Electrochiral effects in nematic liquid crystal-chiral salt mixtures

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Electrochiral effects in nematic liquid crystal-chiral salt mixtures

Zhang Fuliang, Geoffroy Durand

To cite this version:

Zhang Fuliang, Geoffroy Durand. Electrochiral effects in nematic liquid crystal-chiral salt mixtures.

Journal de Physique, 1989, 50 (9), pp.1099-1116. �10.1051/jphys:019890050090109900�. �jpa-00210980�

Electrochiral effects in nematic liquid crystal-chiral ^salt

mixtures

Zhang Fuliang (*) and G. Durand

Laboratoire de Physique ^{des Solides, Bât.} 510, Université de Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^France (Reçu ^{le 25 mai 1988,} accepté ^sous forme définitive ^{le 11} janvier 1989)

Résumé.

Une cellule hybride d’un cristal liquide nématique ^{est un} instrument commode de

mesure de torsion induite, puisque l’ancrage homéotrope peut ^{se tordre sans} contrainte. Nous observons la rotation de polarisation de la lumière qui ^se propage ^{à travers une} telle cellule

hybride, dopée par des ions chiraux. Un champ électrique continu entraîne les ions dans, ^{ou hors} de, ^{la zone où la torsion induite se voit} optiquement. ^{Il en résulte un} effect électrochiral linéaire.

Aux grands champs, ^l’effet quadratique de déformation de texture et les effets électrochimiques

sont clairement séparés. Cette observation permet ^{aussi des mesures} de coefficient de diffusion, d’énergie d’ancrage, ^{et d’effet} flexoélectrique.

Abstract.

A hybrid ^nematic liquid crystal ^{cell is a sensitive} twisting power measuring device, since the homeotropic anchoring ^can be twisted without _any torque. We observe the rotation of

polarization ^{for a} light ^{wave which} propagates ^{across such a} hybrid ^nematic cell, doped with chiral ions. A DC electric field drags the ions inside or outside the optical twisting region ^{of the} hybrid

cell. This results in a linear electrochiral effect. At large field, ^the quadratic effect from texture

change ^and electrochemical effects are clearly separated. ^The diffusion constant, surface

anchoring energy and flexoelectric ^{constant are} also measured.

Classification

Physics ^Abstracts

61.30

78.20

1. Introduction.

Nematic liquid crystals ^are usually made of rod-like non-chiral molecules [1]. In absence of external field, they align spontaneously ^{in a uniform texture} without any twist. It is well known [2] that the dissolution of chiral molecules in a nematic transforms it into a cholesteric material, ^which aligns ^{with a helical texture} indicative of a spontaneous twist. Much work has been done on these mixed systems, ^to relate for instance the helical twisting power ^to the concentration of chiral molecules [1, 3, 4]. Up ^{to now, it seems} that almost no investigation

has been made to study ^the helicity induced in nematics by ^chiral ions, instead of neutral chiral molecules. The reason is -probably ^{related to} the few number of real salts which can be dissolved in usual non-polar nematic materials. In this work, ^we have studied the twisting

power of chiral ions dissolved in ^a nematic liquid crystal, in presence of DC ^or AC electric field. We have used partly dissociated salts giving chiral ions in absence of field, ^{and also}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019890050090109900

undissociated chiral molecules, ^{which can} be ionized by electrolysis under the action of the DC field. To measure the twisting power, ^we have observed the twist of light polarization, propagating ^{across an} hybrid ^cell containing ^the chiralized nematic. Because we have worked

on low concentration systems, ^we have been able to make the ^now classical measurement [5]

of the mass diffraction coefficient of the chiral compounds dissolved in our cells. Finally, working ^with large ^AC field, ^{we can} estimate the anchoring energy of the nematic ^on the

planar ^oriented plate ^{of the} hybrid ^cell.

2. A simple ^{model for a twisted} hybrid ^cell.

The expected ^{texture of a} hybrid ^cell containing ^a weakly twisted cholesteric material is shown in figure 1. The lower plate is treated to give ^a planar orientation along ^x. The upper plate, ^at

a distance d, is treated to give ^an homeotropic alignement along ^z. At any point M, ^the molecular line is twisted by ^an angle q (z ) ^{in the} (x, y) plane, ^and 0 (z) compared ^{to z. The} problem ^{is to calculate} 0 (z) ^and p(z) ^{and to} further estimate the optical ^{twist of} polarized light propagating along ^z through the cell. For simplicity ^{we make the one} constant curvature

(K) approximation. ^A two constant model for a uniform pitch cholesteric has already ^been

made [6]. ^{We call n} the director of the system. The cholesteric curvature free energy density

writes as :

Fig. 1. Fig. 2.

Fig. ^1.

Geometry of molecular alignment ^{in the} hybrid cell. The molecular line starts from 0 at the

planar ^lower plate ^and stops ^{at P on the} homeotropic upper plate. ⁿ is the director.

Fig. ^2.

0(z) ^versus q (z ) ^{in the cell,} for small (a), ^medium (b) ^and large (c) total twist Q max. The dotted curve determines the limit of the Mauguin regime i.e. the effective optical twisting

thickness of the cell between 0

7r/2 ^{down to} BQ. çl is the measured optical ^twist.

where q ^{is the} spontaneous ^{wave vector} of the cholesteric helix (q

² 7T / P, ^P

pitch). ^{With our} notations,

Minimizing (2) compared ^{to 0 and} q gives :

where q ^{is now a} function of z. Equation ^{4 means that the} hybrid cholesteric texture transmits

everywhere ^{the same twist} torque ^{around z,} from the upper ^to the lower plate. ^{With our} hypothesis ^of homeotropic anchoring, ^this torque ^{must be} zero, since molecules cannot transmit torque along ^{n on the} homeotropic plate (the nematic is assumed to be uniaxial).

