Structural transition at the free surface of the nematic liquid crystals MBBA and EBBA

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Structural transition at the free surface of the nematic liquid crystals MBBA and EBBA

P. Chiarelli, S. Faetti, L. Fronzoni

To cite this version:

P. Chiarelli, S. Faetti, L. Fronzoni. Structural transition at the free surface of the ne- matic liquid crystals MBBA and EBBA. Journal de Physique, 1983, 44 (9), pp.1061-1067.

�10.1051/jphys:019830044090106100�. �jpa-00209691�

Structural transition at the free surface of the nematic liquid crystals

MBBA and EBBA

P. Chiarelli, ^{S. Faetti} (*) and L. Fronzoni (*)

Dipartimento ^di Fisica, Universita di Pisa, ^Piazza Torricelli 2, 56100 Pisa, Italy (*) Gruppo ^Nazionale di Struttura della Materia del CNR, Pisa, Italy

(Reçu ^{le 3 dgcembre} 1982, révisé le 4 mai 1983, accepté ^{le 27 mai} 1983)

Résumé. 2014 Dans cet article nous mesurons l’angle 03B8t ^entre le directeur et la normale à la surface libre des cristaux

liquides nématiques ^{MBBA et EBBA. La} technique employée ^est la même que celle de Bouchiat ^et Langevin-Cru- chon, ^{mais nous l’avons améliorée de} façon à ^mesurer l’angle 03B8t ^{avec une} précision supérieure ^{à ± 1° dans} l’intervalle d’existence de la mésophase. ^{Nous observons une nouvelle} transition structurale à la surface libre des nematiques

MBBA et EBBA quand ^la température ^{atteint une valeur} critique T0. Au-dessous de cette valeur, l’angle 03B8t ^tend

vers zéro comme (T0 - T)1/2. Cette transition est en accord avec les prévisions ^{de deux théories} de la surface libre

(Parsons, Mada).

Abstract.

In this paper ^we report measurements of the angle 03B8t between the director and the vertical axis at the free surface of the nematic liquid crystals MBBA and EBBA. The basis of our technique ^{is the same as the one} reported by ^{Bouchiat and} Langevin-Cruchon ^for measurements on MBBA and PAA. However some important improvements ^{make our} technique ^{more suitable and more accurate so that we can} measure 03B8t ^{to within ± 1° over}

the whole range of the nematic phase. ^{We find a new} structural transition occurs in MBBA (and EBBA) ^{when the} temperature ^{reaches a} critical value T0 ^{close to the} clearing temperature of the nematic L.C. Below T0 ^the polar angle 03B8t ^{tends to zero as} (T0 - T)03B2, where 03B2 ~ ^{0.5 is a critical} exponent Information about the anchoring energy at the free surface of MBBA is also obtained. The experimental ^results agree with two recent models of the free surface (Parsons, Mada).

Classification

Physics ^Abstracts

61.30

68.1OC

Introduction.

In the past, ^{a lot of} theoretical and experimental ^work

has been done on the bulk properties ^{of nematic} liquid crystals, ^so that these properties ^{are now well}

understood [1, 2]. ^{On the other} hand, ^the properties ^of

the free surfaces of a nematic L.C. have been little

investigated ^In particular only ^{a few} experimental

measurements of the polar angle Ot between the director n and the axis k orthogonal ^to the free surface have been made [3, 10]. Three different kinds of behaviour have been observed : Ot ^{= 00} [6, 8, 9, 10], Ot ^{= 90°} [3, 4, 5, 7] ^and Ot ⁼ 0(T) [3, 4, 6] (i.e. 6t ^{is a}

function of temperature). ^{This last sort of behaviour}

has been observed by Bouchiat and Langevin-

Cruchon [3, 4] in semi-infinite MBBA samples ^and by

ourselves in freely suspended ^MBBA layers [6]. ^{All the} surface tension theories [ 11-17] explain ^{well the cases} Ot ^{= 0°} and Ot ^{= 90°, but there are some} difficulties in accounting for the MBBA results. In a recent

paper [17] ^Parsons proposed ^a phenomenological

Landau theory of the free surface of a nematic L.C.

