Indian Journal or Pure & /\ppli ed Ph ys i c~ Vo l. 3X. Jul y 2000, pp. 504-5 1 I

Relaxation l110des in ferroelectric smectic C liquid crystals: Effects of bias field

K K Raina & Jasjit K Ahuja

School or Basic & App li ed Sciences. Thapar Institute or Engineering and Technology. Pa 'L i a l ~ 1 147004

Received 20 April 2000. accepted 7 June 2000

Dielectri c properti es or a 1;lrge spontaneous polari sati on rerroe lectri c l iquid crys talline mixture FLC-6430 (Ho Ilman-La-

Roche) h,IVC heen ~t ud i e d in the SmC " and SmA phasc in the rrequcncy range 100Hz to I MH z in planar ori ented cc ll ~ under

the in ri uence or vary ing ex te l'll ;i1 dc hias. Se veral relax at ion modes were ohserved. T he crrect or hi ;IS rield and temperature on

these relax; ltioll lIl ode~ h ; l~ heen inves tigated. The observat ion or a re laxati on mode namely new rcLixation modes (N RM ) in

the high rrcquency range ahove 100 kH z has heen reported. The dielectri c increment o r N RM wa~ very small (L'I£~RM == 5.X4)

a~ compared to the Golds tone mode (L'lE(;M =:l90) .

I Introduction

The ex istence of fe rroe lectri c properti es in chiml smectic C (SmC*) liquid c rys tals was first demonstrated by Meyer e l 0 1.1 and is now firml y es tabli shed on the basis of ex perimental and theorctic ~d in vesti gati om?--'. The fe rroe lectri c stllec ti c C phase is low symmetri c with Cc sy mmetry e lement. It has a layer structure and is forrned due to the modulati on of an incommensurat e structure. The azimuthal angle of long molecular axis processes he licoidall y around layer normal whil e go ing from one smectic layer to anoth er. During this process

I I· I . . I I ~ · IO a le Ica strIpe tex ture appears In t 1e samp c .

Die lectric spectroscopy stud ies of ferroe lec tric smec-ti c C liquid crysta ls (FLC) has been carri ed out in large number of liquid c rystalline cO lnpounds and the ir mi x-ture 1·7 It gives informati on about vari ous collec ti ve and molec ular processes assoc iated with the he li x dynamics. Die lectri c res ponse of FLCs mainl y consists of four re la xati on modes . Two modes are due to the flu ctuati ons of polari zati on order parameter havin g re laxation fre-

quencies o f the order of - SO() MH z. The other two important re lax · ti on 1110des connected to the direc tor fluctuati ons are usuall y referred as the Goldstone mode (GM ) and the Soft mode (SM). These modes occur due

to the phase flu ctuati ons of the azimuthal an gle (

~ [ ( 1' ) [* (CD , 1') =[ + ------

~ I ( . )1 - 11 + I CD 1:0 . .. . (2)

where 1:" and a are the characteri stic re laxation time and di stributi on parameter res pectivel y. ~[( T) is the die lec-tri c strength of the mode.

In this paper, we present die lectri c re laxati on studies in a large spontaneous polarisation Illul ti-component

RAINA & AHUJA: LIQUID CRYSTALS 505

FLC mixture in SmC* and SmA phases and report the observation of new relaxation mode in it. Effects of bias field on various relaxation modes have been investigated in different frequency regions .

2 Experimental Details The frequency and temperature dependence of the

complex dielectric permittivity has been studied in a novel ferroelectric liquid crystal mixture FLC-6430 (ob-tained from Hoffmann-La Roche, Switzerland) . At

22°C, this mixture has short hel ical pitch (- 0.43 ).1m),

large spontaneous polarisation (- 90 nC/cm1) and large

tilt angle 27°. It has a wide SmC* phase from -11 °C to

55°C followed by SmA phaseD .24 .

