Temperature dependence of electrical critical field for one SmC* material

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Temperature dependence of electrical critical field for one SmC* material

S. Dumrongrattana, C.C. Huang

To cite this version:

S. Dumrongrattana, C.C. Huang. Temperature dependence of electrical critical field for one SmC*

material. Journal de Physique, 1986, 47 (12), pp.2117-2120. �10.1051/jphys:0198600470120211700�.

�jpa-00210405�

Temperature dependence ^of electrical critical field for one SmC* material

S. Dumrongrattana (1) ^{and C. C.} Huang

School of Physics ^and Astronomy, University ^of Minnesota, Minneapolis, ^Minnesota 55455, ^U.S.A.

(Recu ^{le 23 mai} 1986, r6vis6 le 19 août, accept6 le 21 août 1986)

Résumé.

Le pas de l’hélice d’un smectique C chiral soumis à

champ électrique croissant à partir ^{de zéro} disparaît pour

valeur critique Eu ^du champ électrique. ^Dans

champ décroissant, le pas hélicoïdal

réapparaît à

^autre champ critique Er. ^Nous

Eu ^et Er ^{dans la} phase smectique ^{C* du} DOBAMBC ;

ces

valeurs suivent

loi en (Tc-T)c,

^exposant

^{voisin de 0,5.} L’hystérésis ^0394E

Eu - Er ^semble

tendre

zéro comme (Tc - T)x

^{0,57 ± 0,09.}

Abstract.

In

increasing applied electrical field from zero, the helical pitch ^{in the} chiral-smectic-C

(SmC*) ^{phase will} disappear ^at

^critical field (Eu). ^{In a} decreasing electrical field, the helical pitch ^will

reappear ^{at another critical} field (Er). ^{Both Eu and Er} have been measured in the SmC* phase ^of

DOBAMBC and behave like (Tc-T)c ^{with exponent}

approximately equal ^{to 0.5. The} hysteresis

0394E

Eu - Er

^to approach

with (Tc - T)x ^and

^{0.57 ± 0.09.}

Classification

Physics ^Abstracts

61.30

77.60

The discovery ^of

pseudo-proper

ferroelectric behaviour in ^one liquid-crystal compound by Meyer

et al. [1] ^{led to} intensive studies of both experimental

and theoretical’ aspects of ferroelectric liquid crystals.

From symmetry consideration, the fundamental

ingredient ^{to create a} ferroelectric state is to remove

the centre of inversion symmetry. ^{In some} liquid- crystal mesophases ^with sufficiently ^low symmetry, this can be accomplished by putting ^{a chiral} asymme- tric part ^to the molecule. Then the helical pitch ^will usually show up in the corresponding liquid-crys-

tal mesophases, namely, ^the chiral-smectic-C

( SmC * ) , chiral-smectic-I ( Sml *), and chiral- smectic-F (SmF*). Among ^these mesophases, ^the

most disordered one, i.e., ^{SmC * has drawn a lot of}

attention. The SmC * phase ^has liquid like molecular

arrangement within the smectic layer ^{and a finite tilt-} angle between the long ^{axis of the} molecule and the smectic layer normal. In heating usually ^{the SmC *} phase ^will undergo ^a continuous phase transition to

the smectic-A (SmA) phase. This transition has been found to be mean-field like [2, 3].

Because of the existence of the molecular chirality,

the smectic layer ^{in the SmC *} phase ^{will form}

helicoidal structure with pitch ^{L about a few microns}

in size which is much larger ^than the smectic layer

thickness d = 25 A. Consequently, ^the interaction associated with helix is very weak. Thus far, ^the

anomalous temperature dependence ^{of the helical} pitch [4, 5] ^{in the} region just ^{below the SmA-SmC*}

transition has been found to be quite ^{common and}

noticeable in the most chiral-smectic-C liquid-crystal compounds. Although ^the simple Landau free energy expansion [6J ^{fails to} predict ^this anomaly,

numerous physical phenomena just ^{below the}

SmA-SmC

transition seem directly ^{related to this}

helical pitch anomaly. ^{At least three} theoretical attempts [7, 8] have been made to account for the helical pitch anomaly. ^{The two different} approaches [7], namely, ^{the critical} fluctuations argument by

Yamashita and Kimura and the anomalous flexoelec- tric coefficient approach by Osipov ^and Pikin, gave

qualitatively reasonable account for the anomalous behaviour of the helicoidal pitch ^versus temperature.

