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Proc. R. Soc. A
doi:10.1098/rspa.2011.0685
Published online
PERSPECTIVE
Twisted and frustrated states of matter
BY JOHN W. GOODBY*
Department of Chemistry, University of York, York YO10 5DD, UK
The World, and much of Nature that we see within it, experiences an environment of
reduced symmetries. For example, living organisms are dependent on asymmetric or
dissymmetric structures for their life processes. In the solid state, a large number of
space groups are chiral. Conversely, in liquids, the effects of reduced symmetries are
smeared out owing to the dynamical fluctuations of the constituent molecules, atoms
or ions. Thus, on progressing from the strongly ordered solid to the amorphous liquid
state, the effects of reduced symmetries weaken as the molecular or atomic correlations
and penetration lengths fall. Between these two states of matter, the fourth state of
organized fluids can be markedly affected by chirality, and over substantial length scales,
owing to both the fluidity and partial ordering of the molecules. In effect, complex fluids
can amplify the effects of chirality at the molecular level. Broken symmetries in selforganizing systems can lead to the formation of novel phases of matter and to the creation
of structured liquids, and to the generation of nonlinear properties such as heli-, ferro-,
ferri- and antiferro-electricity, and electroclinism, which can be harnessed in a wide range
of applications including thermal sensors, imaging devices and information displays, to
name but a few.
Keywords: liquid crystals, chirality, helicity, enantiopurity, ferroelectricity,
liquid crystal displays
1. Chirality and helicity in organized fluids
The term ‘chiral’ was coined by Lord Kelvin in 1904 in his Baltimore Lectures
on Molecular Dynamics and the Wave Theory of Light, in which he stated. . .‘I
call any geometrical figure, or group of points, chiral, and say it has chirality,
if its image in a plane mirror, ideally realized, cannot be brought to coincide
with itself.’ (Kelvin 1904). With this simple concept, Kelvin was able to unify
the understanding of the lack of mirror symmetry by scientists of many different
persuasions. However, Kelvin was unable to quantify the degree to which mirror
symmetry might be broken. Consider an example of a flat glove, as shown in
figure 1a, it has a symmetry plane within the glove and therefore lacks chirality.
As the fingers are bent to create a fist, figure 1b, the glove becomes chiral, and the
‘degree of chirality’ changes as the shape of the glove changes. However, there is
*[email protected]
An invited Perspective to mark the election of the author to the fellowship of the Royal Society in
2011.
Received 21 November 2011
Accepted 23 January 2012
1
This journal is © 2012 The Royal Society
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J. W. Goodby
(a)
(b)
(c)
(d)
CH3
CH3
H3C
*
O
O
H
Figure 1. (a) Flat glove with a symmetry plane in the plane of the page, (b) glove with bent fingers,
the glove has become chiral, (c) chemical structure of ibuprofen and (d) electron density map of
ibuprofen.
no simple measure of the change in chirality, and in analogy, there is no easy way
that we can evaluate the degree of chirality associated with the handed structure
of a chiral molecule, as illustrated by the structure of the common pharmaceutical
ibuprofen (figure 1c,d). Nor is there a way to determine how molecular chirality
is transmitted in bulk systems.
Chiral forms are manifest in the solid state, with many crystal types being
handed, e.g. Pasteur (1848) was able to separate right- and left-handed crystals
of tartaric acid with tweezers! In liquids, the macroscopic structure and related
properties associated with handedness are smeared out. This was demonstrated
in 1812 by Biot, when he compared the optical rotary properties of quartz in
turpentine with turpentine itself (Biot 1812). The phases of matter that are
closest to the processes and structures found in Nature are collectively called
the liquid–crystalline state. Broken symmetries in liquid crystal phases are also
used extensively in modern communication and display technologies, for example,
most common liquid crystal displays (LCDs) possess chiral molecules and are
constructed using asymmetric device structures. Moreover, liquid crystals have
an incredible ability to amplify the effects of molecular chirality, for example, a
plastic strip thermometer possesses a liquid crystal with a temperature-sensitive
helical structure that can rotate plane polarized light many thousands to millions
of times more than the equivalent thickness of the comparative chiral liquid.
Liquid crystals composed of rod-like molecules, such as those of the 4-alkyl4 -cyanobiphenyls prepared by Gray et al. (1973), figure 2a,b, are often called
calamitic mesophases. The nematic phase, where the molecules are depicted as
rods, which are on average parallel to one another (figure 2c), looks like a liquid
and flows like a liquid and has a milky appearance owing to light scattering,
as shown in figure 2d. LCDs, watches, calculators, lap-top computers, monitors
and televisions all employ nematic liquid crystals as the active switching element.
Rotation of the director (parallel order) in an applied electric field is the basic
mode of operation of the many varieties of LCDs. A majority of LCDs are in
fact chiral, as exemplified by the twisted nematic liquid crystal display (TNLCD)
shown in figure 2e (Fergason 1971; Schadt & Helfrich 1971).
