Mechanism of Helix Unwinding in the Ferroelectric Liquid ...pdfs.semanticscholar.org/6f11/72652322f594da28290aa65a3dc9374306aa.pdfGisse, H. T. Nguyen (~) and Ph. Martinot~Lagarde (~)

Mechanism of Helix Unwinding in the Ferroelectric

Liquid Crystal Phase of Compounds Which Display an

Antiferro - Ferri - Ferroelectric Sequence

J. Pavel, P. Gisse, H. Nguyen, Ph. Martinot-Lagarde

To cite this version:

J. Pavel, P. Gisse, H. Nguyen, Ph. Martinot-Lagarde. Mechanism of Helix Unwinding inthe Ferroelectric Liquid Crystal Phase of Compounds Which Display an Antiferro - Ferri- Ferroelectric Sequence. Journal de Physique II, EDP Sciences, 1995, 5 (3), pp.355-368.<10.1051/jp2:1995137>. <jpa-00248163>

HAL Id: jpa-00248163

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Submitted on 1 Jan 1995

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J. Phys. II France 5 (1995) 355-368 MARCH 1995, PAGE 355

Classification

Physics Abstracts

61.30J 64.70M

Mechanism of Helix Unwinding in the Ferroelectric LiquidCrystal Phase of Compounds Which Display

an Antiferro Ferri

-

Ferroelectric Sequence

J. Pavel, P. Gisse, H. T. Nguyen (~) and Ph. Martinot~Lagarde (~)

Laboratoire de Physique de la Matilre Condensde, Universitd de Picardie, 33 rue Saint~Leu,

80039 Amiens Cedex, France

(~) Centre de Recherche Paul Pascal, Avenue A. Schweitzer, 33600 Pessac Cedex, France

(~) Laboratoire de Physique des Sohdes, Universitd de Paris~sud, 91405 Orsay Cedex, France

(Received 21 April 1994, receivedm final form 8 December 1994)

Rdsumd. Nous avons 4tudiA le comportement des lignes de "ddchiralisation" observdes en

microscopie optique polarisantesur

des dchantillonsen gdomdtrie planaire, d'un cristal liquide

antiferro41ectriquesous l'action d'un champ dlectrique continu. Dans la phase ferro61ectrique,

ces lignes de "ddchiralisation"ne sont pas observ6es h champ nul, mais apparaissent h faible

champ. Pour l'expliquer,nous avons montrd en analysant les dnergies d'ancrages des moldcules~

que des "~~disinclinaisons" de surface avec un ancrage antiferrodlectrique du cceur des ddfauts

peuvent exister dans la phase SmC*.

Abstract, The behaviour of planar samples ofan

antiferroelectric liquid crystal under DC

electric field has been studied through observations witha

polarizing microscope In the ferro-

electric phase the dechiralization lines have not been observed under a vanishing electric field.

They appeared with the increasing field. To explain that effect,we

show by analysing the

anchoring energy, that the structure of the planar helicoidal SmC* sample can exist with x~

disclinations on the glass surfaces. The behaviour of such samples under an electric field is also

discussed.

1. Introduction

The texture of thick planar samples of the ferroelectric SmC* phase is characterized by a

system of equidistant parallel lines. By thick sample we mean that the sample thickness is

sufficiently larger than the helical pitch. It was first shown by Brunet and Williams [ii that

these lines are the linear defect 2x~twist disclinations, which originate in the connection of two

incommensurable structures; ahelicoidal structure in the bulk of the sample and an

unwound

@ Les Editions de Physique 1995

356 JOURNAL DE PHYSIQUE II N°3

-2n

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii~»»>~~~iiiiiiiii

~~~~~~~~~~~~~~»~~iiiiiii~~~k'w+-+-~~~~+~a~~~~>~iiiii~~~

k'w+-~~~t,~*~-+~+~a~~~>~iii~~~k'

w-+-+-~~~tt~~w-w~~+~a~~>iiii~~k'w-

+-+-~~~tttf~~w-w~~+~a~~~ii~~k'w+-

+-~~~~tttt~~~w-w~~+~a~~~i~k'w-~+-~~~~tttttf~~~*~~-+~%~~~k'd-++~~