Equation (4) ^{is then} integrated ^{as :}

The total twist _{q maX} = ç (d ) ^{of the texture} from the lower planar plate (z

0) ^to the upper

homeotropic plate (z

d ) ^{is :}

q max does not depend ^{on the} 0 (z) profile. ^It just ^measures the thickness averaged twisting

power q.

The integration ^{of the 0} equation (3) ^is straigthforward when q ^is uniform, ^i.e.

q = q = qo > 0 independent ^{of z.} Integrating (3), ^{we can write :}

since 0 (z) decreases from the planar ^{to the} homeotropic plate. Finally, 0 ^is given by :

The integration ^constant C > 1 is fixed by ^the boundary condition :

qo d is the total twist of the cell across d. We have plotted ⁱⁿ figure 2 the behavior of

0 (z ) ^{versus ’P} (z ) in the cell. For thick enough ^{cells or small} pitch systems (qo d > 1 ), 0 (z) remains close to 7T /2, ^and drops only ^{close to the} homeotropic plate ^{on a thickness}

-

P/4 ^{over which} cp rotates of 7T /2. ^This corresponds ^{to a} situation where cholesteric layers

pile up parallel ^{to the} planar plate (0

7r /2 ). Only the last 1/4 layer ^is destroyed by ^the

imposed 6 ^bend.

For thin cells or large pitch systems (qo ^d 1 ), ^{0 decreases} linearly ^{to zero as :}

e = ’-T 2 ( d-z )_ ^{Figure 2 is useful to} understand the optical properties of the cell.

Normally, for low concentration of chiral molecules, ^the pitch P is much larger ^{than the} wavelength À ^{of the} light ^{used to measure} the twist. One is then in the Mauguin ^limit [2],

where the light polarization ^follows adiabatically ^the twist, provided ^{that :}

àn(O) is the molecular birefringence. ^The point ^is that, ^{close to the} homeotropic region,

0 tends to zéro, and àn(O) accordingly. ^{In this} region, the bended nematic remains

mechanically twisted, ^{but is no more} capable ^{to twist the} light polarization. To estimate the effective thickness of the hybrid cell which can induce an optical twist, we can use the

approximate relationship,

where ne and no ^are the extraordinary ^and ordinary indices of the nematic material. Condition

(10) gives ^{then :}

Calling o p the limit value for 0, ^{which can} twist the light polarization, ^{we can write :}

where ’Pmax == qo d. ^{We have} plotted Oe( ’Pmax) in figure ^{2, for} typical values : d = 10 03BCm, ne - n0

0.2, À

^0.546 um corresponding ^{to our} experiment. Only ^the planar region ^{of the} cell 17 :> 0 :> Of ^{is in the} Maugin limit, ^{i. e. is} capable ^of inducing ^an optical ^twist.

2

The homeotropic region 0l

0 > 0 will behave as a birefringent plate, ^the eigen axis of which

are oriented along Omax and 0max ⁺ ’TT /2. ^In general, ^a linearly polarized light ^wave propagating along ^{z and} entering ^{the cell at the} planar plate with its electric field vibrating along the director n, should be elliptically polarized ^{at the} homeotropic output plate. ^{The axis}

of the ellips ^{should rotate} by ^the angle ’Pe

q ( 0l ) ^{shown in} figure 2. In this first order

analysis, ^{we are not} interested in the polarization ellipticity, ^but simply ^{in the} polarization

twist. As _{lp max} is linear in d, ^{one can} directly visualize the effective fraction dl/d ^of the ^cell

which controls the light polarization twist. The observed twist is not cpmax, but ql

cp (dl) ^{shown in} figure 2. For low cpmax, i.e. for small qo, çi is close _{to cpmax.} The non-twisting part of the cell has then a relative thickness :

which goes ^{to zero as} Q max. For large ’Qmax > ^-u, the twist induced by the cell is the one of the cholesteric layers ^{close to the} planar plate, ^{and cp Q} tends toward Q max - 7r/2. ^{We shall not}

discuss anymore this domain, ^{since we shall} restrict, ^{in what} follows, ^{to the low}

’P max regime.

We discuss now a situation where the total number of chiral molecules is fixed in the cell,

with an inhomogeneous distribution along ^{z, so} that q depends ^{now on z, with a} fixed average

q. ^As previously discussed, cp max = qd ^{will not} depend ^{on the} q (z) distribution. A

measurement of _’Pmax would not give any information ^on q (z ). On the other hand,

cp e depends ^{on the} q (z ) distribution. The Mauguin ^{condition for the} optical ^wave guide regime (Eq. (13)) remains valid locally, ^{as :}

provided ^{we use the} right ^tilt 0 (q (z ) ). ^{In fact,} in the situation ^we consider, the relative variation in space of the twist is small Lq , 1 _{dz d} ^{so that we can estimate 0, (z ) by using its}

calculated value for qo

q, and ^also replace q by q ⁱⁿ equation (15). ^The hybrid ^{cell can then}

be visualized ^as constituted of two regions : ^the optical twisting quasi planar region

(0

Of) ^{close to the} planar plate (z dl) ^{and the} optical ^non twisting quasi homeotropic

region (0 Ol) ^{close to the} homeotropic plate (d p z d ). ^An optical measurement of ,Ql gives ^an information on the total number of chiral molecules in the optical twisting region.

