C. C. Huang, Department of Physics, University of Minnesota Office: Phys. 335, Tel: 4-0861

C. C. Huang, Department of Physics, University of Minnesota Office: Phys. 335, Tel: 4-0861

Outline:

1. Introduction2. Experimental results3. Phenomenological model for the SmC* variant phases4. Predictions of the model5. New experimental results6. 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

Experimental and theoretical studies of the SmC* variant phases

S m CS m A

Conventional molecular arrangements in the SmA and SmC phases

C10H21O C N

H

C C

H H

COCH2C*C2H5

O

CH3

H

DOBAMBC

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.

SmC*

Two unique physical properties associated with the SmC* phase

Sample: DOBAMBC, Tc : SmA-SmC* transition temperature

Spontaneous polarizationSaturation polarization 60 C/m2

Helical pitch

Compounds with large spontaneous polarization

C8H17 C O

O

C O

O

C*(CH3)C6H13

HO

In 1989, A. D. L. Chandani et al., (Jpn. J. Appl. Phys. Part 2 28, L1265) reportedthe discovery of antiferroelectric response from the following compound:

MHPOBC

Saturation polarization > 500 C/m2.

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).

?

??

S m A

Is o tro p ic

fe rro e le c tric(S m C * )

an tife rro e lec tric(S m C A * )

S m C*

S m C FI2*

S m C FI1*

Chiral tilted smectic phases

?

??

x

y

z

c

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:

SmC* phase: uniaxial phase

SmC* phase

AF or SmCFI2* phase: 4-layer structure

SmC* or SmCFI1* phase: 3-layer structure

SmCA* : 2-layer structure

SmCA*SmCFI2* SmCFI1*

Ref.: T. Matsumoto, et al., J. Mater. Chem. 9, 2051 (1999).

O ff R e s o n an c e

= 1 M o lecu le

B o n d in g E n v iro n m en to f R e s o n an t A to m

=

O n R es o n an ce

M o lecu la rA rran ge m en t(A n tife rro e le c tric(S m C A* ) p h as e ): :

Why resonant x-ray diffraction?

Fluorescence spectrum from a 10OTBBB1M7 powder sample

SC10

H O23 6 13

3CO

C OO

C H CC H

*C OO

H

Sample: 10OTBBB1M7

Polarization-analyzed resonant x-ray results from SmC* variant phasesIn

tens

ity (

Cou

nts/

5 se

cond

s)

Qz/Qo

SmC*

SmCFI2*

SmCFI1*

SmCA*

Sample: 10OTBBB1M7

= 5 to 8

= 4

= 3

= 2

Ref: P. Mach et al., PRL 81, 1015 (98).

SC10

H O23 6 13

3CO

C OO

C H CC H

*C OO

H

proposed ruled out

X-ray scattering intensity in the vicinity of the resonant energy

SC10

H O23 6 13

3CO

C OO

C H CC H

*C OO

H

Sample: 10OTBBB1M7

Eo = 2474.8 eV

In the SmCFI2* phase

-90 0 90 180 270-10

-5

0

5

Start Date: 09/17/1999Start Time: 4:30 PMYellow MB10OBC filmProject Name: 9-17-99 MB10 green filmE field magnitude=4VLinear Polarized refl. light, no analyser1 point/1 min.

b)

(deg)

48.50

49.50

49.75

50.00

50.25

(d

eg

)

(de

g)

MHDDOPTCOB

Data: 47 Layer Data: 93 Layer Fit to Data

a)

T = 82.51 °C

Fitting parameters:d = 35.07Å = 31.0°

ne = 1.645

no = 1.485 = 18°

Ellipsometry results from the SmCFI2* phase of MHDDOPTCOB

proposed ruled out

Ref. : P. M. Johnson, et al. PRL 84, 4870 (2000).

Employ a powerful ellipsometer specially designed by our research group

1.24 1.25 1.74 1.75 1.76

0

1

2

3

10

3 C

ou

nts

/Se

c.

Qz/Q

0

High-resolution resonant x-ray scattering results

Sample: MHDDOPTCOB

Ising Model: two equal intensity split peaksClock Model: single peakDistorted Model: Split peaks with different intensity intensity ratio distortion angleseparation size of helical pitch

The measured distortion angle (=15) in good agreement with our opticalresult which yielded =18.

SmCFI2*

Ref: A. Cady et al., Phys. Rev. E (RC) 64, 05702 (2001)

Experimental Results

Experimental advances by resonant x-ray diffraction and optical studies

1. SmC*: incommensurate short-helical pitch with pitch size > 4 layers (1999)

2. SmCFI2*: distorted 4-layer structure (2000, 2001)

3. SmCFI1*: distorted 3-layer structure (2000)

1

2 3

4 112

31

32

4

56

SmC SmCFI2* SmCFI1*

1. M. Yamashita and S. Miyazima, Ferroelectrics 48, 1, (1993). Ising-like structure2. A. Roy and N.V. Madhusudana, Europhys. Lett. 36, 221 (1996). Uniform helical phases and a non-uniformly modulated phases3. 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 structures5. 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.