~~~ttttttff~~~~*'~-+h~~*-*-*~~~~~ttttttttttf~~~~~~~~~~~~

ttttttttttttttttfttttt~tttttt_ttttttttttttttttttttt

+2n

Fig. I. The cross section of the planar SmC* sample. Here we have used for better demonstration of

the orientation of each molecule its polarization which illustrates rather the azimuthal angle because

the polarization is perpendicular to the projection of the molecule to the smectic layer. The cross

section is made perpendicularly to the smectic layers, therefore polarization should be in the smectic

plane I.e. in the plane perpendicular to the figure plane and glass plates We have turned each vector of

polarization by 90° around the axis normal to the glass plates. Therefore the figure does not representthe real geometric situation but it clearly shows the variation of the azimuthal angle in the planarsample. The full circles are cross sections of 2x-disclinations.

homogeneous one close to the glass plates, These lines were called "dechiralization lines". It

was suggested later to call them "unwinding lines" [2] because the unwound region near the

glasses is as chiral as the helical one in the bulk. But in spite of that logical reason it appearsthat the name "dechiralization lines" is still the most frequently used.

As the planar sample is limited by two glass plates, there are two systems of 2x~disdinations

which differ by their sign. The distance between the neighbouring lines of the same sign is

equal to the helical pitch p. When the polar anchoring is realized, which is the case of the

ferroelectric liquid crystals (FLC) with the same treatment of both glasses and when the phase

sequence includes a SmA phase, the system of defects near the one glass surface is generallyshifted by p/2 with respect to the system of defects near the other glass [3,4] (see Fig. I).

If a sufficiently strong DC electric field is applied on the planar SmC* sample, the helical

structure is unwound. In this process the dechiralization lines play an important role [4, 5].In this contribution we investigate the process of unwinding of the helicoidal structure in the

ferroelectric SmC* phase of an antiferroelectric liquid crystal (AFLC). The behaviour in this

phase has been found to be quite different from that of classical FLC.

N°3 MECHANISM OF UNWINDING IN AFLC 357

2. Experimental Observations

The investigated LC was tolan C10:

CnH2n+iO C6H4 C e C C6H4 COO C6H4 COO C*H(CH3) C~H13,

exhibiting the following phase sequence:

Cr--58 °C--SmCA*--94.6 °C--SmC~*--96.I °C--SmC*~-ill.2 °C--SmA--128.6 °C--Is,

where the transition temperatures were determined from DSC measurements. Here wehave

used the labelling of the phases used by the Tokyo group [6, 7], I.e. SmC* is the ferroelectric,SmC~* the ferrielectric and SmC( the antiferroelectric phase. The planar sample 23 ~Jm thick

was observed under the polarizing microscope during the application of the DC electric field.

From the changes of the texture we have constructed the "E-T phase diagram" shown in

Figure 2. Under the electric field we have found up to four different regions. These regionshave been observed during increasing as well as decreasing field.

Region i: The helicoidal structure is formed but the dechiralization lines are not seen. This

region has been found in the SmC* and SmC[ phases for vanishing or small electric fields.

In Figure 2 that corresponds to the areas below the lower solid curves, There is no doubt

j 2°° C~* C~* C * A

~ ] ] ]cn~

iso

j ~

rx~

100

[~',~~ ~

50 "",~"', 2

__----,2

',/~ ,--'~~ 3__----~

~'~~~~ l

85 90 95 100 105 l10 lls

Temperature (°C)

Fig. 2. Temperature dependence of the electric field defining different regions with different tex-

tures, which are observed during the unwinding process in AFLC. Below the lower solid curves the

dechiralization linesare nqt seen

(reg. I). Between upper and lower solid lines the dechiralization lines

are dense (reg. 2). In two regions limited by the dashed lines they are not dense or are not seendue

to their bad contrast (reg. 3). Above the upper solid line the structure is unwound (reg. 4).


that the structure is helicoidal in the ferroelectric SmC* and antiferroelectric SmC( phases at

vanishing electric field. In the SmC* phase we have found on the same sample the contribution

from the Goldstone mode to the dielectric constant [8]. Moreover, the extinction has been

obtained between crossed polarizers for the same orientation of the polarizers as in the SmA

phase. This shows that the mean orientation of the optical indicatrix is in the direction of the

smectic layer normal. The existence of the helical structure was confirmed in both phases bythe measurement of the optical rotatory power [9] in homeotropic cell as well.

Region 2: The dechiralization lines are observed under the optical microscope and are dense.