One now understands the principle of the linear electrochiral effect described in this

experiment : ^{assume that} part ^{of the} twisting power of chiral molecules ^comes from chiral ions. Assume that on the upper and lower plates ^{of the} hybrid ^{cell are} placed transparent electrodes, ^{across which one can} apply ^an electric field E (Fig. 3) [JE 1 = V /d ] . ^We

illuminate the sample by ^a light ^wave linearly polarized along ^x, propagating along ^{z. At the} output ^{of the} cell, ^the light polarization has rotated over an angle cpp defined by the available

twisting power of the lower part of the cell (z dl) ^{in the wave} guide regime. ^{In absence of a} field, the ion concentration is uniform along ^{z. One} can measure a mean twist _’Pe. In presence of field, ^{one will} drag ^{the chiral ions,} according ^{to their} sign, ^{inside or} outside of the twisting region. ’Pe should then depend linearly ^{on E.}

Fig. ^3.

Experimental ^set up. ^{P :} polarizer, ^{A :} analyzer, ^{V : electric} generator. ^{1 ammeter. The field E} drags ^{the ions i in the} twisting (lower) region (i > 0 ) ^{or in the non} twisting (upper) region

(i 0 ), resulting ^{in a linear} change ^{in the} optical ^rotation cpp ^across the cell.

In practice, ^most liquid crystals possess ^a dielectric anisotropy Ba. In presence of ^a field, ^this

causes a texture change quadratic in E. This quadratic effect will be superimposed ^{on the}

previously predicted ^linear electrochiral effect. We can simply describe this quadratic

dielectric effect. Assume Sa > 0, i.e. the nematic director n will align along E, inducing ^an homeotropic ^{texture for} large ^{E. The} twisting power of the cell must decrease, ^{because of the} general decrease of 0. The new texture 0 (z) in presence of E is obtained by adding ⁱⁿ f the dielectric term 1 ₂₄ ^à E2 sin2 0. The _cp equation (4) ^{does not} change ^{since, because of its}

03C0 q (

cylindrical symmetry, ^the coupling ^{of E} with the dielectric anisotropy ^{does not} depend ^{on cp.}

Equation (3) ^{becomes now :}

where the usual [1] ^coherence length e ^is given by :

0 remains given by (8), where qo = q ^{must be} replaced by (ç- 2 - qô )ir2. ^The field reduces the cp, 0 coupling, i.e. it reduces the tendency of 0 to remain around 77-/2 ^{close to the} planar plate,

since E unwinds the cholesteric layers. ^{y For} qo ) ^{° 1, 0} = ’r d z 2 d ^{is the same as the one of a} non-chiral cell. For larger ^field (qo ç 1 ), ^{the curvature of the} 0 (z) dependence changes ^its sign and 0 goes ^more rapidly ^{to zero} (Fig. 4). ^The twisting region of the cell becomes thinner when E increases, ^and accordingly cPf(E) - CPf(O) _d ^{goes also to zero. A more detailed}

description would necessitate a numerical computation, ^non essential for our purpose.

Another difficulty, ⁱⁿ large ^{electric fields,} may be related ^to the finite anchoring strength ^of

the plates. ^{We have not to} consider the azimuthal anchoring strength ^{of the} planar plate, ^since

Fig. 4. Fig. 5.

Fig. ^4.

Variation of 0 (z), ^with E 2 for ^a positive (Ea:> 0) dielectric anisotropy ^material. (a) ^E

^0.

(b) medium field (qo 03BE =1 ). (c) large ^field (qo 03BE=_ 1 ). 0l, independent ^of E, is obtained from CPmax (see Fig. 2). The measured optical ^twist Ql (E) ^decreases continuously ^{down to} zero, for E -> 00.

Fig. ^5.

Variation of 0 ( cp

qo ^z, E2). The surface value of 0 (0, E2)

Os ^{is now allowed to be smaller}

than ir/2, ^{because of weak} anchoring. ^{The z} dependence is restricted to a thickness e: (a)

0 (E

0). (b) intermediate ^{situation 0} (E2). (c) zero optical twist situation Os

Ol.

even in presence of field, ^{there is no azimuthal} torque ^{around z} in the free twisted texture. We have just ^to consider the zenithal anchoring strength ^{of the} planar plate. ^In large field, ^the 7r/2 variation of 0 (z ) is confined to a distance e (Fig - 5) resulting ^{in a} large ^surface torque

K 2 03A003BE . ^{This torque can change the 0}

^Os orientation on the planar plate. ^{Let us} characterize

as usual [1] ^the planar plate anchoring strength ^{with a} surface energy Ws :

where L is the usual extrapolation length [1] (L - ^0.1-1 Um). ^{We must write the balance of}

curvature and surface torques ^{at the} planar plate. ^From equation (16), ^{we obtain a curvature}

surface torque ^{K sin} Os/ 03BE, neglecting ^{the effect of twist, since} qo e ^1. This results in the torque equation :

If ) « L, the solution is Os

^{0, all} of the cell is homeotropically aligned. If ) > L, ^the

solution of equation (19) ^{is :}

or

where Es is the field for which e

^{L. We are not} interested in the 0s - ⁰ limit, ^{but in the}

zero optical ^twist regime. Using equations (12) ^and (10), ^{we obtain :}

i.e. a field Eo ^{for zero twist,} given by :

For typical ^values (À

^{0.5 um,} qo

2 ?r /60 u,m-1, ne - no

0.2) ^{the last term} is of order 1.