We carried out dielectric measurements on the FLC

mixture in 7.5 ).1m thick LUCID ce1l 25 . This cell thick-

ness was large in comparison to the he lix pitch (- 0.43

).1m) of the mixture. The sample was sandwiched be-tween two conducting indium tin oxide (ITO) coated glass substrates . The substrates have been pretreated with polyimide (parallel rubbing direction). The liquid crystal mixture was filled in the cell by the capillary

action at 65 °C (above isotropic temperature of the

sample) and then cooled to SmA phase at 0 . 1 °C/min. in

presence of an ac electric field of (- 10Hz and 10V ) in PI'

a LINKAM tempe rature programmer (model TP90) cum hot stage (THS 6(0) . The effect of the electric field on a randoml y aligned sample was to force the mole-cules in a layer to lie parallel to the rubbing direction so that a mono-domain well aligned sample cell could be obtained. This texture was observed through GETNER polarising microscope . The complex permittivity was measured using Hewlett-Packard Impedance Analyser (model HP-4I92A) in the frequency range 100 Hz-I MHz at diffe rent temperatures. The effect of bias fields and temperature on various relaxation modes was then investigated. The sampl e cell was ca librated using air and benzene as standard reference media.

3 Theoretical Background It is known that due to the presence of chirality in

SmC* phase '} the in-plane polari sat ion perpendicular to the directio n of the tilt is CTiven by P = P X + P Y

b X Y ,

therefore the order parameter (~) and the polarisation (P) can be written as:

S I = 8 0 cos ( q Z) , ~ 1 = 8 ) sin (q Z) - ( .. . (3)

P \. = P ) sin ( q Z ) ,P = P cos ( (I Z) . ( r 0 ... (4)

where Z is the coordinate axis normal to smectic layer

plane, q = 2nlL is the wave-vector of helical pitch (L) 8" and Po are the tilt angle and spontaneous polari sation respectively .

In the absence of an external dc bias GM appears at

low frequencies whereas in the high frequency region (>

50 kHz), SM is observable near T,,*II' The dielectric response in terms of dielectric susceptibility of these two

modes is related to the dielectric strength as X= ca t.c; where ca is the absolute permittivity of free space and t.c = Co - E~, Co and E~ are the static and infinite frequency dielectric constants respectively.

The external dc bias applied to the sample di sturbs

the helix in two ways : firstly in weak fields, the helix is

di sturbed due to the linear coupling between polarisa-

tion (P) and the electric field (E) . The net induced

polarisation thus increases. The dielectric response in

that case will be X = XGM + XSM ' where XGM and XSM are the dielectric susceptibility of GM and SM respectively.

Here GM appears with suppressed dielectric response.

The dielectric response is thus defined as:

< P> X=Lt --' -

. F.~() E ... (5)

where Pi is the average induced polarisation and E is the magnitude of the applied static electric permitti vi ty .

Secondly in presence of both strong dc and ac field,

the coupling between P and E becomes so strong that the helical texture breaks up into the modulated domain

structures as shown in Fig. I . It reduces the electrostatic 26 Th d' I . ener£!v . e Ie ectflc resoonse to the sllsceotibility

,0 ,- ~

;.-:i ~ ----'

~ !-" ~,

~~ ' .... ~

(b)

E>Eo

~" ~ ~

r----:; /J

,C+

(e)

E»Eo

:~ , . :- -t '-->

t--' ,.0-: ~

~ '--'---'

"--6., ~ -: ~.~ -.....

Fig. I - Inrluer.ce of dc and alternating field on the structure of

ferroel ectri c Smecti c C phase. The dc field strength is increas ing

from (b) to (e). En is the zero bi as ;md Ec is the critical field . Nails

represent the molecules and arrows the SmC director

INOlA N J PURE & APPL PHYS. VOL 3R. JULY 2000

wOlild th en be = X I )~ I + X I)~ I ' XIlM and XSM are the domain mode DM and SM susceptibiliti es respecti ve ly.

4 Results and Discussion Fig. 2(a) shows a typical re laxa ti on process in the

form of Co le-Co le pl ot in FLC mi xture at 35°C. It is seen that in ;Idditi on to GM, one more re laxation mode ap-pears Alove 120() kHz. T h is mode could not be CO l11-pletel y suppressed hy an ex tern ;!I dc fi e ld of magnitude

O.67 V/plll. In the absence of ex tern al bias, it was foun ci

th;lt it s die lec tri c increment (~E == 5.i{4) was small as co mpared to that of GM (~£(;~ I ) = 39()). We ca ll it a new re laxa tion mode NRM. The ori gi n of thi s mode can be attributed to the surface d fec ts and th us could ha ve resulted from the surface pinning and tin y domain s, whi ch contribute to he li x unwindin g at the surfaces17-2'J. It is al so c lear from Fi g. li b) 1 in se tl that RM st rongly depends on ce ll thi ckness. Thi s dependence may be due to th > increase in surface anchorin g energy . Fi g. 2(a) Iinse tl .~h()w s contributi on of GM tn die lec tri c permit-

ti vity in the form of abso rpti on 1£'((1)) 1 and di spersion

Ir"((0) 1 curves at 35°C.