From the density of the lines the pitch was estimated to be about 0.5 ~Jm. This texture can be

found in the intermediate fields between two solid lines in Figure 2.

Region 3: The density of the dechiralization lines decreases remarkably. There are areas in the

sample where the lines disappear completely. A very careful observation under the polarizingmicroscope shows that these lines exist but they are difficult to see due to the weak optical

contrast. This region has been found in two islets within region 2. The boundaries of the

region 3 are not well defined.

Region ~: The structure is completely unwound, I.e. the dechiralization lines are really van-

ishing. The unwinding of the helicoidal structure happens under a large electric field, which

corresponds to the area above the upper solid line in Figure 2.

Figure 3 shows the microphotographs of the sample texture of the SmC* phase at the transition

from region I to region 2. Under the increasing DC electric field the dechiralization lines start

to appear and they extend in the direction of the smectic planes (Fig. 3a). This processreminds of the appearance of the dechiralization lines in classical FI,Cs when the DC electric

field is switched off. A further increase of the electric field causes the successive increase of the

density of the dechiralization lines (Fig. 3b). We do not present here the photograph of the

texture in region 3 because the contrast on the lines is very weak.

The transition temperature between the ferrielectric SmC~* and ferroelectric SmC* phases

was determined when the slope change of the upper line in Figure 2 took place. This temper-ature is in a good agreement with the transition temperature found in the DSC measurement

(see the phase diagram above). In Figure 2 the transition temperature between the SmC~*and the SmC( phase was indicated as the temperature where the left lower line crosses the

temperature axis. It results in alarger ferrielectric phase than that found in the DSC. But

in fact we can state that this point corresponds to the transition from ferroelectric to anti-

ferroelectric anchoring on the glass plates (see also the later discussion). Therefore the phaseindicated in Figure 2 as SmC~* corresponds to the ferrielectric or antiferroelectric (for the

lower temperatures) structure in the bulk of the planar sample with ferroelectric anchoringsof the molecules on the glass surfaces. The strong influence of the boundary conditions on the

transition between the SmC~* and the SmC( phases has also been reported in reference [8].From Figure 2 one can see that there is a large interval of temperatures in the ferroelectric

SmC* phase for which the following sequences of textures under an increasing DC electric

field can be observed: The texture without the dechiralization lines-

high density of the

lines-

low density of the lines or their disappearance-

high density of the lines-

total

disappearance of the lines corresponding to the complete unwinding of the helicoidal structure.

3. Theoretical Model

In this section we shall discuss the unusual behaviour of the ferroelectric phase under a DC

electric field. We propose a model which is derived from the optical observation of the textures


4 ,

,~ ~~ , '

_ ~

~

~ ~' "

,~ ~~.~

~~

«b~ ~ ~,

~, ~'

t'("

~i ~ ~)~"

'~ ~

j _~_ ~

~ ~",~~]j~'~)

0 « ~ '~, ,»

"j &~

~~-

b)

Fig. 3. The microphotographs of the texture inthe SmC* phase under a DC electric field. a) The

appearance of the first lines under DC electric field corresponding to the transition from region 1 to

region 2. b) The striped texture in region 2 near region 1


in the polarizing microscope.

For the investigation of the dechiralization lines it is important to know how the molecules

areanchored on the glass surfaces. In order to describe this anchoring we introduce two

polarization vectors

Pi=

Polcos41,sin41), Pi+1=

Polcos41+1,sin41+1) ii)

where ii is the azimuthal angle in the i~~ layer and Po is the magnitude of the spontaneous

polarization. As order parameters it is convenient to use the in-layer polarization

P=

(Pi + Pi+1)/2=

Po(cos #cos~fi~ sin #cos ~fi) (2)

and antipolarization

A=

(Pi Pi+1) /2=

Po sin # sin ifi, cos # sin ~fi), (3)

where #=

(ii + #i+1)/2,~fi =

iii #i+1)/2 (see [8]). Taking into account the symmetry of

AFLC we can write the surface anchoring energy using the lowest order terms as

W= -ii In P/Po)~ -121n P) -131n A)~, 14)

where 11, 12, 13 are the anchoring constants and n is the unit vector to the surface having the

direction of the z-axis- The first term in (4) corresponds to the anchoring energy of non-chiral

