HAL Id: jpa-00231156
https://hal.archives-ouvertes.fr/jpa-00231156
Submitted on 1 Jan 1975
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Ferroelectric liquid crystals
R.B. Meyer, L. Liebert, L. Strzelecki, P. Keller
To cite this version:
R.B. Meyer, L. Liebert, L. Strzelecki, P. Keller. Ferroelectric liquid crystals. Journal de Physique
Lettres, Edp sciences, 1975, 36 (3), pp.69-71. �10.1051/jphyslet:0197500360306900�. �jpa-00231156�
L-69
FERROELECTRIC
LIQUTD
CRYSTALS
R.
B.
MEYER
(*),
L.
LIÉBERT,
L.
STRZELECKI
and
P.
KELLER
Université
Paris-Sud,
Physique
des
Solides
(**),
91405
Orsay,
France
Résumé.
2014
Un
argument
généraI
de
symétrie
est
présenté
et
des
expériences
sur
le
p-décyloxybenzy-
lidène
p’-aminocinnamate
de
méthyl-2
butyle
sont
décrites
démontrant
que
les
smectiques
C
et
H
chiraux
sont
ferroélectriques.
Quelques
propriétés
de
cette
nouvelle
famille
de
ferroélectriques
sont
discutées.
Abstract.
2014
A
general
symmetry
argument
is
presented,
and
experiments
on
newly
synthesized
p-decyloxybenzylidene
p’-amino
2-methyl
butyl
cinnamate
are
described,
demonstrating
that
chiral
smectic
C
and
H
liquid
crystals
are
ferroelectric.
Some
of
the
properties
of
this
new
class
of
ferro-
electrics
are
discussed.
In
spite
of
speculation
on
the
possibility
of
ferro-
electric
liquid
crystalline
phases
[1],
there
has
never
been
a
compelling
fundamental
reason
for,
or
expe-
rimental
demonstration
of
the
existence
of
ferro-
electricity
in
these
systems.
In
this
letter
we
show
by
symmetry
that
smectic
C
and
H
liquid
crystals
composed
of
chiral
molecules
must
have
a
sponta-
neous
polarization.
The
synthesis
of
a
new
material
exhibiting
these
phases
is
reported,
and
experiments
are
described
which
determine
the
existence
and
approximate
magnitude
of
the
spontaneous
polari-
zation.
Some
of
the
unusual
properties
of
these
fluid
ferroelectrics
are
discussed.
In
a
smectic
C
liquid
crystal,
rod-like
molecules
are
arranged
in
layers,
with
the
long
molecular
axes
parallel
to
one
another
and
tilted
at
an
angle
0
from
the
layer
normal.
Each
layer
is
a
two-dimensional
liquid.
In
the
smectic
H
phase
(also
called
tilted
B),
the
molecular
layers
are
crystalline;
there
remains
some
question
about
the
degree
of
correlation
of
the
lattices
on
different
layers.
These
properties
are
well
established
by
x-ray
[2]
and
optical
studies
[3].
_
Both
these
phases
have
monoclinic
symmetry,
the
point
group
for
which
contains
only
a
two-fold
rotation
axis
parallel
to
the
layers
and
normal
to
the
long
molecular
axis,
a
reflection
plane
normal
to
the
two-fold
axis,
and
a
center
of
inversion.
However,
if
the
phase
is
composed
of
chiral
molecules
(not
(*) Alfred
P.
Sloan
Foundation
Research
Fellow.
Present
address,
Division
of
Engineering
and
Applied
Physics,
Harvard
University,
Cambridge,
Massachusetts,
U.S.A.
02138.
(**)
Laboratoire
associe
au
CNRS.
superposable
on
their
mirror
image)
then
the
mirror
plane
and
the
center
of
inversion
are
eliminated.
The
remaining
single
two-fold
axis
allows
the
exis-
tence
of
a
permanent
dipole
moment
parallel
to
this
axis.
