Observation of Transient Alignment-Inversion Walls in Nematics of

Article pubs.acs.org/JPCB

Observation of Transient Alignment-Inversion Walls in Nematics of Phenyl Benzoates in the Presence of a Magnetic Field Hristo P. Hinov,*,† Leonard K. Vistin’,‡ and Yordan G. Marinov† †

Institute of Solid State Physics, Bulgarian Academy of Sciences, 72, Tzarigradsko Chausse Bulvd., 1784 Sofia, Bulgaria Moscow State Regional University, 10a Radio Street, 105005 Moscow, Russia

‡

ABSTRACT: Formation of new transient walls by a constant magnetic field at the Fréedericsz critical value has been observed. They are oriented along the initial alignment of the nematic phase of phenyl benzoates and appeared only in relatively thick samples with a thickness between 50 and 100 μm of the cells. The excellent planarity of the liquid crystal orientation is considered to be the most important condition for their presence These magnetic walls are transient as they disappear either after a few seconds for 100 μm thick nematic cells or after parts of a second for thinner (50 μm) nematic cells. Nonregular stable magnetic walls, incorporating disclinations with core, appear immediately after the relaxation of the transient walls, when the planarity of the nematic orientation is not perfect. In thinner nematic cells of 20 μm or less, a Fréedericksz transition has only been observed. The formation of transient magnetic walls can be described by a model taking into account alignment-inversion, twisted along Y regions. The transient walls accompanied by a system of Becke lines relax by going through three-dimensional twist−splay−bend deformations.

1. INTRODUCTION Helfrich1 and Brochard2 have theoretically considered various kinds of alignment-inversion walls in nematic liquid crystals. The formation of alignment-inversion π-walls has been regarded for the case of a strong magnetic field H and strong surface forces which oppose to the action of the magnetic field.1 These interactions affect the alignment of the nematic in the cells. In the middle, far enough from the boundaries, the alignment of the nematic is along the magnetic field whereas in the boundary regions it changes to the “easy axis” of the director defined by the surface forces. On the other hand, Brochard2 considered the walls formation around the Fréedericksz transition.3 These two kinds of walls were discussed by de Gennes.4 The Brochard’s walls were experimentally obtained and studied by Léger.5,6 Such types of walls were also considered by Rey7 and Ranganath.8,9 In this paper, we present observations and suggest explanation of new ±θ alignment-inversion transient walls which appear in the middle of the nematic cells under study. They are observed just at the beginning of splay Fréedericksz transition when the magnetic field H is applied in the Z direction (normal to the glass plates forming the liquid crystal cells) and the initial orientation of the liquid crystal director n is in the X direction. The director orientation jump in ±θ relaxes via three-dimensional twist−splay−bend deformations,10 accompanied by formation of a system of Becke lines.

eutectic mixture H-1 consists of 67 mol % of the liquid crystal 4-butylbenzoic acid 4-(hexyloxy)phenyl ester

and 33 mol % of the liquid crystal 4-hexyloxybenzoic acid 4butylphenyl ester

The two liquid crystals were synthesized for the first time in 1972 by Steinsträsser11 (see also the data presented in the book under the edition of Zhdanov12). This eutectic mixture is a chemical product of Merck with the following phase transition temperatures: K − 0 °C − N − 42 °C − I

where K, N, and I designate crystal, nematic, and isotropic phases, respectively. The dielectric anisotropy Δε of the first chemical component (1) at room temperature is −0.2, whereas the dielectric anisotropy Δε of the second chemical component is +0.2.13 Using the formula14 Δε1,2 = Δε1x1 + Δε2x 2

2. EXPERIMENTAL RESULTS 2.1. Liquid Crystals. We have used a mixture of two eutectic mixtures H-1 and H-106 of phenyl benzoates. The first © 2014 American Chemical Society

(3)

(4)

