C. C. Huang, Department of Physics, University of Minnesota

1
Experimental and theoretical studies of the SmC
variant phases
C. C. Huang, Department of Physics, University of
Minnesota Office Phys.
335, Tel 4-0861

• Outline
• Introduction
• 2. Experimental results
• 3. Phenomenological model for the SmC variant
  phases
• 4. Predictions of the model
• 5. New experimental results
• 6. Summary and questions

Collaborators D. Olson, X. F. Han, A. Cady, H.
T. Nguyen,H. Orihara, J. W. Goodby, R.
Pindak, W. Caliebe, P. Barios, and H. Gleeson
2
Conventional molecular arrangements in the SmA
and SmC phases
In 1975, R. B. Meyer et al., proposed and
synthesized the following chiral compound that
displays ferroelectric response in the SmC
phase. Spontaneous polarization is perpendicular
to the tilt plane.
DOBAMBC
SmC
3
Two unique physical properties associated with
the SmC phase
Sample DOBAMBC, Tc SmA-SmC transition
temperature
Spontaneous polarization Saturation polarization
? 60 mC/m2
Helical pitch
4
Compounds with large spontaneous polarization
In 1989, A. D. L. Chandani et al., (Jpn. J. Appl.
Phys. Part 2 28, L1265) reported the discovery of
antiferroelectric response from the following
compound
MHPOBC
Saturation polarization gt 500 mC/m2.
5
Thermal studies of MHPOBC sample
Refs A. D. L. Chandani, et al., Jpn. J. Appl.
Phys. 28, L1261 (89). K. Ema, et al.,
Phys. Rev. E 47, 1203 (93).
6
Chiral tilted smectic phases
?
q
z
?
y
?
x
c
f
7
Sequence of SmC variance phases and their
preliminary properties
By employing various electro-optical techniques
to study these phases, the following properties
have been obtained Upon Cooling SmCa phase
uniaxial phase SmC phase AF or SmCFI2 phase
4-layer structure SmCg or SmCFI1 phase 3-layer
structure SmCA 2-layer structure
SmCA
SmCFI2
SmCFI1
Ref. T. Matsumoto, et al., J. Mater. Chem. 9,
2051 (1999).
8
Why resonant x-ray diffraction?
9
Fluorescence spectrum from a 10OTBBB1M7 powder
sample
Sample 10OTBBB1M7
10
Polarization-analyzed resonant x-ray results from
SmC variant phases
p
Sample 10OTBBB1M7
p
n 5 to 8
SmCa
p
p
SmCFI2
s
proposed
ruled out
n 4
Intensity (Counts/5 seconds)
p
p
SmCFI1
n 3
p
SmCA
n 2
Ref P. Mach et al., PRL 81, 1015 (98).
Qz/Qo
11
X-ray scattering intensity in the vicinity of the
resonant energy
Eo 2474.8 eV
In the SmCFI2 phase
Sample 10OTBBB1M7
12
Ellipsometry results from the SmCFI2 phase of
MHDDOPTCOB
Employ a powerful ellipsometer specially designed
by our research group
proposed
ruled out
T 82.51 C Fitting parameters d 35.07Å q
31.0 ne 1.645 no 1.485 d 18
Ref. P. M. Johnson, et al. PRL 84, 4870 (2000).
13
High-resolution resonant x-ray scattering results
Sample MHDDOPTCOB
Ising Model two equal intensity
split peaks Clock Model single
peak Distorted Model Split peaks with
different intensity intensity ratio
distortion angle separation
size of helical pitch The measured distortion
angle (d2 15?) in good agreement with our
optical result which yielded d2 18?.
SmCFI2