SmC, the second one reflects the polar character of anchoring arising from the ferroelectricityand the third one describes the antiferroelectric interaction. Using (2) and (3), equation (4)

can be rewritten as

WAF II, ~fi) "cos~ # cos~

~fi iF cos # cos ~fi IAFsin~ # sin~

~fi,is)

where

7F "P072/71 and IAF "

Pi13/11. (6)

The anchoring energy is) exhibits local or absolute minimum only in three cases:

1)#=

0,~fi =

0, WAF (0, 0)=

WI, (7)

2)4" ~, lfi "

0, WAFI4, 0)=

W2, (8)

3)j=

), ~fi=), w~~j),))=w~, j9)

Figure 4 shows schematically these three possible anchorings. The energies WI, W~ and W3

are the corresponding anchoring energies. One should be aware of the fact that anchorings(7), (8) and (9) take place when the influence of [he bulk is not considered. Depending on

the anchoring coefficients iF and IAF, there can be different inequalities between energies WI,W2 and W3. It can also happen that one or out of from three possible anchorings cannot be

achieved because the corresponding minimum does not exist. Analysing the energy (5)we can

obtain 8 different cases:

1) WI < W3, there is no minimum for W2,

2) WI < W2, there is no minimum for W3,

3) WI, there are no minima for W2 and W3,


4) W3, there are no minima for Wi and W2,

5) W3 < WI, there is no minimum for W2,

6) WI<W2<W3,

7) Wi<W3<W2,

8) W3<Wi<W2.

In cases 3) and 4) only one anchoring is possible, in cases 1), 2) and 5) two different anchorings

can be achieved, one of which is metastable, and in cases 6), 7) and 8) all three anchorings

can exist, two of them are metastable. Which case takes place as a function of iF and IAF is

shown in Figure 5.

We suppose that constants 11, 72, 73 in (4) do not depend on the temperature. In this

case the temperature dependence of the coefficients iF and IAF is given by the temperaturedependence of Po. One can assume that Po depends on the temperature as (T~ T)~/~. In

this case 7F is proportional to (T~ T)~/~ and 7AF to (T~ T). Excluding PO from definition

(6) we get for coefficients iF and iAFi

7AF "

k7', (10)

where k =11 73Ill The dependence (10) is represented in Figure 5 by the dashed lines (it is a

straight line in the logarithmic scale) for two values of k. We can call this line a "temperatureaxis" due to the temperature dependence of the coefficients iF and IAF. As Po increases

with decreasing temperature, iF and IAF also increase. At the transition SmA SmC* both

constants vanish. For different values of k the "temperature axis" defined by (10) crosses

different regions in Figure 5.

Figure I shows the cross section of the thick planar sample of the ferroelectric SmC* phaseof the FLC. Each 2~-twist disclination is attracted by the nearest surface. However the lines

cannot approach the surface because the boundary conditions are fixed. What happens when

the lines are even pushed to the surface by the electric field? This case was observed for thin

planar samples of FLC [10, iii. In these samples the helix was unwound but there always exists

a twist in the direction of the sample thickness due to the polar anchoring. There can exist

regions of the opposite sense of the twist, which are separated by 2~-twist disclinations (seeFig. 6a). When the electric field is applied, the disclination is pushed towards one glass plate.At some critical field the 2~-disclination reaches the surface where it splits into two surface

~-disclinations. Between them the anchoring with higher anchoring energy takes place which

becomes favorable under the electric field [10, iii (see Fig. 6b).

~ ~ ~4~4~4~4~ tttt t4~t4~

1)j=0,y=0 2)j=1r,y=0 3)j=lra,y=1r/2Wi W2 W3

Fig. 4 The three possible anchorings corresponding to the minima of the anchoring energy is)

The arrows represent the local polarizations


The thick SmC* planar sample with the helicoidal structure in the bulk cannot exist without

disclinations. These disclinations can be realized as 2~-disdinations in the bulk or as ~-

disclinations on the surfaces. The second possibility is shown in Figure 7a. The elastic energy

of the 2~-twist disclination per unit length of line can be written as (see Ref. [12] or [10]):

E~n=

~(BiB3)~~~m~ In(R/r2«)"