Received: December 27, 2013 Revised: March 26, 2014 Published: March 26, 2014 4220

dx.doi.org/10.1021/jp412685h | J. Phys. Chem. B 2014, 118, 4220−4227

The Journal of Physical Chemistry B

Article

where x1 and x2 designate the molar fraction of the first and second compounds, respectively, we obtained the dielectric anisotropy Δε for the H-1 eutectic mixture to be 0.1 in agreement with the data pointed out by Vistin’ et al.15 The second eutectic mixture designated by H-106 consists of three compounds: the liquid crystals determined by the relations (1) and (2) and by a third liquid crystal (4{[(butyloxy)carbonyl]oxy}benzoic acid 4-ethoxyphenyl ester):

benzoates forming in this way the studied liquid crystal cells. The inner surfaces were covered with thin polymer (polyvinyl alcohol (PVA)) layer24,25 rubbed by the Chatelain−Berreman method to ensure planar orientation of the nematic26−28 with strong polar θ-anchoring.29 It is well-known that such treatment of the glass plates gives a weaker azimuthal φ-anchoring of the nematic (Wsθ > 0.5 erg/cm2 versus Wsφ ∼ 7.10−3 erg/cm2) where the surface coupling coefficient is designated by W.30,31 At weak anchoring to the polar θ angle (Wθ ∼ 10−2−10−3 erg/ cm2), de Gennes calculated the magnetic threshold: Hc =

The dielectric anisotropy of this liquid crystal has been measured by de Jeu and Lathouwers.16 Some data of the eutectic mixture H-106 were given by Vistin’ et al.17 as follows: K − 1.5 °C − N − 59 °C − I

(K 22/K33) = 0.273

(8)

where b = K/Wθ < d, K is the mean elastic constant, and d is the thickness of the nematic layer.4 The anchoring energy value Wθ was found from the formula

(6)

ε∥ = 5.79, ε⊥ = 5.74, and Δε = +0.05, at room temperature T = 23 °C. The elastic constants of H-106 were established by Valkov et al through the thermal fluctuations method.18 K33 = 1.1 × 10−6 dyne,

1/2 π ⎛ K ⎞ ⎜ ⎟ d + 2b ⎝ Δχ ⎠

Wθ =

⎛ H π⎞ Hc πK11 tan⎜ c ⎟ Hco Δχ ⎝ Hco 2 ⎠

(9)

Hc and Hco are respectively the threshold magnetic fields corresponding to finite and infinite strong (W → ∞) anchoring at the liquid crystal−substrate interface.

(K11/K33) = 0.863, (7)

We mention that mixtures of phenyl benzoates were used for three purposes: (1) causing Fréedericksz transition when the dielectric anisotropy changes its sign with growing frequency (the so-called nematic two-frequency addressing mixture),14 (2) provoking dynamic scattering effect of the transmitted light through the liquid crystal cell,19 and (3) formation of the Vistin’−Pikin−Bobylov flexoelectric domains (the so-called variable grating mode liquid crystal device for optical processing and computing).20 2.2. Setup and Magnetic Anisotropy Susceptibility Δχ. The constant magnetic field has already been used in various investigations, among them observations and study of longitudinal flexoelectric domains21 (Figure 1). The anisotropy

Hco =

1/2 π ⎛ K11 ⎞ ⎜ ⎟ d ⎝ Δχ ⎠

(10)

and K11 is the splay elastic constant.32 2.4. Observations: Metastable Walls, Irregular Stable Walls, and Fréederiksz Transition. The liquid crystal cells prepared with a planar orientation of the director were placed between the poles of the magnet shown in Figure 1 in the way that the constant magnetic field H is perpendicular (along Z) to the nematic layer. The optical observations were effected between two polarizers (polarizer and analyzer) that are parallel to the initial alignment of the liquid crystal. The walls were not observable in crossed nicols. The intensity of the light incident normally on the cells can be presented in the following form:33 ⎛ δ⎞ I = Io⎜1 − sin 2 2φ sin 2 ⎟ ⎝ 2⎠

(11)

The maxima in the transmitted light are at the following values of the angle φ: φ = 0, π /2, π ...

(12)

The minima disposed between the maxima are determined by the relation sin 2φ = ±1, i.e., at the following φ angles: φ = π /4, 3π /4, 5π /4...