Theoretical advances: phenomenological approach

Phenomenological model for the SmC* variant phases

Chiral: the simplest chiral term is f1(k x k+1)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 phaseSmCA*: antiferroelectric phase

SmCFI1*: distorted structure with a 3-layer unit cell

SmCFI2*: distorted structure with a 4-layer unit cell

SmC*: incommensurate nano-scale helical pitch structure with pitch size > 4 layers

The molecular tilt in k-th layer can be described by k = (cos(k), sin(k)).

x

y

z

k

Various interlayer coupling terms

A) n.n. coupling term: a1(k . k+1) a1 < 0 ferroelectric coupling a1 > 0 anti-ferroelectric coupling

B) 3-layer unit cell: requires 3rd n.n. coupling term: a3(k . k+3) and a3 < 0C) Thus the free energy expansion can be written as:

G = [a1(k . k+1) + a2(k . k+2) + a3(k . k+3) + f1(k x k+1)]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 > 0 as well as both a1 and a3 are not too large.

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 Cepic’s approach.

k

One crucial additional term: b(k . k+1)2

Thus:

G = [a1(k . k+1) + a2(k . k+2) + a3(k . k+3) + f1(k x k+1) + b(k . k+1)2]

b > 0 bi-layer model which has been considered previouslyb < 0 stable 3- and 4- layer distorted unit cell.

We are mainly interested in minimizing the free energy G for variousmolecular 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 thefollowing phase diagram as a function of a1 and a2.

The final free energy which yields the all the observed phases

k

Path 2

Path 1

-0.5

d3Sm-C*

2Sm-C*d4Sm-C*

1Sm-C*

1

0.5

0

-1.5 0 1.5

Sm-C*

ASm-C*

-180-170-160-150-140-130-120-110-100-90-80-70-60-50-40-30-20-12-9-6-3-2-101236912

a1 (K)

a 2 (K

)Phase diagram generated by the phenomenological model

a3 = -0.07K, f1 = 0.12 K

b2 = -0.2K

a2 < 0 n.n.n. synclinic

a1 < 0 SmC*

a1 > 0 SmCA*

a1 0, a2 0 and a3 < 0

SmCd3*

a2 > 0 n.n.n. anticlinic

small a1 SmCd4*

a2 - a1 SmC1*

a2 a1 SmC2*

SmCd3* and SmCd4*:3- and 4- layer distorted structure.

SmC1* and SmC2*:INHP structure with pitch> 4 and < 4 layers

Ref: D. A. Olson, X. F. Han, A. Cady, and C. C. Huang, PRE 66, 021702 (2002).

-1 0 11

10

100

1000

a1 (K)

0.4 0.6 0.80

25

50

b)

a)

a2 (K)

Pitch evolution along two different pathsP

itch

len

gth

(lay

ers)

a) pitch versus a2 along the path 1 for the SmC1*-SmC* transition.b) pitch versus a1 along the path 2 for the SmC1*-SmCd4*- SmC2* transition.

SmC1*SmC*

SmC1*

SmC2*SmCd*

Optical rotatory power vs. temperature from two compounds

10OTBBB1M7 11OTBBB1M7

pitch inversion no pitch inversion within the SmCFI2* phase window

Ref: F. Beaubois, et al., Eur. Phys. J. E 3, 273 (2000).

-0.5

d3Sm-C*

2Sm-C*d4Sm-C*

1Sm-C*1

0.5

0

-1.5 0 1.5

Sm-C*

ASm-C*

-64-60-56-52-48-44-40-36-32-28-24-20-160

a1 (K)

a 2 (K

)The distortion angle () in 4- and 3-layer distorted phases

a3 = -0.07K, f1 = 0.12 K

b2 = -0.2K

In the SmCd4*,

arcsin(- f1/(2 b2))if pitch length is large.

1

2 3

4

114 116 118

5

6

7

8a)

Temperature (oC)

Pit

ch (

in l

ay

ers)

cooling heating

84 85 86 87

20

40

60

80b)

film 1 heating film 1 cooling film 2 heating film 2 cooling

a) The helical pitch of 10OTBBB1M7 decreases monotonically on cooling through the SmC

* 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).

Temperature variation of pitch (> 4 layers) from two compounds

-10 -5 02.01

2.02

2.6

2.8

3.0 221L 163L 62L ellipsometry

Pitc

h (

laye

rs)

T-Tc (K)

Pitch evolution in MHPOCBC

SmCA*

SmC*

A new SmC* phase with pitch < 4 layers is experimental found by an optical probe!

Layer thickness 3nmLaser wavelength = 630nm.

C8H17 C O

O

C O

O

C*(CH3)C6H13

HC O

O

Ref. A. Cady et al., PRL 91, 125502 (2003).

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 SmC2* phase with pitch less than four layers. Experimentally we have shown the existence of such a phase.Question Some critical properties of the SmC2* 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.

Path 2

Path 1

-0.5

d3Sm-C*

2Sm-C*

d4Sm-C*

1Sm-C*

1

0.5

0

-1.5 0 1.5

Sm-C*

ASm-C*

-180-170-160-150-140-130-120-110-100-90-80-70-60-50-40-30-20-12-9-6-3-2-101236912

a1 (K)

a 2 (K

)

Phase sequences upon cooling

SmA –SmC1*-SmC*-SmCFI2*-SmCFI1*-SmCA*

Additional questions

1. 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 (k .k+2) + b(k . k+1)2 four- layer structure

a3(k . k+3) + b(k . k+1)2 ?

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