that explained the tilted alignment of the director at the free surface of MBBA. This alignment ^is interpreted

as being ^{due to the} competition ^{between two different}

forces : Van der Waals forces of quadrupolar sym- metry ^{that tend to} align ^{the director} parallel ^{to the}

surface and polar forces that tend to align ^it orthogo-

nal to the surface. Parsons shows that a structural transition to a homeotropic alignment ^{can occur at a} given ^critical temperature. ^More recently [12, 13]

H. Mada proposed ^{a different} phenomenological

model of the surface tension ^that explains ^{the tilted} alignment of MBBA in terms of a distortion of the director-field below the free surface. Mada deduced an

analytical expression ^{for the} angle 0, ^{as a} function of the scalar order parameter ^S [1]. ^{With a} proper choice of a fitting parameter a, Mada’s results show a tempe-

rature dependence of 0, ^that agrees qualitatively ^with

the experiment.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019830044090106100

1062

In a previous paper [6] the authors investigated ^the

director orientation in freely suspended layers ^of

MBBA and found that the angle 0, vanishes when the temperature approaches ^a critical value To ^that depends ^on the thickness of the layer. This effect was not observed in semi-infinite ^MBBA samples [3, 4].

In this paper ^we report ^new experimental ^results

obtained by using ^an improved version of Bouchiat’s and Langevin-Cruchon’s technique [3, 4] that allows

us to obtain the angle 0, ^at the free surface of ^a semi- infinite MBBA sample ^{to an} accuracy greater ^than

± ^{1° over} the whole _range of the nematic phase.

In the first part of the paper ^we describe the principle

of this measurements, the ^sources of errors and the

improvements ^we have introduced. In the second part

we discuss the experimental ^results obtained for MBBA and EBBA. The measurements on MBBA

were performed ^{both at} the air-L.C. interface and at the vapour-L.C. interface. We find ^{a new} structural transition occurs when the temperature approaches

a critical value To ^{close to the} clearing temperature T c.

Below this critical temperature ^the angle 0, ^{tends to}

zero as (To - T)fJ, where fl

^{0.5 ± 0.04 is a critical}

exponent. ^{The same} orientational transition has also been observed at the air-L.C. interface in EBBA. In the third part ^{of this} paper ^we show that both the theories of Parsons [17] ^{and Mada} [12, 13] ^{for the}

free surface are able to explain the transition to the

homeotropic alignment.

1. Experimental procedures.

The technique ^used by B. and L.C. [3, 4] consists of

measuring the relative anisotropy Ro ^{of the} reflectivity

coefficients for a polarized monochromatic beam that

impinges orthogonally ^on the free surface. This relative

anisotropy ^is given by :

where p || and P 1. represent ^the reflectivity coefficients of the extraordinary ^and ordinary waves, respectively.

The expressions ^for _p II and P 1. for the free surface of a

monocrystal ^{are :}

and

where Ot ^{is the} angle between the director and the vertical axis and nl and n II ^are the ordinary ^and extraordinary refractive indices of the nematic L C.

If n-L ^and n are known, Ot ^{can be deduced} directly by measuring Ro.