~(BiB3)~~~ ln(R/r2«), Ill)

where Bi, 83 are the elastic constants, m is the strength equal for 2~-disclination to I, R is a

dimension of the sample (the precise value of R is not very important, because it enters only

in alogarithm), r~n is the radius of the core of the defect which is of the order of molecular

dimensions. Equation (11) does not include the contribution of the core, because it is hard to

calculate. But it may be lumped together in (11) by a slight change in the argument of the

logarithm [12j.For the energy of the ~-disclination on the surface we can take one half of the energy of

the 2~-di~clination expressed by ill). For two ~-disclinations on the surface we can therefore

write the elastic energy as:

E~jrj=

~(BiB3)~~~ ln(R/rn) ~/2(Bi 83)~~~ ln(d/rn), (12)

where rn is the radius of the core of the ~-disclination and d is the distance between two

~-disclinations. The second term in (12) corresponds to an interaction energy between two

~-disclinations on the surface. As the ~-disclinations have the same sign, this interaction

~Q 4

~

~fi k=

100~

5'~'AF~

~

~

~

lo -~ ~

6y

~

~

~

l 0 ~k

=10~~

~

~

~

~

~

~

z 3

~° ~~

0.I 1 10'~'F

Fig 5 The phase diagram of the anchoring of AFLCS The x-axis is the ferroelectric and y-axisthe antiferroelectric anchoring energy. The numbers of the areas

in the diagram indicate the following

cases, where WI, W2 and W3 are the energies of the possible anchorings: 1) WI < W3, 2) WI < W2,3) WI, 5) 11'3 < II'i, 6) WI < W2 < W3, 7) WI <11'3 < W2< 8) W3 < WI < W2. The dashed lines

are

"the temperature axes" where lower values of ~F and ~AF correspond to the higher temperatures.


iiiiiiiiiiiiiiiiiiiiiiiiiii

iiiiiiiiiiiiiiiiii~~~~i~~««««<~iiii~~~~~~~~~~~

~~~~~~~~~~<~ii~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~

~-~-~-~-~-~-~-~-~-~-~-~~~~-~-~-~-~-~-~-~-~-~-~~~~~~~~~~~~~-6~-~--~-~-~-~~-~-~-~~-~-~-~-~-~-~-~-~~~~,,~~,,~~~~~~~

~~~~~~~~~~~~,t~~~~~~~,,,,

~~~~~~~~~~~~i+i~~~~~~~~~~

~~~~~~~~~«ti+tii~~~~~~~~«tttttttiiittttttttittttttttttttttttitttttttttttt

11

~~

-2n

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii~~~~~~

~~~~~~~~~iiiiiiiiiiiiiiii~iiiiiiiiii~iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

~((((~~~~~~~~~~~~~~~~~~~~ E

~~iiiiiiiiiii~~~~~i~~~i~~iiiiiiiiiiiii~~iiiiiiiiii

iiiiiiiiiiii~ii~~~~~~~~~~

~~~~~~~~<~i~~~~~~~~~~~~~~

-~~--+-~ii~~~+-+~~~~~~~~~

ttttttttttJ~~itttttttttttJ

b) -n -n

Fig 6. The cross section ofa

thin planar SmC* sample. The structure is unwound due to the

boundary conditions The arrowsindicate the local polarization. a) E

=0, two regions of the opposite

sense of the twist are separated bya

2~-twist disclination b The same sample under DC electric field.

The 2~-disclination has been pushed to the lower glass plate where it splits into two ~-disclinations.

decreases elastic energy. For the estimation of the energy of two ~-disclinations on the surface,

we should also take into account the change of the anchoring energy between the lines, because

it has changed from WI to W2 The energy of two ~-disclinations per unit length in the

JOURNAL DE PHYSIQUEII T 5.N°3.MARCH 1995


-n -n -2nii

4444rffr44444444444444444 4444444444444444444444444ill~*'~f?~+~~iiiii~44444111 4441111iiii14444444444444/~~/+~f?-~+~~~~ii14441111/ 4111111j~~iii144444444444

~*'*'~~~f~'~~+~~~~ii144111~~ ill~~*'~'~+~~~iiii144444441++~'~~tfY~'++~*~~~i14111~~- ll~~*'~~?~~+~~~ii1444444ii/-~'~~tfY?'-~~~*~~~141/~~*'- /~~~~*~tY»~~~~~ii1444iiill~'~~~~ff~~'-~~~~~141/~~*'- ~~~*'~~tY'~~+~~~~ii144iill/ (El

