10 October 2011
The nematic phase of liquid crystals (LC), used in most LC display applications, is a fluid state formed by orientationally ordered molecules. The direction of their alignment, and hence the overall optical response of the material, is easily modified by the application of an electric field
and elastically relaxes back to a well-defined off-state when the field is removed. It has been recently shown that hybrid materials formed by nematic LCs incorporated in complex micro-structured porous matrices are often capable of indefinitely retaining the alignment direction imposed by an electric field. Such multistability is ultimately due to the interactions of the porous material with the lines of topological defects that develop within the confined nematic. Controlling the defect lines and their interactions is crucial to the design of materials whose optical properties
are electrically driven but spontaneously preserved.
Francesca Serra, Marco Buscaglia, and Tommaso Bellini*
Dipartimento di Chimica, Biochimica, Biotecnologie per la Medicina, Università di Milano, Milano, Italy
Current liquid crystal displays exploit the anisotropy, flexibility, and elasticity of the long-ranged molecular ordering of the nematic phase. Because of the intrinsic fluidity and the dielectric uniaxiality, the orientation of a nematic liquid crystal (NLC) within a pixel is readily controlled by an electric field E1. In turn, the direction of molecular alignment affects the polarization state of transmitted light, thus determining the on and the off state of each pixel. Upon removal of the field, the weak elasticity of nematics drives the pixel back to its off-state, which is a stable, unique, and well-defined state determined by the cell surface alignment. In Fig. 1a and 1b two of the most common schemes used in commercial displays are shown: twisted nematics 2(TN) and in-plane switching 3, 4(IPS), respectively. An alternative concept for display technology is the use of bistable or multistable materials, in which the electric field is needed to switch the system between two or more states that remain stable without the need for a continuous supply of energy. Several solutions for nematic-based bistable devices have been investigated over the last 30 years, without offering, so far, a practical alternative to the dominant technology used in conventional flat displays. However, the e-book concept and similar applications requiring a refreshable printed paper-like display without an embedded illumination source, is stimulating interest in new multistable display concepts.
Despite their differences, all of the LC-based bistable devices that
have been proposed make use of flat cells whose surfaces couple to
the LC to frustrate the development of uniform molecular alignment.
Bistability emerges when the nematic can satisfy the external
constraints with (typically) two different configurations that cannot be
transformed into each other by continuous rearrangement of the local
alignment. These two states should be topologically distinct, so that
the thermal energy cannot induce a state switch.
While the first bistable displays were based on special LC molecules,
like ferroelectric LCs5
, or used phases with complex symmetry, like the
, the first generation of bistable devices based on NLCs
was developed in the 90s by Durand and co-workers7,8
(see Fig. 1c). In
that scheme, the frustration was obtained in a cell with slightly tilted
planar parallel boundary conditions by doping the NLC with a small
amount of chiral molecules9
to induce a spontaneous twist distortion
in the nematic ordering (chiral nematic phase). In this way, the NLC
can match the surface conditions by adopting either a twisted or a
slightly splayed configuration, which are both stable and long-lived.
Hydrodynamic coupling to the LC director (the preferred direction of
orientation) enables switching between the two states by using electric
field (E) pulses with different shapes: slowly removing the electric
field drives the nematic to the unwound, splayed state, while abruptly
removing the field leads to the twisted state.
A second generation of chiral nematic-based bistable devices was
developed in the late 90s10-14
(see Fig. 1d). In this case, the boundary
conditions and LCs were chosen so that a uniform helix across the
cell spontaneously developed, with a pitch low enough to reflect
the illuminating light through a Bragg-like mechanism 1
. Applying an
electric field parallel to the helix direction induces a transition to the
so-called focal conic state, where the uniform helical order is disrupted,
and helical arrangements develop locally in random orientations. In this
state, the Bragg reflection is suppressed and the cell becomes rather
transparent, letting the transmitted light be collected by an absorbing
layer on the back of the device (Fig. 1d). Whether the system relaxes
back in the reflecting uniform twist phase or remains stuck in the focal
conic state again depends on the kinetics of the field removal. Fujitsu’s
FLEPia reader is based on this technology (Fig. 1f15
), as well as the
Binem display by Nemoptic.
