interfacial phenomena between nematic liquid ...2000/03/04 · 3 interfacial phenomena between...

Romanian Reports in Physics, Vol. 52, Nos. 3–4, P. 317–331, 2000

ATOMIC AND MOLECULAR PHYSICS

INTERFACIAL PHENOMENA BETWEEN NEMATIC LIQUID CRYSTALS AND OTHER MEDIA

MIHAELA ÞÎNÞARU

National Institute for Materials Physics, R-76900, Magurele-Bucharest, P.O. Box MG 7, Romania

(Received March 25, 1999)

Abstract. Several contributions to the study of interfacial phenomena between liquid crys-tals and other media are described. Contributions to the control of molecular orientation in liquid crystal cells are presented. Temperature induced surface transitions in homogeneous and hybrid nematic liquid crystal cells are experimentally studied and theoretically explained with the elastic theory. Temperature dependence of liquid crystal surface tension is studied and an improved phe-nomenological theoretical model is discussed to explain the experimental results.

Key words: liquid crystals, surface transitions, surface tension.

1. INTRODUCTION

The interface phenomena between liquid crystals and other media have been widely studied from both experimental and theoretical points of view for their importance concerning liquid crystal display devices [1–5].

The thesis entitled “Interfacial phenomena between nematic liquid crystal and other media”, describes contributions to the study of such phenomena in nematics, for example the control of the molecular orientation in liquid crystal cells, temperature induced surface transitions, and temperature dependence of nematic liquid crystal surface tension.

In Section 2, the contributions to the control of the molecular orientation in nematic liquid crystal cells are described. A new experimental method for ob-taining a variable tilt angle is given. An improved interferometric method for tilt angle measurement is also described.

In Section 3, an experimental study of temperature induced surface transi-tions is presented. The results are well explained by using the second order elas-tic theory.

In Section 4, the experimental study of temperature dependence of surface tension for some nematic liquid crystals, followed by a suited phenomenological theoretical model, is presented.

In Section 5, the main results presented are summarised.

318 Mihaela Ţînþaru 2

2. CONTROL OF MOLECULAR ORIENTATION AND THE TILT ANGLE DETERMINATION IN LIQUID CRYSTAL CELLS

2.1. CONTROL OF THE TILT ANGLE IN NEMATIC LIQUID CRYSTAL CELLS

The tilt angle is a fundamental property that characterises the liquid crys-tal-surface interaction. Therefore, an accurate control of this parameter is very important for liquid crystal devices. We proposed a new method for producing tilt angle in liquid crystal cells [6]. The proposed method requires an alignment substrate obtained by SiO vacuum deposition layer that is subsequently covered with a polyvinyl alcohol (PVA) layer, by dipping it in aqueous solution. By changing the PVA concentration in the solution, it was possible to obtain tilt an-gles (θ), measured from the surface, between 7° and 30°.

The sample used in our experiments is of the sandwich type and is sche-matically represented in Fig. 1. It consists of two glass plates treated for liquid crystal alignment.

mylarliquid crystal

glass

conductive layeralignment layer

spacer

filling hole

Fig. 1. – Schematic view of a liquid crystal cell.

We used two methods for tilt angle measurement: the crystal rotation method [7] and the null magnetic method with optical detection [8].

nL CH M L P P V

12 21

S PH

Fig. 2. – The experimental set-up for crystal rotation method. L1 – lamp; CH – chopper; M – monochromator; L2 – lens; P1, P2 – polarizers; S – liquid crystal sample; PH – photo diode; V – nanovoltmeter.

The crystal rotation method is based on the determination of the sample po-sition for which the phase difference between the two optical modes of propaga-tion of a monochromatic wave through the crystal has an extreme value. The precision of this method in tilt angle determination is of maximum 20′.

The null magnetic method with optical detection consists in finding the posi-tion of the nematic liquid crystal cell for which the application of a strong magnetic

3 Interfacial phenomena between nematic liquid crystals and other media 319

H

LP1 PC P2 F

S Fig. 3. – Experimental set-up for measuring the tilt angle by the null mag-netic method. L – laser; P1, P2 – polarizers; S – liquid crystal sample; C – compensator; F – band-pass filter; P – digital photometer.

field does not produce any modification of the intensity of the transmitted light. In that position, called “null magnetic position”, the director of the liquid crystal layer is parallel with the magnetic field H, acting on the sample. So that the tilt angle can be directly measured. The maximum error in tilt angle measurement is of ± 30′.

Fig. 4. – Tilt angle versus PVA concentration (weight %) of the dipping aqueous solution for liquid crystal ZLI 1132 (Merck).