-'~~~t~ff~?~'-~~+~~1411'*'*'- ~~*'-+~~Y~M+~+~~~~i14iill/~~~~~~tfft?~~'M~~+~~4/~*'-- *'a-d-~~~t,~»~+~~~~~14il~~~~~~~t~tffft??~'-~~~j/k'4-~~~ -~*~~~tt~'»~~-+~~~14/~k'k'/d-

~tt~ff++ffY~~~'--+~j~d-+-~~~ *~~~~~tffY~~'»---K~~j/k'd--~+-tttttfffffffYY~~-~4~~-~~tt ~~~~tttffYY~?~~'~~4/~~~~~fffffffffffffffff,444,fffff fffffffffffffffff,444,fffff

]i

a) +~ +l~ b) + +fl +lt +

-2n -2n11

4444444444444444444444444 44444444444444444444444444iiii14iiii14444444444444 44iiii1444444444444444444

41111~~~~~iii144444444444 4411/~~j~~ii1444444444444ill/kf*'~'~+~~~i~~~444444444 iill~*'~'~+~~iii14444444444ill~*'~~?~~~~iii~~4~~4444i 11/~~~~?~~~~iii~~44444441

llkf*'~-tY'~+~*~iii1444441411j~ 11/~*'~-t~-~+~~ii14444414441 E3ll~~+-+-tt'+~~~ii~44444441i 2111~*"t~'~+~~ii144444444ii1/~~-*~tt'+~~~iii~44414144 ii/~*"tt'~+~~ii~~~~~~l14411/~~+-~tY'+~~~iii141444141

/~*'~-~~-~+~~ii14144444111~

1/~~+-~tY'+~~iii1444444441 li/~~~~?~~~~ii14444444441ii/~*'~~f'~+~~i144444444444 411/~*'~'~+~~i1444444444444411/~~tf~~~i1444444444444 4111ill'~ii14444444444444

44444,ffff,4444441144444444 44444441144444441444444441-.

C)~ +n +n + d) +2n

Fig. 7 Thecross

sections ofa

thick planar SmC* samples of AFLC. a) E=

o. b), c), d) show the

different states under an increasing DC electric field (El < E2 < E3) The types of disclmationsare

Judicated

direction of the y-axis (y-axis is perpendicular to the plane of Fig. 7) is then:

E~jnj + WI W2=

~(BiB3)~~~ ln(R/rn) ~/2(Bi 83)~~~ ln(d/rn) + 21Fd. (13)

As 2~-disclination is in the volume and ~-disclination is on the surface, one can write between

their radii the inequality r2« < rn, from which it follows that always E2j«j < E2«. The value

of the anchoring coefficient ~F increases with decreasing temperature. Thereforewe suppose

that below the transition SmA SmC* we can obtain E2j«j + WI W2 < E2« and the structure

with two ~-disclinations (Fig. 7a) is realized. One can see from Figure 5 that the "temperature

axis'~ crosses region 6 for large intervals of values of the constant k. In this region all three

anchorings are possible. This suggested to us that the anchoring of the molecules in the inner

region of the ~-disclination may be antiferroelectric (with energy W3). The structure of such

~-disclination is shown in Figure 8. The angle~fi

varies smoothly from the value~fi = ~

/2on the


surface to the value~fi =

0 in the bulk. In this case the core of the ~-disclination can be much

larger than that of the 2~-disclination (r2« « rn). The optical contrast on ~-disclinations is

smaller than on the 2~-disclinations in the bulk. This may be one possible explanation whythe dechiralization lines are not seen for E

=0 in some temperature range in the ferroelectric

SmC* phase.We suggest the "antiferroelectric" core of the ~-disclination because antiferroelectric anchor-

ing is permitted But if this is not the case, the inequality r2« < rn is always fulfilled. Moreover,

another difference exists between a ~-disclination on the surface and a 2~-disdination in the

bulk. The first one is not charged but the second one is charged by a bound charge comingfrom non vanishing value of div P. This local charge may be an additional cause for a higher

contrast on 2~-disclmations. One can imagine, for example, that the electrostatic field in the

vicinity of 2~-disclination created by its charge may influence refractive indices around the

line.

When a DC electric field is applied on the structure illustrated in Figure 7a, one can logicallyexpect the following behaviour. The electric field is directed from the upper to the lower

glass plate (see Figs. 7b, c, d). The upper ~-disclinations move to one another, because the

anchoring between them is unfavorable. When two ~-disclinations come together they make

one 2~-disclination in the volume (see Fig. 7b), which can be seen under the microscope

(region 2 in Fig. 2). The region between lower ~-disclinations increases, ~-disclinations move

in the direction of the arrows. In Figure 7c two ~-disclinations are just below the upper

2~-disclination.