In order to measure the relative anisotropy Ro,

the director must be oriented uniformly ^{all over the}

free surface. This uniform orientation is obtained by applying ^a magnetic field in the vertical x-z plane

that forces the director to lie in this plane. Figure ¹ schematically shows the director orientation in a semi- infinite nematic L.C. subjected ^{to a} magnetic ^{field H}

that makes an angle On, ^ranging between 00 and 90°, with the orthogonal z-axis. The polar angle ^{0 of the}

director changes continuously from the surface value 0

00 ^{to the} bulk value 0 ⁼ eH. ^{The order} of magni-

tude of the thickness of the distorted layer ^{is about}

the same as the magnetic ^coherence length ^defined by :

where K is a Frank elastic constant and _xa is the

anisotropy ^{of the} diamagnetic susceptibility. ^{If the} anchoring energy of the nematic L.C. at the free surface is high [18], ^the magnetic ^field changes ^the

azimuthal angle 0 of the director with the x-horizontal axis but is not able to modify appreciably the surface

polar angle 00 ^{and thus,} 00 - 0,. If OH is different from 900 and 00, the director is aligned along only ^one easy direction at the free surface (o

00). ^If On

^90°,

there are two possible preferential orientations _sym- metric with respect ^{to the z-axis in the x-z} plane (o ^{= 00} and 0 ⁼ 1800). ^{In this} case, domains will be present ^at the free surface aligned along ^these

directions and separated by magnetic ^walls [19].

Fig. ^1.

Orientation of the director near the free surface of a nematic liquid crystal subjected ^{to a} magnetic ^{field H.}

We note that equations [1-3] have been written down for a uniform nematic sample, whereas the actual orientation of the director in a nematic L.C.

in the presence of ^a magnetic field is stratified in the bulk. Corrections to equation ^{2 due to} the presence of the director distortion below the free surface can be evaluated by using ^the theoretical procedure given

in reference 20. In the present experiment ^{the ratio of}

the magnetic ^coherence length ^{to the} wavelength ^of

the incident beam is high (ç/ Å > 5) ^{and thus} xhese

corrections can be neglected (AR 0.000 1).

Apparatus.

Our experimental apparatus ^{is shown} schematically

in figure ^{2. The cell} containing the nematic sample

Fig. ^2.

Schematic view of the experimental apparatus.

is inserted between the poles ^{of an} electromagnet

oriented in such a way ^{as to} generate ^a magnetic ^field making ^an angle of 800 with the vertical axis z in the

x-z plane. ^The magnetic ^field intensity ^{can be varied}

between 0 and 7 000 G. The He-Ne laser beam

(A ⁼ 6, ³²⁸ A) ^{is reflected} by the mirror M and

polarized by ^the polarizer ^{P at an} angle ^{of 450 to the}

x-axis in the _x-y horizontal plane. The laser beam

impinges ^on the free surface of the nematic sample

at an incidence angle - 0.20. The reflected beam _goes

through ^{a Wollaston} prism (WP) ^that splits ^the optical

rays into ones polarized orthogonal ^and parallel ^to

the vertical plane ^x-z. The intensities Il ^and III ^{of the}

two beams are measured by ^two photodiodes (PH,

and PH2). ^{Further on, an} electronic circuit furnishes the ratio R ⁼ lll - Il _to an accuracy of better than

1. ^Y

0.5%.

The nematic samples ^{are enclosed in a} glass ^cell

inside an aluminium block thermostated within 0.1 OC in the temperature range 20 °C-80 OC.

The nematic L.C. used for the present experiment

were commercial N-(p-methoxybenzilidene)-p-n-buty- lanyline (MBBA) by ^{Hoechst and} N-(p-Ethoxybenzi- lidene)-p-n-butylaniline (EBBA) by Eastman Kodak.

These samples ^had clearing temperatures ^of T c ⁼ 43.5 °C and T c ⁼ 72°C, respectively. ^{The meas-}

urements are performed by heating (or cooling) ^the

nematic samples ^{at the} temperature ^{rates= 0.2} oC/min.

and by recording ^the signals R ^and Il ^{on the two}

channels of a x-t _pen recorder. Very ^{close to the} clearing temperature ^the temperature ^{rate is reduced}

to 0.01 OC/min. We verified that the experimental

results were independent ^{of the} temperature ^rate.