When the structures of the molecules in the nematic phase are made to have
handed structures, i.e. chiral, see the steroidal system cholesteryl benzoate (CB)
in figure 3a,b, then the nematic phase itself becomes chiral, with the chirality
manifesting itself in a fluid, helical organization of the molecules, as shown in
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Perspective. Liquid crystals and chirality
(a)
(b)
(c)
(d )
(e)
director n
C
N
molecular
associations
orientational
ordering
quasiliquid
TNLCD
Figure 2. (a) The structure of 4-pentyl-4 -cyanobiphenyl (5CB), (b) molecular associations of 5CB
in the nematic phase, (c) the local structure of the nematic phase with the molecules shown as
rods (the average parallel ordering is called the director), (d) the milky appearance owing to light
scattering of the nematic phase at room temperature and (e) the twisted nematic liquid crystal
display (TNLCD).
(a)
O
(b)
(c)
(d )
(e)
O
chiral
molecules
chiral molecular
associations
helical
orientational
ordering
iridescent
fluid
thermometers
cosmetics
Figure 3. (a) The structure of cholesteryl benzoate (CB), (b) a space filling model of the chiral
material CB that exhibits a twisted structure, (c) the spiralling structure of the calamitic nematic
phase with the molecules shown as rods where the twist direction is dependent on the molecular
stereochemistry, (d) the opalescent appearance of the chiral nematic phase at room temperature
and (e) the use of chiral nematic phases in cosmetics.
figure 3c. When the pitch of the helix is similar to the wavelength of light, the
mesophase iridescently reflects incident light, as shown by the bulk chiral nematic
phase in figure 3d. The pitch of the helix can be affected by external fields, e.g.
electric, magnetic, mechanical, thermal, and thus the chiral nematic phase can
be used in sensing, e.g. strip thermometers, etc.
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J. W. Goodby
helical axis
O
O
O
O
molecular chirality
and point symmetry
H CH
3
space symmetry
C2 axis
molecular
layers
layers
molecules
form chirality
helical macrostructure
spiralling polarization
P
Figure 4. The three levels of chirality in the smectic C∗ phase, where the dynamically fluctuating
molecules are represented as ellipsoids. The exemplar chemical structure (top left) is shown in its
(S )-stereochemical form.
In organized fluid systems of calamitic nematic and smectic (layered) liquid
crystals, there are three levels of chiral complexity to consider. Consider the
example of the smectic C∗ phase (the asterisk denotes the smectic C phase is
chiral), where the rod-like molecules are tilted in soft or diffuse layers. The first
level is point asymmetry or structural dissymmetry associated with molecular
stereochemistry, where the stereochemical centres are designated as R or S (Cahn
et al. 1966), figure 4. The second level is related to broken space symmetry, where
the local molecular organization is asymmetric or dissymmetric (C2 in the case
of the chiral smectic C∗ phase and C2h for the non-chiral analogue). The broken
local environmental symmetries are associated with physical properties such as
ferroelectricity (Meyer et al. 1975; Meyer 1977), antiferroelectricity (Chandani
et al. 1989), electroclinism (Garoff & Meyer 1977, 1979) and secondary properties
such as pyroelectricity (Glass et al. 1986) and electrostriction (Patel & Meyer
1987). The third level of chiral complexity is form chirality associated with the
bulk organization of the molecules. This is usually manifested in the form of
helical macrostructures (designated as dextro, d, or laevo, l); in the case of the
smectic C∗ phase, the twist is generated by a preferred rotation of the tilt of
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5
Perspective. Liquid crystals and chirality
(a)
(b)
local structure of the
smectic C phase
local structure of the
smectic C* phase
local
dipoles
centre of
inversion
chiral molecules
as many molecules
pointing up as down
mirror
plane
two-fold
axis of rotation
two-fold
axis of rotation
local symmetry, C2h
local symmetry, C2
Figure 5. Symmetry breaking in the smectic C phase where the molecules are tilted in layers. The
figure shows the arrangement of just two molecules that can be used to represent the bulk phase: (a)
shows the organization and symmetry for non-chiral molecules, whereas (b) shows the arrangement
for chiral molecules.
the molecules about an axis perpendicular to the layers, whereas the helix in
the chiral nematic phase is caused by a lateral twist in the packing of adjacent
molecules. The helical macrostructuring can be associated with properties such
as helielectricity, thermochromism and electrochromism.
For applications of smectic C phases in displays, as there are as many molecules
pointing up as down in the layers, the local environmental symmetry elements are
a centre of inversion, a mirror plane and a twofold axis of rotation, so the phase
has C2h symmetry, as shown in figure 5. However, when the molecules are handed,
as shown in the right-hand section of figure 5, the symmetry is broken, resulting
in the presence only of a C2 axis, and the phase subsequently has C2 symmetry.
The electron distribution along the C2 axis is not symmetrical, and, therefore,
there is a spontaneous polarization associated with this arrangement. Application
of a DC electric field means that the direction of the spontaneous polarization
can be inverted and hence so too the molecular tilt. The response time for the
molecular reorientation can be in the sub-millisecond to nano-second regime, i.e.