In the SmC* phase the die lec tri c permitti vity consists of contributi ons due to the GM and NRM. In alternatin g fi eld. contributi ons to the co mpk x permitti vit y due to these modes I,~ shall be:

~ E (;~I + I + ( i ()) 1 (; \1 ) I - (\ ; ~ I

~ r N R ~ I ... (6) I + ( . r" T )1 " .' I(~ I I UJ ' N 1< ~ I

~f(;:d and ~£N R ~. I arc the die lec tric strength s. whereas 1( ancl a represent s the re laxa t ion times and the d istri but ion par;1Il1eters of GM ancl NRM respec ti ve ly. T he NRM

relaxati on frequency (J;NI{~ I ) in 5 pm cell at 35°C \vithout hias was cal cul ated to be 427.8 kH z. T hef I (~ I has not

been meas ured un 7.Sp m ce ll due to its partial refl ec tion as show n in Fi g.2( h) 1 in se t 1 The empty ce ll diclnot show any re i;J xati on Li p to I MH z (mc;lsura ble range of fre-quency in our case). As we approach near 7 ~"i\' the SM domina tes over both GM and NRM as in show n in Fig .

3(a.h). We found that the bias 0.67 V/pm was not suffic ient to suppress the GM . In order to stud y the presence of other re laxat ion processes. we app li ed a dc

field up to 2.0 V/p m to the sa mpl e ce ll to suppress the GM mode. The typi ca l frequency dependence of the illlagina ry part of the cOlllpl ex permitti vity at diffe rent

bias fi e lds is shown in FigA. We noti ce that at 1.3 V Ipm ,

£" decreases rapidly due to the suppress ion of he li x.

Here NRM is c learl y re fl ec ted due to the surface pinning

at hi gher bias as can be seen in Fig. 4 1 in setl Fig. 5 shows the effec t of bias on the re laxat ion

frequency of GM . It is seen that with the in crease of

ex ternal dc fi e ld ,fGM increase from 0 .6 k Hz at 1.3 V l~lIll

to 2.86 kH z at 2.0 V/j..lIn. Corres pond ing di stributi on

parameter a lso changes from 0.1 8 at (l.G7 V 1p.1ll to 0.27

~

~ w

450~~45cOG===========~~~-----:~((~) 3S'c 350C a

400

350

300

250

'" 200

150

100

50

0 0

600

5.50

' 500

450

400

350

300

250

200

150

100

50

a

>- 400 Po4nI O .~TVI~ ~ 350 -0-, -.- , • 0.0 V/llm ~ -.-... - ...-. ... . ~ 300 '" 0.67V/llm Cl. 250 u U 200 .9! !1 150 o

100

0.01 0.1 1 10 100 1000

• lit'"

Frequency (kHz)

NRM

50 100 150 200 250 300 350 400 450

14 (b ) - . - 5 .0~m r • 501-1 111 12 ...... 7 5~m

NRM j / • 7.51-1111

10

8

E£ " 6 /:>~."-.J 4

2

0 0 2 4 6 8 10 12 14 .::

•••• • • ,. ........ III I i ¥ • "j ..... " .. I",'I,','I""'·,"I"···II,'I' ... ,III.," ••. a 50 100 150 200 250 300 350 400 450 500 550 600 ,

E

ri g. :2 - (,I) Cole-Col e r l o t~ or GM and IRM in the SIllC"

pha~c. Il n~c I I show~ Ihc dispcrsi()n iE'(Ul) 1 curves;l1 c1 i lTcrcnl

cx tcrn

RAINA & AHUJA LIQUID CRYSTALS 507

at 1.3V/pm and thcn increases furt her. At bias greater

than 1.3 V /p m, we be l ieve that the changes ina. andfa re

20~~--________________________ ~ (0 )

54°C 15 • 0.0 V/~m

T 0.67 V/~1I1

__ ... "".re ...... T .. T..;.T T 'r" ............... 10 15 20 25 30 35

12~~------______________________ ~

(b) 10

8

6 rOO 4

2 .-o

o 2 4

-

6, 8 E

f.'