The results for tilt angle versus PVA concentration used in obtaining the alignment substrate are given in Fig. 4. From this figure we observe that the tilt angle linearly decreases as the PVA concentration rises.


2.2. THE TILT ANGLE DETERMINATION BY AN INTERFEROMETRIC METHOD

We proposed a new method of tilt angle determination in liquid crystal homogeneous cells [9]. This method is based on the determination of the bire-fringence of liquid crystals by a new manner of processing the experimental data in the interference method [10].

The intensity of the transmitted light through a liquid crystal sample situ-ated between crossed polarizers making an angle of 45° with the optical axis of the sample passes through successive minima and maxima when the wavelength of the incident light, λ, is variable.

The condition for an interference minimum to be reached is:

0( )i

i

h n k i∆ λ= +λ (i = 0, 1, 2…) (1)

where h is the thickness of the sample, ∆n is the birefringence of the liquid crys-tal, k0 denotes the unknown interference order corresponding to the minimum with the greatest λ in the used spectral range, and (k0 + i) is the interference order.

For small variation of λ, ∆n is usually considered λ-independent [11, 12]. From our experiments, performed for the 5CB liquid crystal, we observed

that ∆n shows an important variation with λ, and consequently, the mean bire-fringence cannot be considered λ-independent. In ref. [10] we supposed that ∆n is well described by a power series of the type:

20

12in n i i∆ = ∆ + ε + α (2)

where ∆n0, ε, and α are constants. Supposing ε/∆n0 << 1 and α/2∆n0 << 1, and using eq. (2) in eq. (1), the ratio h/λ is calculated like a polynomial of third de-gree and, then, the birefringence can be determined.

The results for 5CB using the above method are in a very good agreement with those from ref. [13, 14] that used other measuring methods.

The proposed method for the tilt angle determination, suitable for a liquid crystal with negative dielectric anisotropy, is based on the comparison of the sample birefringence in the absence and the presence of an electric field, deter-mined through the interferometric method described above.

The tilt angle value, Φ, measured from the normal to the substrate, is given by:

12 2

cos 1 1o o

o ef o

n n n nn n n

− + ∆ + ∆ Φ = − − + ∆ (3)


where ∆nef is the Φ-dependent effective birefringence, and no is the ordinary re-fractive index.

The experiments were performed for the nematic liquid crystal ZLI 2659 from Merck (with no = 1.486 for λ = 0.59 µm), in tilted samples, obtaining: Φ = 52.8 ± 0.4°.

For comparison, the tilt angle was also measured by the null magnetic method, experiment from which we obtained 52 ± 0.5°. As can be remarked, the concordance is quite good.

3. TEMPERATURE INDUCED SURFACE TRANSITIONS IN LIQUID CRYSTAL CELLS

Temperature induced surface transitions both in homogeneous [15] and hy-brid [16, 17] liquid crystal cells were experimentally studied. The results were theoretically explained by an elastic theory of surface transitions [18]. This the-ory explains the tilt angle variation by the difference between the temperature variation of the effective splay-bend elastic constant, 13,k and the usual elastic constant, k. The temperature dependencies for the ratio of these constants are given by:

13 .C

k DCk T T= +

− (4)

T is the absolute temperature and TC is a temperature a little higher than the nematic-isotropic temperature transition, C and D are constants.

For both types of samples, the bulk and the surface tilt angles are fitted in the strong and weak anchoring hypothesis, respectively.

For tilted homogeneous cells, in the case of strong anchoring, the bulk tilt angle, Φb, is given by:

( )1 sin 22b S sC

DCT T

Φ = Φ − + Φ −

(5)

with

,S eΦ = Φ (6)

ΦS being the surface tilt angle and Φe, the easy direction in the Rapini-Papoular theory [19].

For weak anchoring:


( )

( )( )

2

1/ 22

4

/1 arccos2 /

( / )1 / 12 /

Cb

C

CC

C

A B T T

C D T T

A B T TC D T T

C D T T

+ − Φ = − + −

+ − − + − ⋅ − + −

(7)

with

[ ] 213sin 2( )

.sin(4 ) 2S e

S

kLb k

Φ − Φ = Φ

(8)

L is the extrapolation length and b is a mesoscopic length, near the surface, in which a sharp variation of the nematic orientation is introduced. A, B, C and D are the fitting constants.