10–100 times faster than the response times of the materials used in modern
televisions (approx. 5–10 ms), which are based on nematic technologies. Moreover,
the switched states are bistable and so only a voltage is required to effect switching
(Clark & Lagerwall 1980). The fast switching and bistable operation make such
device concepts (see figure 6 for an outline of the device construction) of interest
in combination with silicon back-planes, for use in projection applications and
spatial light modulators in order to create real three-dimensional, volumetric,
imaging systems, i.e. switchable holograms. Such light processors can be used in
amplitude modulation or phase modulation of light. With amplitude modulation,
very high-resolution professional monitors, and near-to-eye three-dimensional
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J. W. Goodby
polarized light
polarizer
glass
alignment
layer
Ps
–V
liquid crystal
+V
Ps
optic
axis
alignment
layer
polarizer
(crossed to top polarizer)
glass
dark state
light state
optical path
length
adjusted to give
a phase shift of
l /2
Figure 6. Construction of the surface-stabilized bistable ferroelectric display device showing the
two stable switched states, one with its spontaneous polarization pointing down (left), the other
with it pointing up, in response to the direction of an applied DC electric field.
imaging can be achieved. Compared with digital mirror devices, ferroelectric
liquid crystal devices can have considerably higher pixel density, leading to more
pixels on the same chip area and cost effectiveness for high pixel numbers.
Moreover, because of the fast switching speed of ferroelectric liquid crystals, using
frame sequential colour illumination (i.e. red, green, blue LEDs as backlights),
colour images can be realized using a third as many pixels used in conventional
displays. This would reduce the power consumption of a typical television display
down to the level of an energy-saving light bulb.
2. Frustrations in helical mesophases and the formation of new phases
of matter
In the chiral nematic phase, the director orientation changes smoothly along the
helix axis, and so too does the twist in the molecular packing, figure 7 (upper left),
but now consider what happens if the molecules become arranged into layers
at the transition to a smectic phase. For example, the smectic A phase has a
similar local organization of the molecules as the nematic phase, except that it
has layers where the molecules are arranged perpendicular to the layer planes, as
shown in figure 7 (upper right). At the transition, the lateral twist in the packing
orientations of the molecules would be expected to be in a direction along the layer
planes. However, the twist cannot overcome the strength of the layer ordering,
and so the twist is expelled at the phase transition. But what happens if the
layers are soft? In this case, the twist is only expelled over a defined wavelength,
and so the helical structure becomes discontinuous, and the rotation in the lateral
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Perspective. Liquid crystals and chirality
chiral nematic
transition
to smectic
smectic A
cool
competition between
twist and layering
screw dislocations
form grain boundaries
lb
twist
axis
Dq
block of
smectic
layers
ld
molecules
Figure 7. Transition from a chiral nematic phase to the layered smectic A phase via the formation
of a new phase of matter, the twist grain boundary (TGB) phase.
packing of the molecules becomes localized at defect sites. The defects allow for
blocks of defined size of the smectic A phase to be rotated relative to one another
through the introduction of rows of screw dislocations that form grain boundaries,
as shown in figure 7 (lower). This novel frustrated phase of matter was called the
twist grain boundary (TGB) phase (Renn & Lubensky 1988), predicted by de
Gennes (1972), and was brought into reality via the material, 14P1M7 (Goodby
et al. 1989a) shown in figure 8.
The screw dislocations, because of the frustrated helical structuring, permeate
the normal smectic A phase in the form of a lattice, which caused de Gennes
to draw a physical analogy between the structure of the TGB phase and the
vortex liquid phase that separates the normal and Abrikosov phases in type II
superconductors (Abrikosov 1957; de Gennes 1972). The relative analogies are
shown together in table 1.
In type II supercoducting systems, in addition to the Meissner effect, there
can be associated entangled and/or disentangled melted flux phases that are
accessible in fields slightly above Hc1 , as described by Gammel et al. (1987) and
Nelson (Nelson 1988; Nelson & Seung 1989). In liquid crystals, such as 14P1M7,
chiral-induced phases occur in the liquid at higher temperatures than the liquid
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J. W. Goodby
screw dislocations
spiralling
layer order
93.8
isotropic liquid
C14H29O
TGB phase
O
O
89.7
CH
O * 3
C6H13
O
14P1M7
polarization
P
P
P
P
42.5
53.4
P
antiferroelectric
ferrielectric
smectic C*
phases
P
ferroelectric
Figure 8. The phases and transitions (◦ C) of (S )-1-methylheptyl 4 -[(4 -n-tetradecyloxyphenyl)
propioloyl]oxybiphenyl-4-carboxylate, 14P1M7.