This remains valid for small À qo. Using Ea ~ ^{4 7T and K - 10- 6} cgs, ^one expects Eo ^{values in}

the range of Ego - Vo/d - 0.3 L V/cm independent of qo. In principle, ^the observation of

Eo ^allows for calculation of L. The 0 (z ) variation for 0s # ir/2 is shown in figure ^5. Apart ^for

a thickness e ^{close to the} planar plate, ^the sample ^is expected ^{to be} homeotropic. ^Above Eo ^the twisting power is expected ^{to increase} linearly ^{in field.}

Finally, ^we could also in principle suspect ^{another linear electric} field effect to occur in our

system. ^The hybrid ^cell presents ^a flexoelectric polarization P f [1], associated with the splay-

bend texture. A DC electric field will couple linearly ^with Pf, through ^the coupling energy

density - ^{E .} P f. This situation has already been studied [7]. Following ^the work of the Bordeaux group [8], ^we can assume that Pf ^has mostly ^a quadrupolar origin, ^i.e.

Pf = e o . (nn - Î /3 ) where e is the sum el ⁺ e3 of the usual [1] flexoelectric coefficients.

2

Assume now E uniform. The volume energy density integrates ^{out as a surface term on the} planar plate + e E ^{cos2 OS.} Because there is no flexoelectric polarization associated with a

2

twist distorsion, this surface term, independent ^{of Q,} changes only the zenithal anchoring

energy. We expect now a more complicated ^behavior. Equation (19) ^{becomes :}

K03BEa, 1/2

For small flexoelectric coefficient e«- ( K03BEa ir ) ^{one expects now two} différents critical For small flexoelectric coefficient e

4 03C0

^{one expects now two} differents critical fields to produce ^the complete homeotropic alignment (Os

0 ). These fields ^are solution of :

For most liquid crystals, e ^is positive. ^A positive ^E (aligned along ^{z from the} planar plate ^to

the homeotropic one) will then decrease e, i.e. increase the critical field. A negative ^{E should}

decrease the critical field.

Kea ^1/2

For large flexoelectric coupling e ( 4 ir ) 1/2 ^{there is just one critical field, of same}

polarity ^{as e which} aligns homeotropically the cell. Of course, the flexoelectric coupling

should become zero when using ^AC fields, ^of frequency larger than the relaxation frequency

of the splay ^{bend texture.}

3. The expérimental set up.

We have prepared ^a hybrid ^cell filled with ^room temperature ^5CB (pentyl cyanobiphenyl)

which undergoes ^a nematic --> isotropic phase transition at T,

^{34.5 °C. Our} experiments ^are

made at T

19.5 ± 1 °C, ^{i.e. 15° below} Tc. ^For this material at T

19.5 °C, ne

1.739 and no

1.536 for À

5 461 Â, the green mercury wavelength [9]. ^{The elastic}

curvature_ ^constants are [10] Kl (splay)

^{6.2 x 10-7} cgs, K2 (twist)

^{3.1 x 10-7} cgs and

K3 (bend)

^{8.8 x 10-7} cgs. The dielectric anisotropy ^is [11] e.

12. The plates ^{are ITO} (indium ^tin oxyde) transparent electrodes. The upper ^one is coated with DMOAP silane [12],

to induce homeotropic orientation. The lower one is obliquely evaporated ^{with SiO, at an} angle ^{of 66°} compared ^{to the normal,} which results in ^a planar orientation [13]. ^A linearly polarized light ^beam (Fig. 3) ^{is send across the cell, with the} optical ^{E vector} along P//x along ^the planar plate. ^The sample ^{is observed} through ^a polarizing microscope. ^An analyzer inside the microscope ^measures the rotation _Ql of the output polarization, ^{from the}

rotation of the light extinction angle. Accuracy ^and reproductibility ^{are in the one} degree

range. Note that ^a positive algebraic Ql in the (x, ^y, z) ^frame corresponds ^{to a} negative

cpe for the opticians. ^{In what} follows, ^{we have} kept ^the optical convention for the sign ^of

Qlof. For comparison, ^we give in table 1 the sign ^{of the} rotatory power in solution of the chiral

compounds ^{used to} dope ^the hybrid ^cell.

To observe a possible electrochiral effect, ^{we can} apply ^{an electric} field 1 E 1 = V /d between the two electrodes. The electric generator ^{can be an AC or DC source with} adjustable polarity, ⁱⁿ the range ^± 30 V. The sample thickness d is 10 _um, obtained using

silica sphere spacers. We ^can also measure the DC current I through ^{the cell} using ^{a sensitive}

ammeter. The measured voltages ^are always referenced compared ^{to the} grounded ^lower planar plate. ^{This means} that in the x, y, ^z frame a positive ^{V induces a} negative ^{E. For} convenience, ^when reporting ^our observations, ^we have chosen for positive ^{the sense of E} along - ^{z, so that E} and V have the ^same sign.

To calibrate our set-up, ^we have made various samples with different concentrations of ^a

chiral dopant, ^the cholesteryl oleyl ^carbonate (COC). We have first measured the pitch ^{of a}

Table I.