(13)

The phase difference between the extraordinary and ordinary rays usually is written in the following form:34

Figure 1. Diagram of apparatus: (1) video camera; (2) electromagnet winding; (3) clamp; (4) test speciment; (5) microscope barell; (6) long distance microscope objective; (7) electromagnet yoke; (8) OP24 light source; (9) polarizer; (10) analyzer.

δ=

2π ⎡ ⎢ λ ⎢⎣

∫0

d

none dz [no 2 cos2 θ(z) + ne 2 sin 2 θ(z)]1/2

⎤ − nod ⎥ ⎥⎦ (14)

of magnetic susceptibility Δχ = χ|| − χ⊥ > 0 has not been measured for the mixture H-1/H-106. Nevertheless, there are sufficient data exposed in refs 22 and 23 permitting us to estimate Δχ = 0.5 × 10−7 (in CGSM units). 2.3. Liquid Crystal Cells: Preparation and Anchoring. The gap between two glass plates separated with equal spacers of 10, 20, 50, and 100 μm was filled with the mixture of phenyl

where λ is the wavelength of the incident light, d is the thickness of the liquid crystal layer, and no and ne are the ordinary and extraordinary indices of aligned nematic, respectively. The magnetic walls shown in Figure 2 are observed at a threshold value of the magnetic field Hc = 1.8 kOe when the cell was with a thickness of 100 μm. 4221



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These domains have been observed by various authors.35,36 The comparison of the images shown in Figures 2 and 3 clearly indicates that the walls (Figure 2) are very regular whereas those shown in Figure 3 are irregular and in some rare cases they are closed. Let us stress that this is a typical picture for all the samples studied. The diagonal orientation of the static domains is connected with the initial twist in the middle part of the cells, which accompanied the relaxation of the transient magnetic walls. On the other hand, the relaxation of the transient walls at the switching off of the magnetic field relaxes completely after an hour and at application of a magnetic field one can see again the formation of the transient walls at the Fréedericksz transition. Further, they disappear at magnetic field increase up to a value of 5 kOe and one can often observe the existence of thin threads only. At the same time, the period of the transient magnetic walls was measured to be around 13 μm independently of the thickness of the studied thick liquid crystal layers.

3. DISCUSSION The particular kind of transient magnetic field-induced walls clearly shows that one domain consists of two (1/2) gray parts, surrounding the bright and dark parts. All of them appear periodically in a similar manner in the systems of walls (Figure 2). We suggest that the bright lines are fringes of Becke (or the so-called “Becke lines”),37 which occur at strong change or discontinuity of refraction when the rays pass through the liquid crystals.38 Furthermore, two such lines can be seen at direct observations of Williams domains in some cases when the nematic is excited simultaneously by both electric and magnetic fields.39,40 In our opinion, the two lines, the bright and the dark, appear due to the strong refraction and/or local total internal reflection of the extraordinary ray.41 The extension in micrometers does not coincide with the real change in the liquid crystal orientation as mentioned also by Lavrentovich42 for the case of disclinations with core. It is important to point that our model is only based on our experimental observations. Initially, we suggest that a number of reverse twisted along Y regions are formed at the beginning of the Fréedericksz transition (Figure 4).

Figure 2. Metastable alignment-inversion walls in a nematic cell with a thickness of 100 μm. The polarizer and analyzer are parallel to the initial alignment of the nematic no.

They appear only at a thickness of 50 μm and above of the liquid crystal layers (we have studied liquid crystal cells with a thickness of 10 μm, 20 μm, 50 and 100 μm). In the case of thinner cells with a thickness of 20 μm and below, only Fréedericksz transition was observed. The second important feature of these walls is that they are transient and after 2−5 s they disappear in cells with thickness of 100 μm. The duration decreases considerably for thinner liquid crystal cells as follows: for 50 μm cell, the magnetic walls exist only parts of a second. Third, they disappear with no threads, which unambiguously shows that there are no linear disclinations with core incorporated in them. As noted, a very important requirement for the observation of these walls is the excellent planarity of the liquid crystal layers. Because of that, the second application of the magnetic field (after the formation and disappearance of the walls) only leads to the formation of other, nonregular domains shown in Figure 3.