In this case the contrast of 2~-disdination may decrease, which corresponds to the region 3

in Figure 2. The next step is the formation of the lower 2~-disclination from two ~~disclinations

(Fig. 7d). The optical contrast on the lines may increase (upper part of the region 2). The

last step is the anihilation of two 2~-disclinations of opposite signs and complete unwinding of

the helicoidal structure (region 4 in Fig. 2).

4. Discussion and Conclusions

We have observed the unusual behaviour of the planar SmC* samples of AFLC under DC

electric field. At zero electric field we have not seen the dechiralization lines but they appeared

on increasing electric field.

When the dechiralization lines are not seen, one can expect the following possibilities:

1) the structure is unwound,

2) the structure is hehcoidal but the defectsare not seen because of the short pitch,

3) the structure is hehcoidal but the defects are not seen because of their small contrast.

The structure of the planar FLC sample can be unwound by the influence of the boundary

conditions (see surface stabilized ferroelectric liquid crystals [13] ). It happens when the sample

thickness is small, comparable with the helicoidal pitch Recently, another case of the unwound

structure of the thick planar sample of FLC with high Ps was observed [14]. In this case the

helix was not formed for a sample thickness of about two orders of magnitude larger than the

helical pitch. The authors of reference [14] suggest that the helix formation is connected with

the increase of the electrostatic energy because the dechiralization lines are charged.

Another example of the unwound structure of short pitch FLC in the planar geometry has

been reported by Fiinfschilling and Schadt [15]. In their case a stripe texture has been created

at the transition SmA SmC*. The origin of these stripes is in the chevron-like deformation of


the smectic layers in the sample plane (the smectic layers remain perpendicular to the glassesand not deformed in the sample bulk). After the structure is unwound by the electric field and

the field is switched off, the dechiralization lines develop slowly because the stripe boundaries

represent an obstacle for the formation of the helix. In this way the structure may remain

unwound at vanishing electric field for several hours [15].

The Goldstone mode contribution to the dielectric constant, as well as the extinction found

between crossed polarizers revealing the mean orientation of the molecules in the direction of

the layer normal, show that the helix is formed for the investigated planar sample of C10 in

the ferroelectric phase. For topological reasons some disclinations should exist between the

homogeneous structure near the glass plate and the helix in the bulk. As the helicoidal pitchdoes not depend on the electric field, especially for a small field, we cannot explain by a short

pitch that the defects are not visible at vanishing field It also contradicts the way in which

the lines appear under electric field (cf. Fig. 3).

The only remaining explanation is that the defects have a small contrast for a small electric

field and they change their contrast and character when the electric field increases.

The structure of the planar sample under zero electric field is helicoidal. Therefore there is

a necessity of the existence of defects as a consequence of the helicoidal structure in the bulk

and unwound structure near the surfaces. We have sho,vn by analyzing the anchoring energythat these defects can be surface ~-disclinations. The temperature region of the existence of

the ~-disclinations is given by the temperature dependence of the coefficients iF and IAF. The

"temperature axis" crosses probably region 6 in Figure 5. It means that all three anchorings(see Fig. 4) can exist. We have suggested that the anchoring m the inner region of the ~-

disclination can be antiferroelectric (Fig. 8). The optical contrast of such a ~-disclination is

weak and it is the reason why the lines are not seen under the microscope.The difference between the ferroelectric phase of AFLCS and that one of FLCS is in the

-R

tttttitititititit~titi~~ittttt~t~t~tit~t~t~t~t~~~~

ttttt~t~t~tit~titititi~~i~t~~~~t~~~~~~it~t~~~~~l~l~~

~~~~~~~~~~~~~~~~~~~~~~~&~

~~~~~~~~~~~~~~~~~~~~~~~'~~

~~~~~~~~~~~~,~~~~~~~~~~~~~

~~~~~w~~ar~~~~~~~~~~~~~~~~~~

-~-+-+-w»~-~~-+-~-w~-~~~w~-~~-w~~+~~~~

-w-+-w-+-w~-w-+-+-%-+-+-w-%-~-%--%-+-%~-%-%-%-%

Fig. 8. The cross section ofa

"magnified" ~-dischnation. The antiferroelectric structure onthe

surface in the inner region of the ~-disclination changes smoothly to the ferroelectric structure in the

bulk


constant 13. This constant should be small for substances which do not exhibit the antifer-

roelectric phase. In that case, the "temperature axis" crosses regions 2 and 3 in Figure 5,I.e. the antiferroelectric anchoring cannot be achieved, thus the structure of the i-disclinationproposed in Figure 8 is not probable.

