Dielectric method for determining the electrical critical field in ferroelectric liquid crystals

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Dielectric method for determining the electrical critical field in ferroelectric liquid crystals

A. Levstik, Z. Kutnjak, B. Zeks, S. Dumrongrattana, C. Huang

To cite this version:

A. Levstik, Z. Kutnjak, B. Zeks, S. Dumrongrattana, C. Huang. Dielectric method for determining

the electrical critical field in ferroelectric liquid crystals. Journal de Physique II, EDP Sciences, 1991,

1 (7), pp.797-803. �10.1051/jp2:1991110�. �jpa-00247556�

J

Phj.s

II France ₁

(I99I)

797-803 _JUILLET 1991, PAGE 797

Classification Phv>ic> Ab.itracts

61 30 77 60

Dielectric method for determining the electrical critical field in ferroelectric liquid crystals

A. Levstik

('),

Z

Kutnjak ('),

B Zeks

('),

_S.

Dumrongrattana

_(~

*)

and C C

Huang(2)

(')

J Stefan Institute. University of Ljubljana, 61II I

Ljubljana,

Jamova 39, Yugoslavia (~) School of Physics and Astronomy.

University

of Minnesota,

Minneapolis,

MN 55455 U S A

(Rc,ceived J4 January J99J, accepted 27 March 199J)

Abstract. Both the electrical critical field and the dielectric _constant so

Ae~)

associated with the Goldstone mode _m the ferroelectnc

liquid

crystals are related _to the helical

pitch

A direct relation between these two

physical

quantities is established We have calculated the electrical critical field for both DOBAMBC and DOBA-I-MPC

compound

from the measured temperature

variation of _so AeG and polarization without any adjustable parameter ^Just below the transition

temperature _region, the results obtained _agree

qualitatively

with the

expenmental

data

Away

from the transition temperature, ^there exist systematic deviations

In 1975,

Meyer

et al

[I]

discovered

pseudo-proper

ferroelectnc behavior _{m a}

liquid-crystal mesophase

that does not

display long-range

translational

order, namely

the SmC*

phase.

In

these studies the _now

widely

characterized

compound

DOBAMBC

(p-(n-decyloxybenzy-

lidene)-p-amino-(2-methyl-butyl) cinnamate)

was used To

date,

ferroelectric properties ^have been found not

only

_m the chiral-smectic-C

(SmC*) phase

but also _m the chiral-smectic-I

(Sml*)

and chiral-smectic-F

(SmF*) phases Among

these three

mesophases.

the most disordered _one,

SmC*,

has been the focus of _a lot of _attention, because it has

high potential

<ipplications

for fast

electro-optical switching

devices

[2] Upon heating.

the SmC*

phase

_can

undergo

a continuous

phase

transition to the smectic-A

(SmA) phase

which has _a

high enough

symmetry ^{such that} it does _not exhibit the ferroelectnc behavior Considerable

experimental

<tnd theoretical work has been carried out m the vicinity ^{of the} continuous SmA-SmC*

transition to

gain insight

into nature of the _more ordered SmC*

phase Nevertheless, only

<titer _a number of _{years was} it realized that the sixth order _{terms m} the _mean field free energy expansion had _to be included _{to account} for the unusual temperature variation of the heat capacity ^{and tilt}

angle (R)

and

accurately

describe the SmA-SmC* transition

[3].

The necessity ^{of the sixth order} terms indicates that the _{transition is m} the close vicinity of _{a mean-} field tncritical point

('j Pie,e,ii ac/dress King

MongJut's

Institute of Technology Thonburi, Pracha-Utit Road,

Bangmod, Raj-Burana,

Bankok, Thailand

798 JOURNAL DE

PHYSIQUE

II bt 7

Among

numerous

outstanding experimental efforts,

_one of the most celebrated works _is the

discovery

of the

anomaly

m the temperature

dependence

of the ratio

Pig through high-

resolution and simultaneous measurements of both tilt

angle (R

and

spontaneous polariza-

tion

IF)

_near the SmA-SmC* transition of DOBAMBC [4] ^Since

then,

the similar

anomalous behavior has been observed _{m many} other ferroelectnc

liquid-crystal compounds

by

various research groups

[5-7]

In order to

explain

the temperature

dependence

of the

polarization,

helical

pitch

and other

physical

_properties

(m particular

the

anomaly

_m the ratio

(FIR )),

_we

need,

at

least,

eleven expansion terms m the mean-field free _{energy expansion}

(the

_so

called, generalized

mean-field model

[4, 8, 9]).