Sign of optical rotatory power, in solution, o f the ^{various chiral} compounds ^{used in}

this work. (Optical convention).

cholesteric mixture 5CB + COC for various mole concentration c of COC, using ^{the Cano} wedge [14] method. The two plates forming ^the wedge ^are SiO coated to give parallel planar

orientation. We observe ^a periodic ^set of disclination lines parallel ^{to the} wedge ^{corner. The}

Fig. 6. Fig. 7.

Fig. ^6.

^Pitch measurement with a Cano wedge. ^{c mole} concentration of the solution, ^P pitch (um). ^a

and b planar aligned plates. ^X disclination lines.

Fig. ^7.

Optical ^twist cpe calibration versus the total twist The figures ^are the mole concentration

of COC in 5CB.

change ^of wedge ^{thickness between two} adjacent lines is taken as P _{2 (half} the pitch). ^The

result is shown in figure 6, which shows the classical c-1 dependence ^{of P} [1]. ^{We have now}

measured the rotation _cpe versus c, in our hybrid cell, for the 5CB-COC ’mixtures. We have

plotted cpî versus ’Pmax

qo d, calculated from the measured pitch P, ⁱⁿ figure ^{7. The data}

show clearly ^that çi tends toward _{cp max} only for small concentrations typically in the range QmaX 90°, ^as expected. ^{In the} following experiments ^{we have} always worked in this small rotation regime ^{where the} Mauguin criterium works and for which there is no 180° error

possible ^for cpQ.

4. The electrochiral effects.

4.1 POSITIVE CHIRAL IONS.

We have first tried to observe the electrochiral effect on

mixtures of 5CB doped ^{with a} chiral salt. Obviously, the dissociation of a « salt » is not

expected ^to be very large ^{in a} weakly polar material like 5CB. We have first used benzyl quininium ^bromide (BQB) ^{at C}

^{0.5 %, which is} expected ^to dissociate to give ^a positive

chiral ion BQ+ and ^a non-chiral negative bromide ion. We have measured the optical ^rotation

Q p ^versus E, in the range ± 6 V/10 J,Lm. We do observe (fig. 8) ^{around E}

^{0 a} linear variation of _cpe, followed by sharp variations at ± V 1/d ^and finally ^{a decrease at} large ^{E. The} large 1 E 1 decrease is easy ^to understand. On the same figure 8, ^we have shown the observed

’Pi variation versus the ^rms value of a high frequency ( f

³ kHz ) ^E field, which results only

into a dielectric quadratic effect. This quadratic effect is the expected ^E2 decrease of the cell

Fig. 8. Fig. 9.

Fig. ^8.

Electrochiral effect for a 5CB + BQB mixture. (0) : lpf (E) (DC field) ; (+) : lpf(E) (AC field, f

³ kHz). V1/d ~ ^{3 V/10} um corresponds ^to VI ⁱⁿ figure 9, and is the threshold for electrochemical reaction.

Fig. ^9.

^{Current I versus DC} voltage ^{V across the 5CB +} BQB cell of figure ^8. V1, corresponding ^{to a} large increase of current, is ^an electrochemical threshold.

’

twisting power, due ^to the induced molecular tilt. For large ^values of 1 El, ^{, the DC} field results also in the same quadratic decrease of _çt, when molecules align along ^E. The low field observed variation of 1 CPt 1 corresponds ^{to a} larger (smaller) ^{twist for} positive (negative) voltage ^on the upper plate. ^If positive chiral ions are present ^{in the} cell, they ^must concentrate close to the negative planar electrode, in the active region for twist of the hybrid cell, increasing ^the rotation 1 cpe 1 ^{as observed. We then} interpretate this linear variation as the

expected electrochiral effect from positive ^BQ+ ions. Note that _Ql is negative ^{for thisl}

mixture. The singularities ^{observed at ±} V 1/d ^with Vi - ^{3 V can} be understood if one looks at the measured electric current I through ^{the cell} (Fig. 9). ^{1 is linear} (ohmic like) ^{for low} voltage, ^{due to} the presence of ions. Above ± V 1, ^{we observe a} sharp increase of the current.

V corresponds probably ^{to the onset of an} electrochemical reaction which results in a large

increase of the total ions density. ^{The ±} signs indicate that this reaction can happen ^{on both}

electrodes. In figure 8, ^{we do see} that, ^{below -} V 1/d, the rotation increases and that above

V 1 /d, the rotation decreases sharply. ^{This means} probably that the electrochemical reaction decreases the density of chiral ions BQ+ ^{or create} negative chiral ions. We cannot be more

specific ^{at this} stage.

We have reproduced ^the experiment ^{with a} mixture of 5CB plus benzyl quininium ^chloride (BQC), which is also expected ^to give positive ^{BQ+ ions. We} do observe the same linear effect for the low field variation of Ql (E) (Fig. 10), ^{with the same} sign ^{for the} slope, ^as expected. The electric current in the cell shows now sharp variations for V

± Vs ^{1 V} (Fig. 11), for which the linear effect on cpe ^{seems to} increase slightly. It may be that ^at this

voltage ^the density ^{of BQ+} chiral ions increases.

Fig. 10. Fig. 11.

Fig. ^10.

Linear electrochiral Ql (E) (DC) ^{for a SCB + BQC mixture.} V 1/d corresponds ^to Vs ^{1 V/10} um in figure ^11.