In light ^{of our recent} high-resolution experimental

results [9-11] ^{on the} temperature dependence ^{of the}

tilt angle ^and spontaneous polarization, ^{we have}

demonstrated that it is not sufficient to simply

propose ^a theoretical model to fix up the tempera-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198600470120211700

2118

ture anomaly ^{in the} helicoidal pitch. ^{The details of}

our argument ^are given in reference [11]. ^{On the}

basis of our high-resolution experimental ^{data on the}

temperature variation of ^heat capacity, ^tilt angle,

and spontaneous polarization ^{near the SmA-SmC*}

transition of DOBAMBC (p-decyloxybenzylidene- p’-amino-2-methylbutyl cinnamate), ^we have propo- sed a generalized mean-field theory [9-11], ^{which is}

an extension of the model suggested by ^Zeks [8] ^in,

an attempt ^to explain ^the helicoidal pitch anomaly,

to describe the nature of the SmA-SmC* transition.

Specifically, ^this generalized mean-field _{model gave} very good fitting ^results [11] ^{on the} temperature variation of heat capacity, ^tilt angle, spontaneous polarization ^{and the} anomaly in the ratio of the spontaneous polarization ^{to tilt} angle. Furthermore,

reasonable fitting [11] ^{can be obtained for the} existing ^{two sets of} helicoidal pitch ^{data. As an}

extension of our characterization of the SmA-SmC * transition of DOBAMBC, ^{here we will} report ^our electrical critical field measurements in the chiral- smectic-C phase ^{of DOBAMBC.}

At least five measurements [5, 12-15] ^{have been} reported ^{on the} electrical critical field for DOBAMBC in the SmC * phase. Recently ^{we have}

achieved in preparing high quality large ^area single

domain (- 18 mm by 12 mm) ^{SmC *} samples. ^In

addition to our high-resolution measurements on the spontaneous polarization ^{and tilt} angle [9,10], ^these samples ^{allow us to obtain} good quality ^{data from}

the electrical critical field measurements. The impor-

tant steps [16] ⁱⁿ preparing ^our sample ^{cells are the} following. ^{First, a thin film of} nylon polymer ^was spin ^{coated on a cleaned} glass ^{slide. Then unidirec-}

tional rubbing ^the polymer ^{film was done on cotton}

cloth. The sample ^cell consisting ^{of one} pair ^of glass

slides with one of them being prepared in this way will provide ^a unique direction for liquid-crystal

molecules to align ^{in a slow} cooling ^{from the} isotropic ^{to the SmA} phase. ^Further cooling ^{down to}

the SmC * phase, ^the sample retains the planar alignment. ^{Under a} polarizing microscope, ^{one can}

see uniform and well-aligned dechiralization lines

throughout ^the sample. ^The dechiralization lines are

the defect lines to accommodate the balance of an

alignment ^{force on} molecules created by the walls of the sample cell and the intermolecular twisting

force. It has been demonstrated that the spacing

between dechiralization lines is closely ^{related to the}

helical pitch [17].

Our DOBAMBC sample ^was purchased ^from.

Frinton Laboratories [18] ^and recrystallized ^twice

from methanol. For a thickness of 25 _Rm, our typical sample resistance ^over the area 18 mm by ^{12 mm is}

about 40 Mfl. This indicates the high quality ^{of our} sample. ^The sample ^{cell was} kept ^{inside a Mettler}

hot stage, ^an FP80 central processor controlled the

sample temperature ^{with a} resolution 0.1 K. The

sample ^{was examined under a} polarizing microscope

to determine ^the disappearance and reappearance of dechiralization lines while the applied electrical field

was changing step by step ^or slowly increasing (decreasing) ^through Eu Er ^{with rate approxima-}

tely 0.5 V/min. Our high quality samples with very

good alignment ^and high resistance value (about

40 MQ) ^{allow us to determine the} critical electric field E. ^for dechiralization lines disappearing ^from

entire field of view (0.3 ^mm dia) ^and Er ^{for the first}

reappearance of dechiralization lines with high ^confi-

dence. The location of the last group of dechiraliza- tion line(s) ^{in the} increasing field and that of the first group of dechiralization line(s) ^{in the} decreasing