So far detailed

experimental

tests of this

generalized

mean-field model have

only

been

carried _{out on} DOBAMBC

[9],

DOBA-I-MPC

[6]

and HDOBAMBC [5] ^{which have} very

similar chemical structures. All of these

compounds

_are Schiff-based

compounds

which _are not stable at elevated temperature

Many

_new and stable chiral smectic-C

liquid-crystal compounds

have been

synthesized

for device

applications

It would be very important to

demonstrate that the

generalized

mean-field model is _not just

applicable

to the

homologous

~enes similar to DOBAMBC On the other

hand,

the major motivation

[4]

^of proposing the

generalized

mean-field model _is the

experimental discovery

of the

anomaly

in the temperature v;triation of

FIR

which has been

subsequently

confirmed _m two other SmC*

compounds [7]

that _{are not} Schiff-based

compounds

Intuitively

_it sounds unrealistic that eleven terms m the mean-field free energy expansion

;tre needed to describe the SmA-SmC* transition But

judging

from the number of non-trivial anomalous behaviors m

physical

_properties to be

described,

the

eleven-parameter fitting

~cheme _no

longer

_seems unwarranted.

Moreover,

the three

leading

_{parameters m} the free

energy expansion can be determined

fairly precisely by fitting

to both the heat

capacity

and tilt

;tngle

data which _can be measured with very

high

resolution. The other

independent experimental

measurements give us a very

good

idea about the

magnitude

of another four coefficients

Consequently.

there _are

only

four parameter to be determined

entirely

from the

fitting

to the anomalies _m

FIR

and helical

pitch [9]

Under these circumstances, the

generalized

mean-field model gives an excellent _account for the temperature ^{vanation of heat} capacity, ^tilt

angle, polarization

and the _ratio

F/6,

but

only

_a

qualitative description

of the temperature

dependence

of the helical

pitch Meanwhlle,

we have tned to find _a

simpler

model to describe all these anomalies and failed As _a result, before _we add _more terms to the

generalized

mean-field model _to improve our

fitting

for the helical

pitch,

two different

,ipproaches

_can be taken to get further

insight

into the _nature of the SmC*

phase. First, direct, independent

confirmation of these four _new parameters ^{from other}

expenmental

_measure-

ments would be

extremely

useful The _most important one is the

biquadratic coupling

term

(F~

_{6~) between the}

polarization

and tilt

angle

This _is not _an easy

task,

because it involves the

high

order terms _m the free _{energy expansion.}

Secondly,

it _{is a}

good

idea to find _some consistency check of the

physical quantities

^which are

relatfid

_to the helical

pitch

In this spurt

we present one of these evidences from the temperature variation of the spontaneous

polarization,

electrical critical field

(E~)

and the dielectric constant

(so As~)

^associated with the Goldstone mode Both the electrical critical field and the dielectric constant _are

directly

i-elated to the helical

pitch.

Thus these _two

physical

quantities can be related to each other without the

knowledge

of the helical

pitch

The

temperature dependence

of electrical critical field _m the SmC*

phase

of DOBAMBC h;ts been measured

by

_many research _groups

ii

0,

iii

The data

reported by Dumrongrattana

,ind

Huang [10]

are

displayed

_m

figure

I Details of _our

expenmental

measurements _are

presented

m reference

[10]

Some of the

important

^facts are listed _m reference

[12]

Two s;thent features revealed

by

this set of data _are the

following I)

There exist

hystereses

N 7 ELECTRICAL CRITICAL FIELD 799

5

o

4

DOBAMBC

~ O

~s

~

£

~ ~

~

f+

+ + ^{~ +} + + ^{~ + + +}

+O+ ^{+ ~}

O

%/

~

+* ^~

,

°

$ ^{° ~}

O

j

² ~

(

~

o

~ ~

O

~ O

~ O

I

o

o s lo is

Tc.T (K)

Fig -Measured temperature

dependence

of the electrical critical field E~

(open

diamonds) and E~j (open circles) for DOBAMBC For comparison, the calculated values from equation (3) _are shown

,> + 's

between the

disappearance

and appearance of dechirahzation lines while the

applied

electrical field _is increased _or decreased

through

the critical field _region Here

E~

and E~j ^are the critical field for

disappearance

and appearance of dechirahzation

lines, respecti- vely ?)