Ref A. Cady et al., Phys. Rev. E (RC) 64, 05702
(2001)
14
Experimental Results
Experimental advances by resonant x-ray
diffraction and optical studies 1. SmCa
incommensurate short-helical pitch with pitch
size gt 4 layers (1999) 2. SmCFI2 distorted
4-layer structure (2000, 2001) 3. SmCFI1
distorted 3-layer structure (2000)
SmCa
SmCFI2
SmCFI1
15
Theoretical advances phenomenological approach
1. M. Yamashita and S. Miyazima, Ferroelectrics
48, 1, (1993). Ising-like
structure 2. A. Roy and N.V. Madhusudana,
Europhys. Lett. 36, 221 (1996).
Uniform helical phases and a non-uniformly
modulated phases 3. M. Skarabot et al., Phys.
Rev. E 58, 575 (1998). Short
helical pitch and bi-layer structures 4. S.
Pikin et al., Liq. Cryst. 26, 1107 (1999).
Short helical pitch structures 5. M.
Cepic and B. Zeks, Phys.Rev. Lett. 87, 85501
(2001). Short helical pitch
structures None of them predicts the stability of
distorted 3- or 4-layer structures.
16
Phenomenological model for the SmC variant phases
The molecular tilt in k-th layer can be described
by xk q(cos(fk),
sin(fk)).
Chiral the simplest chiral term is f1(xk x
xk1) Phenomenological model one with a minimum
number of expansion terms which yields all the
observed SmC variant phases and offers new
predictions. The description of observed SmC
variant phases (ignore the long optical helical
pitch) SmC ferroelectric phase SmCA
antiferroelectric phase SmCFI1 distorted
structure with a 3-layer unit cell SmCFI2
distorted structure with a 4-layer unit
cell SmCa incommensurate nano-scale helical
pitch structure with pitch size gt
4 layers
z
q
y
fk
x
17
Various interlayer coupling terms
A) n.n. coupling term a1(xk . xk1) a1 lt 0 ?
ferroelectric coupling a1 gt 0 ?
anti-ferroelectric coupling B) 3-layer unit cell
requires 3rd n.n. coupling term a3(xk . xk3)
and a3 lt 0 C) Thus the free energy expansion can
be written as G ? a1(xk . xk1) a2(xk .
xk2) a3(xk . xk3) f1(xk x xk1) D) Do we
need 4th n.n. coupling term to describe SmCFI2
with a 4-layer unit cell? The key feature
for SmCFI2 is that n.n.n. orientation is
anti-clinic. Thus this requires that a2 gt
0 as well as both a1 and a3 are not too large.
k
Simulation results f1 ? 0, leads to simple
helical structures and no well-defined phases
with 3- or 4-layer unit cell and is
similar to Cepics approach.
18
The final free energy which yields the all the
observed phases
One crucial additional term b(xk .
xk1)2 Thus G ? a1(xk . xk1) a2(xk .
xk2) a3(xk . xk3) f1(xk x xk1) b(xk .
xk1)2 b gt 0 bi-layer model which has
been considered previously b lt 0 stable 3-
and 4- layer distorted unit cell. We are mainly
interested in minimizing the free energy G for
various molecular azimuthal orientation with a
given set of coefficients a1, a2, a3, f1, and b.
It is expected that a1 and a2 are the two most
important ones. Thus for a given set of
parameters (a3, f1, and b), we have identified
the following phase diagram as a function of a1
and a2.
k
19
Phase diagram generated by the phenomenological
model
a3 -0.07K, f1 0.12 K bq2 -0.2K
SmCd3 and SmCd4 3- and 4- layer distorted
structure. SmCa1 and SmCa2 INHP structure
with pitch gt 4 and lt 4 layers
a2 lt 0 n.n.n. synclinic a1 lt 0
SmC a1 gt 0 SmCA a1 ? 0, a2 ? 0 and
a3 lt 0 SmCd3 a2 gt 0
n.n.n. anticlinic small a1 SmCd4
a2 ? - a1 SmCa1 a2 ? a1
SmCa2
Ref D. A. Olson, X. F. Han, A. Cady, and C. C.
Huang, PRE 66, 021702 (2002).
20
Pitch evolution along two different paths
SmCa1
SmC
a) pitch versus a2 along the path 1 for
the SmCa1-SmC transition. b) pitch
versus a1 along the path 2 for the
SmCa1-SmCd4- SmCa2 transition.
Pitch length (layers)
SmCa2
SmCd4
SmCa1
21
Optical rotatory power vs. temperature from two
compounds
11OTBBB1M7
10OTBBB1M7
no pitch inversion within the SmCFI2 phase
window
pitch inversion
Ref F. Beaubois, et al., Eur. Phys. J. E 3, 273
(2000).
22
The distortion angle (d) in 4- and 3-layer
distorted phases
a3 -0.07K, f1 0.12 K bq2 -0.2K
In the SmCd4, d ? ?arcsin(- f1/(2 bq2))? if
pitch length is large.
23
Temperature variation of pitch (gt 4 layers) from
two compounds
a) The helical pitch of 10OTBBB1M7 decreases
monotonically on cooling through the SmCa
phase as measured using resonant x-ray
diffraction by P. Mach et al., Phys. Rev. E
60, 6793 (1999). b) A much different helical
pitch evolution in MHR49 as measured using
resonant x-ray diffraction by L. S. Hirst et al.,
Phys. Rev. E 65, 041705 (2002).
24
Pitch evolution in MHPOCBC
A new SmCa phase with pitch lt 4 layers is
experimental found by an optical probe! Layer
thickness ? 3nm Laser wavelength 630nm.
SmCa
SmCA
Ref. A. Cady et al., PRL 91, 125502 (2003).
25
Summary
1. Our phenomenological model with five expansion
terms has given theoretical support to the
existence of the SmCd3 and SmCd4 with 3- and 4-
layer distorted structures. Question Can
the SmCd3 and SmCd4 fully describe the
corresponding SmCFI1 and SmCFI2 phases?
More research work needs to be done to answer the
question. At least, the predicted helical
pitch inversion in the SmCFI2 phase has been
observed in one liquid crystal compound. 2.
The model also predicts the existence of the
SmCa2 phase with pitch less than four
layers. Experimentally we have shown the
existence of such a phase. Question Some
critical properties of the SmCa2 phase have to
be experimentally tested. Related work is in
progress. 3. The proposed model may not be the
complete one. On the other hand, it contains
the minimum number of terms to yield the
stability of all observed SmC variant
phases. Definitely, it will form the starting
point for the future theoretical modeling for
the SmC variant phases.
26
Phase sequences upon cooling
SmA SmCa1-SmC-SmCFI2-SmCFI1-SmCA
27
Additional questions

• With liquid-like molecular arrangements within
  each layer,
• what are the physical origins of the
  next-nearest-neighbor
• and the 3rd nearest neighbor interactions,
  required for this
• phenomenological model?
• Recently, M. B. Hamaneh and P. L. Taylor (PRL,
  in press)
• have offered one plausible explanation.
• 2. At least, two theoretical models have
  predicted the stability of
• a phase with the six-layer structure. So far,
  there is no experimental
• support of such a six-layer structure. Can a
  phase with the six-layer
• structure be stable in our simple model?
• a2 (xk . xk2) b(xk . xk1)2
  four- layer structure
• a3(xk . xk3) b(xk . xk1)2 ?

Research work is supported by NSF, PRF, and DOE
through BNL