Fig. ^11.

1 ( V ) relationship for the 5CB + BQC, mixture of figure ^10. Vs ^{1 V is an} electrochemical

threshold.

Many ^other compunds which could give positive chiral ions have been found poorly ^soluble

in 5CB and give ^a weak effect. This is the ^case for instance of Alanine ethyl ^ester hydrochloride (AEEH). ^{A saturated} (unknown) concentration of this compound gives ^{a zero}

field rotation _{’Q e - -} 1 ° . A positive ^E increases 1 Q e 1 ^{as expected, but} the effect is too weak to be quantitatively analyzed.

4.2 NEGATIVE CHIRAL IONS. - We have ^now made the same experiments ^on salts which can

dissociate to give negative chiral ions. We have prepared ^{a c}

^{4.95 %} solution of phenyllactic

acid (PhLA) in 5CB. Our results are plotted ⁱⁿ figure 12. For this compound, ^{the twist is now} optically positive. ^{For low field, we do observe a} linear variation of _Qe, with a negative slope,

as expected ^from negative chiral ions (PhLA)- ^{which for} positive voltage ^{on the} homeotropic

upper plate, ^should get ^out from the efficient twisting region ^{of the} hybrid ^{cell. We also find at}

E = V 1 V1 _d

^{+ 2 V/10} 03BCm ^a sharp ^{decrease of ’Pi. This is} correlated with the current voltage

curve of the cell (Fig. 13). I(V) ^{shows an ohmic} region between - 2 V and + 2 V, ^{and a} large

increase beyond these values. As _Ql decreases more sharply ^above V 1/d, ^{we can infer that} electrolysis ^creates probably ^above V 1 a larger concentration of the negative chiral ions

responsible for the twist.

We have reproduced ^the experiment with another related compound which is also expected

to give negative ^{chiral ions, the} potassium phenyl ^lactate (KPhL). ^{We have} prepared ^a

c

0.43 % solution of KPhL in 5CB. In absence of field, we measure ’Ql

⁺ 57°. A positive

field of 2 V/10 ut ^decrease ’Pi down to 55°, ^as expected for chiral PhL- ions.

Fig. 12. Fig. 13.

Fig. ^12.

^Linear electrochiral effect for a 5CB + PhLA mixture. V 1/d ~ ^{2 V/10} um corresponds ^to Vi in figure ^14.

Fig. ^13.

I (V ) ^curve for the 5CB + PhLA, mixture of figure ^1. V = 2 V is an electrochemical

threshold.

4.3 UNDISSOCIATED CHIRAL DOPANTS. - For comparison, ^{we have} studied chiral com-

pounds ^{which are not} expected ^to spontaneously dissociate, like chiral alcohols and esters.

We have checked octanol-2 (OC-2), cholesterol (CH) ^{and its esters.} The behavior of a c

0.64 % mixture of CH in 5CB is shown in figure 14. For low field ( 1 E 1 ^{2 V/10} f.Lm)

Ql does not depend ^{on E.} Increasing ^the voltage drop ^across the cell above 2 V, ^{one observes}

a sharp decrease of _Ql for E > 0 and ^an increase for E 0, which indicates the appearance of

negative chiral ions. These variations are deduced in comparison ^{with the} purely ^dielectric quadratic effect demonstrated on the same figure, measured with ^a 3 kHz AC field. The observed _{cp p} variation must be correlated with the I (V ) ^curve of this cell (Fig. 15). ^{We do find}

an ohmic region ^{between ±} V ^{= ±} 2 V. As there is no change ^{in çt in this} region, ^{we must} accept the idea that the ions responsible for this conduction are non-chirals. Beyond ^{± 2} V,

we observe a large increase of I, ^{and a further one above} V2

^{6 V. We can} say that

V1 1 and V2 ^are the thresholds for electrolysis ^to produce ^chiral negative ^ions (CH- ?).

Cholesteryl ^octanoate (CO) (c = 0.4 % ) ^{shows an} equivalent ^behaviour (Fig. 16) : ^no

variation of _{ç l} for low field, ^an abrupt decrease of Ql above E

1 V/10 itm and an increase of _Ql (compared ^{to the} quadratic ^AC curve) ^{for E -1 V/10} um. This also ^can be correlated with the non-linear behavior of the I (V ) ^curve (Fig. 17). ^{The same} behavior has been found for cholesteryl ^nonanoate (CN), cholesteryl ^decanoate (CD), cholesteryl propronate CP, cholesteryl oleylcarbonate (COC) ^and cholesteryl ^chloride (CC). Note that all these cholesterol compounds result in negative çt for low concentration, ^as already reported [4].

Fig. 14. Fig.15.

Fig. ^14.

Electrochiral effect, for a 5CB + CH mixture. (0) : ^{DC field ;} (+) : ^{AC field} (3 kHz). ^No

linear effect is observed at low field. V 1/d ~ ^{2 V/10 lim} corresponds ^to VI ⁱⁿ figure ^15. V2 ~ (6- 8) ^{V/10 iim} corresponds ^to V2 in figure ^15.

Fig. ^15.

1 (V ) ^{curve for the} 5CB + CH mixture of figure ^14. Vi-2V ^and V2 ~ 6 V ^are

electrochemical thresholds.

Fig. 16. Fig. 17.

Fig. ^16.