The
typical
liquid
crystal
molecule
has
a
permanent
dipole
moment
and
is
of
low
enough
symmetry
so
that
it
has
only
two
degenerate
minimum
energy
positions
in
a
monoclinic
environment,
connected
by
the
two-fold
rotation.
If
the
molecule
is
non-chiral,
the
mean
orientation
of
its
permanent
dipole
must
be
normal
to
the
two-fold
axis.
However,
the
skewed
form
of
a
chiral
molecule-forces
the
permanent
dipole
to
have
a
component
parallel
to
the
two-fold
axis.
If
all
the
molecules
are
identical
this
produces
a
net
polarization
of
at
most
a
few
Dehye
per
molecule.
A
racemic
mixture,
however,
will
have
no
net
pola-
rization.
Two
effects
tend
to
reduce
the
magnitude
of
the
spontaneous
polarization.
First,
the
coupling
of
the
molecule
to
the
monoclinic
environment
may
be
weak,
so
that
the
molecule
is
almost
freely
rotating
about
its
long
axis.
Second,
if
the
chiral
part
of
the
molecule
is
only
weakly
coupled
to
the
polar
part,
then
internal
molecular
rotations
may
reduce
the
polarization.
With
these
considerations
in
mind,
a
new
chiral
material,
p-decyloxybenzylidene
p’-amino
2-methyl
butyl
cinnamate
(DOBAMBC),
was
synthesized.
By
analogy
with
similar
molecules
it
was
expected
to
have
a
smectic
C
phase,
and
because
the
chiral
2-methylbutyl
group
is
next
to
the
polar
ester
group,
it
was
hoped
that
the
problem
of
internal
rotation
would
be
minimized.
The
thermal
phase
diagram
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0197500360306900
L-70
was
determined
by
polarized
light
microscopy
and
x-ray
studies :
Crystal
76’
Smectic
C
-- 95’ +
Smectic A
1~
Isotropic
’"
~3°
Smectic
H
The
smectic
C -~
smectic
A
transition
appears,
by
differential
scanning
calorimetry
and
optical
measurements,
to
be
second
order,
with
0
going
continuously
to
zero,
while
the
other
transitions
are
first
order.
In
both
the
C
and
H
phases,
a
helicoidal
structure
is
observed,
in
which
the
molecular
tilt
direction
precesses
around
the
normal
to
the
layers,
with
a
pitch
of
several
microns.
There
are
two
causes
for
this
helix.
First,
as
in
a
cholesteric
liquid
crystal,
there
is
a
chiral
component
to
the
intermolecular
interac-
tions
which
induces
a
spontaneous
twist
in
the
ground
state
structure
[4].
Second,
the
same
symmetry
argu-
ment
that
predicts
a
spontaneous
polarization
also
requires
in
the
ground
state
a
spontaneous
bending
curvature
[5].
In
fact,
this
helicoidal
structure
is
a
state
of
uniform
torsion
and
bending
of
the
molecular
alignment.
(This
was
expected
for
the
smectic
C
phase
[6],
but
it
raises
fundamental
questions
about
the
H
phase
to
which
we
will
return
later);
because
the
helix
results
from
two
different
interactions,
it
should
be
possible
to
find
conditions
where,
in
a
pure
material,
the
helix
disappears
(pitch
-~
oo),
while
the
spontaneous
polarization
does
not.
Another
way
to
get
the
same
situation
could
be
to
mix
different
materials,
compensating
for
the
pitch
but
not
for
the
local
dipole.
To
detect
the
spontaneous
polarization,
the
electro-
optical
properties
of
DOBAMBC
were
examined.
First,
samples
were
prepared
between
glass
plates
treated
with
hexadecyltrimethyl
ammonium
bromide,
which
induces
the
smectic
planes
to
lie
parallel
to
the
glass,
in
the
smectic
A
phase.
Upon
cooling
into
the
C
phase,
this
ordering
is
preserved.