The main improvements ^{to the B. and L.C.} experi-

mental apparatus [3, 4] ^{are the} following :

i) ^the measurements of Il ^and III ^are simultaneous

so that we avoid the uncontrolled and annoying

deflections of the laser beam due to the introduction of a half wave plate [3, 4].

ii) ^{The use of an} analogue ^{divider allows us to}

eliminate the effects due to fluctuations of the laser

intensity.

iii) ^The magnetic field is tilted with respect ^to the free surface and thus the director is uniformly aligned ^at the free surface. Thus we avoid spurious

effects due to the _presence of magnetic ^walls [19]

at the free surface.

Exrimental ^errors.

In our experiments ^we believe that the largest ^source

of errors in vacuum sealed glass cells is due to the residual anisotropy ^{of the} glass windows. If we assume that the glass window behaves locally ^{as a} monocrystalline plate, ^{we can} show that the experi-

mental signal R (for R I)canbewrittenas:

where Ro(T) is the effective relative anisotropy ^{of the} reflectivity coefficients, R(T ;) ^{is the} spurious signal

in the isotropic phase ^{at a} temperature ^{T =} Ti, h(T)

is a coefficient that accounts for the variations of the

glass anisotropy ^with temperature ^and L(T) ^{is a} multiplicative coefficient that accounts for the varia- tions of R due to the interference between the aniso- tropy ^{of the} glasses ^{and the} anisotropy of the L.C.

The contribution R( Ti) ^{to the} spurious signal ^{is the}

most relevant to our experiment (R(Ti) - 0.02). ^{It can}

be easily ^removed by measuring R(T) ^{in the} isotropic phase (T ⁼ T ;, R(T) ⁼ R(Ti)) ^and by rotating ^the glass cell in such a way ^to cancel R(T). ^{In order to}

evaluate the effect of the two last terms of equation ⁵

we have repeated measurements of R( T) ^{on the same}

nematic sample with different orientations of the glass

cell around the vertical axis. The largest ^difference

between the values of R(T) - R(T;) ^{obtained in this}

way in different runs was less than 2 %. ^{The uncer-} tainty AO, ^{in the} polar angle ^{is due to the} inaccuracy AR( ² %) in the relative reflectivity anisotropy ^and

the inaccuracies Anl ^and An,, ⁱⁿ the refractive indices of the nematic L.C. given ⁱⁿ the literature. By compar-

ing ^different experimental measurements of the refrac- tive indices of the nematic L.C., ^{we estimate} Ani - An 11 - ^{5 x 10-3 . For 0, 350, the uncer-}

tainty 06, is lower than 1 °.

2. Experimental measurements in MBBA and EBBA.

In this section we present ^our experimental results for MBBA and EBBA.

2.1 MBBA FREE SURFACE. - Figure ^{3 shows the} temperature-dependence ^{of R for a MBBA} sample

enclosed in a vacuum-sealed cell and subjected ^{to a}

2 kG magnetic field The noise in R is mostly ^{due to}

mechanical vibrations of our apparatus. ^{In order to}

measure the clearing temperature ^{of the} sample ^we

record the intensity Il of the reflected beam polarized

1064

Fig. ^3.

Dependence ^of the relative reflectivity anositropy

R on the difference between the clearing temperature ^{and the} temperature. The noise in R is mostly ^{due to mechanical}

vibrations of the apparatus.

orthogonal ^to the director. At the transition point ^this intensity ^{curve exhibits a} step ^{due to the} sharp ^varia-

tion of the ordinary refractive index of the nematic L.C. We note that in general ^the clearing temperature

can be different from that of the bulk [11, 15]. By measuring simultaneously ^the intensity ^{of a laser}

beam transmitted through the L.C. between two crossed polarizers ^{and the} intensity of the reflected beam we find that the clearing temperature ^{of the} surface and of the bulk do not differ to within 0.3 °C.

This uncertainty ^{is due to} the coexistence of the

isotropic ^{and the} anisotropic phase ^{in the} sample ^{in as}

temperature range of about 0.3 OC around Tc [21].