Electrochiral effect for a 5CB + CO, ^mixture. (0) : DC measurement ; (+) : ^AC

measurement ( f = 3 kHz ). No linear electrochiral effect is observed. V 1/ d~ ^{1 V/10 um and} V2/d ~ ^{3 V/10 um} correspond ^to V1 ^and V2 in figure ^17.

Fig. ^17. -1 (V ) ^curve for the 5CB + CO mixture of figure ^16. V 1, V2 electrochemical thresholds.

All these compounds show the appearance of chiral negative ^{ions from} electrolysis, ^{above a} voltage ^threshold V1 ~ ^{1-2 V.} Finally, the chiral octanol-2 (OC-2) ^{at c}

^{4.3 %} shows also a

similar behavior but the weak initial rotation (Ql = - 3° ) ^{does not allow for a} good enough

accuracy.

4.4 DISCUSSION. - We have not made any detailed calculation ^to modelize the expected change in ions concentration across the cell, ^{versus the} applied voltage ^V. Nevertheless, ^we

can consider two limiting cases : assume first that the used compound ^{is a} perfect salt, ^{i.e. its} ionisation energy qV 1 in the nematic is lower, ^or comparable, ^to kB ^T (q ^ion charge). ^The compound ^{should be} completely dissociated at room temperature. The linear electrochiral effect should saturate for V > kB T/q ~ ^{25 mV,} since the chiral ions will segregate ^{on one} side of the cell. In case, now, where qV o is ^much larger ^than kB T, ^{no effect should be}

observed until V - V 1, for which an electrochemical reaction can be triggered. ^{This last}

situation corresponds ^{to the case of the} cholesteryl ^esters described in part c), ^{where we}

observe a simultaneous increase of the current and the onset of a large electrochiral effect for

V1 - 2 V. We have ^not observed the first situation. It is likely ^{that the} compounds ^{we have}

used are not fully dissociated. We can just estimate that the maximum relative change ^{of twist}

must compare with the relative density ^of ions, ^{i.e. to} the dissociation factor. From our data,

we can estimate this factor at about 5/75 - 8 % for PhLA, 3/60 - 5 % for KPhL, 8/40 - 20 % for BQC and 5/30 - 16 % for BQB. The benzyl quininium derivative are the one which behave closer to real salts. In fact, ^we have observed that the instantaneous current through

the cell is much larger than the measured stationnary ^{current. This means} that the used non-

blocking electrodes are polarized. ^The potential drop ^{across the} cell will be localized closed to the electrodes, ^which explains ^{also the} observed absence of saturation for the electrochiral effect, since the effective voltage inside the cell is much smaller than the applied voltage ^{V. A} quantitative ^{model of the} charges ^and potential distribution across the cell cannot be made at the present stage, ^with just ^the integrated data of the electrochiral effect and the electric current.

5. Diffusion and anchoring energy measurements.

5.1 DIFFUSION.

When trying ^to make solutions of chiral salts with 5CB, ^{we had some}

difficulties to dissolve the chiral molecules. One method was to prepare ^an hybrid ^cell of pure 5CB, ^{and to} place ^{on the} edge of the cell small crystallites ^{of the} compound ^to dissolve. The chiral molecules, ^{at the} constant saturation concentration on the edge ^{of the} cell, diffuse into the nematic cell along ^{the x} direction. The optical measurement of the twist allows for ^a measurement of the local concentration c (x, t ) ^{at time t. We have then a method to measure}

the mean diffusion coefficient D of a chiral compound in the cell. This method is akin to a

previously demonstrated experiment [5], ^{with the} advantage ^{of a better} spatial accuracy, and the drawback of the averaging process due ^to the splay bend of the hybrid ^{texture. We}

demonstrate this method with a solution of PhLA in 5CB. Figure ^{18 shows} microphotographic pictures ^{of the cell,} placed ^{between the} polarizer ^P (Fig. 3) ^{and the} analyzer. ^A turned from the extinction direction by 10°, 20°,

up ^to 90°, 24 h after placing ^the crystallites ^{on the left of}

the pictures. The horizontal scale represents ^{4 mm.} From these pictures, ^{we can draw the}

cpe (x, to) ^at to

^{24 h} (Fig. 19). Taking ^{the same data at times t}

² h, ⁴ h, ⁸ h, ^{we obtain in} figure ^{20 an} ensemble of curves çt (x, t ). ’Pi is the same at the edge ^{of the} sample, ^{because it} corresponds ^to the saturated concentration. We could analyse exactly ^the analytical profiles ^of

these curves, which represent the classical smoothing ^{of a constant} concentration step function, by diffusion. In fact, the accuracy of the observation is ^not terribly good. ^{It is} simpler ^to derive D from the definition :

aQ and a2Q ^are measured in figure ^{20. This results in D = 1.7 x} 10-7 cm2/s. This compares

at ax2

well with the data from reference [5] ^for cholesteryl ^esters in MBBA. We do not know of _any

measurements of cholesteryl ^{esters diffusion constant in 5CB.}

5.2 ANCHORING ENERGY. - We can now interpretate ^the large field behavior of the

quadratic electrochiral effect as shown in figure ^{14 for} instance, for the 5CB + CH mixture.