The
electric
field
was
applied
parallel
to
the
layers
between
a
pair
of
200
J1II1
diameter
copper
wires
imbedded
in
the
sample
1.5
mm
apart;
the
wires
also
served
as
spacers
for
the
glass.
For
these
samples,
the
conoscopic
image
was
observed,
using
crossed
linear
polarizers.
With
no
field,
due
to
the
presence
of.
the
helix
a
uniaxial
inter-
ference
figure
was
seen,
centered
on
the
layer
normal,
and
consisting
of
a
series
of
concentric
rings,
just
as
in
the
A
phase,
and
an
extinction
cross,
the
center
part
of
which
is
more
or
less
distinct,
depending
on
the
molecular
tilt
angle.
With
a
small
applied
field,
this
figure
shifts,
without
apparent
distortion,
in
a
direc-
tion
normal
to
the
field.
This
effective
rotation
of
the
macroscopic
optical
axis
is
linear
in
the
field,
changing
direction
when
the
field
is
reversed.
At
higher
fields,
,
the
helicoidal
structure
is
completely
unwound,
with
the
molecular
tilt
direction
uniformly
oriented
normal
to
the
field,
producing
the
typical
biaxial
interference
figure
of
a monodomain
smectic
C
sample.
Again,
reversing
the
field
reverses
the
tilt
direction.
This
behavior
is
consistent
with
ferroelectric
coupl-
ing.
At
high
field
the
polarization
is
uniformly
aligned,
producing
the
observed
monodomain
structure.
The
low
field
behavior
results
from
distortion
of
the
helix,
in
which
regions
of
favorable
polarization
grow
at
the
expense
of
the
intervening
regions
of
opposite
polarization.
This
shifts
the
mean
optical
axis
toward
the
high
field
direction.
The
helix
serves
as
an
ideal
ferroelectric
domain
structure,
although
it
arises
from
local,
not
long
range,
interactions.
For
quantitative
measurements,
the
ferroelectric
coupling
must
be
separated
from
the
ordinary
dielectric
coupling
due
to
the
anisotropy
of
the
,
dielectric
constant
[7].
Since
the
ferroelectric
coupling
requires
the
tilt
direction
to
rotate
with
the
field,
this
response
is
damped
by
the
rotational
viscosity
of
the
fluid,
and
in
practice
disappears
above
a
few
hundred
Hertz.
The
dielectric
coupling,
which
is
quadratic
in
field,
produces
a
static
response
which
persists
at
high
frequency.
-
By
preparing
samples
between
glass
slides
coated
with
transparent
tin
oxide
electrodes,
a
focal
conic
texture
is
obtained
in
which
the
applied
field
is
again
parallel
to
the
smectic
layers,
in
some
regions.
In
these
regions,
the
helix
produces
a
series
of
parallel
stripes,
allowing
direct
measurement
of
the
pitch
and
the
critical
field
Ec
for
unwinding
the
helix.
The
high
frequency
value
of
Ec
was
typically
at
least
a
factor
of
20
higher
than
the
d.c.
value,
meaning
that
the
dielectric
coupling
can
be
ignored
at
low
frequency.
The
ferroelectric
coupling
results
in
a
critical
field
Ec = 1t4
K/(4 lP),
in
cgs
units,
with
I
the
full
pitch
of
the
helix,
P
the
polarization,
and K
a
torsional
elastic
constant
for
the
helix
[8].
Using
measurements
at
86 °C,
Ec
=
2 400
V/cm,
and
I
=
1.5
~m.
Esti-
mating K ~
10-6
dyne,
then
P ~
125
statcoul./cm2,
or
about
0.25
Debye/molecule,
which
is
not
unreaso-
nable ;
estimating
the
anisotropy
of
the
dielectric
constant
2~/4
1t ’"
1,
the
electric
polarization
induced
by Ee
( N
8
cgs)
is
much
smaller
than
our
estimated
value
for
P,
showing
the
consistency
of
our
inter-
pretation.
Ec
varies
from
600
V/cm
at
94 °C
to
6
500
V/
cm
at
63.5
°C.
