Electro-optical and thermal studies of one ferroelectric liquid-crystal compound with a polarization sign reversal

(1)

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Electro-optical and thermal studies of one ferroelectric

liquid-crystal compound with a polarization sign reversal

C.C. Huang, T. Min, D.S. Lin, B. Zhou, J.W. Goodby

To cite this version:

(2)

Electro-optical

and thermal

studies

of

one

ferroelectric

liquid-crystal compound

with

a

polarization sign

reversal

C. C.

_Huang

_(1),

T. Min

_(1),

D. S. Lin

_(1),

B. Zhou

₍₁₎

and J. W.

_Goodby

₍₂₎

(1)

School of

_Physics

and

_{Astronomy, University}

of Minnesota,

Minneapolis,

Minnesota 55455,

U.S.A.

(2)

School of

_Chemistry,

The

_University,

Hull HU6 7RX, G.B.

(Received

on _January_{11, 1990,}revised on

_April

_23,1990 and

_accepted

on

_April

26, 1990)

Abstract. 2014

Temperature

variations of heat

_{capacity, optical}

tilt

angle, polarization,

and helical

pitch

have been measured in the

_vicinity

of the smectic-A

_{(SmA)-chiral-smectic-C (SmC*)}

transition of one

_{liquid-crystal}

_compound

which exhibits an unusual reversal behavior in

polarization

at about 25 °C while the SmA-SmC* transition occurs at 50 °C.

Unexpectedly,

from our detailed calorimetric and

optical microscopy

studies, we have found that the

_{recrystallization}

also occurs around 25 °C

_during

a

_reasonably

slow

cooling experimental

run.

Classification

Physics

Abstracts

61.30 - 64.70 - 64.70M

Ferroelectric

_{liquid-crystalline mesophases,}

in

_particular,

the chiral-smectic-C

_{(SmC*) phase}

have been demonstrated as

_potentially

useful

_operating

media in

_{electro-optical applications}

with

_{switching speeds}

in the microsecond range

[1].

Compared

to conventional

_{liquid-crystal}

devices

_employing

nematic

materials,

electro-optical

devices based on the ferroelectric

liquid-crystal

materials

_have,

at

_least,

one

_important

new feature.

_Namely,

the

_{switching speed}

can be much faster. Numerous new

_homologous

series of

_{liquid-crystal compounds}

have been

synthesized

to

_explore

the various

_{physical properties}

related to device

_{applications.}

Meanwhile,

the

_interplay

of the

_polarization

and other molecular

_properties

has created very

rich and

_{interesting physical phenomena,}

e.g.,

polarization

reversal

_[2,

_3].

In _{this paper,}we

report

our detailed thermal and

_{electro-optical investigations}

on one

_{liquid-crystal compound}

which exhibits this unusual behavior near room

_temperature.

The smectic-A

_(SmA)

and smectic-C

_(SmC)

_{liquid-crystal mesophases}

can be characterized as

_{orientationally}

ordered fluids with a

layer

structure. The

_layer

normal is

_along

the

_long

axis of the molecule

_{(molecular director)}

in the SmA

_phase

or at an

angle

to it in the SmC

_phase.

The order

_parameter

_{characterizing}

the SmA-SmC transition is the tilt

_angle.

The inclusion of a chiral center within the molecular structure will break the mirror

_symmetry

in the SmC

phase

and create a new

_{mesophase, namely,}

the SmC*

_{phase [4].}

In the SmC*

_phase,

the molecular _{director precesses around the}

_layer

normal and forms a helicoidal structure with a

pitch

about several microns. The

_breaking

of the mirror

_symmetry

allows for a

_spontaneous

polarization

to be

_{generated along}

the two-fold rotational axis which is

_{perpendicular}

to the

plane containing

both the

_layer

normal and the molecular director. The existence of a

(3)

1750

spontaneous

polarization

within each smectic

layer

leads us to call the SmC*

_phase

a ferroelectric

_{liquid-crystal mesophase.}

Thus in addition to the molecular tilt

_angle,

both

polarization

and helical

_pitch

are essential

_macroscopic

quantities

to describe the nature of the

SmC*

_phase

or the SmA-SmC* transition.

