.
(23) For a preliminary communication, see: Roberts, J. C.; Kapernaum,
N.; Giesselmann, F.; Lemieux, R. P. J. Am. Chem. Soc. 2008, 130,
13842–13843.
(20) Kamien, R. D.; Selinger, J. V. J. Phys.: Condens. Matter 2001, 13,
R1–R22.
(21) The SmA*-C* layer contraction in a homologous series of chiral
mesogens was shown to decrease with increasing temperature range
of the SmA* phase: Bezner, S.; Krueger, M.; Hamplova, V.;
Glogarova, M.; Giesselmann, F. J. Chem. Phys. 2007, 126, 054902.
(22) The 5-phenylpyrimidine analogue of PhP1 only forms a SmA phase
(Cr 84 SmA 117 I): Hegmann, T.; Meadows, M. R.; Wand, M. D.;
Lemieux, R. P. J. Mater. Chem. 2004, 14, 185–190.
(24) Brown, D. J.; Lee, T.-C. J. Chem. Soc. C 1970, 214–219.
(25) The assignment of a SmX phase is based on the relatively low enthalpy
of the SmX-SmC transitions for 2(4) and 2(5) (11-15 kJ/mol) as
compared to those of the Cr-SmC transitions for the higher homo-
logues (37-53 kJ/mol), and the observation of recrystallization
exotherms on heating the higher homologues before the Cr-SmC
transitions.
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Design of Liquid Crystals with “de Vries-like” Properties
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angle increases with the length of the nonsiloxane side-chain,
which is consistent with normally observed trends;18 at T -
TAC ) -10 K, θopt increases from 15° to 25° for 2(n), and from
24° to 43° for 3(n) (see Table S2 and Figure S1 in Supporting
Information). Because the tilt angle is the primary order
parameter describing the SmA-SmC phase transition, the
temperature variation of θ is described by the power law:
θ ∝ |T - Tc|ꢀ
(3)
where ꢀ is the order parameter exponent related to the nature
of the phase transition and Tc is the phase transition temperature
of a theoretical second-order phase transition (critical temper-
ature).32 According to the generalized mean-field theory of phase
transitions (Landau theory), a ꢀ value of 0.5 is expected in the
case of a pure second-order transition, whereas a ꢀ value of
0.25 is expected in the case of a SmA-SmC transition at the
crossover (tricritical) point from second- to first-order transi-
tion.33,34 The plots of θopt versus |T - Tc| for 3(4), 3(7), and
3(10) are compared to the best fits to eq 3 in Figure 6.35 These
fits give ꢀ values of 0.28, 0.12, and 0.08, respectively, which
are consistent with the trend observed in the ∆HAC measure-
ments and suggest a change in the nature of the SmA-SmC
transition from tricritical to first-order at n ) 7. The corre-
sponding fits to eq 3 for 2(4), 2(7), and 2(10) give ꢀ values of
0.21, 0.22, and 0.14, respectively, which are also consistent with
the ∆HAC measurements and suggest that the SmA-SmC phase
transition in this series is tricritical up to n ) 8 and changes to
a first-order transition at n ) 10.
Reduction Factor Measurements. Accurate measurements of
smectic layer spacings (d) as a function of temperature were
carried out by small-angle X-ray scattering (SAXS). As shown
in Figure 7, the d/dAC versus T - TAC profiles for series 2(n)
are qualitatively similar and show a negative thermal expansion
in the SmA phase that persists in the SmC phase to such an
extent that the layer spacing in the SmC phase (dC) exceeds the
spacing at the SmA-SmC transition (dAC) at reduced temper-
atures as high as -20 K. The maximum layer contraction
increases with the length of the chloroalkoxy side-chain, from
0.5% for 2(4) to 1.5% for 2(10), which correlates with the
increase in θopt. The d/dAC versus T - TAC profiles for series
3(n) also show a negative thermal expansion in both the SmA
and the SmC phases. However, these profiles show two separate
trends with a break that may correspond to the apparent change
in SmA-SmC transition from tricritical to first-order. As shown
in Figure 7, the profiles for the lower homologues 3(4) to 3(6)
are very similar and show a maximum layer contraction of 0.5%,
which jumps to 1.4% with 3(7) and then progressively decreases
with increasing alkoxy chain length to 0.5% with 3(10). The
SmA temperature range of 3(12) is too narrow to detect any
layer contraction, and the profile only shows dC increasing due
to the negative thermal expansion.