The
pitch
varies
from
3
~n
at
94 °C
to
1
Jl1Il
at
73 °C,
below
which
it
was
too
small
to
be
measured
in
this
experiment.
Unfortunately,
K
is
not
known,
so
that
P
cannot
be
determined.
The
properties
described
above
are
the
most
impor-
tant
for
classifying
a
material
as
a
ferroelectric,
namely
the
presence
of
a
spontaneous
polarization
which
is
easily
oriented
by
an
applied
field.
The
analogy
with
crystalline
ferroelectrics
extend
further
than
this.
The
smectic
A H
smectic
C
transition
of
DOBAMBC
is
actually
a
Curie
point.
This
transition
is
driven
by
intermolecular
forces
producing
the
tilt,
and
not
by
the
ferroelectric
coupl-
ing
[1,
9].
This
is
confirmed
by
comparing
the
transi-
tion
temperature
?c
of
the
chiral
and
racemic
versions
L-71
of
DOBAMBC,
which
differ
by
less
than
1 ~c.
The
situation
is
then
fundamentally
different
from
what
happens
in
usual
ferroelectric
transitions in
solids,
where
dipole-dipole
interactions
are
directly
respon-
sible
for the
phase
change.
By
symmetry,
then,
the
polarization
P
is
proportional
to
0,
going
to
zero
continuously
at
Tc.
The
linear
coupling
of
P
and
6
also
produces
a
piezoelectric
effect
in
the
smectic
A
phase.
Sh~ar
of
the
smectic
layers
over
one
another
produces
tilt
[10]
which
in
turn
produces
a
polarization
transverse
to
the
shear.
Conversely,
an
electric
field
in
the
plane
of
the
layers
produces
a
polarization
and
therefore
a
tilt
normal
to
the
field.
The
latter
effect
is
easily
observed
in
DOBAMBC,
although
quanti-
tative
measurements
have
not
yet
been
made.
As
the
Curie
point
is
approached
from
above,
the
piezo-
electric
coefficients
diverge,
which
also
leads
to
a
divergent
dielectric
constant.
The
molecular
tilt
mode
plays
the
role
of
a
soft
optical
phonon
at
the
transition.
In
this
case
it
is
an
overdamped
mode,
and
its
viscous
relaxation
frequency
tends
toward
zero
at
the
transition.
This
should
be
observable
in
electro-optic
or
dielectric
constant
measurements.
Ferroelectric
liquid
crystals
should
have
a
number
of
unusual
properties,
An
ordinary
smectic
C
mate-
rial
exhibits
curvature
elasticity
for
spatial
gradients
of
the
tilt
direction,
much
like
a
nematic
liquid
crys-
tal
[4, 11].
The
presence
of
the
ferroelectric
polari-
zation
fundamentally
alters
this
situation,
since
any
divergence
in
P
produces
space
charge
and
long
range
coulomb
interactions.
A
bending
mode
of
the
tilt
direction,
with
wave
vector q
parallel
to
the
smectic
layers,
is
a
divergence
mode
of
P.
The
electrostatic
energy
of
this
mode
is
independent
of
q,
in
contrast
to
the elastic
energy
which
varies
as
q ~ 2.
The
elec-
trostatic
interaction
therefore
makes
this
a
non-
hydrodynamic
mode
with
finite
relaxation
frequency
at
zero
wave
vector.
The
role
of
ionic
impurities
will
further
complicate
the
problem.
Another
unusual
effect
will
be
flow
induced
pola-
rization.
As
pointed
out
by
L.
Leger,
shear
of
the
layers
over
one
another
will
distort
the
helix,
producing
a
preferred
alignment
of
the
molecules
and
therefore
a
polarization
transverse
to
the
flow.
A
similar
dis-
tortion
and
polarization
can
be
induced
by
a
magnetic
field
obliquely
oriented
to
the
layer
normal.
We
are
grateful
to
I.
W.