_{Experimentally,}

it has been demonstrated that the

primary

order

parameter

for the SmA-SmC* transition of the well-characterized DOBAMBC

compound

is the tilt

_{angle [5,}

_6].

Here DOBAMBC refers to

p-(n-decyloxybenzylidene)-p-amino-(2-methylbutyl)

cinnamate.

Much of our

knowledge concerning

the SmA-SmC* transition has been

acquired

from the

experimental

work on the renowned DOBAMBC

_compound

[7,

8].

Recently,

Mikami et al.

[2]

and

_{Goodby et}

al.

[3]

have

_reported

an unusual

_polarization

reversal behavior in the SmC*

phase

of

_{(S)-2"-methylbutyl}

_{4’-n-alkylcarbonyloxy-(I, l’-biphenyl)- 1 -carboxylate}

(2MBnCBC).

For

_example,

the

_polarization

of 2MB8CBC increases from zero at the

SmA-SmC* transition

temperature

(42

°C),

reaches a maximum value around 37

°C,

gradually

approaches

zero around 22 °C and reverses the

_sign

of the

_{polarization.}

The

tilt-angle

measured

_by

an

_{optical technique}

on 2MB9CBC also

_displays

reversal behavior

[2].

Subsequently, Skarp et

al.

_[9]

have carried out several

_{electro-optical}

measurements on 2MB9CBC to

_investigate

the nature of the SmC*

_phase.

In

_addition,

_employing

two

_sample

cells with different

thicknesses,

the thicker one in the presence of the helix and the other one without the

_helix,

Eidenschink et al.

_[10]

obtained different

_temperature

variations of

tilt-angle

near the reversal

_temperature

of 2MB8CBC. Later Musevic et al.

[11]

]

obtained the

temperature

dependence

of tilt

_angle

from both measurements of

_rotatory

power and x-ray

diffraction on _{2MB8CBC. Both results gave}a tricritical-like behavior without _any

anomaly

near the

_polarization

reversal

_temperature.

To

_get

a better

understanding

of this

family

of

homologous

compounds

with unusual reversal behavior in

_{polarization,}

we have carried out

high-resolution

measurements on the heat

capacity,

tilt

angle, polarization

and helical

pitch

in the

_vicinity

of the SmA-SmC* transition of

_{(S)-2"-methylbutyl}

4’-n-decylcarbonyloxybi-phenyl-1-carboxylate (2MB(10)CBC).

Its chemical formula is

and transition _sequenceis

Isotropic (62 °C)

SmA

_{(51 °C)}

SmC*

_{(29 °C) Crystal.}

The details of our measurement

_techniques

for heat

_capacity

and

_{electro-optical properties}

have been described in references

_{[7, 12] respectively.}

The thickness of our

_well-aligned

sample

in the

_{planar configuration}

for

_{electro-optical investigations}

is 25 um.

Separations

between the laser diffraction

_spots

from dechiralization lines in the SmC*

_phase

are

_employed

to determine the helical

_pitch.

The tilt

_angles

are obtained from the

_{extrapolation}

of

«

_{apparent »}

_tilt-angles

measured at several

_applied

electrical fields. Due to the existence of the

_{pretilt angle}

between the

_{liquid crystal}

and the substrate and the

_possible

chevron

structure inside the

_{sample [13, 14],}

some concerns have been raised in this

_approach

in

determining

the tilt

_angle.

_However,

the

_{justification}

for this

_approach

has been demonstrated

nicely by

the work of

_{Seppen et}

al.

_[15].

In the case of

DOBAMBC,

the

_tilt-angle

obtained

_by

our research group

_[6]

from such an

_{extrapolation}

scheme is in excellent

_agreement

with the one from the measured

_rotatory

_power

_[15].