Within _one

degree

_range below the _transition

temperature,

in a very narrow region of

applied

electrical field

(8

x 10~

v/m)~

the system ^exhibits a reentrant

behavior, namely,

existence of the SmC*-SmC-SmC* transition sequence as temperature ^decreases under _a

constant electrical field. One very important

point

should be mentioned here Because of the

hysteretical

behavior of the measured electrical critical field, _{a concave}

upwards

_{curve in} the temperature

dependence

of

E~

^is not sufficient _to guarantee ^{that there} exists a reentrant hehavior _{as a} function of temperature ^For

example,

_{a system} with temperature

dependence

of _E~~ and

E~

as sketched _in

figure

2 wJll _not have _{a reentrant} behavior The second

feature, n<imely,

the up ^turn of the electrical critical field _in the

immediately

_vicinity of the _transition

temperature is

directly

related to the decrease _in the _size of the helical

pitch.

Eu

Ec

Ed

Tc.T

Fig ^{? A} sketch of the temperature

dependence

of the electrical critical field E~ ^and E~ The dashed tile indicates the _minimum of the E~ Even though there exist upward turns near the transition

temperature m both E~ and E~, _m this special case one cannot find _any constant

applied

electrical field lh<il will leads _{to a reentrant} behavior _{as a} function of temperature

800 JOURNAL DE

PHYSIQUE

II N 7

Based _on the balance of elastic energy associated with the helix and electrostatic energy associated with the

polarization

and

applied

electrical

field,

_one obtains

[10]

an

expression

for the electrical critical field _to unwind the helical

pitch, namely,

E~

= ar ~K@

~/(4 PL~) ₍₁₎

Here K _is the elastic constant, L the _size of the helical

pitch.

The _same expression can be obtained from _one soliton solution to

electncally

unwind the helical

pitch _[13]

This

approach

has been discussed _in detail

by

de Gennes _in the context of

unwinding

cholestenc

pitch by

_an

<ipplied

_magnetic field

[14]

Figure

3

displays

the

anomaly

of

Ae~

^obtained from _a dielectric relaxation measurement of

DOBAMBC below the SmA-SmC* _transition

[15]

The

peak,

located just ^{below the}

transition temperature, is

directly

related to the

anomaly

_in the helical

pitch.

Now let _us derive _an expression of

Ae~

in term of relevant

physical

parameters. ^The order parameter

,issociated with the SmA-SmC

(or -SmC*)

transition can be written as x exp

(14

where _is the

magnitude

of the

angle

between the _smectic

layer

normal

(say

the _z

axis)

and the

long

_axis of the molecule and _~b the azimuthal

angle

of the molecule tilt with respect to, say, the _{y axis}

While the

angle

_{~b is} fixed within _a given domain in the SmC

phase,

_it

gradually changes along

the _{= axis in} the SmC*

phase

^{This leads} to the formation of helical

pitch Typically

the

pitch

size is on the order of _a few _microns. Since the molecular

length

_is

only

about 25

I,

_the

change

_{in ~b} between _successive smectic

layer

_is

quite

^small.

Consequently,

_{in a} moderate electrical field

applied

to unwind the helical

pitch,

_we will _assume that the

magnitude

of tilt

angle

_remains constant With the

applied

electncal field

being along

the _x-axis, the free- energy

density

_in the SmC*

phase

_can be written as

g = K@

~(d~b/dz)~/2

K@^~ L

(d~b/dz)

EP _{cos ~b}

Here _ii

= 2 _r

IL

_is the _wave vector associated with the helical

pitch (L Minimizing

this free energy

density,

_one obtains

K@

~(d~~b/dz~)

EP _sin d

=

0

60 8

DOBAMBC °

° o

o

~ o

o~ .