Table 1. The analogies between TGB phases in liquid crystals and Abrikosov phases in type II
superconductors.
type II superconductor
liquid crystal
normal metal
normal metal in a magnetic field
Meissner phase
Meissner effect
London penetration depth
superconducting coherence length
vortex (magnetic flux tube)
Abrikosov flux lattice
entangled/disentangled flux phases
nematic phase
chiral nematic (N∗ ) phase
smectic A phase
twist expulsion
twist penetration depth
smectic correlation length
screw dislocation
TGB phase
structured liquids
crystal phases. Optical rotary dispersion studies show that before the formation
of the liquid crystal state on cooling from the isotropic liquid, the liquid actually
becomes structured (Kang et al. 1995). This observation is supported by an
associated enthalpy determined via calorimetry. At higher temperatures above
the enthalpy, the liquid appears normal. Thus, materials such as 14P1M7 appear
to possess two liquid forms in addition to the TGB phase (Goodby et al. 1989a,
1989b, 1993), the lower temperature phase being driven by chiral interactions,
whereas the higher temperature phase is not.
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Perspective. Liquid crystals and chirality
9
Figure 9. A section through the stacked helical organization of fibrils in box-fish ‘scutes’ (adapted
from Bouligand 1969). The region highlighted by the dark lines shows a defect pattern often seen
in electron microscopy.
In addition to the TGB phase and the possibility-entangled/disentangled liquid
phases, 14P1M7 also exhibits two other chirally frustrated phases of matter at
lower temperatures with respect to the smectic C phase, as shown in figure 8
(Goodby et al. 1989b). The spontaneous polarization will try to minimize the
system’s polarity, and it does this by alternating the tilt direction from one layer
to the next. In doing so, the resulting phase becomes antiferroelectric. To get
from the ferroelectric to the antiferroelectric phase, it is possible to pass through
a phase or phases where the opposed tilts are not equal in number, but are in a
sequential order, e.g. two layers with molecules tilting to the left followed by one
to the right, with a repeat of this sequence. Other sequences, including a Devil’s
staircase phase, are also possible for this Ising model (Chandani et al. 1989).
Alternatively, it has been suggested that there could be a twist in the tilt on
passing from one layer to the next, such that three layers might give one full 360◦
rotation. This is called the clock model (Mach 1999; Hirst et al. 2002). These
intermediary states are collectively known as the ferrielectric phases. For nonchiral systems, the alternating tilted phase is still found, whereas the ferrielectric
equivalents are not. Thus, the formation of the ferrielectric phases appears to be
chirality driven.
Although twist frustrations are found at a molecular level, there are possibilities where they can be seen in Nature, for example, in a wide variety of
biological structures, including crustacean and insect cuticles, vertebrate bones,
chromosomes (Bouligand 1969) and box-fish scales (Besseau & Bouligand 1998).
Interestingly, Besseau & Bouligand (1998) have described the structures of boxfish ‘scutes’ as possessing twisted (helical) networks of collagen that they compare
to sheets of ‘plywood’, where the fibrils align parallel within superposed layers of
uniform thickness, with their directions changing from layer to layer, with each
showing a constant orientation, but with abrupt angular change at the transition
from one layer to the next (figure 9), i.e. similar in effect to that of the TGB phase.
Furthermore, certain beetle cuticles were shown to act as circularly polarizing
reflectors. Figure 10 shows photographs of the Christmas (scarab) beetle,
Anoplognathus aureus (Scarabaeidae, Rutelinae) viewed under (a) normal light,
(b) left-hand circularly polarized light and (c) right-hand circularly polarized
light. Clearly, the beetle reflects polarized light with a left-handed, anticlockwise,
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J. W. Goodby
(a)
(b)
(c)
Figure 10. Christmas (scarab) beetle, Anoplognathus aureus (Scarabaeidae, Rutelinae), (a) normal
light, (b) left-hand circularly polarized light, (c) right-hand circularly polarized light.
rotation. This effect, which is only found for Scarabaeidae beetles, was first
reported by Michelson (1911), who suggested that the cuticles could have helical
structures. Scientists working in the field of liquid crystals have always presumed
that this phenomenon must be related to the presence of chiral nematic phases
frozen into the structures of the cuticles. For example, Neville & Caveney (1969)
attributed the circularly polarized reflection to arrangements of ‘helical stacks’
of chitin microfibrils. Chitin, structure 1, is essentially a linear polysaccharide,
and although it is chiral, its ability to hydrogen-bond is likely to drive the
formation of parallel associations of the main chains, resulting in fibrils. However,
lateral twist between the chains, caused by chirality associated with the polymer
backbone, will compete with the hydrogen bonding in soft phases, and the
resulting frustrations could possibly result in the formation of TGB phases.
Indeed in a recent article, Seago et al. (2009) depicted the twisted structure as
stacks of microfibrils in a TGB-like arrangement.
CH3
OH
O
HO
NH
O
HO
O H
O
O
HO
n
NH
OH
O
CH3
Structure 1
3. Chirality-driven rotary motion
For some materials that exhibit TGB phases, helix inversions in the TGB phase
have been observed as a function of change in temperature (Takatoh et al. 1994),
see compounds of structure 2. This means that as the inversion point is
approached, the grain boundaries move, decrease in number, and some dissolve.
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11
Perspective. Liquid crystals and chirality
suspended
film
metal
plate
TGB
chiral nematic
smectic A
Figure 11. Schematic of a free-standing film of a smectic A phase that has been heated to the point
where a droplet of the chiral nematic phase forms on its surface. The layers of the smectic A phase
are in the plane of the metal plate.