Frustration, and therefore bistability, can also be induced through
surface patterning. The zenithal bistable display (ZBD)16-20
, the most
famous of this class of device, uses thin cells, where one surface has
a complex morphology (such as the saw-tooth shape in Fig. 1e) and
forces perpendicular molecular anchoring. A commercial example of this
is the Epop display by ZBD, shown in Fig. 1g21
. Here, once more, the LC
has two possible long-lived states that can be switched using E pulses of
different shapes. The different optical properties of the two states can
be used in the design of bistable pixels, becoming light and dark when
between crossed polarizers. Extensions of this concept to three-state
cells have been also proposed22
The explanation of why the configuration shown in Fig. 1e is a
stable state relies on an understanding of the topological defects,
i.e., regions where the nematic ordering is not define d1
(red and blue
dots in the figure), which develop in the cell. As will be explained, the
geometrical constraints of defects represent a fundamental descriptor
of confined liquid crystals.
Fig. 1 Mono and bistable nematic displays. (a,b) Schemes of common monostable displays: (a) TN and (b) IPS. Black dashes represent NLCs, indicating their average
orientation. (c-g) Bistable NLC devices, based either on (c, d) chiral phases or on (e) patterned surfaces. Scheme of the chiral nematic ordering is shown in violet. Some
bistable displays are commercially available, such as (f) the flexible e-paper by Fujitsu (courtesy of Fujitsu) and (g) the Epop display by ZBD. (Courtesy of ZBD)
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Memory effects in disordered nematics
A new perspective on the notion of topologically distinct metastable
states is offered by nematics incorporated in micron-sized pores of
solid matrices. This class of system is optically interesting because they
are generally extremely turbid, but become clear when an electric field
is applied. Optical turbidity, τ, represents a intensive property of the
material, corresponding to the inverse mean free path that the photons
can travel within the material before being scattered. A large turbidity
indicates a short photon mean free path and thus a small transmitted
intensity. The large turbidity of these systems is a consequence of the
intrinsic birefringence of nematics and of the orientational disorder
induced by their interactions with the surfaces of the host matrix.
The confinement of NLC in micron-sized pores results in big spatial
fluctuations of the refractive index on the length scale of optical
wavelengths, a property that produces a large scattering cross section
for light, as happens in white materials, like paper, fabric, and paint.
By applying a strong enough electric field, orientational order is forced
along the field direction, and the refractive index thus becomes more
uniform and the scattering cross section decreases.
It was observed that some of these systems show memory
: after the electric field is removed, the light transmittance
does not grow back to its original value (Fig. 2a). This means that the
field-induced orientational order is partially recorded in the system. This
memory can be erased by heating and cooling, transitorily melting the
nematic order. From their study in the early 90s of nematics dispersed
in polymer structures with different morphologi es 25,26,28
and co-workers showed that disconnected pores (such as in the scanning
electron microscope photograph of Fig. 2c, schematized in Fig. 2e) do
not yield significant memory effects. These effects are instead observed
in (some) cases where the pores form a multiply connected structure in
which the NLC alignment is continuously distorted, as sketched in Fig.
2f. In Fig. 2b the behavior of NLC embedded in polymeric matrices with
disconnected (Fig. 2c) and connected (Fig. 2d) pores are compared by
plotting the light transmittance of these structures during (full dots) and
after (open dots) the application of an electric field as a function of the
field ampli tude28
. In the interconnected structures, after the removal of
the field, the transmitted intensity decreases only partially. It would thus
be useful to maximize this effect and have materials that, once made
transparent (or opaque) by an external field, would permanently preserve
that state. The problem is that the amount of memory displayed by
different structures is difficult to predict. Our research group has studied
the behavior of nematics incorporated in the disordered porous cavities of
Millipore filter membranes (Fig. 2h) or colloidal gels made of aggregated
(filled nematics, Fig. 2i). These structures differ
in chemical composition, in morphology, and in their characteristic size.
However, both confining structures lead to similar memories after the
removal of E, as shown by the field dependence of the turbidity reported
in Fig. 2g. By means of appropriate scattering models33
turbidity, τ, can be used to estimate the overall molecular orientational
order of the LC within the porous network, as expressed by the nematic
order parameter Q (Q = 0 indicates no ordering, while Q = 1 indicates
. In the most relevant cases, a simple approximate
linear dependence can be derived: Q ≈ 1 – τ/τ
, where τ0
is the turbidity
of the unperturbed s ystem31
Fig. 2 Memory effects in disordered nematics. (a) Transmittance, T, as a function of the applied field. (b-d) Transmittance in polymer-dispersed nematics in (c, red)
disconnected and (d, violet)connected cavities. (e, f) Schematics of NLC orientation in cavities. (g) Turbidity, τ, of nematics embedded in disconnected pores
(red), in (h, blue) Millipore filters and (i, green) filled nematics. τ = −ln(T)/d, d being the sample thickness. Scale bar in (c), (d), and (h) is 10 μm, and in (i) is
0.2 μm. (b-d) A dapted from28
. (h) Courtesy of Dr M. Carpineti.