Figure 4. Possible initial realignment of the nematic director.

We conclude that this kind of arrangement is due to the perfect planar alignment of the nematic orientation. Probably, the Becke lines appear in places of planes where the orientation of the director is discontinuous. Physically, this is not justified and according to de Gennes4 such an orientation of the director must relax. We show this process schematically only along the Y direction (Figure 5). As a result, the relaxation into one-dimensional Zdeformations is more complex and is effected through threedimensional twist−splay−bend deformations. In addition, one has to take into account the dynamic behavior of the

Figure 3. Stable alignment-inversion walls in a nematic cell with a thickness of 100 μm. 4222



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where the Hc1 designates the applied magnetic field which is greater than Hc, ηa = (1/2)α4

nematic.10,43−45 The end of relaxation is accompanied by disappearance of the metastable regions of orientation of the director. In our opinion, the bright lines are Becke’s focal lines and the accompanying dark lines are “shadows” of the bright lines, as explained by Lavrentovich42 for the case of disclinations in nematics. Transient walls which appear at the Fréedericksz transition and above, were both theoretically and experimentally studied by many authors in the following more important cases: (a) The initial alignment of the nematic is along X and the applied constant magnetic field is along Z, i.e., along the normal to the glass plates confining the liquid crystal,46−50 and case (b) the constant magnetic field is applied along Y, in the plane of the glass plates.51−57 Specifically, we are interested only in the theoretical results obtained at a linear approximation of the nemato-dynamic equations. Next, we will discuss only the main results obtained in these papers and simultaneously we will compare them with our observations and suggestions. The transient walls mentioned above, follow the experimental and theoretical results obtained by Guyon, Meyer, and Salan.47 Namely, these walls appear well above the value of Hc, causing the appearance of the Fréedericksz transition58−62 to decrease the value of rotational viscosity γ1 at the dynamics of the nematic. This process includes the backflow effects63−65 when either the magnetic field is switching on (suddenly) with a big amplitude of the constant magnetic field H or a big magnetic field is switching off and the nematic relaxes to the initial position. We have to stress that our walls are obtained at a value of H which is close to Hc. For the case of 100 μm nematic cell Hc is about 1.8 kOe (compare with the experimental measurements of Magakova et al.59 applying a constant magnetic field H on a similar nematic cell with a twisted orientation and obtaining a value of 1.4 kOe (see curve 1 in Figure 1 in ref 59)). Let us mention that this measured value for the case of phenyl benzoates is greater compared to that obtained by Gerritsma et al.60 for the case of MBBA. This is due to the smaller value of the anisotropy of the magnetic susceptibility of the mixture of phenyl benzoates and the bigger value of Keff:14

sin 2 θm

(17)

2

( ) f (θ ̅) + sin = dθ ̅ dz

|Δχ |H2

2

θ̅ z =−d /2, +d /2

(18)

where f (θ ) = K11 cos2 θ + K33 sin 2 θ θ̅ → 0

sin 2 θm

2

( )K ≅

nx = cos θ

dθ ̅ dz

|Δχ |H

11

2

ny = 0

(19)

nz = sin θ

Hx = Hy = 0

Hz = 1

Figure 6. Possible orientation of the twist wall. The period 2ξ is shown.

It is seen that the period

(15)

⎛ K 22 ⎞1/2 1 2ξ = ⎜ ⎟ ⎝ Δχ ⎠ H

The backflow effects cannot be significant for the walls creation observed by us because they are weak for planar layers and for small deviation of the deformation angle in the middle part of the cell. Further, estimations in the frame of a linear analysis and the concept of the fastest mode of some authors55−57 led to the following formula: ⎛ Hc1 ⎞2 K ηγ ⎜ ⎟ = 1 + 3 a 21 K 2 α2 ⎝ Hc ⎠