At the inversion point, no grain boundaries would be expected to exist, thus the
associated screw dislocations are liquid-like and mobile. At the transition from
the TGB phase to the liquid, it is thought that the screw dislocations melt first
before the bulk liquid crystal phase, thereby creating a structured liquid, which
may be analogous to an entangled or disentangled flux phase predicted by Nelson
(1988) for type II superconductors.
F
H
O
CnH2n+1OCH2
H
O
C3H7
Structure 2
The mobility of the defect structure of the TGB phase can be further exemplified
through the observation of rotatory motion in TGB films. For example, compound
3 (Slaney & Goodby 1991) exhibits a blue phase–chiral nematic and smectic A
phase sequence on heating, but on cooling, a TGB phase is injected between the
chiral nematic and smectic A phases owing to supercooling, as shown in figure 11.
O
C9H19O
O Cl
O
O
Structure 3
∗
∗
SmC 121.0 SmA 144.6 TGB 145.4 N 145.5 BPI 148.6 BPII 149.9 BPIII 150.2 ◦ C Iso Liq
A freely suspended film of the material can be drawn across a 1–2 mm hole in
a metal plate while in its smectic A phase, such that the molecules have their
long axes perpendicular to the plane of the film, and the film is several hundred
molecular layers thick (figure 11, lower). As the nematic phase does not support
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J. W. Goodby
(a)
(b)
Figure 12. (a) Filaments forming on the surface of a free-standing film of a smectic A phase,
(b) the rotation of the droplet caused by the filamentary growth (in transmission, crossed polars,
magnification ×100).
film formation, when the material is heated in its smectic A phase until it just
starts to undergo a phase transition, droplets of the chiral nematic phase appear
upon the surface of the smectic film.
If a small temperature gradient is introduced across the film, at the transition
temperature when the chiral nematic phase returns to the smectic A phase, at the
edges of the droplets a TGB phase is injected. At the edges, spiral filaments of the
TGB phase grow, and because of the chirality of the material, the filaments start
to curve in a preferred direction, see upper part of figure 11. This growth causes
the chiral nematic droplet to rotate on top of the smectic A film. Rotational rates
were found to be tens of seconds. Figure 12a shows the filaments of a TGB phase
of a droplet of the chiral nematic phase starting to spin on the free-standing film
of the smectic A phase (Goodby et al. 2009a). In this photomicrograph (×100),
the filaments appear white, whereas the homeotropically aligned film appears
black under the crossed polars. Figure 12b shows a photomicrograph of the
rotating droplet as it approaches maximum velocity. The smeared-out filaments
are indicative of the speed (film speed American Standards Association (ASA)
400). The speed of rotation of the droplet shows that the interfacial viscosity
between film and droplet is relatively low.
The rotation is probably driven by a convective effect owing to the small
temperature gradient in the oven. As there is a slight hysteresis in the transition
temperatures, the material from the centre of the film is converted from a smectic
A phase directly into a chiral nematic phase. Cooling at the edges of the droplets
introduces the formation of a TGB phase, which subsequently converts back
to a smectic A phase, thereby completing the thermal cycle. The rotation is
driven by the formation of the filaments, whose direction of spiralling curvature
is dependent on the stereochemistry of the material.
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Perspective. Liquid crystals and chirality
4. Frustrated twist in molecular structures – molecular boojums
So far, we have seen how twist in condensed phases can be compromised via frustrations, which can lead to new phases of matter. Twist can also be compromised
at a molecular level, leading to a new concept of frustrated molecular structures.
Consider the example of a supermolecule possessing a spherical scaffold with
chiral mesogenic units laterally (side-on) linked to the scaffold, as shown, for
example, in structure 4 (Campidelli et al. 2006). The lengths of the rodlike mesogens are of similar size to the diameter of the scaffold, which is
composed of a [C60 ] fullerene cage with short methylene (−C6 H12 −) linking
chains. The mesogenic units are chiral by virtue of possessing asymmetric terminal
aliphatic chains derived from (S )-2-butanol. The linking units to the C60 core
are bifurcated, thereby allowing for the attachment of two mesogenic units per
binding site. Thus, 12 mesogenic units surround the spherical core of the scaffold.
Modelling shows that the mesogens cannot pack together around the fulleroscaffold without twisting. As they are chiral, the twist is in one preferred direction
around the scaffold, i.e. the director field spirals, hence a ‘molecular boojum’ is
potentially formed with defects at the poles, as shown in figure 13. The material
itself, because the mesogens are laterally attached, exhibits a chiral nematic
phase from a glassy state at 47◦ C to the transition to the liquid at 103◦ C. Thus,
the nano-structured supermolecular material has a chiral surface, which in turn
affects its abilities to self-organize as a ‘chiral object’.
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O O
O
O
O
O
O
O
OO
OO
O
O
O
O
O
O
O
O
scaffold
O
O
O
O
O
O
O
O
O
O O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
Structure 4
(Note that the conjugative double bonds of the C60 cage have been removed for clarity and
the structure of the material to the rear of the drawing is coloured grey.)