On cooling the iF coefficient can become larger than 2 and in this case the anchoring with

energy W2 cannot exist (see Fig. 5). Thus the defects cannot be ~-disdinations on the

surface but 2~~disdinations in the bulk. This corresponds to the experiment, in which the

dechiralization lines are observed without electric field for low temperatures in the SmC*

phase.

if the structure of the planar sample involves ~-dischnations, we cali expect the same be-

haviour in electric field as has been shown in Figure 7. Although the observation under polar-izing microscope is difficult, due to the short pitch, we can state that the behaviour of AFLC

is not in contradiction with our model. But, for more precise studies~ it would be better to

increase the helical pitch.Recent measurements of the Raman scattering on planar samples of AFLCS (16,17] show a

correlation between the Raman tensor terms and the existence of the dechiralization lines in

the volume. The Raman intensity increases for light polarization parallel to the smectic layers

or decreases for the light polarized perpendicularly to the layers when the dechiralization lines

appear. Large changes of the Raman intensity for E=

0 have been observed at the ferrielectric

phase in the temperature range where the dechiralization lines are observed [16]. A similar

effect has been found when the DC electric field was applied in the ferroelectric phase. The

Raman intensity shows step-like dependence on the electric field with the jump correspondingto the field at which the dechirahzation lines appear [17].

Raman experiments may contribute to a confirmation of our model, I-e- the existence of the

~-disdinations on the surface at vanishing field and 2~-disclinations in the bulk under electric

field. The two situations differ in the inner distribution of the bound electric charges which giverise to an inhomogeneous electrostatic electric field in the sample. This local field becomes largein the second case because 2~-disdinations are charged. The electric field induces variations

in the terms of the polarizability and thus the Raman tensor is affected. But the numeric

evaluation of this effect have not yet been done. These results will be published in more detail

elsewhere [18].We did not discuss in this paper the behaviour of the fernelectric and antiferroelectric phases.

The problem of these phases is more complicated because there are changes in the phase

structure in the bulk under electric field (the angle~fi is very sensitive to E). We shall discuss

this problem elsewhere.

Acknowledgments

The authors are greatly indebted to Dr. L Lejcek~ as well as to Dr. V. L. Lorman, for

stimulating discussions, and to Prof. R. Farhi for the critical reading of the manuscript. This

work was supported in part by the Region of Picardie.

References

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Janovec V and Fousek J,

Mol. Cryst Liq Cryst. 91 (1983)309

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[8] Gisse P, Pavel J., Nguyen H-T and Lorman, V L. Ferroelectrics 147 (1993) 27

[9] Gisse P and Martinot-Lagarde Ph., unpublished results.

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The Physics of Liquid Crystals (Clarendon Press, Oxford, 1974) p 131

[13] Clark N A. and Lagerwall S-T, Appl. Phys. Left 36 (1980) 899.

[14] Glogarova M., Sverenyak H, Holakovsky J, Nguyen H T. and Destrade C., 15th International

Liquid Crystal Conference~ J-P16, Budapest 1994, to be published in Mol. Cryst Liq Cryst

[15] Ffinfschilling J. and Schadt M.~ Jpn J Appl Phys. 30 (1991) 741

[16] Gisse P, Sjdir M Pavel J Lorman V-L- Farhi R. and Nguyen H T 15th International LiquidCrystal Conference, B~P17, Budapest 1994, to be published in Mot Cryst.

[17] Sidir M.~ Nguyen H-T- and Farhi R 4th Condensed Matter Meeting of the French PhysicalSociety, Rennes, France~ 1994

[18] M Sidir et al, to be published.

Documents

Mechanism of Helix Unwinding in the Ferroelectric Liquid ...pdfs.semanticscholar.org/6f11/72652322f594da28290aa65a3dc9374306aa.pdfGisse, H. T. Nguyen (~) and Ph. Martinot~Lagarde (~)