field may ^{not occur} in the same region. ^This

indicates that our glass surface is fairly homogeneous

and will not preferentially ^nucleate dechiralization lines in ^some particular ^{area. This} observation only

holds in the centre area of ^our sample. ^{Near the} edge

of our sample, ^{a few} dechiralization _{lines may} stay while E

E. ^{and the rest of} sample already ^{in the}

uniform polarization ^state. Furthermore, the diffe-

rence of the critical fields from the helix to the twisted and the twisted to the uniform state is within

our experimental resolution (about 0.07 V for ^our 25 _pm samples). Glogarova ^{et al. have} reported

similar observation [17]. Among ^all our measure-

ments, hysteresis ^was found between E. ^and E,. ^The

temperature dependences ^of E. ^and Er ^are displayed

in figure ^{1 as} log-log plots ^of Eu ^and E, ^versus Tc - T, respectively. ^Here T, ^{is the SmA-SmC*}

transition at zero applied ^electric field and is about 93.7 °C for our sample. ^{In order to be sure that our}

surface treatment does not have any significant

effect ^{on our} experimental results, measurements have been done on samples with thickness of 25 _pm and 75 _JLm. The same results were obtained within

experimental ^errors. Our results can be fitted to a

simple power law E oc (Tc - T) c ^{with exponent}

c =

0.53 ± 0.03 and 0.51 ± 0.02 for Eu ^and Er, respectively, ^{in the} temperature range 0.7 K Tc - ^{T 18 K.} Beyond this range the criti- cal field E. ^and E, ^{start to deviate from a linear fit in}

the log-log plot. ^{The deviation in the} region far away from Tc ^{is much} smaller than that near the Tc. ^The

Fig. 1.

^A log-log plot ^{of the} temperature dependence ^of

critical fields E. (circle) ^and E, (square).

latter one is due to the anomalous behaviour of the helical pitch ^{in the} vicinity ^of Tc.

The difference of Eu ^and Er ( AE ^{= Eu -} Er ⁱⁿ

our critical field measurements is plotted ^{as a}

function of T, - ^T in another log-log plot ⁱⁿ figure ^2.

Although ^{the data are somewhat} scattered, the

simple power law ð.E oc

(Tc - T) x ^{with x =}

0.57 ± 0.09 ^seems to describe the ata in a wide

temperature range from 0.1 K ^to 22 K below

T,. ^{Our results suggest that the} unwinding ^transition

between the SmC * and the SmC phase always ^has hysteresis. ^This contradicts with the theoretical pre- diction by Michelson et al. [19].

Fig. ^{2. - A} log-log plot ^{of AE with} temperature

( Tc - T) .

In addition to the hysteresis ^between E. ^and Er,

the deviation in the high temperature ^{side of} figure ¹

shows clearly ^{the reentrant} SmC *-SmC-SmC * beha- viour in some range of applied electric field. Similar

reentrant behaviour has been reported in the magne- tic field-temperature phase diagram by ^{Musevic et}

al. [20]. ^In comparing ^{with the} existing data, Rozanski and Kuczynski [14] and Takezoe et al. [15]

have reported ^{the reentrant} behaviour but not the

hysteresis. ^{Kai et al.} [13] ^{have seen the} hysteresis ^but

failed to reveal the upturn ^{of the critical field}

because of relatively large uncertainty of the data in the immediate vicinity of the transition temperature.

The existing phenomenological ^theories predicts

both hysteresis [13] ^{and reentrant behaviour} [21].

Based on the balance of elastic energy associated with the helix and electrostatic energy associated with the spontaneous polarization ^and applied ^elec-

tric field, ^{one obtains an} expression for the electrical critical field to unwind the helical pitch, namely,

Ec = 1T4 K02/ 4 PL 2 Here K is the elastic cons-

tant, ^{P the} spontaneous polarization, 0 ^{the tilt} angle, ^and Lo the helical pitch ^without applied ^field.