• O.OV/pm _ 0.67V/lJm

10 12 14 16

Fig. 3 - (a ) Co le-Co le represe nt ali on oJ' GM ;lI1d SM in lhe

vicini ty or transil ion teillperatu re T,.* /\ al 54 DC

Ih) Culc-O'le plOl or FLC-(,4 :1 0 in the ahsence or dc bias and al

(l.(,7 V/~Ill ; 1I 57DC (SIllA phase) rel"iccling SM

due to the appearance of OM (considered to be a res id-ua l l :; part of GM ). In our opinion, the OM has appeared due to the formation of modulated domain structures in bulk interface in the presence of stron g e lectric fi eld l '). We ca ll it Bu lk domain mode BOM. An obscrvati ollto this effect has bee n made in one of our expcriment s

di sc ussed elsewhere27 . Thef 'R ~ t - 198 kHz was fo und to be almost independent of bias from 1.3 V/pm to

2.()V /J-lm . We assume that due to the bulk prope rti es of sa mple (large ce ll thick ness to pitch rati o) , the contribu-tions to OM may be due to the bulk domainlllode BOM and the NRM . Wrobel el l/1. l.l IS have also hinted at the appearance of such modes in large P, material s. In bulk region, the helix is co mpl etely unwound above the threshold field , whereas it is suppressed at the surfaces .

Under these cond iti ons the compl ex permitt i vi ty shall beco me:

c '" = C I _ i c " = c + _______ "" __ c-'I.'-'I ',,-) ,,-,~t _____ + ~ 1 +( i(J)'T )1 - O: n l )f\ l

IlDM

"" C N R M

I + ( i CD 'tN i{ M ) I - 11 N R M ... (7 )

By sp litting Eg. (7) into real and imaginary parts we ge t:

c/(CD)=£~ +

200 ~--------------~==============~

si nh A

no. NRM

20 ----..to.-1.3V/~m - ... -2.0V/~m

150

100 10 100

w - . -. 0.0 V/ jJlll

50 - e - 0.67V/jJl1l ----A-- 1.3 V/jJ fTl

- -T- 2.0 V/ jJm

o

0.01 0.1 10 100 1000 10000

Frequency (kHz)

Fig. 4 - Frequency dependence or [/I( w ) al 35 DC

sox INDIAN J PURE & APPL PHYS, VOL ::lX, .I UL Y 20()U

3.0

FLC-6430 7.5tJm

2.5

2. 0

N 1.5 I ~ -~

1.0

0.5

0.0 0.0 0.5 1.0 1.5 2.0

Applied Electric field (V/~m)

Fig. :'i - I':xlcrnal de hi ;ls dependencc of lhc relaxalion frcqucncy of GM

+ £(11 1) l - EON RM [_1_ sinhB ] 2 coshfJ +sin(rra 12)

II Il M

... (8a)

E I I ( (J) ) =

EON I( ~ l - E ..

2 [COS ( rr ('f. 101 12) 1

cosh A+s in(rra 12) N R 1

E 0 II Il M - Eo N I( M +

:2 [ cos ( rr all I) ivI 12) ]

co~h fJ+s in (na 12) IIIH I

... (8b)

whcre!\ = ( l-aNRM ) In (un:NRM)' /J = ( 1- (Xllml) In Cur-cHml ) and olher terms have their usual meanings. The relaxa-

ti ons corresponding to NRM and BDM at 2.0 Y/~ll11 in the rorm or Co le-Co lc plOI are shown in Fig. 6. So l id linc represents the BDM ,lIld NRM cvaluated by rittin g

ex perimcntal data in Eq. X(a ,b). A good agreement be-

tween theory and our ex perimcntal results has been

round . A typi cal dependence of relaxat ion frequency (f;) and

dielec tric st rength (t.E) or abovc relaxation modes as a

functi on or temperature is shown in F ig. 7(a ,b). As seen,

.I;;M and .I;'NRM are allllo.-t i ndepcndent of tcmperature i 11 the SmC* phasc. As we approach 7: ,, /\, SM appears wit h a sudden ri se in the relaxat ion frequency . Measurements

very c lose to T, .. ;\ have not becn taken due to large

20

Fitting parameters Domain mode 35°C, 2V/~m 18 &NRM = 11.07 &BDM = 5.25 • I' E: 16 aNRM = 0.012 a BOM = 0.295

f,NRM = 198.83kHz freDM = 2.86kHz 14

12

;w 10

8

NRM 6

4 ~~ BOM 2 0 I I I I I ~ I I , I

0 2 4 6 8 10 12 14 6 18 20 E:

Fig. () - Colc-Co le rcprcscntalion of 8 DM ami IRvt in lhe SI11C* ph ;lse (Solid lincs ;Irc th e hest f il corresponding lolhe . Eq.(7))

fluctuation s in the ex periment;d values . It could bc due to the segregati on and pre-transiti onal effec ls at thi .~

temperature because of the Illulti-component nature or

the FL C mi xtures. lt is seen that SM obeys Curie-Weiss

law governed bY .l;.s~ 1 = (/ (T- Tl" " \ ) + /J , where (/ and /J ,Ire

constants.