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The memory effects described in Fig. 2 are scientifically interesting
but not significant enough for applications. Given the complexity of the
problem, the optimization of NLC memory on the basis of the structure
of the microporous confining material has to be approached through
3D computer simulations. This strategy, which lets us look inside the
structure of nematics in these complex environments, has recently led
to new insights on the emergence of memory in these systems.
The secret ingredient: topological defect lines
As it turns out, memory is better understood when topological
defects are included in the description of NLC confined in porous
matrices. Defects are points or lines in the proximity of which the
nematic order is los t34,35
. Topological defects typically arise within the
nematic fluid when boundary conditions do not allow the formation
of uniform ordering. This phenomenon is exemplified in Fig. 3, which
shows the necessity of a topological defect in a brick-made apse of
a Romanesque church: the boundary conditions, i.e., the orientation
of the bricks along the perimeter of the apse, cannot be smoothly
joined with aligned bricks. In this condition, both in the apse (Fig. 3a
and 3b) and in nematic s36
(Fig. 3c), a topological defect (red dot in
the figure) is formed. Defects concentrate distortions, at the same
time enabling the surrounding material to be locally ordered. In real
3D nematics, topological defects often develop in lines (Fig. 3d) that
cannot terminate within the nematic bulk, and are thus typically closed
in loops. In transient situations, the application of an external field
leads to line defects expanding in plane defects, before nematic order
The role of topological defects in the behavior of nematics confined
in complex geometries has been elucidated by computer simulation
based on the Lebwohl-Lasher (LL) spin lattice model41,42
nematic LCs. This is a simple approach in which nematic order develops
in a system of freely orienting spins on a lattice as a consequence of their
mutual interaction. A first set of LL-based simulations was performed by
mimicking the effect of disordered and interconnected confinement by
adding a strong and randomly oriented field acting on a randomly chosen
fraction of the spins43
. In this way, a portion of the spins is constrained
in disordered orientations, as are the molecules in contact with the solid
interface in real systems, while the rest of them try to find a compromise
between the disordering forces and their “natural” orientation
ordering. This random-field model is conceptually very simple and has
demonstrated that nematics with random disorder are populated by a
large number of defect loops, whose length and trajectory characterize
the difference between the metastable states. In this approach, the
system becomes rich with pinning sites for the defect lines. The outcome
is a network of defects resembling a 3D “connect the dots” game, in
which however the dots (i.e., the pinning sites) can be connected in a wide
variety of ways (each corresponding to one of the multiple metastable
states). The various options of connectivity can be switched by sufficiently
strong external fields acting on the locally oriented nematic, which in turn
is coupled to the geometry of the defect lines.
Random-field computer simulations have thus unraveled an
essential and intriguing characteristic of NLCs confined in porous
media. In addition to the “real” components of these hybrid materials
(the porous matrix and NLC), a third, immaterial constituent is present
Fig. 3 Examples of topological defects. (a,b) Disclination defect in the apse of “Rotonda di san Lorenzo”, Mantova, and (c) in an NLC: the molecular alignment
is made visible by polymer bundles36
. In 3D NLC, disclinations are arranged into (d, red line) lines which are found near microspheres (e, f, g) immersed in a
NLC. (h,i) Topological defects are also predicted by computer simulations of NLC incorporated into bicontinuous regular or random lattices. (c) Courtesy of
Dr I. Dierking. (e,f,g) Reprinted figure with permission from45
. © 2007 by the American Physical Society. (h,i) Courtesy of Dr T. Araki.
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in the system: the network of topological defect lines, which determine
the variety of metastable states and their stability.
Crocheting complex structures with defect lines
The analysis of disordered nematics based on random-field models is
interesting from a fundamental standpoint, but offers no tools to design
real structures that would maximize multistability and memory effects.
Inspiration about how to approach the problem from a different angle is
presented by an independent set of experimental observations, theory, and
computer simulations, showing how topological defects arise when smooth
regular surfaces favoring perpendicular NLC alignment (i.e., no randomness)
are inserted in a nematic. In particular, many studies have been devoted
to NLC hosting microspheres44-52
. Interestingly, even in the simple case
of two spherical microinclusions, it is found that the overall topological
constraints exerted by the combined surfaces on the NLC can be matched
by more than one choice of defect line trajectory: the two states in Fig. 3e
and Fig. 3f, are topologically distinct, although the energy barrier between
the two metastable states is rather low. Topological defects can mediate
colloidal assembly when more spherical inclusions are considered (Fig. 3g).