Our

_experimental

measurements

_required

to

unwind the helical

_pitch

and the

_rotatory

_powermeasurements did not. Three

_typical

sets of data are shown in

_figure

1.

_Except

in the

_vicinity

of the transition

_temperature

_{(see Fig. 1 c),}

the field

_dependent

_apparent

_tilt-angle

exhibits a nonlinear effect

_{(see Figs.}

la and

_b).

This

nonlinear effect is enhanced as the

_sample

_temperature

is decreased. It is

_plausible

that the

deviation in the low field

_region,

which is still

_larger

than the critical electric field

(4)

Fig.

1. -

Apparent

tilt

angle

versus

_{applied voltage}

for three different _temperatures

_(a)

Tc -

T = 16.02 K ;

(b) Tc -

T = 2.21 K ;

(c) £ -

T = 0.37 K with

Tc

= 50.66 °C.

temperature

region

or the surface

_anchoring

_effect,

_e.g.,the well known chevron structured smectic

_{layers [13].}

The chevron structure tends to reduce the measure

_tilt-angle.

The deviations of the

_apparent

tilt

_angle

from the linear

_{extrapolation}

were not seen in our

measurements of two other ferroelectric

_{liquid-crystal compounds}

which have moderate size in

_polarization

with well-behaved

_temperature

variations. As a

result,

the

tilt-angle

data

reported

in this paper are determined from

high-field extrapolation

if nonlinear behavior exists. Here

_{Ee ( 8 X 105}

V/m)

is the electrical field

required

to unwind the helical

_pitch.

Moreover,

Takezoe et al.

_[16]

have

_argued

that the tilt fluctuations are a

_plausible

cause for the non

_linearity

in the

_apparent

tilt

angle.

We believe that the deviation of the

_apparent

tilt

angle

in the low field and low

temperature

region

should not be due to the fluctuation effect of the tilt

_angle.

This kind of fluctuation should be much

stronger

near the transition

temperature

range than in the low

temperature

region.

Finally,

the

_polarization

was also measured as a function of the

applied

field. The

polarization

remains constant for the field

strength larger

than twice the critical field.

(5)

1752

respectively.

While both heat

_capacity

and helical

pitch

behave similar to the SmA-SmC* transition of DOBAMBC

_(Refs.

_{[7, 17],}

the

_polarization

acts _very

_differently.

Similar to

2MB8CBC,

the

_polarization

increases from zero at the SmA-SmC* transition

_temperature

(about

50 °C),

reaches a maximum value around 42 °C and exhibits a reversal behavior around 25 °C.

Our

_{heat-capacity}

data

_{(Fig. 2a)}

demonstrated that there exists another transition near

25 °C which is in the

_neighborhood

of the

_polarization

reversal

_temperature

_{(see Fig. 5).}

The

melting point of 2MB(10)CBC

is 46 °C and

_{reported recrystallization}

_temperature

is - 6.6 *C

(Ref. [3]).

In order to

_investigate

the nature of this transition

_just

above room

_temperature,

we have

_employed

a

_{polarizing optical microscope equipped}

with a Mettler hot

_stage.

The

sample

can be

_{quickly supercooled}

from any

high

temperature

phase

to room

_temperature

without

_{crystallization. Upon cooling}

from the SmA

_phase

to 30.5

_°C,

the

_sample

was

_kept

at

30.5 °C. It remained in the SmC*

_phase

for more than three

_days

without any

_sign

of

crystallization. Cooling

further to and

_monitoring

at 29.2

°C,

the

_{sample crystallized}

in about 5Hr. Another

_{quick cooling}

run from the

_{isotropic phase}

down to 29.2 °C

_directly

gave the

same result.

_Namely,

the

_{sample crystallized}

within 5Hr at 29.2 °C.

_{Consequently,}

the

recrystallization

is the

_primary

cause of the second transition in our

heat-capacity

result

Fig.