In figure ^{3 we} distinguish ^{two different} regions : a) ^{for T} T o(T 0 ⁼ T c - ^0.9 OC), R ^{decreases on} increasing ^the temperature and becomes zero as the temperature reaches the critical value To. This critical temperature ^{is the same} for either increasing ^or decreasing temperature-sweeps.

b) ^For T o ^T Tc R ^{is zero to} within the

experimental noise due to mechanical vibrations

(AR = ± 0.001). ^{In this} temperature range both the free surface and the bulk of the L.C. are anisotropic

and the director is orthogonal ^to the free surface.

Near the clearing temperature ^one observes random fluctuations of R (AR ⁼ 0.01) ^{with zero} average value due to the coexistence of small regions ^of isotropic ^and anisotropic phase ⁱⁿ the bulk of the sample. ^These

fluctuations ^occur just ^above T c ^{when the} sample

is heated starting ^{from the} anisotropic phase ^and just

below T c ^{in the other case.}

2.2 STRUCTURAL TRANSITION. - Figure ^{4 shows} Ot ^{at the} vapour-MBBA ^{interface versus the difference}

between the clearing temperature T, ^{and the tem-} perature ^{T of the MBBA} sample. The accuracy of the

experimental ^values of 0, is better than ± ^{1 ° over the} whole temperature-range. Figure ^{5 shows the} depen-

dence of 01 ^{on T near} the critical temperature To.

The behaviour of Ot ^near To is well described by equa- tion 6

Fig. ^4.

Behaviour of the director angle 6, ^at the vapour- MBBA interface versus the difference between the clearing temperature ^{and the} temperature. 0, is deduced by ^substitu- ting ^into equations ^{1-3 the} experimental values of R and the refractive indices of MBBA [21]. Crosses and circles corres-

pond to two measurements performed ^with decreasing ^or increasing temperature-sweeps, respectively.

Fig. ^5.

^Behaviour of the square of the surface angle 0, ^at

the vapour-MBBA ^{interface as a} function of the difference between the clearing temperature ^{and the} temperature.

Triangles ^{and circles} correspond ^{to two} measurements

performed ^with decreasing ^or increasing temperature- sweeps, respectively.

where

and

All these results are completely reproducible ^to

within + 10 ^over the whole range of the nematic

phase.

The same transition to a homeotropic alignment ^is

observed also at the air-MBBA interface. However,

the critical temperature for the air-MBBA interface

is slightly ^{lower than} the critical temperature ^cha-

racterizing ^the vapour-MBBA interface. By plotting

Ot against the difference between the critical tem-

perature ^{and the} temperature ^{we obtain two curves} for the air- and vapour-MBBA interfaces _respec-

tively, which coincide to within 20. Anyway, Ot ^is systematically slightly lower in the air-MBBA case.

The same qualitative behaviour has been observed also in samples ^of very low purity (T. ⁼ 37°C) ^for

the same values of To - ^T.

By comparing ^our results with the previous ^ones [3, 4], ^we observe that the values of Ot ^obtained by ^B.

and L.C. are systematically smaller than our values.

This difference is in part ^{reduced if we take into account}

a trivial computational ^{error made} by the authors of references 3, ^{4 in} evaluating Ot ^from equations 1, ^3.

The correct computation increases the values of Ot by - ^50. Also these corrected values are systema-

tically smaller than ours at room temperature ^as is shown in figure 6. However we point ^{out that the}

differences between these curves could be due to the different origins ^and purities ^{of the} samples ^{used for}

the experiments. ^In fact differences of this type ^have

already been observed at the isotropic-anisotropic

interface of different MBBA samples [26]. ^Therefore experiments with purer compounds ^{are needed}

All the previous ^{results are} independent ^{of the} intensity of the laser beam.

Fig. ^6.