Figure 3. Phase transition temperatures for 2(n) and 3(n) measured by
DSC on heating.
Figure 4. Polarized photomicrographs (100×) of compound 3(8) in a
parallel rubbed glass cell with a spacing of 19 µm at (from left to right) 76,
74, and 70 °C. The change in interference color from 76 to 70 °C
corresponds to an increase in birefringence of ca. 20%.
Furthermore, the Cr/SmX-SmC transition point shows the
expected odd-even effect in 2(n) but not in 3(n), which shows
a gradual increase in the Cr-SmC transition point from n ) 5
to n ) 9. The liquid crystal temperature ranges are generally
broader in series 2(n) than in 3(n), and the two shortest
homologues in series 2(n) are mesogenic in the SmC phase at
room temperature.
The DSC analysis suggests that lengthening the alkoxy side-
chain causes a change in the nature of the SmA-SmC phase
transition of 2(n) and 3(n). As shown in Figure 5, the increase
in enthalpy change for the SmA-SmC phase transition of 3(n)
(∆HAC) with increasing alkoxy chain length, from <0.1 to
1.6-1.7 kJ/mol, and the hysteresis of the peak temperatures on
heating and cooling for the higher homologues suggest a
crossover from a second-order or tricritical SmA-SmC transi-
tion at relatively short chain lengths (n e 6) to a first-order
transition at longer chain lengths.26 This trend is consistent with
previous observations in homologous series of a second-order
SmA-SmC transition becoming discontinuous with decreasing
temperature range of the SmA phase.27-30 On the other hand,
the SmA-SmC phase transition in series 2(n) is undetectable
by DSC except for the highest homologue 2(10), which suggests
that the crossover to a first-order transition occurs further down
the series, between n ) 8 and n ) 10.
Optical Tilt Measurements. Optical tilt angles (θopt) in the
SmC phase were measured as a function of temperature by POM
by applying a field of 10 V across surface-stabilized FLC films
(5 µm) in ITO glass cells with rubbed Nylon alignment layers
using liquid crystal samples doped with the chiral additive 9
(1-2 mol %).31 In both series 2(n) and 3(n), the optical tilt
(32) Chandrasekhar, S. Liquid Crystals, 2nd ed.; Cambridge University
Press: Cambridge, 1992.
(26) Thoen, J. In Physical Properties of Liquid Crystals; Demus, D.,
Goodby, J. W., Gray, G. W., Spiess, H.-W., Vill, V., Eds.; Wiley-
VCH: Weinheim, 1999; pp 208-232.
(33) Birgeneau, R. J.; Garland, C. W.; Kortan, A. R.; Litster, J. D.; Meichle,
M.; Ocko, B. M.; Rosenblatt, C.; Yu, L. J.; Goodby, J. Phys. ReV. A
1983, 27, 1251–1254.
(27) Huang, C. C.; Lien, S. C. Phys. ReV. E 1985, 31, 2621–2627.
(28) Ratna, B. R.; Shashidhar, R.; Nair, G. G.; Prasad, S. K.; Bahr, C.;
Heppke, G. Phys. ReV. A 1988, 37, 1824–1826.
(34) Landau, L. D. Statistical Physics, 3rd ed.; Pergamon Press: Oxford,
1980.
(35) Because of the relatively low temperature resolution in the optical tilt
angle measurements ((0.5 K), a precise value of the critical temper-
ature Tc cannot be obtained; TAC < Tc for a first-order transition,
whereas TAC ) Tc for a second-order transition. The fits to eq 3 over
the full temperature range of the SmC phase are primarily intended
to confirm the trends in ∆HAC observed by DSC.
(29) Prasad, S. K.; Raja, V. N.; Shankar Rao, D. S.; Nair, G. G.; Neubert,
M. E. Phys. ReV. A 1990, 42, 2479–2481.
(30) Heinrich, B.; Guillon, D. Mol. Cryst. Liq. Cryst. 1995, 268, 21–43.
(31) Roberts, J. C.; Kapernaum, N.; Giesselmann, F.; Wand, M. D.;
Lemieux, R. P. J. Mater. Chem. 2008, 18, 5301–5306.
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Figure 5. Partial DSC traces of compounds 3(5-9), 2(8), and 2(10) showing the SmC-SmA and SmA-I phase transitions on heating and cooling at 5
K/min, and the enthalpy change for the SmA-SmC phase transition ∆HAC in kJ/mol.