2. -

Temperature

variation of heat

_capacity

over a wide temperature range

(a)

and in the

vicinity

of

(6)

(Fig. 2a).

Because the

_peak

_position

of the

_polarization

is about 10 K above the

_{crystallization}

temperature,

it is

_{highly unlikely}

that the

_{crystallization}

will have any effect on the

polarization

reversal behavior. Without any further direct

experimental

evidence,

we can not

entirely

rule out this

_possibility.

On the basis of their

_{high-resolution}

_{heat-capacity}

measurements on another

liquid-crystal

compound,

Huang

and Viner

_{[18] proposed}

the

_following

free energy

expansion

to describe

the

temperature

variations of the heat

_capacity

and tilt

_angle

near the SmA-SmC* transition : :

By

minimizing

this free energy, the

temperature

dependence

of the tilt

_angle

and heat

capacity

near the transition

_temperature

can be obtained and are

and

respectively.

Here A =

a 3/2 /(2(3

C)I/2

T c 3/2)

Tm

=

Tc(l

₊

to/3 )

and B ₊Dt is the

background

heat

_capacity

obtained from the

_non-singular

part

of the free energy

Go.

We have also defined a dimensionless

quantity to

=

b 2/ (ac )

which characterizes the cross-over from the

_ordinary

meanfield

_region

₍

_t

₁

_{to )}

with

_{(b 0}

_{4) >- (ctP 6)}

_{and tP = tP olt 11/2 to}

the meanfield tricritical

region

(1 t 1 >- to)

with

_{(btP 4) - (ctP 6)}

_{and tP = tP olt 11/4.}

The

coefficients a, b,

and

c are

positive

constants for a continuous

transition, 0

is the

_magnitude

of the order

_parameter

and

t(= ( T -

Tc)lTc)

is the reduced

_temperature.

The

_fitting

of our

heat-capacity

data to

equation (3)

is shown as the solid line in

_figure

2b over the

_temperature

range from 35 °C to

53 °C. The

_important

dimensionless

parameter

obtained from this

_fitting

is found to be

to = 3.37 _x

10 - 3.

The

reported tilt-angle

data on 2MB9CBC with tricritical-like behavior

by

Musevic et al.

_{[ 11 agree}

with this small value in

_to.

_{Thermodynamically,}

in a mean-field

_phase

Fig.

3. -

Temperature dependence

of helical

_pitch

in the SmC*

_phase.

Fig.

4. - Tilt

angle

versus _temperaturein the SmC*

phase.

The solid line is calculated

(7)

1754

transition,

the anomalous

_part

of heat

_{capacity (AC)}

and the order parameter

(0)

are related

by [ 19]

Here AC = C - B - Dt. The solid line in

figure

4

displays

the calculated result from _our

heat-capacity

data

_except

for an overall constant factor.

_They

are in reasonable

_good

agreement except

the

_drop

in tilt

angle

for

_{T,, -}

T > 20 K. We believe that this

_drop

is caused

by

the great reduction in the

_polarization

near the reversal

_temperature.

In the case of

DOBAMBC

_{(Ref. [6])}

and DOBA-1-MPC

_{(Ref. [20]),}

we have demonstrated that AC and tilt

_{angle satisfy equation (4)}

and concluded that the tilt

_angle

is the

_primary

order

parameter

for the SmA-SmC* transition of these two

_compounds.

In the immediate

_vicinity

of the SmA-SmC*

_transition,

the helical

_pitch

exhibits a

_sharp

_drop

and reaches a finite value at

the transition

_temperature.

_{Correspondingly,}

the ratio of the

_polarization

to tilt

_angle

exhibits a

_{pronounçed drop}

and reaches a finite value in the

_{immediately vicinity}

of the transition

temperature.

This _agreeswith the

prediction

based on the

_generalized

mean-field model

proposed by

Zeks

_[21]

and

_{Dumrongrattana}

and

_Huang

_[22].