,

_p

~ o o o

o o~

~ ~ o o o _o ° ° °

~

~ _°

° Co°

m

E ~$

o

4 C'

~

~ o

o

o o

3

j

C-

/

o

o o

0 4 8 12

Tc.T

(K)

~ig 3 Temperature variation of

polarization (solid dots)

and dielectric

strength

(open circles) _m the SmC~

phase

of DOBAMBC

N 7 ELECTRICAL CRITICAL FIELD 801

In the case of _a small

applied

electrical field and _in the limit of the linear response region, we

obtain

go

Ae~

=

(PL)~/(8

ar ~K@ _~)

(2)

Here _{s~ As}

~ is the dielectric

strength

in the Goldstone-mode of the induced

polarization

due to the

applied

electrical field

Combining _equations (I)

and

(2),

_one obtains the

following

relation

E~

=

(ar

^~ P

)/(32

_go

Ae~) (3)

Here the electrical critical field _is

directly

related to the

polarization

and dielectric

strength.

Near the SmA-SmC* _transition of DOBAMBC and

DOBA-I-MPC,

_we have measured the

temperature ~anation of both

polarization [4, 6, 15]

^{and dielectric}

strength [15]

The results

<ire

reproduced

m

figures

3 and 4 for DOBAMBC and

DOBA-I-MPC, respectively

Without

any

adjustable

parameters, equation

(3)

allows _{us to} calculate E~ ^{from P and} go

&e~

^The calculated results _are

displayed

_in

figure

I and

figure

5 for DOBAMBC and

DOBA-I-MPC, respectively

The measured temperature

dependence

of the electrical critical field

E~

and

E~ near the SmA-SmC* _transition of DOBA-I-MPC _is shown _m

figure

5

(see

Ref

[12])

Qualitatively,

_equation

(3)

_gives reasonable relation among the three

physical _quantities

_in

describing

the _nature of the SmC*

phase

of both DOBAMBC and DOBA-I-MPC. The difference between the measured and calculated electrical critical field _is

clearly

not

negligible, particularly

_m the region away from the transition temperature. ^{At this}

point,

^the effect of the surface treatment used for

alignment

_on the measured results _is not clear to _us

Note, _in the _case of dielectric measurements, a magnetic ^field was used _to

align

the

samples

Careful measurements on the _same

sample

for all three

physical

quantities,

namely,

E~~ ^P and _so

Ae~

may allow _{us to} eliminate this

plausible problem.

One final remark _is that the major difference between the two

compounds,

_we

presented

_in

this paper, is that the chiral group of DOBA-I-MPC _is closer to the central part ^{of the}

molecule than that of DOBAMBC. This results _{in an increase} of factor of three in the

200

~°

/

^~~° ~ _o

~ ~ ~ o o o o o

o

I ^°~

^:

°

loo

~

^°

,o°

t

~°°

j.?

^c~m

~

Cl

°

50

S DOBA.i-MPC

o o

o s lo is

Tc-T

(K)

~ig 4 Temperature dependence of polarization (solid dots) and dielectric strength (open circles) in

[he SmC'

phase

of DOBA.I-MPC

802 JOURNAL DE

PHYSIQUE

II N 7

DOBA-I-MPC o

~

o

o a

o

~

O a

I _O

~ _O a

a ~

~

^0.6

~

°

~ ~ .

~ ~ ~ a ~ .

j '$'~

^~

o-o

o s io

Tc-T

(K)

Fig

5 -Measured temperature variation of the electrical critical field E~ (open circles) ^and

E~j (open squares) for DOBA-I-MPC For comparison, ^{the calculated values from} equation (3) are

,hown _as solid dots

magnitude

of

polarization

for DOBA-I-MPC

(see Figs.