In the case of hybrid cells, for strong anchoring we have for the experimen-tal measured tilt angle, Φexp:

( ) ( )exp 2 21 11 sin 22 C

DCe T T

Φ ≈ Φ + − + Φ − (9)

with 1 eΦ = Φ (10)

and for weak anchoring:

( )

exp 2

1/ 22

4

/1 arccos2 ( / )

( / )1 11 12 ( / )

C

C

C

C C

A B T TC D T T

A B T TDCe T T C D T T

+ −Φ = +

+ −

+ −+ − + ⋅ − − + −

(11)

with 2 2

13

/cos(2 )( / )

b Lk k

Φ ≈ (12)

Φ1 and Φ2 are the tilt angles at the two surfaces of the hybrid cell. In our studies, various types of alignment were used. In the case of homo-

geneous cells, the measurements were made on three types of alignment which led to: I – bulk tilt angle of about 60° with the normal to the substrate, II – high tilt angles of 70÷80°, and III – low tilt angles, strongly dependent on the liquid crystal. For the hybrid cells, the limiting surfaces were treated so that the pla-nar-homeotropic and planar-tilted orientations may be obtained.


The liquid crystals used, both in homogeneous and hybrid cells, are: NP 8A, NP 9A, NP 997, ZLI 1623 (from Merck) and MBBA (from Eastman).

The tilt angle was obtained from measurements of optical path difference between the ordinary and the extraordinary waves introduced by the cell.

The experimental results of tilt angle versus temperature were fitted both in the strong and the weak anchoring hypotheses. To choose a better set of fitting parameters, several types of experiences were performed: using the same liquid crystal in various cell geometries or the same liquid crystal and the same align-ment substrate in homogeneous and hybrid cells.

I chose, for exemplification, the liquid crystal NP 9A, studied both in homo-geneous and hybrid geometries. The experimental results for planar-homeotropic hybrid cells are given in Fig. 5, and those for homogeneous cells, in Fig. 6.

Fig. 5. – Tilt angle versus temperature for NP 9A in a planar-homeotropic hybrid cell. experimental results. The best fit according to eq. (11). TC = 61°C; A = 0.2; B = –0.1; C = –0.5; D = 0.09; χ2 = 3⋅10–5; Φe = 0°. 13 / 0.5k k = − (at 20°C).

Comparing the results obtained for liquid crystals in all the geometries studied, we may conclude that:

1. A good agreement for the fitting parameters and the value of 13 /k k for the same liquid crystal on the same type of surface, but in different geometries is observed.

2. The liquid crystals may be classified in function of 13k constant in: liq-uid crystals with 13 0k > and liquid crystals with 13 0.k <


Fig. 6. – Average tilt angle, Φb, versus temperature for NP 9A (III) type surfaces. experimental results. Continuous curve – the best fit according to eq. (7). TC = 61°C; A = 0.3; B = 0.6; C = −0.9; D = 1.6; χ2 = 2⋅10–4; Φe = 0°. Dotted curve – the best fit according to eq. (5). TC = 61°C;

ΦS = 0.644; C = –1.1; D = 4.3; χ2 = 9⋅10–413 / 0.6k k⋅ = − (at 20°C).

3. Interesting results were obtained in experiments made on homogeneous type III cells. In this type of samples, for liquid crystals with 13 0,k > a tilt initial orientation, negative with the deposition direction of SiOx, was observed. With increasing temperature, the bulk tilt angle increases from negative to positive values passing through homeotropic alignment. For the same substrate type, but for liquid crystal with 13 0,k < the initial tilt angle (positive with the deposition direction of SiOx) decreases, tending to low values with the increasing temperature.

4. The surface tilt angle measured for III type surface (Φ2 or ΦS at T = 20°C), is the same for almost all the liquid crystals used. Therefore, we considered that the surface tilt angle value is more dependent on the surface topography than on the mesophase nature.

5. The method can give indications whether the anchoring is strong or weak.

We remark that the temperature induced surface transitions are well de-scribed using the elastic model. That is why these experimental results are new arguments for the validity of the elastic model for the temperature induced sur-face transitions and, also, allow an evaluation of the elastic constant ratio 13 / .k k


4. TEMPERATURE DEPENDENCE OF LIQUID CRYSTAL SURFACE TENSION

The experimental measurements of surface tension versus temperature for liquid crystals show a variety of behaviours near the phase transition: for some liquid crystals that dependence has a positive slope in contrast to isotropic liq-uids, and for others, a jump of the surface tension value at the phase transition is present. Moreover, in a small temperature range above the transition point, for some liquid crystals, the surface tension rises.

We studied the temperature dependence of the surface tension of four liq-uid crystals from the alkyl-cyanobiphenyl homologous series with the general chemical formula:

CNCnH2n+1 (n = 5, 6, 7, 8).