γ1 = α3 − α2

Taking into account the values of the viscosity coefficients for MBBA65 at room temperature, we have obtained that the eventual correction is (1/2)(K3/K2). However, this correction can increase with the real viscosity coefficients of the studied mixture of phenyl benzoates. The application of a high constant magnetic field (in the range of 5 kOe) led in our case to quick disappearance of the walls in 1 s instead of in several seconds. Their kind and period, however, did not change. Next to be discussed is the second important parameter, the period of the walls. The period of the walls in cited experiments decreases significantly with the increase of the value of the applied magnetic field. In our case, however, it is not changed. The Fréedericksz transition and the well-aligned nematic trigger the appearance of the walls which are created by the maximal angle θm in the middle part of the cell:

Figure 5. Possible relaxation of the nematic director along Y.

Keff = K11 + (1/4) (K33 − 2K 22)

and

(20)

is inversely proportional to the value of the magnetic field H.4 As the deformation angle in the middle part of the cell is not π/ 2, we suggest that in regions where θm and −θm meet, we observe the system of Becke lines. The appearance of the twist walls instead bend−splay walls along Y likely is connected with the smaller elastic energy and validity of the following inequality:

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2K 22 < K11 + K33

lines due to the existence of bulk θ, φ deformations. Consequently, in our opinion, only one bright line, or a bright line accompanied by a gray line cannot be interpreted as Becke lines. As noted, the shadowgraph method is useful to study the Becke lines.75,78 However, the use of two polarizers permits us to study not only the polar angle deformations but also the azimuthal angle deformations.79,80 The lines of Becke are also important for walls, observed by many authors.81 It was showed that the two bright and dark lines appear during the early stage development of Néel inversion walls. On the other hand, there is a picture, representing the Becke lines in Grandjean−Cano wedge.82 A small part of this picture is shown in Figure 7. Here we focus our attention on several points: (a) The walls are stable as they were formed in one largepitch cholesteric. In our case, however, the patterns observed are transient because they correspond to a system of alternating right-handed and left-handed twisted regions, which annihilate each other in the process of relaxation (see also the comment of the authors of ref 76). (b) There is no discontinuity inside these structures. The discontinuity in our model can be simply removed during the relaxation process by rotation of director on a cone in one place or on cones in various places (Figure 8). In this way, the twist is not only in Y but also in Z.

(21) 54

for the studied mixture of phenyl benzoates. In addition, for higher initial deformations in the nematic layer, it is probable to form twist−bend walls55,56 that are more stable and at application of a high magnetic field one can observe the appearance of (+1/2) or (−1/2) disclinations during the process of “pincement” of the walls. In accordance with suggestions of Sogo et al.66 we believe that the wall disappear with three-dimensional twist−splay−bend deformations. Finally, we will comment two important questions: the appearance of Becke lines and the validity of the model proposed. The lines of Becke are well-known in crystallo-mineralogy as Becke41 first discovered a method for measuring the index of refraction of the minerals based on the appearance of two lines: black and bright, which are situated around the boundary crystal-liquid. It is observed that as the focus of the light changes, the bright and dark lines can exchange their places (Figure 7). This experimental finding is well explained in the

Figure 8. Possible escape from the discontinuity.

(c) There are thickness-independent regions of the domains due to two reasons: the first one is connected with the behavior of the spiral along Z82 and the second one is connected with the so-called optical threshold described by Van Doorn.83 (d) The patterns do not appear in thin nematic layers because in such layers the twist region cannot exist. In the case of pure θ-deformations, one cannot prevent the discontinuity. (e) The existence of a twist deformation along Z leads to a slow relaxation of the nematic toward its initial planar orientation. (f) The optical picture of Becke lines indicates that the image of Figure 2 is taken slightly out of the focus. However, in part of the picture shown in Figure 7, one cannot see the Becke lines.68 Here at the end of this discussion we should mention first that the dynamics during the disappearance of the pattern49,84 is also important. However, it requires a special setup and we cannot perform such studies. Second, the discovered transient texture cannot be studied optically further for different orientation of input linear polarization because our samples are fixed and cannot rotate in the (x, y) plane or be inclined with respect to the magnetic field. Under these circumstances, according to the considerations of Madhusudana, Karat, and