3 and

4) According

to equation

(I),

we believe that this _is the major factor that the electrical cntical field for DOBA-i-MPC _is about three _times smaller than that for DOBAMBC

This work _was

supported

_in part

by

the U

S.-Yugoslavia

Joint Board

Program

for Scientific and

Technological Cooperation sponsored by

^the National Science Foundation One of _us

jCCH)

would like _to

acknowledge

the support of the Donors of the Petroleum Research Fund~ administered

by

the American Chemical

Society

References

Ii

MEYER R B, LIEBERT L, STRzELECKI L and KELLER P., J Phys France Leii 36 (1975) L69

[2] ^{CL~RK N A and LAGERWALL S} T,

Appl

Phys Len 36

(1980)

899

[3] ^{HUANG C C and VINER J} M, Phys Rev A 25 (1982) 3385,

DUMRONGR~TT~NA S.. NouNEsis G and HUANG C C, Phys Rev A 33

(1986)

2181

[4] DUMRONGRATTANA S and HUANG C C~ Phys Rev Len 56 (1986) 464

[5] ^EzC~RRA A PEREz JuBmDo M A.. DE LA FUENTE M R, ETXEBARRIA J.. REMON A, TELLO

M J.

Liquid

Crysi 4 (1989) 125 and references found therein Here HDOBAMBC refers to

(S)-2-hydroxy.4.decyloxybenzyhdene.p.amino.(2-methyl.butyl)

cinnamate

[6] ^{H~ANG C} C, DUMRONGRATTANA S NouNEsIs G. STOFKO J J and ARIMILLI P A, Phys

Ret A35 (1987) 1460 Here DOBA.I.MPC refers to

p.decyloxybenzylidene.p"amino-I-

methylpropyl cinnamate

[7] PARMAR D S., HANDSCHY M A and CLARK N A., llthlnternational

Liquid

Crystal

Conference,

Berkeley,

California, 1986, Abstract b-046.FE, SKARP K private communication

[Xi ZFKS B. Mot Cr_~si Liq Crysi l14 (1984) 259

[9] HUANG C C and DUMRONGRATTANA S

Phys

Rev A34

(1986)

5020

[10] DUMRONGRATTANA S and HUANG C C, J Phys France 47 (1986) 2117

bf 7 ELECTRICAL CRITICAL FIELD 803

IIII M~RTINOT-LAGARDE Ph, DUKE R, DURAND G, Mot

Crysl Liq Crysl

25 (1981) 249

KONDO K. SATO Y, TAKEzOE H, FUKUDA A, KuzE E, Jpn J

Appl

Ph_vs ²⁰

(1981)

L871,

K~i S, T~KATA M, HIRAKAWA K, Jpn ^J

Appl Phys

22

(1983)

938,

RozANsKi S A, KuczYNsKi W., Chem Phys Len 105 (1984) 104,

TAKEzOE H~ KONDO K, MIYASATO K, ABE S, TSUCHIYA T, FUKUDA A, KuzE E,

Ferroelectrics 58

(1984)

137

[1?]

The DOBAMBC

compound

_was purchased from Fnnton Laboratones, Inc~ PO Box 2310,

vineland, NJ 08360~ U-S A. The

compound

was

recrystallized

twice from methanol

by

_us.

The DOBA-I.MPC compound was synthesized

by

Mr J J Stofko _in 3M Center, St Paul, MN 55113. US A We did _not check the optical _purity of the samples ^The

well-aligned liquid-crystal

sample _in planar

configuration

_{was grown} between _a pair of ITO (indium.tin- oxide) coated

glass

slides To achieve

high-quality alignment,

the

glass

slides _were

spin-coated

with nylon and then rubbed _{on cotton} cloth The

samples

of 25 _~Lm and 75 _{~Lm in} thickness

were used

Experimental

results from the

samples

with these _two different thicknesses _{are in}

good

agreement

[13] ^URBENC B, ZEKS B. and CARLSSON T, Ferroelectncs, to be

published

II 4] DE GENNES P G The Physics of

Liquid Ctystal

»

(Clarendon

Press-Oxford, 1974)

[15] LEVSTIK A, KUTNJAK Z FILIPIC C, LEVSTIK I, BREGAR Z., ZEKS B, CARLSSON T, Phys Rev A 42 (1990) 2?04