Behaviour of the surface angle et ^at the air-MBBA interface in the present experiment (circles) and in the Bouchiat and Langevin-Cruchon experiment. ^The triangles correspond ^to the values of 0, calculated by B. and L.C. [3, 4]

while the crosses correspond ^to the corrected values calcu- lated by ^us by using ^the experimental ^{values of the aniso-} tropy ^{of the} reflectivity coefficients reported ^{in the same}

reference 3, ^4.

Z . 3 SURFACE _TORQUE.

In order to test the influence of the magnetic ^{field on the} measurements of R, ^we varied H between 1 500 G and 7 000 G without

observing any variation of R within the experimental

noise - 0.001. For this measurement we oriented the

magnetic ^field along the horizontal x-axis in such a way

as to avoid spurious effects due to the Faraday ^effect

in the glass windows of the cell containing ^{the nematic}

L.C. The result of this measurement shows that Ot

is not modified appreciably by ^the magnetic ^beld

This gives information about the value of the restoring torque ^at the free surface of MBBA. By using ^{the one-}

elastic-constant approximation (K;;

K) ^and by assuming that the surface tension for Ot - ^{0° can be}

written as F ⁼ Fo ⁺ W(O - Ot)2 ^{one obtains} (after ^a straightforward calculation) :

where X,, ^{is the} anisotropy ^{of the} diamagnetic ^sus- ceptibility, ^K is the Frank elastic constant and A0 is the variation of the surface angle ^induced by ^the

variation OH of the magnetic field. It should be noted that W corresponds ^{to an} energy barrier rather than to an anchoring energy ^as defined by ^{Vitek and}

Kleman [18], ^{as was shown} recently by ^{J. E. Proust and}

L. Ter-Minassian-Saraga [10] ^and by ^{R. G. Horn}

et al. [27].

At room temperature Ot ~ ^30°, 00,IOR - ^1.5 rad,

xa N 10-’ u.e.s., K ⁼ 6 x 10-’ dynes ^and AR/AH ^{2 x} 10-7 G- i. Therefore W >- 0.4 erg/cm2.

In order to evaluate the influence of the magnetic

field we also took some measurements of R after

switching ^{off the} magnetic ^{field In this case, there are}

no preferential directions in the _x-y horizontal plane,

so the director arrangement ^at the free surface beco-

mes conically degenerate. ^{When the} magnetic ^field

is switched off, differently oriented domains come across the laser spot ^on the surface and generate variations in the signal ^{R At a} given temperature R shows some oscillations having ^{a maximum} ampli-

tude equal ^to R(T), ^where R(T) denotes the relative

anisotropy ^{of the} reflectivity coefficients measured at the same temperature in the presence of the magnetic

field. This measurement confirms that the 0t-angle ^is

not affected by ^the magnetic field and shows that the

angular correlation length of domains on the free sur-

face is larger than the diameter of the laser beam

( 1 mm).

2.4 EBBA FREE SURFACE.

Figure ^{7 shows the}

surface angle 0, ^at the air-L.C. interface of the nematic

liquid crystal N-(p-ethoxybenzylidene)-p-n-butylani-

line (EBBA) ^{versus the} difference between the clearing temperature T, (72°C ^{in our} sample) ^{and the tem-}

perature ^T. The 0, angle ^was deduced from the meas-

ured value of the relative reflectivity anisotropy by using the refractive indices of EBBA reported ⁱⁿ

reference 22. Unfortunately, this reference does not

give ^the experimental values of the refractive indices

over the whole _range of the nematic phase. ^Therefore

the experimental ^values of 0, ^{indicated by crosses in} figure 7 have been obtained by using ^{values of these}

refractive indices extrapolated ^{to lower} temperatures.

The estimated _accuracy of the measured values of Ot

1066

Fig. ^7.

^Behaviour of the director angle 9t ^at the air-EBBA interface versus the difference between the clearing tempera-

ture and the temperature. 9t is deduced by substituting ^into equations ^{1-3 the} experimental values of R and the refractive indices of EBBA [22]. ^Points corresponding ^to T c - ^T > 28°C have been obtained by using refractive indices extrapolated

from reference 22.