A recent experimental study51
has shown that it is indeed possible to tie
and untie knots of defect lines around colloidal particles, thus showing that
defect lines can be effectively treated as real objects and manipulated.
A recent LL-based computer investigatio n53
has studied the topological
state of nematics incorporated in bicontinuous solid structures having
various geometries, both periodic and disordered (Fig. 3h and 3i). This
analysis confirms that bicontinuous porous structures with perpendicular
surface anchoring of the NLC molecules induce the formation of a large
number of defect loops, a fraction of which encircle the solid portions.
A quantity which is commonly used to define topological states is
the topological charge, M. More technically, a topological charge can
be assigned to every topological defect and it represents the angle by
which the nematic director “turns” around the defect, divided by 2π. In
the example shown in Fig. 3b and 3c the nematic director makes a 180°
angle around the defect, therefore the topological charge is ½. Rigorous
definitions of topological charge can be found elsewhere54,55,34
. In the
simple cases, for porous systems with perpendicular boundary conditions,
the modulus of the topological charge equals the number of elementary
defect loops. The amount of topological charge in a confined NLC
depends on the symmetry of the porous network. This is demonstrated
in a recent experimental and theoretical analysis56
of the topological
state of NLCs in porous networks such as the 3D cubic arrangement of
cylindrical channels shown in Fig. 4a. By viewing these structures as a
combination of elemental units as in a jigsaw puzzle, it can be shown that
the number of defects (more rigorously expressed by the total topological
charge) depends on the valence v of the nodes of the network, i.e., the
number of channels merging in the vertices of the network (nodes of
valence 3 and 4 are shown in Fig. 4b). For example, the prediction
for a bicontinuous cubic structure (as the one of Fig. 4a), obtained by
combining nodes of valence 6, is of two defect loops per unit cell. Ten
years ago Kang and coworkers57
studied NLCs in the interstitial spaces
of a colloidal crystal of closed packed microspheres (face-centered-cubic
lattice) with perpendicular anchoring. In order to calculate the topological
charge for such a complex geometry, it is important to identify a relevant
unit node, as the one sketched in Fig. 4d. In this structure, the prediction
of ref erence 56 is of five elementary loops per unit cell. Similarly, with
the formula reported in Fig. 4c, it is possible to calculate the topological
charge per unit cell for lattices with various symmetries.
It is expected and found that NLCs in bicontinuous porous matrices are
populated by defect lines that permeate the structure, adopting one of the
many possible choices of trajectories. Many of these loops are stuck to their
trajectories. Indeed, changing the path of loops that encircle solid handles
of porous matrices as in Fig. 3h and 3i would require “cutting” the loops
and reconfiguring large portions of the nematic order. This operation costs
much more energy than is provided by the thermal noise, and gauges the
magnitude of the energy barriers that separate the distinct configurations.
Moreover, the presence of the solid structure makes these loops irreducible
Fig. 4 3D network filled with NLC. (a) Network of glass microfabricated channels (diameter 30 μm). (b) Detail of the structure and combinable elements of the
structures. (c) Formula for topological charge and table with the topological charge of unit cells with various symmetries: cubic, body-centered-cubic (bcc), facecentered-cubic (fcc) lattices, and random porous network obtained by spinodal decomposition (SD rand)56
. (d) An FCC-type structure made from closely packed
spheres and detail of LC alignment in the interstice. Reprinted figure with permission from57
. ©2001 by the American Physical Society.
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by preventing them from contracting to point defects; quite different, for
example, from defect loops around spheres that can slide along the sphere
and contract to a point. The irreducible character of the loops combined
with the importance of the energy barriers is the cause of the multistability
of NLCs confined in smooth bicontinuous porous media.
The basic symmetry (random, cubic, hexagonal, random) of the porous
matrices and their detailed morphology have relevant roles in determining
the amplitude of the memory effects and in the kinetic response of
these hybrid systems. Fig. 5 shows the trajectories of defect lines within
porous media having periodic and random geometry, as obtained (i) by
cooling the system into the NLC phase with no electric field applied
(Figs. 5a and b), a condition in which the NLC is locally ordered but
globally disordered, and, (ii) after the application and removal of an
electric field (Figs. 5c and d). Figs. 5e and f show, for the two structures,
the global orientational order of the NLC molecules, as expressed by the
order para meter Q, before, during and after the application of the field. It
is found that random porous media, such as those provided by Millipore
filter membranes, have weak memory (the ordering forced by the field is
largely lost as the field is removed) and very slow relaxations, reminiscent
of a glassy behavior31
. On the contrary, bicontinuous cubic matrices
are found to maximize memory and minimize the response time. The
comparative analysis of these two structures and their behavior indicates
that the improved performances of the bicontinuous cubic structure
are due to the optimized combination of symmetry and local curvature.