The dependence 0 1 "f'~ 1Ij)~1 and t.Enml as a fu ncti on 01

temperat ure at 2Y Ipm is shown i 11 Fig. R( a.h ). We not ice

RAINA & AH UJA: LIQUID CRYSTALS

400 ~----------------------------------------~

350

300

250

N 200 I c.. 150 '+--

100

50

o

(0 ) GM SM NRM

OVllJm - .- - e -O.13V/lJm - A - - T -O.67V/lJm - +- -+-1.3V/lJm -x- -*- - I -

1'-:--- I - 1----/ I"" NRM

GM

a.-a-I-35 40 45 50

I

SmA

55 60 0.201.-:-----------------------------------,

(b)

0.15

0.10

0.05

0.00

OM SM NRM

O .OV/~m -.- -0-O.l3V/~rn -A- -'1-O.67V/llm-+ - -0-I.)V/III" - 0 - -0- - 6.-

o

<

6.__ r: -SM

J6.____ '" NRM 6._~6. \ ~~

.~OoY

GM Snit' ~ t SmA O----d [J 0 -.---a • a-a 35 40 45 50 55

Temperature (DC)

60

Fi g. 7 - Temperature dependence or (a) relaxat ion rrequency./;· and

(h) dielectric strength 6£ orG M , SM ;lIld NRM in the SmC* and SmA pha~c

that./;NR~ 1 is much hi gher in magnitude than/;'BDM (f~NRM >f;I\DM)' Similarl y, th e di e lec tri c strength of NRM (l'.E.NRM ) is found to be 2 times more than that of l'.E.IlD~ 1

(l'.E. R 1 "" 2l'.E. lIDivJ These results sugge. ts that the sur-face anchorage energy dominate over the bu lk property or thc sample.

compl ete refl ec tion of NRM is observed at hi gher bia:-;

( 1.3 V I~m) due to the coupling or surface domains with

electric fi eld. The '/; NRM is almost independent or tem-

perature but strongly depends on sample thi ckness. The

'/;'NRM) 198 kH z and its l'.E.NR ~ 1 = 11 .07 at 35 °C.

Goldstone mode GM and Bu lk domain mode BDM

appear in low frequency region . BDM is basicall y a

residual part of the GM and appears due to the formation

or mod ulated domain structures in the bulk interface .

5 Conclusions Dielectric relaxation modes ha ve been investigat ed in

a novel FLC-6430 mi xture under the influence of ex ter-nal bias in the low and hi gh frequ cncy regions. It is round

that :

A new relaxati on mode namely RM appears both with and without ex ternal bias . NRM is a consequence of the st rong surface interacti ons and contributions from the tin y domains formed at the surfaces, which in turn contribute to the heli x un winding at the surfaces. A

The./;(;M andj;BDM arc 0.83 kH z at O.OV I~m and 2.86 kHz

at 2 .()V/~m res pecti vely at 35 °C. Their corresponding

dielectric strength is l'.E.GM = 390 and l'.E. IIDM = 5.25 .

Soft mode SM parameters sat isfy the Curie-Weiss

law as we approach near Tc*,,'

:'lIO TNDIA J PURE & APPL PI-IYS. VOL 3X, JULY 2000

250 (0)

1::,.

200

RAINA & AHUJA: LIQUID CRYSTALS 511

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17 Hiller S. Biradar AM . Wrobe S. & Haase W. Phys Rev E. 53 ( 1996) I.

I~ Marzec M. Haase W . Jakob E. Pfeiffer M, Wrobel S, & Geelhaar. Liquid Cry.Ha/'l . 14 1967 ( 1993).

19 Beresnev L. Pfeiffer M. Pikin S. Haase W & Blinov L, Fer-roelectrio. 132 ( 1992) 9