3(10), the layer spacing dAC is restored at T - TAC ) -10 K
due to the negative thermal expansion, within (0.1 Å.
To assess the contribution of negative thermal expansion in
offsetting the layer contraction due to increasing tilt, the f factors
were calculated for 2(n) and 3(n) (eq 2). The negative thermal
expansion of the layer spacing d in the SmA phase is due
primarily to an increase in orientational ordering according to
eq 4, where L corresponds to the molecular length l, assuming
a monolayer structure, and S2 is the orientational order parameter
(vide infra).3,36 The latter can be expressed by a power law
function (eq 5), according to the general theory of phase
transitions and critical phenomena, where T* is the superheating
limit in K (T* > TI) and 1 - R is the power law exponent (R e
1).37 Hence, the layer spacing in the SmA phase can be
expressed as a function of T according to eq 6:
dA ) L/3(S2 + 2)
S2 ) (1 - T/T*)1-R
(4)
(5)
(6)
dA ) L/3[(1 - T/T*)1-R + 2]
For materials that exhibit only a small negative thermal
expansion in the SmA phase, the power law exponent R
converges toward zero. In their original calculation of f for 3M
8422, Ratcliffe et al. assumed that R ) 0 near the SmA-SmC
phase transition and extrapolated dA into the SmC phase
according to a least-squares fit of the data points at T - TAC g
0.10 In the present case, the f factors were calculated for 2(n)
and 3(n) by fitting the data points in Figure 7 at T - TAC g 0
to eq 6 and extrapolating dA according to these fits into the SmC
phase at T - TAC ) -10 K (see Figure 9, for example, and
Figure S2 in Supporting Information). As shown in Figure 10,
the f factors of all compounds in series 2(n) and 3(n) are larger
than the corresponding R factors. This suggests that negative
Figure 6. Optical tilt angles θopt versus reduced temperature T - Tc for
(a) compounds 2(4) (O), 2(7) (4), and 2(10) (0), and (b) compounds 3(4)
(O), 3(7) (4), and 3(10) (0). The solid lines represent the fits to eq 3.
Although the maximum layer contractions measured for
compounds 2(n) and 3(n) upon SmA-SmC phase transition
are in the same range, the R values for 3(n) are significantly
smaller than those for 2(n) because of the difference in optical
tilt angles (eq 1). As shown in Figure 8, the R values in series
2(n) range from 0.36 to 0.47 at T - TAC ) -10 K, whereas the
R values in series 3(n) range from 0 to 0.30; in the case of
(36) In the case of organosiloxane mesogens, which form partially bilayered
smectic phases, l < L < 2l: Ibn-Elhaj, M.; Skoulios, A.; Guillon, D.;
Newton, J.; Hodge, P.; Coles, H. J. J. Phys. II France 1996, 6, 271–
279.
(37) Stanley, H. E. Introduction to Phase Transitions and Critical Phe-
nomena; Oxford University Press: Oxford, 1971.
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368 J. AM. CHEM. SOC. VOL. 132, NO. 1, 2010

Design of Liquid Crystals with “de Vries-like” Properties
A R T I C L E S
Figure 7. Relative smectic layer spacing d/dAC versus reduced temperature
T - TAC for (a) compounds 2(n) and (b) compounds 3(n). The measurements
were performed on heating from the crystalline phase for all compounds
except 3(9) and 3(10), which were performed on cooling from just below
the clearing point due to the narrow SmC temperature ranges. The data for
2(8) are from ref 17.
Figure 9. Smectic layer spacing d versus reduced temperature T - TAC
for compounds 3(4) and 3(9). The dashed lines show the layer spacing at
the SmA-SmC transition. The solid lines represent the fits to eq 6 for the
data points at T - TAC g 0. The arrows indicate the difference in layer
spacing for calculating the R and f reduction factors.
and lies near the solid line corresponding to R ) f. More
significantly, the points corresponding to compounds 3(n) are
clustered around that corresponding to 3M 8422, except for
compound 3(10), which shows no layer contraction at T - TAC
) -10 K.