Figure 7. Lines of Becke in Grandjean−Cano wedge.

scientific sources.37,38,67,68 Becke lines always appear as two lines: black and bright. However, two lines (bright and dark) often accompany the appearance of various disclinations in liquid crystals42,69−72 and in many of the cases they cannot be recognized as Becke lines. This can be only checked by the Becke test. Further, the bright line is formed following refraction or total internal reflection of the rays, which occur in the region observed. The total internal reflection is a very important tool for the study of liquid crystals.73,74 The shadow images described by Richter, Rasenat, and Rehberg75 can aid in our opinion at the study of Becke lines. In other words, it is sufficient to use only the polarizer that should be oriented along the Becke line. The use of a liquid crystal is better than the crystals and isotropic fluids,38 which do not require application of nicols. We discuss the results of Cramer et al.76 as an example thereof. In our opinion, they obtained Becke lines at the two edges of the electric stripes, which follow the sign in the gradient of the optical index. In addition, the azimuthal φ-deformation is not important for the appearance of Becke lines. For instance, the observations of Léger77 for wall motion in nematics, clearly shows that the wall appears to be bright below the free surface of the MBBA drop whereas near to the free boundary one sees bright and dark 4224



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Chandrasekhar,85 it is not possible to obtain additional information for the optics of the transient walls. It is evident that this problem requires a special setup and we cannot perform such an experiment.