_However,

detailed

_descriptions

of both

_polarization

and tilt

_angle

data within one theoretical model are not

_available,

because we do not

_truly

understand the

_origin

of the reversal behavior in the

_{polarization.}

In the

following paragraph,

we will

_present

two

_preliminary

_attempts

in

_fitting

the

_temperature

dependence

of

_{polarization.}

After

discovering

the

_polarization

reversal

_phenomena

in two

_{liquid-crystal homologous}

series,

Goodby

and co-workers

[3]

tried to describe the

_polarization

data

_by

the

_following

empirical

form

with four

_adjustable

_{parameters PA,}

_PB,

A and

_3.

_{The basic idea is that among}numerous

confirmational

_{configurations}

of the

_{given liquid-crystal}

molecule,

two of them dominate all of the others.

_They

are

_{separated by}

an _{energy barrier} à and have

_polarization

PA

and

_PB,

_{respectively.}

So the Boltzmann factor accounts for the

_probability

that a molecule will be in confirmational

_{configuration}

with

_polarization

_PA

which has an

_{opposite sign}

from

PB.

In this

_argument,

the different

_sign

for

_PA

and

_PB

is the

_major

source of the

_polarization

reversal behavior.

_Fitting

_results,

based on

_{equation (5),}

are shown in

_figure

5a as solid line and lead to

_PA

= 397

uC/m2,

PB

= - 42.4

uC/m2, A

= 670

K,

and {3 =

0.53 which

qualitat-ively

agree with the results

reported

before

[23].

However,

it has been

clearly

demonstrated that a

_{simple power-law expression}

is not sufficient to describe the

_temperature

_dependence

of either tilt

_angle

or

polarization

near the SmA-SmC* transition of

ordinary liquid-crystal

compounds [6]. Temperature

variations of both tilt

_angle

and

_polarization

_experience

evolution from one value of the critical

_exponent

near the transition

temperature

region

(7c-T1K)

to another value away from the transition

temperature.

For

_example,

the

temperature

dependence

of the tilt

_angle

has an

_ordinary

mean-field critical

exponent

(/3 =

1/2) just

below

_T,

and a tricritical-like

_exponent

_{(3 - 1/4)}

_{away from}

T,,

(Tc -

T >

_to

x

_T,).

A tricritical-like behavior in the

_temperature

dependence

of

tilt-angle

has been

_{reported by}

Musevic et al.

_[11].

Thus the value

_{of 3}

obtained from the

_fitting

of

equation (5)

may not be realistic. Our

_{high-resolution heat-capacity}

measurements

_give

the value of the

_important

_{parameter to}

to be 3.37 x

10- 3.

This means that the cross-over from the

ordinary

mean-field behavior to the tricritical one occurs around

Tc -

T = 1 K.

(Note :

(8)

Fig.

5. -

Temperature

variation of

polarization

in the SmC*

phase.

The solid lines in

_(a)

and

_(b)

are

fitting

results from

equations (5)

and

_(6),

_{respectively.}

Consequently, simple power-law description

for either tilt

_angle

or

polarization

with

/3 =

1/2

is not

_appropriate.

The

_temperature

_dependence

of the

_primary

order

_parameter

( 03A6 )

is known from

_{equation (2). Assuming}

that

_polarization

is

_proportional

to

_03A6,

we tried to

fit our

polarization

data to

_{equation (5) using}

the

_expression

for 0 in

_{equation (2),}

instead of

1 t 1 B.

No reasonable

_fitting

results can be obtained.

Instead,

the

_{following expression gives}

a

_fairly

_{good description}

of our

_polarization

data :

Our

_fitting

results are

_displayed

in

_figure

3b as the solid line and

_{give Pc = -}

2.23 x

10-10

_uC/m2,

_{P D}

= 10.3

uC/m2,

à’ = 7 380 K.