Smith
for
a
very
useful
discussion
of
such
an
experiment.
The
smectic
H
phase
presents
fundamental
struc-
tural
problems.
The
observed
helicoidal
structure
is
incompatible
with
a
three
dimensional
lattice,
sug-
gesting
that
the
two
dimensional
lattices
in
the
smectic
layers
rotate
with
the
tilt
direction
in
the
helix
[12].
This
requires
weak
coupling
between
the
layers,
and
perhaps
an
equilibrium
network
of
screw
dislocations.
The
electro-optical
effects
seen
in
the
C
phase
are
observable
in
the
H
phase
as
well,
but
with
a
much
longer
relaxation
time,
varying
from
about
a
tenth
of
a
second
near
the
smectic
H-smectic
C
phase
change
to
several
seconds
at
lower
temperatures.
The
mecha-
nism
of
the
apparently
uniform
rotation
of
the
tilt
direction
in
response
to
an
applied
field
may
involve
the
motion
of
dislocations
within
the
lattice
of
each
layer.
In
conclusion,
we
have
demonstrated
the
existence
of
a
new
class
of
ferroelectric
materials.
Their
unusual
combination
of
fluid
and
ferroelectric
properties
leads
to
some
novel
phenomena.
The
ferroelectric
and
piezoelectric
properties
of
these
materials
should
provide
useful
probes
for
the
study
of
their
phase
changes
and
their
basic
structure.
The
authors
are
grateful
to
J.
Doucet
for
perform-
ing
x-ray
measurements.
R.
B.
Meyer
wishes
to
thank
G.
Durand
for
a
critical
reading
of
the
manuscript,
R.
Ribotta
and
Y.
Galeme
for
help
with
experimental
problems,
I.
W.
Smith
for
both
experimental
assis-
tance
and
numerous
valuable
discussions
of
this
project.
References
[1]
MCMILLAN,
W.
L.,
Phys.
Rev.
A
8
(1973)
1921.
[2]
DOUCET,
J.,
LAMBERT,
M.,
LEVELUT,
A.
M.,
J.
Physique
Colloq.
32
(1971)
C
5A-247.
DE
VRIES,
A.,
Proc.
of
Fifth
Intl.
Conf.
on
Liquid
Cryst.,1974,
J.
Physique
Colloq.
36
(1975)
C
1,
to
be
published.
[3]
TAYLOR,
T.
R.,
FERGASON,
J.
L.,
ARORA,
S.
L.,
Phys.
Rev.
Lett.
24
(1970)
359.
[4]
FRANK,
F.
C.,
Disc.
Faraday
Soc.
25
(1958)
19.
[5]
MEYER,
R.
B.,
Lectures
in
Theoretical
Physics
(Les
Houches)
1973,
to
be
published.
[6]
HELFRICH,
W.,
OH,
C.
S.,
Mol.
Cryst. &
Liquid
Cryst.
14
(1971)
289 ;
URBACH,
W.,
BILLARD,
J.,
C.
R.
Hebd.
Séan.
Acad.
Sci.
272
(1972)
1287.
[7]
CHEUNG,
L., thesis,
Harvard
Univ.,
1973 ;
GRULER,
H.,
SHEFFER,
T.
J.,
MEIER,
G.,
Z.
Naturforsch.
27a
(1972) 966.
[8]
The
calculation
is
formally
identical
to
that
of DE
GENNES,
P.
G.,
Solid
State
Commun.
6
(1968)
163.
[9]
DE
GENNES,
P.
G.,
C.
R.
Hebd.
Séan.
Acad.
Sci.
274B
(1972)
758.
[10]
BROCHARD,
F.,
thesis,
Université
Paris-Sud,
Physique
des
Solides
(1974).
[11]
DE
GENNES,
P.
G.,
The
Physics
of
Liquid
Crystals
(Oxford
Univ.
Press,
London)
1974,
chapter
7.
[12]
This
point
was
clarified
in
a
discussion
with
DE
GENNES,
P.
G.