In addition to spherical supermolecular materials, with laterally attached
mesogens, that possess defect structures (figure 14a), a number of materials have
been prepared (Goodby et al. 2008, 2009b) that have related gross molecular
shapes. They include materials with helical topologies based on rod-like central
scaffolds, which can potentially possess molecular line defects (figure 14b),
and materials that have chemically differing faces (figure 14c). The packing
together of such nano-structured supermolecular systems may be through surface
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J. W. Goodby
molecular defect
spiraling
director field
spherical
scaffold
mesogens
molecular defect
Figure 13. Schematic of the chiral nano-particle.
molecular recognition processes, as in the formation of helical macrostructures,
or face-to-face interactions, as described for the packing of ‘Janus grains’
together (de Gennes 1991). Janus supermolecules may have two faces of strongly
differing chemical character, e.g. hydrocarbon–fluorocarbon, aromatic–aliphatic,
hydrophobic–hydrophilic, achiral–chiral. Structure 5 shows a Janus supermolecule
with one face being achiral and favouring smectic mesophases, and the other
face being chiral and favouring chiral nematic phases. Remarkably, this material
glassifies below zero and forms a liquid just above room temperature, with a chiral
nematic phase occurring between these temperatures.
Structure 5
g − 7.9 N∗ 38.2 Iso Liq
For large molecular systems with laterally attached mesogens, by virtue of
their topologies, it is possible to have more than two defects. Colloidal liquid
crystal systems having defect structures associated with nematic director fields
confined in spherical geometries have been previously envisaged (Nelson 2002;
Fernandez-Nieves et al. 2007; Bates 2008a,b); for example, figure 15 shows a
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Perspective. Liquid crystals and chirality
direction of
orientation
of mesogens
15
line
defect
Figure 14. Topologies for supermolecular materials: (a) the direction of the orientation of laterally
attached mesogens spirals around a spherical scaffold, (b) mesogen orientation spiralling around
a rod-like core and (c) a ‘Janus’ supermolecular architecture where one hemisphere may be
chiral and the other not, thereby giving different molecular recognition surfaces. Adapted from
Goodby et al. (2009b).
Figure 15. An example of a nematic director field confined in a spherical geometry where there are
four defects. Adapted from Goodby et al. (2009b).
nematic director field confined in a spherical geometry where there are four
defects. Nelson (2002) suggested that such systems may be created in ABA
triblock copolymers (i.e. segment A–segment B–segment A), and that large-scale
structures and condensed phases might be created through linking points at the
defects by using ligands (Vitelli & Nelson 2006). In a similar way, it may be
possible for large-scale organization of supermolecular materials via interactions
between the defect sites of neighbouring molecules.
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J. W. Goodby
5. Frustration of twist in sensing chirality and determining enantiomeric excess
In this discussion, it has so far been presumed that the molecules in each example
are of one hand, i.e. they are defined as right-handed (R) or left-handed (S ) by
application of the rules of Cahn et al. (1966). However, this is rarely the case,
and most chiral materials are composed of unequal mixtures of left- or righthanded molecules (enantiomers). The relative proportions of left- to right-handed
enantiomers in a mixture are termed the enantiomeric excess (ee). The percentage
ee can be defined as:
%ee =
no. of moles of enantiomer A − no. of moles of enantiomer B
.
no. of moles of both enatiomers
(5.1)
In terms of materials whose molecular structures possess one seterogenic centre
of defined spatial configuration (R or S ), ee is given by
R−S
ee =
× 100
R+S
S −R
or ee =
× 100.
R+S
(5.2)
Thus, for a material that exhibits a helical macrostructure in a condensed
mesophase, e.g. a chiral nematic phase, the pitch length of the helix is proportional
to enantiopurity. At zero ee, the pitch length will become infinite, and at 100 per
cent ee, the pitch will reach a minimum value. Assuming a linear relationship,
the pitch of the helix will be inversely proportional to the ee. The measurement
of enantiopurity of a material can be achieved using either nuclear magnetic
resonance spectroscopy with chiral shift reagents, chiral gas chromatography,
chiral high-pressure liquid chromatography or optical rotary dispersion. However,
these methods are not generally applicable to all varieties of materials, and their
accuracies are often no better than ±2%.
As noted earlier, liquid crystal systems have advantages in amplification of
physical properties, it is therefore possible that liquid crystal systems might also
be capable of quantitatively determining enantiopurity as well as qualitatively
sensing chirality. For example, twist can also be induced into nematic phases,
where the molecules are not handed, simply via surface anchoring. This technique
is used in practice in the construction of the TNLCD shown in figure 2.