Again

an

_{opposite sign}

for

_Pc

and

_{P D}

is

responsible

for the reversal behavior.

_Obviously,

both

_{equations (5)}

and

_{(6) give fairly good}

fit to the

_polarization

data.

However,

in

_{equation (6),}

there exist

_only

three

_adjustable

parameters,

instead of four as in

_{equation (5). Although}

we do not

_precisely

know the

microscopic origins

for the activation energy term in

_{equation (6),}

several

_{physical quantities}

(e.g., viscosity)

exhibit an activation _{energy form in}

_{liquid-crystal mesophases.}

The

magnitude

of the

_spontaneous

_polarization

in the SmC*

_phase

is

_closely

related to

_damping

of

the molecular rotation around its

_long

axis. A trend similar to the reversal

_polarization

phenomenon

has been observed in recent NMR studies of the

_temperature

_dependence

of the

polar

order

_parameter

_{of the C=O group in 2MB8CBC}

_{(Ref. [24]).}

Furthermore,

while

investigating

the

_diverging

behavior of the twist

_viscosity

near the nematic-SmA transition of another

_{liquid-crystal compound,}

_{Huang et}

al.

_[25]

have found that the

_{non-divergent}

_part

of the twist

_viscosity

has an activation energy form with activation energy

B = 5.3 x 10 3 K.

This

value of B is

_comparable

to _{the activation energy à’}obtained from data

_fitting

to

equation (6).

On the basis of these facts and our current

_knowledge

on the nature of the SmA-SmC*

_transition,

we believe that

equation (6)

with

_only

three

_adjustable

_parameters

_maybe a more realistic model to describe the

polarization

reversal behavior.

Here we assume that both à in

equation (5)

and A’ in

equation (6)

are

_temperature

independent

variables. These

_quantities

are related to the

_phase

transition and are in the

argument

of the

_exponent.

_Any

small

_temperature

_dependence

will have a dramatic effect on the

_temperature

variation of the

_{polarization.}

At this moment, we do not have any

appropriate

theoretical model to describe the

_possible

_temperature

variation of these two

important

parameters.

Furthermore,

the

_existing

data

_fitting

can’t rule out these two

(9)

1756

theoretical advances are essential to understand the

_{physical origin}

of this unusual

polarization

reversal

_phenomenon.

In

_conclusion,

we have

investigated

the

_temperature

variation of heat

capacity, polarization,

tilt

_angle

and

_pitch

for one

_{liquid-crystal compound}

with reversal

_polarization

behavior. In the

vicinity

of the

_polarization

reversal

_temperature,

the

_sample

exhibits a

_phase

transition from the SmC*

_phase

to the

_{crystalline phase, provided}

that the

_sample

is cooled

_slowly

_enough.

However,

the

_{recrystallization}

can not be

_{fully responsible}

for the

_polarization

reversal

phenomenon.

The

_{microscopic origin}

of this reversal

_phenomenon

is

_still

_lacking.

Without a

satisfactory microscopic explanation

or a _{proper free energy}

_expansion

for the

_temperature

variation of

_{polarization,}

_fitting

our

_experimental

data to

_{equation (5)}

and

₍₆₎

is rather tentative. Further

_experimental

information is needed to unfold this unusual

_phenomenon

in

polarization.

Acknowledgments

The authors would like to

_{acknowledge help}

from H. Y. Liu in data

_analysis.

This work was

supported by

the Donors of the Petroleum Research

Fund,

administered

by

the American Chemical

_{Society. Major}

_part

of this paper was

_prepared

while one of us

_(C.C.H.)

visited J. Stefan

Institute,

University

of

_{Ljubljana, Yugoslavia}

under the

_{U.S.-Yugoslavia}

Joint Board

_Program

for Scientific and

_{Technological Cooperation.}

Numerous discussions were made with Prof. B. Zeks and R. Blinc

_concerning

the

_{possible physical origins}

of the reversal

polarization phenomenon.

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