4.1. THE EXPERIMENTAL METHOD

To measure the surface tension, the pendant drop method was used. The variant proposed by us [20] uses the photographic image and can be applied to any drop shape having a maximum diameter or not. The method is based on the location of the inflexion point of the shape, also used in ref. [21], but expressed in function of the radius of the curvature at drop apex. The experimental results were processed by a computational method carried out in our laboratory.

4.2. THE MEASUREMENT OF LIQUID CRYSTAL SURFACE TENSION

The experimental curves for surface tension versus temperature of the four studied liquid crystals, both in nematic and in isotropic phases, are shown in Fig. 7. It can be shown the differentiate behaviours of all compounds, in nematic, isotropic phases and at the phase transition. We observe that for T < TNI, the surface tension versus temperature has a negative slope for 5CB, 6CB and 8CB. This slope changes its sign from positive to negative for 7CB, on the same temperature range. At T = TNI there is a down jump of the surface tension value, for 5CB, 7CB and 8CB. For T > TNI, we observe that from 5CB to 8CB, the curve trend changes by emphasising its maximum together with the increase of the alkyl length.

It can also be seen that, for the same reduced temperature, the surface ten-sion value decreases with the increasing of the alkyl length. This result is in good agreement with those from ref. [22].

Fig. 8 shows the temperature dependence of surface tension for 8CB in the smectic phase.


28.5

30.0

31.5

33.0

34.5

–15 –10 –5 0 50

5CB6CB7CB8CB

T–TNI

γ [d

yne/

cm]

Fig. 7. – The surface tension versus reduced temperature for: 5CB; 6CB; ∇ 7CB; 8 CB.

29.2

29.4

29.6

–6 –4 –2 0

T–TNI

γ [d

yne/

cm]

Fig. 8. – The surface tension versus reduced temperature for 8CB in the smectic phase.


4.3. THE SURFACE TENSION IN THE IMPROVED PHENOMENOLOGICAL THEORY

The results are theoretically explained by an improved phenomenological theory taking into account the dependence of the surface free energy from the surface tilt angle (Φ0) and the calculated surface order parameter (S0) [23] and considering that all the phenomenological coefficients from fb are temperature dependent [24].

In a first step, the Landau-de Gennes theory of phase transitions was used. According to this theory, the total free energy of a semi-infinite system (F) is given by:

( )2

0

1 d ,2b SF f L S z f∞

′= + +∫ (13)

where d / dS S z′ = with S – the z dependent order parameter and L is an elastic constant. fb is given by the expansion in function of the order parameter S:

( ) 2 3 40

3 1 9( ) 4 4 16b Cf f T a T T S BS CS∗= + − + + (14)

where a, B, C are phenomenological coefficients considered constant for a nar-row temperature range near the nematic-isotropic transition, *

CT is the lowest temperature up to which the isotropic phase is allowed. The surface free energy (fS) expansion is:

( ) ( ) ( )22 2 2

0 11 20 0 21 0 22 01 2 1 1 1( , ) (0) 3 3 3 3 3S S of S x f S x S S x S x= + β − + β + β + + β − (15)

In the surface free energy we denote with S0, the surface order parameter, and with 2

0cos ,x = Φ where Φ is the nematic tilt angle with the normal to the sub-strate. βij are phenomenological coefficients, temperature independent.

As the measurements were made within a wide temperature range, follow-ing ref. [24], we considered further, that also the phenomenological coefficients B and C in fb are linearly temperature dependent.

The surface tension temperature dependence for a liquid crystal is given by:

γ(T) = γiz(T) + ∆γ(T) (16)

where the isotropic part of surface tension is

2 / 31 2( )iz Mv D D Tγ = + ⋅ (17)

with Mv µ= ρ – molar volume, µ – molar mass, ρ – density, D1 and D2 – constants.


0

0 02 ( ) ( ) d ( , )bS

b b b SS

L f S f S S f S∆γ = − + Φ∫ (18)

represents the contribution to γ due to the presence of bulk and surface ordered phases. Sb is the bulk order parameter, far from the surface z = 0.

With this model, and with B/a and C/a values from [24], the temperature dependence of surface tension for 5CB was studied. We chose the same values for β20, β21 and β22 and different values for β11. We made this choice because β11 is the coefficient of the most important term from fS, that describes the direct interaction between liquid crystal and surface. In these circumstances, in function of the values of β11, states with S0 > Sb and S0 < Sb (for T < TNI) can arise. The sur-face phase remains ordered also at T > TNI, for great absolute values of β11.