Using ^the existing ^available experimental ^informa-

tion around Tc - ^{T =} 5 K, i. e. , ^P

⁴² I-LC/m2

(Ref. [9]), 0

^{0.37 radian} (Ref. [9]), Lo

^{2.5 03BCm}

(Ref. [22]), ^and K = 3 X 10-12 N (Ref. [11]), ^we

have Ee

^{4 x 104} V/m which is in reasonable agree-

ment with our experimental results. In addition, Ee ^is inversely proportional ^to L02 ^and Lo ^{has a} peak

within Te - ^{T 1 K.} Consequently, E, ^{should have}

a dip ^{at the same} temperature [21]. ^This explains ^the

reentrant behaviour. Michelson et al. [19] ^have proposed ^{a Landau} theory ^{of the} transition between

a uniformly polarized ^SmC phase ^{and a distorted}

SmC * phase in the presence of ^an electric field

parallel ^{to the smectic} layers. ^{Here the distorted} phase ^means that the molecular helical arrangement

is deformed under the applied ^electric field. In the

field-temperature ( E - T ) phase diagram, they

show that a tricritical point Et, Tt ^{will separate a}

continuous SmC *-SmC transition for a small applied

field from a discontinuous one for ^a large applied

field. Here T,

T, - ^0.24 (Tc - Trc) , ^{and T, is the}

SmA-SmC * transition temperature ^without applied

field and Tc, ^{the SmA-SmC} transition temperature

for the racemic mixture of the same liquid-crystal compounds. ^{In the case of DOBAMBC,} T, - T,’ =e ^{0.7 K} [23] ^thus Te - Tt = ^{0.17 K. This} disagrees ^{with our results.} Hysteresis ^{is still} clearly

detectable with Te - ^T

0.1 K. This semimicrosco-

pic theory ^{based on one} important assumption, ^i.e.,

the spontaneous polarization (P) ^is proportional

to the tilt-angle ( 0 ) . Recently ^{our detailed} experi-

mental work has revealed that P / 0 ^is slowly ^decrea- sing function of temperature ^for Tc - ^T

2 K and shows a dramatic drop ^near T, [9,10]. Consequently,

this theory ^{is not} sufficient to provide ^{a correct} picture ^{near the} T,. Kai et al. [13] ^have proposed ^a

mean field theory and attributed the hysteresis ^{to the}

internal electric field caused by ^the polarization alignment by ^the applied ^field. Away ^{from the}

transition temperature Tc, ^the predicted temperature dependence ^{of the} unwinding ^field Eu ^{and rewin-}

ding ^field Er , ^{i.e., E,} (Tc - T) , ^{is in fairly}

good agreement ^{with our results.} Finally, Glogarova

et al. [17] ^have argued ^{that the} activation energy is involved in the annihilation and the creation of dechiralization pairs ^{and thus} hysteresis should exist

during these processes. So far all the theories give qualitative argument ^{for ours and the} existing experi-

mental results on the temperature dependence ^{of the}

critical field. However, quantitative description ^or fitting by any existing theory ^{seems still} fairly

remote. The complication may be related to the

sample-thickness dependence of the helicoidal pitch reported by Takezoe et al. [24] ^and/or Complicated

nucleation processes of dechiralization pairs ^{on the}

substrate surface.

To justify ^our electrical critical field ^measure-

ments, ^{let us} compare the size of the P . E term with the dielectric anisotropic ^term ( 8 I1T ^{EE 2 For}

example, ^at T, - ^{T = 5 K, P}

⁴² JLC/m2, ^and

E ⁼

2.1 x 10-11 F/m, ^with Eu

^{3 x 105 VIm,} we

2120

have 8117 ₀ ^eE2/ P . E >

^{6 x 10- 3. Thus, the} strength ^{of the} applied ^{electric to} unwind the helix is small enough ^{that the} dielectric ^{term can be} ignored.

In conclusion, ^both hysteresis in the critical field and the SmC *-SmC-SmC * reentrant behaviour in some

range of applied electric field have been observed in

our well-aligned ^DOBAMBC samples. It would be

interesting ^{to test our} observation with different surface alignment technique. Once different surface

alignment being identified, ^we will carry ^out this test. A comprehensive theoretical calculation to

explain ^our results is not yet ^available.

Acknowledgments.

We would like to thank J. Novack for helping ^us

with the recrystallization process, W. Huffman for

providing ^{the ITO coated} slides, ^{and S.} Sidiqi ^{and L.}

Wong ^for help ⁱⁿ carrying ^{out the} experiments. ^This

work was partially supported by ^{a research contract}

from Minnesota Mining ^and Manufacturing Company, the Centre for Microelectronic ^and Infor- mation Sciences, University ^of Minnesota, ^{and the}

National Science Foundation, Solid State Chemistry,

Grant No. DMR-8503419.

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technique

^{similar to}

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et al. (Ref. [24]).

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