Let ^us observe first the saturation effect of the AC field for which ^we do not expect any flexoelectric effect. The optical ^twist çt goes linearly ^{to zero for a finite} Eo

^{10 V/10 J,Lm.}

Using ^formula (23), ^{we can} estimate L

0.3 _um. This value is a bit larger ^{than the} already

measured L

0.1 _u,m for strong planar anchoring [15]. It may be that chiral molecules, ^or ions, trapped ^{at the} interface, decrease the anchoring energy, ^{or even} change ^the orientation of minimum energy. This could explain the very large ^observed Eo dispersion (2-20 ^V/10 )JLm)

between cholesteryl ^{esters and BQB} respectively. ^One possible mechanism would be the

following : ^surface ions, trapped ^{on the} electrode, ^{create a} surface field Es ^{normal to the}

electrode, ^{over a thickness} equal ^{to the} Debye screening length. ^The coupling ^of

Es ^{with the} positive anisotropy ^of 5CB would decrease the planar anchoring energy, since it

orients the nematic director normal to the electrode. This mechanism has already ^been

Fig. ^18.

Optical appearance of ^the hybrid ^{cell under} microscope 24 h after placing crystallites ^of

PhLA on the left edge. The x distance ^to the edge is indicated in mm. The black line corresponds ^{to the} region ^{where the} optical rotation is _{cpe :} a) cpe

90° ; b) cp = 80° ; c) cpe

60° ; d) cpp

30° ; e) cpe

20° ; f) ç

10°. The x displacement of the dark line indicates a concentration gradient ^of

chiral PhLA.

proposed [16] ^to explain the so-called

spontaneous Freedericksz ransitions

More carefull observations would be necessary ^to clarify ^this point.

We now observe the large ^DC field saturation effect of _cpe, also visible for instance in

figure ^14. Compared ^{to the AC behavior, we} do observe ^a decrease of 1 Eo 1 ^{for positive V,}

and an increase of Eo ^for negative V, ^as expected ^{for a} flexoelectric contribution to the surface energy, with e

0. The relative variation of Eo is of the order of 30 %. This is reasonable with

4 03C0 ^1/2

our model which predicts ^{p a relative} change - e ( B ^{4 ’r 112 EaK}

^{With Sa - 12 and K - 0.7 x}

10-6 _cgs, we find ^{e -} 2.5 x 10-4 cgs. This value is ^too low by ^{a factor 2 or} 3, ^{from the one}

measured [3] ^{in AC by} the Bordeaux Group. ^This effect is probably ^{due to the} partial

Fig. 19. Fig. 20.

Fig. ^19.

Ql (x, t

²⁴ h ) for the 5CB + PhLA inhomogeneous sample ^of figure ^18.

Fig. 20. - Same as figure 19, ^for various t, ^{from t = 2 h to 24 h.}

screening of the field by the ions close to the non-ohmic electrodes. It would also be important

to know the associated non uniformity of E which would give ^{a direct} coupling ^{with the}

electric quadrupole density ^of the nematic material. As always, ^{the DC} behavior of nematic cells remains essentially unexplained.

Conclusion.

A nematic hybrid cell is the simplest liquid crystal ^texture which allows to measure the

twisting power of chiral compounds, ^since by definition the homeotropic plate ^cannot

transmit twist torque, and then will not disturb a weak induced helicity. We have used this property ^{to measure the} twisting power of chiral molecules and salts in the nematic 5CB, ⁱⁿ

presence of DC ^or AC electric field. A small DC field drags the chiral ions in the region ^of large visible induced helicity (the planar side) ^{or in the} region where twist is not visible,

because of molecular tilt (the homeotropic region). Although the total twist of the texture remains the same, because the optical ^wave guide condition of Mauguin ^is non-linear, ^this

chiral ion drag results in a linear electrochiral effect. For large field, ^the quadratic effect of the dielectric anisotropy of the nematic changes ^the hybrid texture to an homeotropic ^{texture and}

suppresses the linear effect. At large ^AC field, the twist vanishes for a finite field value, ^which gives ^{a new method to measure} surface zenithal anchoring energies. ^{For DC field, the same}

observation gives ^a measurement of the flexoelectric constant of the nematic material. The twist in the hybrid ^{cell can} also be used to probe concentration changes in space and time, through diffusion process for instance. Our results ^on 5CB room temperature ^nematic liquid crystal demonstrate the existence of the polar electrochiral effect, ^{for both} positive ^and negative chiral ions. Benzyl quininium derivative seems to be 10 to 20 % dissociated :

phenyllactic derivative can give ^{5-8 %} ions. In its present form the effect is too weak to lead to

practical applications. For this purpose ^one should use more dissociated chiral salts and zero

dielectric constant anisotropy mixtures. Other geometries ^{can also be} considered, ^{where the}

electric field is parallel ^{to the} plates ^for instance. This allows for a nice 2 dimensional mapping

of the chiral agent concentration, ^but leads, in presence of chiral ions, ^to complicated ^flows

and could be the subject of further work. Finally, ^{we have estimated the mean diffusion}

constant of Phenyllactic acid in the cell [D

^{1.7 x} 10-7 cm2/s ^at T

20 °C ] ^{and the} anchoring energy ^on the planar plate (extrapolation length ^{in the 0.1} jim ^to 1 _f.Lm range). ^The

observed dispersion ^{of this} anchoring energy is ^not really understood.

Acknowledgments.

We thank Pr. H. Kagan ^{for the} supply ^{of the} benzyl quininium derivatives and a critical

reading ^{of the} manuscript. We thank Dr. C. Germain for mixtures preparations. ^{This work}

was supported by ^{a CNRS} grant ^{to one of us} (Z.F.L.).

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