Order Parameter Measurements. Recent theoretical models
by Osipov and Saunders support the experimental evidence3
that smectogenic materials combining low orientational and
high translational order are likely to exhibit de Vries-like
properties.15,16 To test this prediction, orientational (S2) and
translational (Σ) order parameters were measured in the SmA
phase as a function of temperature for the representative
compounds 2(8), 3(5), and PhP1. The order parameter S2 is
a measure of the long-range orientational ordering of long
molecular axes relative to the director n. In the nematic or
smectic A phases, it is derived experimentally from the
intensity profile I(ꢁ) around the wide-angle arc of diffuse
X-ray scattering.38,39 The order parameter Σ is a measure of
the one-dimensional translational ordering (i.e., lamellar
ordering) in the SmA phase.2 It is defined as the amplitude
of the density wave arising from the 1D-periodic smectic
layer structure; Σ was determined experimentally by a method
previously described by Kapernaum and Giesselmann.40 As
shown in Figure 11, both organosiloxanes 2(8) and 3(5)
exhibit unusually low orientational order in the SmA phase,
with S2 values in the range of 0.45, as compared to the
conventional parent compound PhP1 with a S2 value of ca.
0.65. The translational order of both 3(5) and PhP1 is very
Figure 8. Bar graphs showing reduction factors R at T - TAC ) -10 K
(9) and maximum layer contractions (0) for compounds 2(n) and 3(n).
thermal expansion in the SmC phase does counterbalance to
some extent the layer contraction caused by increasing tilt and
results in enhanced de Vries-like properties relative to the parent
compound PhP1, which shows little negative thermal expansion
9
J. AM. CHEM. SOC. VOL. 132, NO. 1, 2010 369

A R T I C L E S
Roberts et al.
according to the theoretical predictions of Osipov and
Saunders.15,16
Conclusions
In comparison to the parent compound PhP1, the reduction
factors measured for series 2(n) and 3(n) support our
hypothesis that combining structural elements promoting the
formation of SmA and SmC phases in the same molecules
causes a frustration that enhances de Vries-like properties.
A comparison of R and f factors suggests that such enhance-
ment may be due in part to a pronounced negative thermal
expansion in the SmC phase that counterbalances the layer
contraction caused by increasing tilt. Although enhancement
in de Vries-like properties is observed in both series, only
compounds in series 3(n) may be considered “de Vries-like”
with properties comparable to that of 3M 8422. This is
consistent with the finding that, of the three representative
compounds for which order parameters were measured, only
3(5) shows a combination of low S2 and high Σ, which is in
agreement with theoretical predictions made by Osipov and
Saunders.15,16 According to the generalized mean-field theory
developed by Saunders, the SmA-SmC phase transition of
materials with low orientational and high translational order
should be either second-order near the tricritical point or first-
order, which is consistent with the DSC and optical tilt angle
results obtained for 2(n) and 3(n).16 From a practical point
of view, materials such as 3(5), which forms a SmC phase
near room temperature and has a saturated tilt of ∼27°, may
be useful as a component of FLC formulations with bookshelf
geometry.
Figure 10. Plot of R versus f for compounds 2(n) (9), 3(n) (b), PhP1
(0), and 3M 8422 (O) at T - TAC ) -10 K.
Acknowledgment. We are grateful to the Natural Sciences and
Engineering Research Council of Canada (NSERC), the Canada
Foundation for Innovation, and the Deutsche Forschungsgemein-
schaft (DFG) for support of this work.
Figure 11. Plots of order parameters S2 and Σ versus reduced temperature
T - TI (TI is the SmA-isotropic transition temperature) for compounds
2(8) (9), 3(5) (b), PhP1 (0).
Supporting Information Available: Syntheses of compounds
2(n) and 3(n), tables of phase transition temperatures and
enthalpies of transition, layer spacings and reduction factors,
and plots of θopt versus T-TAC and d/dAC versus T-TAC. This
material is available free of charge via the Internet at http://
pubs.acs.org.
high, which is somewhat unexpected in the case of PhP1
considering that it lacks a nanosegregating siloxane-end
group. On the other hand, the chloro-terminated organosi-
loxane 2(8) exhibits a much lower translational order than
3(5), which is consistent with the higher R values of series
2(n). Of the three representative compounds, only 3(5)
combines low orientational and high translational order,
which may explain why the R values for series 3(n) are
comparable to, and even lower than, those reported for
established de Vries-like materials such as 3 M 8422
JA9087727
(38) Davidson, P.; Petermann, D.; Levelut, A.-M. J. Phys. II France 1995,
5, 113–131.
(39) Giesselmann, F.; Germer, R.; Saipa, A. J. Chem. Phys. 2005, 123,
034906.
(40) Kapernaum, N.; Giesselmann, F. Phys. ReV. E 2008, 78, 062701.
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370 J. AM. CHEM. SOC. VOL. 132, NO. 1, 2010