Predicted Properties of Nematic Eutectic Mixtures of Esters. Mol. Cryst. Liq. Cryst. 1984, 111, 103−133. (14) Stettin, H.; Kresse, H.; Schäfer, W. The Development of a Nematic Two-Frequency Addressing Mixture. Cryst. Res. Technol. 1989, 24, 111−120. (15) Vistin’, L. K.; Yakovenko, S. S.; Chicherin, A. E.; Yarosheva, A. I. The Behavior of Domains of a Second Kind in Nematics under Electric Fields with Above threshold Values. Kristallografia (USSR) 1981, 26, 871−874 (Sov. Phys. Crystallogr. 1981, 26, 496−499). (16) De Jeu, W. H.; Lathouwers, Th. W. Nematic Phenyl Benzoates in Electric Fields I. Static and Dynamic Properties of the Dielectric Permittivity. Mol. Cryst. Liq. Cryst. 1974, 26, 225−234. (17) Vistin’, L. K.; Gotra, Z. Yu.; Yakovenko, S. S.; Molochko, B. A.; Kalinina, T. A.; Kleinman, I. A. Formation of Domains of the Second Kind in Nematic Crystals with Positive Dielectric Anisotropy. Zh. Eksp. Teor. Fiz. (USSR) 1977, 73, 1981−1983 (JETP 1977, 46, 1038−1040). (18) Val’kov, A. Ju.; Zubkov, L. A.; Kovshik, A. P.; Romanov, V. P. The Selecting Scattering Effect of a Polarized Light in a Oriented Nematic Liquid Crystal. Pis’ma Zh. Eksp. Teor. Fiz(USSR) 1984, 40 (N7), 281−283 (JETP Lett. 1984, 40, 1064−1066). (19) David Margerum, J.; Lackner, A. Ester Liquid Crystal Mixtures for Dynamic Scattering at Elevated Temperatures. Mol. Cryst. Liq. Cryst. 1981, 76, 211−230. (20) Barnik, M. I.; Blinov, L. M.; Trufanov, A. N.; Umanski, B. A. Flexo-Electric Domains in Liquid Crystals. J. Phys. (Paris) 1978, 39, 417−422. (21) Hinov, H.; Vistin’, L. K.; Magakova, Yu. G. The Flexoelectric Character of Longitudinal Domains in Liquid Crystals. Kristallografiya (USSR) 1978, 23, 583−587 (Sov. Phys. Crystallogr. 1978, 23, 323− 325). (22) Hardouin, M. F.; Achard, M.-F.; Gasparoux, H. Evolution des Propriét és Magnétique d’une Phase Mésomorphe lors d’une Transition Smectique A − Nématique. Etudie de Deux Exemples. C. R. Acad. Sci. Paris C 1973, 277, C-551−C-553. (23) Zhuk, I. P.; Karolik, V. A. The Investigation of Temperature Dependence of the Magnetic Susceptibility of Nematic Liquid Crystals. Acta Phys. Polon. 1979, A55, 377−384. (24) Kutty, T. R. N.; Fischer, A. G. Planar Orientation of Nematic Liquid Crystals by Chemisorbed Polyvinyl Alcohol Surface Layers. Mol. Cryst. Liq. Cryst. 1983, 99, 301−318. (25) Kubono, A.; Onoda, H.; Inoue, K; Tanaka, K.; Akiyama, R. Liquid Crystalline Alignments on Polar Surfaces Covered with Amino and Hydroxy Groups. Mol. Cryst. Liq. Cryst. 2002, 373, 127−141. (26) Chatelain, P. Sur L’Orientation des Cristaux Liquides par les Surfaces Frottés: Étude Expérimentale. C. R. Acad. Sci. Paris 1941, 213, 875−876. (27) Berreman, D. W. Solid Surface Shape and the Alignment of an Adjacent Nematic Liquid Crystal. Phys. Rev. Lett. 1972, 28, 1683− 1686. (28) Wen, B.; Rosenblatt, Ch. Planar Nematic Anchoring Due to a Periodice Surface Potential. J. Appl. Phys. 2001, 89, 4747−4751. (29) Yablonskii, S. V.; Nakayama, K.; Ozaki, M.; Yoshino, K.; Palto, S. P.; Baranovich, M. Yu.; Michailov, A. S. Control of the Bias Tilt Angles in Nematic Liquid Crystals. J. Appl. Phys. 1999, 85, 2556−2561. (30) Iimura, Y.; Kobayasi, N.; Kobayashi, Sh. A New Method for Measuring the Azimuthal Anchoring Energy of a Nematic Liquid Crystal. Jpn. J. Appl. Phys. 1994, 33, L434−L436. (31) Zhou, Y.; He, Zh.; Sato, S. Generalized Relation Theory of Torque Balance Method for Azimuthal Anchoring Measurements. Jpn. J. Appl. Phys. 1999, 38, 4857−4858. (32) Podoprigora, V. G.; Gunyakov, V. A.; Parshin, A. M.; Krustalev, B. P.; Shabanov, V. F. Liquid Crystals on Solid State Surface − The Determination of Anchoring Energy Under an Applied Magnetic Field. Mol. Cryst. Liq. Cryst. 1991, 209, 117−121. (33) Born, M.; Wolff, E. Principles of Optics; Pergamon Press: Oxford, U.K., 1968; pp 640−641. (34) Berezin, P. D.; Kompanets, I. N.; Nikitin, V. V.; Pikin, S. A. The Orienting Effect of an Electric Field on Nematic Liquid Crystals. Zh.

4. CONCLUSIONS We have observed for the first time the formation of transient magnetic field-induced walls matching the planar orientation of the director at the two boundaries with the orientation of the director at the bulk. The magnetic walls appear in thick cells (with a thickness of 50 μm and above) at very good planarity of the nematic layer and a slow increase of the field. They are transient and disappeared in a few seconds (thick cells) or in parts of a second (thin cells). In thick cells and nonperfect planar orientation of the director, immediately after the relaxation of the transient walls, we have observed stable walls containing in their structure sharp disclinations (probably of strength ±1/2). In the case of thinner nematic cells with a thickness of either 10 or 20 μm, we have observed only the well-known Fréedericksz transition. A simple model is suggested incorporating reverse-twisted regions along Y and the appearance of a system of Becke lines. According to Figure 7, we have observed the lines slightly out of the focal plane of the light. They relax to the initial one-dimensional Fréedericksz transition via three-dimensional twist−splay−bend deformations.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The work of one of the authors has been carried out as a part of Bulgarian-Russian interacademy BAS-RAS joint research project.

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REFERENCES

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