The electric field forces defect loops to be localized along the black lines
in Fig. 5h, i.e., where the pore surface is laying parallel to the field. As
the field is removed, defects modify their paths to minimize the elastic
energy of the nematic, typically moving close to the areas with the largest
negative Gaussian curvature, marked by magenta lines in Fig. 5i. In the
case of the bicontinuous cubic, the local curvature of the surface favors
the defect lines being held along the same paths where they are driven by
the electric field, thus largely maintaining the alignment induced by the
How good could it get?
The performance of bicontinuous cubic matrices in terms of retaining
memory are much better than those of the random porous network (see
Fig. 5g) and better than other pore g eometries49
. From the simulation
studies it appears that the topology and the geometry of the hosting
matrix determines the memory properties of the NLC. The upcoming
challenge is to experimentally realize porous materials with tailored
geometries to be exploited in bistable devices. The recent improvement
of 3D microfabrication technologies53
, such as soft lithography,
self-assembly, femtosecond laser microfabrication, and two-photon
polymerization are making the exploration of microconfined nematics
progressively viable and enabling the downsizing of single pixels.
E-paper seems to be a suitable application for these composite
materials. The ideal e-book visualization should have the characteristics
of printed paper, be readable in all ambient lights, and permanently hold
images until rewritten. Current LC technologies are not used for e-book
applications because of their poor display in strong ambient light and
their significant energy consumption. The low consumption of the new
composite materials is granted by their multistability. Moreover, choosing
the geometry appropriately also leads to a lowering of the threshold field
that is needed to switch the device between its metastable states.
Confined NLCs also have significant potential in matching the other
criteria. The readability of paper comes from its strong turbidity. Confined
nematics are quite promising in this respect since they enable high levels
of turbidity to be achieved. Specifically, the fact that turbidity is produced
by the distortion of a highly birefringent uniaxial material, such as the
Fig. 5 Memory effects in (yellow box) random and (cerulean box) cubic porous structures (computer simulations). Defect lines (red) before (a,b) and after (c,d)
field pulse. (e,f) Average molecular ordering, Q, evolving with the number of Monte Carlo cycles (MCC). (g) Q during (full symbols) and after (open symbols)
field application vs field amplitude. The superior memory of the cubic structure is understood by comparing the defect trajectories in (h) high field to the (i) loci of
largest negative Gaussian curvature. Adapted from53
(d) (h) (i)
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nematic, allows values of turbidity of among the highest possible in any
material to be reached31
. Therefore cells of confined nematics as thin as a
few tens of microns could provide the white state necessary for efficient
visualization in ambient light illumination.
At the same time, the confined NLC-based device could be
switchable from a transparent state to a turbid one. This can in principle
be done using various strategies. One approach is to use electric fields
perpendicular to the cell to induce alignment, and thus transparency,
while using in-plane electric patterns to generate distortions.
Another strategy is to employ dual-frequency materials, a promising
development in NLC-based display technology59,60
. The dielectric
anisotropy of these materials changes sign with frequency, thus enabling
switching between the transparent (axial alignment) and the scattering
(degenerate planar alignment) states using the same electrodes.
The value of frustration and defects
In this article we discussed how confinement generally leads to a
conflict between the long-ranged orientational ordering of nematic
LC and the orientational constraints exerted on the molecules in
contact with the surfaces of the porous matrix. This frustration of the
NLC ordering results in the loss of a well-defined ground state, which
is instead replaced by a multiplicity of metastable 3D patterns of
alignment. In this way, metastability can be achieved by functionalizing
the nematic via geometric confinement.
Quite interestingly, the behavior of these two-component hybrid
materials formed by nematics in bicontinuous porous matrices is
dominated by the behavior of a third component: topological defect
lines. Their trajectories, their connectivity, and their interactions with
the local curvature of the hosting matrix determine the characteristics
of the metastable states, the energy required to switch between them,
and the kinetic response of the system. “By nature we have no defects
that could not become a strength” (J.W. Goethe)61
The authors wish to thank T. Araki, M. Carpineti, R. Cerbino, G. Cerullo,
I. Dierking, R. Osellame, H. Tanaka, and R. Yamaguchi for providing
images, and useful discussion, and Fondazione Cariplo for financial
support (grant 2008-2413).
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61. Von Natur besitzen wir keinen Fehler, der nicht zur Tugend […] werden koennte,
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