∆γ [d

yne/

cm]

∆γ [d

yne/

cm]

–0.75

–0.45

–0.15

0.15

00

–10 –6 –2 20

4a3a

2a

1a

β11>0

T– TNI

–2.0

–1.5

–1.0

–0.5

0

0.5

0

–10 –6 –2 20

4b3b

2b

1b

β11<0

T–TNI Fig. 9. – Anisotropic contribution to surface tension versus relative temperature for the case (a) β11 > 0 and (b) β11 < 0; a = 1.12×106 erg/cm3 K, β20 = 0.9 dyne/cm, β21 = −0.9 dyne/cm, β22 = 0.9 dyne/cm. Curve 1(a): β11 = 4.5 dyne/cm; 2(a): β11 = 2.7dyne/cm; 3(a): β11 = 0.32 dyne/cm; 4(a): β11 = 0.09 dyne/cm. Curve 1(b): β11 = −4.5 dyne/cm; 2(b): β11 = − 2.7 dyne/cm; 3(b): β11 = 0.32 dyne/cm; 4(b): β11 = 0.09 dyne/cm.

The results for the temperature dependence of the contribution to the sur-face tension due to the presence of an ordered phase are given in Fig. 9. In function of the absolute value of β11, various temperature behaviours can be obtained:


curves with positive or negative slope for T < TNI. At T = TNI, all the calculated curves present a jump either in the positive or the negative sense.

The coefficient β11 determines, also, the alignment type. We showed that for β11 > 0 and great, planar stable alignments are obtained, while for β11 < 0 and great, the homeotropic ones are allowed. For small absolute values of β11, the tilted stable alignments are obtained. For certain values of this coefficient, surface transi-tions from tilted to planar or homeotropic alignment could be described.

This theory can describe the great variety of the behaviour of liquid crystal surface tension with temperature. By means of this theory, a similar curve with the experimental one was calculated for 5CB and is given in Fig. 10. The calcu-lated curve was obtained for great in absolute value and negative β11, which corre-sponds to homeotropic orientation at the free surface for 5CB, as experimentally determined [25].

–0.2

0

0.2

0.4

0.6

0.8

–10 –6 –2 20

∆γ + Cγ= ∆γ– 0.03x(T–TNI) + C

T–TNI

γ [d

yne/

cm]

Fig. 10. – The calculated surface tension, γ, with phenomenological coefficients: a = 1.12×106 erg/cm3 K; β11 = –2.7 dyne/cm; β20 = 1.9 dyne/cm; β21 = 1.9 dyne/cm; β22 = 1.9 dyne/cm. B and C are temperature-dependent coefficients.

We remark a good agreement with our experimental data: the theoretical curve reproduces the decreasing behaviour of γ for increasing temperature, and the jump value at the phase transition.


5. CONCLUSIONS

The most important original results obtained in the thesis are: 1. A new method of obtaining the tilt alignment in nematic liquid crystal

samples, was imagined. The method consists in achievement of an orientation substrate by SiO deposition that is subsequently covered with a polyvinyl alco-hol (PVA) layer, obtained by dipping in aqueous solution. By changing the con-centration of PVA in the solution, it was possible to obtain different tilt angles for the used liquid crystals.

2. A new method for tilt angle determination was proposed. This method, suitable for liquid crystals with negative dielectric anisotropy, is based on the comparison of the sample birefringence in the absence and the presence of an electric field. The birefringence was determined by a new manner of processing the experimental data in the interference method, improving the results.

3. Experimental studies on temperature induced surface transitions in liquid crystal cells were made. The results were theoretically explained by the elastic theory of surface transitions. According to this theory, the tilt angle changing is due to different temperature dependence of the splay-bend and of the usual elas-tic constants. The experimental value of 13 /k k for various liquid crystals was determined. From our experimental observations, we can conclude that the elas-tic model describes well the temperature induced surface transitions for the stud-ied liquid crystals. Therefore, these results are also new arguments for the validity of this model.

4. The temperature dependence of the surface tension for four liquid crys-tals from homologous series of alkyl-cyanobiphenyls was determined using the pendant drop method. For the first time, the surface tension for the smectic phase of 8CB was accurately obtained. The experimental results were explained using a model based on an improved phenomenological theory. In this theory, all the phenomenological coefficients in the bulk free energy are considered tempera-ture dependent and in the surface free energy expression we take into account the equilibrium value of the surface tilt angle and the calculated surface order pa-rameter. This theory can describe o great variety of surface tension behaviours for nematic liquid crystals, including those studied by us.

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