In the TNLCD, the surfaces are coated with polyimide, which is then
unidirectionally buffed. The direction of the buffing, i.e. the alignment direction
for the molecules, is set at right angles to one another for the two inner
surfaces (top and bottom). A nematic phase, composed of non-chiral materials
such as the commercial mixture E7 (Raynes et al. 2009), acting as an elastic
fluid, twists through a quarter helix from one surface to the other, as shown
in figure 16a. As the device constraints are energetically degenerate, left- and
right-hand twists are possible, and compete with each other, to give a domain
structure with disclination walls between the left- and right-handed domains
(figure 16b). In display devices, the two twist domains degrade contrast, which is
solved by incorporating a small amount of a chiral dopant into the liquid crystal,
thereby favouring one domain over the other, and as a consequence producing a
monodomain.
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17
Perspective. Liquid crystals and chirality
white
light
(a)
polarizer
polarized light
disclination line
glass
left-hand
helix
1/4 twist
right-hand
helix
1/4 twist
rotation of
plane of
polarization
by 90°
rotation of
plane of
polarization
by 90°
molecules
achiral host
liquid crystal
e.g. E7
spacers
disclination
glass
polarizer
(c)
(b)
left-hand
domains
right-hand
domains
E7 host mixture
doped with
commercial
ibuprofen
curved
disclination lines
spacers
E7 host mixture
non-chiral
Figure 16. (a) A twisted nematic cell containing a non-chiral host nematic material showing
competing twist domains, (b) looking vertically at the cell, the defect lines appear straight for the
host mixture E7 (×100) and (c) the left- and right-hand domains for E7 doped with commercial
‘racemic’ ibuprofen (×100), the curved disclination lines demonstrate that the sample of ibuprofen
is really chiral. Adapted from Raynes et al. (2009).
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J. W. Goodby
This concept can be turned on its head, for instance, Raynes et al.
(2009) demonstrated that the twisted nematic (TN) display device could
be used as a very sensitive instrument for examining molecular chirailty.
Without a chiral dopant, the non-chiral nematic material in the device
exhibits straight defect lines that are pinned to the thickness controlling
spacers in the display, as shown in figure 16b; however, for liquid crystals
containing very small amounts of a dopant, the defect lines curve. The radius
of curvature is a measure of the helical pitch and of the enantiopurity
of the dopant, and hence the direction of the curvature directly relates to which enantiomer is in excess. Thus, in practical applications, this device
concept can be used to quantify the ee and to qualitatively investigate if a material
is chiral or not. Obvious candidates for investigation are chiral pharmaceuticals,
where the degree of chirality is important to drug efficacy. As de Camp noted
‘Regulatory guidelines are interpreted for applications for the approval of a
pure enantionmer in which the racemate is marketed, for the approval of
either a racemate or a pure enantiomer in which neither is marketed, and for
clinical investigations to compare the safety and efficacy of a racemate and its
enantiomers. Examples of the basis for such regulation are drawn from historical
situations (thalidomide and benoxaprofen) as well as currently marketed drugs
(arylpropionic acids, disopyramide and indacrinone)’ (de Camp et al. 1989). So,
when is a drug enantiomerically pure (ee = 100) and when is it racemic (ee = 0)?
Figure 16c shows the qualitative result for commercially purchased, racemic,
ibuprofen that had been added to the commercial nematic liquid crystal mixture
E7, that is composed of non-chiral molecules. Racemic ibuprofen, which would be
expected to be composed of a 50–50 mixture of left- and right-handed molecules,
clearly shows that the bounding lines between the domains are curved, and
therefore ibuprofen on this basis is chiral (optically active). One might think that
the surfaces of the upper and lower plates may not have been at right angles,
but it is also possible to off-set the glass plates, thereby biasing one domain over
another; however, the results are the same, even for off-set geometries.
This interesting result for ibuprofen raises a further question; if ibuprofen had
been prepared by standard chemical methods that did not involve stereochemical
transformations, how did the material become weakly chiral? Thus, the ‘TN
device sensor’ can be used to investigate the mechanisms of chemical reactions
by which materials are prepared.
For example, the liquid crystal material of structure 6 was prepared in its
chiral (both enantiomers) and racemic forms. In its chiral forms, the material
exhibits smectic A∗ and smectic C∗ phases, and therefore should possess reduced
C2 symmetry in the smectic C∗ form where the molecules are tilted in layers,
as shown in figure 4. Rotational C2 axes are polar, and so the phase should
be expected to be ferroelectric, which was demonstrated to be the case. By
contrast, the smectic C phase composed of a racemic mixture should have
C2h symmetry and be non-ferroelectric and exhibit dielectric switching. The
material was prepared starting from commercial 2-octanol, which is available
in both chiral forms and the racemate. Additionally, the racemate can be
prepared from 2-octanone by reduction with sodium borohydride. Subsequent
esterification with protected hydroxybenzoic acid, as shown in figure 17, yields
an important intermediate in the preparation of structure 6. It is possible to
prepare the intermediate ester by two different methods, i.e. the Steglich approach
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Perspective. Liquid crystals and chirality
Mitsunobu esterification
Steglich esterification
H
CH3
PO
COOH
potential
source of
chirality
H O C R
PO
COOH
H O C R
CH3
DMAP
EDAC
HO R
H
CH3
R OH
H
starting with equal amounts
of enantiomers,
(a racemate)
then after esterification, the
product should be a
racemate,
as nothing changes at
the stereogenic centre
COO
PO
CH3
attack
R
H
C R
COO
PO
CH3
C R
CH3
O
O
O (CH2)11O
H O C R
CH3
DIAD
PPh3
H
CH3
H
H
H
H O C R
O
O
O
CH3
C6H13
H3C
OH
H
attack should be equal
at either face,
therefore the product
should be racemic
should the attack be unequal,
the product will have some
degree of chirality
Structure 6
Figure 17. Comparison of the preparation of compound 6 via the synthesis of an intermediate ester
using Steglich and Mitsunobu conditions. In the scheme shown, P is a protecting group and R is
C6 H13 −.