(circles ⁱⁿ Fig. 7) is better than ± ^20. We notice that the angle 0, ^{shows a similar sort of} behaviour both in EBBA and in MBBA. In particular, ^{we have also}

in EBBA a transition to a homeotropic alignment ^at a critical value To ^{of the} temperature. Figure ^{3 shows}

0f ^{as a function} of the difference between the clearing

temperature ^{and the} temperature. ^{From a best fit}

to the experimental points ^near the critical tempe-

rature we obtain : where

and

Fig. ^8.

^Behaviour of the square of the angle 6t ^{at the}

air-EBBA interface versus the difference between the clearing temperature ^{and the} temperature.

3. Discussion.

The transition to homeotropic alignment ^observed

at the free surface of MBBA and EBBA can be easily

explained ^{in terms} of the Landau theory of the free surface proposed by ^Parsons [17]. According ^to

Parsons the surface tension of the nematic L.C. near

the critical temperature ^can be written as :

where Fo ^{is a} function of the temperature ^{that does not}

depend ^{on the} angle 0,, ^{B is a} coefficient with a smooth

dependence ^{on the} temperature ^{and A =} Ao(T - To).

Below the critical temperature AIB 0 and the value of 0 minimizing equation ^{9 is} given by :

On the other hand 0,

^{0° for T} > TO(AIB > 0).

For small values of the difference 0 - Ot, the surface tension (Eq. 9) ^can be written as :

By using equations ^{9-11 we find} (for ^T TO) :

Therefore we expect ^{W to} vary ^as (To - T). ^Measur-

ements of W versus the temperature confirm this

prediction [25].

Also the Mada theory [12, 13] ^{is able to} explain ^the

structural transition at the free surface of MBBA and EBBA. By using (28) ^and (28’) ^{of reference 13 and} by assuming 0, ^{1, we} obtain the following dependence of Ot ^on temperature :

where _y denotes the temperature coefficient OSIOT

of the scalar order parameter ^at the critical tempe-

rature To ^{and a is a} parameter ^{of the Mada} theory.

To is defined as the temperature ^at which the scalar order parameter ^{S is} given by :

where

the relative anisotropy ^{of the} splay ^and bend elastic constants of the nematic L.C.

In our experiment ^{in MBBA we find} To

Tc - ^{0.9 OC.}

From references 23 and 24 one obtains So ^{= 0.33 ± 0.03,}

y ^{= -} 0.035 ± ^0.01 (OC) -’ ^and n ^{= -} 0.25 °+ ^0.05.

By substituting these values into equations ^{13 and 14}

one obtains

and thus

in satisfactory agreement ^{with the} experimental ^value

C ⁼ 14.5 ± 0.6 0/(OC)1/2.

In the case of EBBA we have To ⁼ Tr - ^1.2°C.

From reference 22 one obtains Sa ^{= 0.357 ± 0.03 and}

y

0.025 ± 0.004 (oC) - 1. By assuming tj - - 0.25,

we obtain : and

which is in good agreement ^{with the} experimental

value C = 11.8 ± 1.60/(OC) 112 . However, ^the agre- ement between the Mada theory ^{and our} experimental

results is rather _poor at room temperature.

4. Concluding ^remarks.

In the theoretical section we have shown that both the Parsons and the Mada theories are able to explain

the main features of the structural transition occurring

at the free surface of MBBA and EBBA. However we

point ^out that these theories are based on very diffe- rent physical mechanisms. Parsons explains ^{the tilt}

of the director in terms of the competition ^between polar ^and quadrupolar ^forces, while Mada explains

the tilt as being ^{due to} the effect of an elastic force caused by ^vertical gradients of the director polar angle.

Further experiments ^are needed in order to discover the true mechanism responsible for this tilt.

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