using the reagents 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDAC) and
dimethylaminopyridine (DMAP), or via the Mitsunobu method that uses
triphenylphosphine (PPh3 ) and diisopropyldiazodicarboxylate (DIAD). The
Steglich method retains the stereochemistry of the 2-octanol, whereas the
Mitsunobu approach allows for the possibility of inversion at the steroegenic
centre. For the chiral starting 2-octanols, the ester intermediates were found
to be chiral using the TN method described above. However, for the racemate,
from both the starting racemic 2-octanol and the reduced form of 2-octanone, the
Mitsunobu method yielded chiral products, with enantiopurities of approximately
2 per cent. Following through the synthesis to the final products of structure 6,
the results show that all of the materials prepared via the Mitsunobu reaction are
chiral and ferroelectric, whereas the preparation of structure 6 via the Steglich
reaction gave a racemic product for the preparations starting with racemic 2octanol, and chiral products for the materials starting from the chiral 2-octanol
enantiomers. Thus, there appears to be chiral induction at the esterification
stage using the Mitsunobu method. This was confirmed in the final product,
structure 6, which showed ferroelectricity in the material starting from racemic
2-octanol with the preparation proceeding via the Mitsunobu method using
diethylazodicarboxylate (DEAD) in place of EDAC (Cowling et al. 2005a,b).
Why the enantiopurity should increase via the Mitsunobu reaction is not clear, it
may be that a chiral by-product of the reaction has been generated. However, in
comparison to decreasing enantiopurity upon reaction, increasing enantopurity
starting from the racemate is very unusual. Nevertheless, these results show
that chiral liquid crystal technologies can act as incredibly good sensors via
chiral amplification using either the bending of the disclination lines in twisted
nematic devices or by obtaining ferroelectric responses from smectic C phases.
As a consequence, these methodologies have potential for the investigation of
chemical reaction pathways and mechanisms.
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20
J. W. Goodby
Although the discussions in this perspective article are concerned with
materials that possess molecules that are rod-like and chiral, it is also possible
to generate broken symmetries with systems where the molecules are bent in
shape, i.e. ‘banana phases’. Again, analogous phases to the TGB, ferreoelectric
and antiferroelectric phases for rod-like systems are found, but in this case, these
phases have domains of left and right twist/spontaneous polarization. Because
of their lower fluidities, relative to calamitic systems, the left- and right-hand
domains are stable. This branch of liquid crystals represents another collection
of phases that are stabilized by frustrations, this time by bend rather than twist.
Furthermore, frustrated cubic phases, such as blue phases, smectic blue phases
and quasi-crystals have not been touched upon, but they too represent yet further
classes of novel chiral mesophases.
From the point of discovery of thermotropic liquid crystals in 1880, broken
symmetries in organized fluids have produced a rich variety of fascinating and
novel phases of matter, many of which have only been discovered over the last
20 years. Our abilities to unlock the structures and properties of such mesophases
have led to rapid and practical innovation, which has been used to underpin many
of our everyday applications such as flat screen displays.
The author would particularly like to thank Prof. Raynes FRS and Drs Saez and Cowling of the
University of York for their collaborative support, Drs Bradbury and Oxford (York University) and
Di Logumov (Manchester University) for their photographs of scarab beetles, and present and past
research students and research fellows for their inputs into this work. He is also grateful to AT&T
Bell Laboratories, where he was employed, and to DERA (now QinetiQ), Kingston Chemicals Ltd,
Merck Chemicals, The Leverhulme Trust and the EPSRC for financial support.
AUTHOR PROFILE
John W. Goodby
John Goodby studied for his doctorate in liquid crystals
at the University of Hull under the guidance of Prof.
George Gray CBE, FRS before moving to AT&T Bell
Laboratories, where he became Supervisor of the Liquid
Crystal Materials Group. After nearly 10 years in the
USA, he moved back to the UK to become the Thorn
EMI-STC Reader in Industrial Chemistry at Hull. After
2 years, he became the Head of the Liquid Crystals and
Advanced Organic Materials Group, and subsequently
the Head of the School of Chemistry. Currently, he is
Chair of Materials Chemistry at the University of York.
His research is focused on directed self-organization and self-assembly in materials
through nanophase segregation, the development of materials for bistable displays, and
polymers and dendrimers for photonics and gels for use in biomedical applications. John
Goodby was elected a Fellow of the Royal Society in 2011.
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Perspective. Liquid crystals and chirality
21
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