measurement of anchoring coefficient of homeotropically aligned nematic liquid crystal using a polarizing optical microscope in reflective mode

Measurement of anchoring coefficient of homeotropically aligned nematic liquid crystal using a polarizing optical microscope in reflective mode Sang-In Baek, Sung-Jo Kim, and Jong-Hyun Kim Citation: AIP Advances 5, 097170 (2015); doi: 10.1063/1.4931950 View online: http://dx.doi.org/10.1063/1.4931950 View Table of Contents: http://aip.scitation.org/toc/adv/5/9 Published by the American Institute of Physics AIP ADVANCES 5, 097170 (2015) Measurement of anchoring coefficient of homeotropically aligned nematic liquid crystal using a polarizing optical microscope in reflective mode Sang-In Baek, Sung-Jo Kim,a and Jong-Hyun Kim Department of Physics, Chungnam National University, 99 Daehak-ro, Daejeon 305-764, Republic of Korea (Received 27 June 2015; accepted 16 September 2015; published online 24 September 2015) Although the homeotropic alignment of liquid crystals is widely used in LCD TVs, no easy method exists to measure its anchoring coefficient In this study, we propose an easy and convenient measurement technique in which a polarizing optical microscope is used in the reflective mode with an objective lens having a low depth of focus All measurements focus on the reflection of light near the interface between the liquid crystal and alignment layer The change in the reflected light is measured by applying an electric field We model the response of the director of the liquid crystal to the electric field and, thus, the change in reflectance By adjusting the extrapolation length in the calculation, we match the experimental and calculated results and obtain the anchoring coefficient In our experiment, the extrapolation lengths were 0.31 ± 0.04 µm, 0.32 ± 0.08 µm, and 0.23 ± 0.05 µm for lecithin, AL-64168, and SE-5662, respectively C 2015 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4931950] Liquid crystals (LCs) have fluidic properties, and substrates that surround LCs are essential in applications and research The interaction between an LC and a substrate can affect the properties of the LC A uniform alignment is induced from a uniform interaction between an LC and a substrate, which is a necessary condition for the widely used LC display The alignment itself and the alignment techniques used are key factors in controlling the interaction between an LC and a substrate An external electric field compels the LC director to rotate The rotational properties are influenced by the interaction of the LC with the substrate, in addition to the internal properties of the LC The overall substrate effect is expressed as the anchoring energy, which is the energy necessary to rotate the director at the interface.1,2 In general, the interaction of the LC with the substrate hinders the response of the director to the external field The interaction for a typical LC displays is quite strong As techniques have advanced to allow more sensitive and detailed control, the controlled alignment of the strength and orientation has become a topic of much research interest The anchoring energy is generally expressed as the product of the anchoring coefficient and the square of the deviation angle of the director from the easy axis at the interface The anchoring coefficient represents the strength of the interaction of the LC with the substrate for a particular rotation For a given director, there are two anchoring coefficients with polar and azimuthal orientations of the deviation from the easy axis There are several well-established techniques for measuring the anchoring coefficients for planar and tilted alignments The standard method for measuring the polar anchoring coefficient for planar alignment entails observing the response of the director near the interface with a relatively strong external field.3,4 This method allows us to ignore the response of thick-bulk director, which cancels out the optical response, and to focus only on the director in the very thin layer near the interface, which is effective for obtaining the polar anchoring coefficient a e-mail: jxk97@cnu.ac.kr 2158-3226/2015/5(9)/097170/7 5, 097170-1 © Author(s) 2015 097170-2 Baek, Kim, and Kim AIP Advances 5, 097170 (2015) A method similar to that used for planar alignment cannot easily be applied for homeotropic alignment It is difficult to hide a large bulk response, which overwhelms a small response from the interface Therefore, when the expected signal is masked by a large bulk response, it is difficult to obtain the desired results.5 There are several methods for measuring the anchoring coefficients in homeotropic alignment.6–13 The reflectance at the interface of interest was used in these methods A wedge cell was used to remove the effect of the unimportant substrate in one method While controlling the observation angle and electric field, ellipsometry was used to measure the reflectance in another method In addition, a method using the fully leaky waveguide technique was reported However, all of these methods require the preparation of an appropriate cell structure or complicated processes In the present study, we introduce a technique to measure the anchoring coefficient of a nematic LC in homeotropic alignment We use a polarizing optical microscope in the reflective mode with an objective lens of low depth of focus to observe the change in the orientation of the director near the interface The rotation of the director with the electric field changes the reflectance of light linearly polarized parallel to the electric field The director rotation is calculated using a given coefficient The experimental results are fitted with the calculated results to obtain the appropriate coefficient This technique uses a common tool, relatively easy processes, and a typical LC cell, enabling widespread usage For our technique, we made several assumptions to simplify the experiments and to help understand the measuring process The LC cell we considered consisted of two parallel substrates and, in general, the light reflected from the cell consisted of light reflected from both substrates To avoid the effect of unnecessary reflection, we used an objective lens with a low depth of focus in optical microscope We adjusted the depth of focus of the objective lens to be much smaller than the cell gap and focused the lens at the upper interface between the LC and alignment layer Even when the director was rotated, the change in reflectance was small Adjustments of the microscope, such as increasing the exposure time and removing unnecessary light, are essential to enhance the signal Assuming that the signal is obtained from an interface, the other substrate was considered to align uniformly along the electric field for ease of calculation Because observations were focused near the interface and neighboring layers, the thickness and refractive index of each layer should be known We checked the change of the director orientation in homeotropic alignment with the planar electric field First, several parameters were considered such as the cell gap (d), electric coherence 1/2 length (ξ E ), and extrapolation length (b) The electric coherence length (ξ E = 4πK/∆εE ) is the distance from substrate of the infinitely anchoring to the director rotated in the direction of the electric field, where K is the appropriate elastic constant, ∆ε is the dielectric anisotropy, and E is the strength of the electric field.1 Here, we consider the case of ∆ε > The extrapolation length (b = K/W ) is the distance from the substrate surface to the virtual surface of infinitely anchoring in the substrate, where W is the anchoring coefficient.1 We considered only the case of d >> ξ E to simplify the calculation If the anchoring is not too weak, the change of the director orientation at the interface would be sufficiently small, and the condition would apply for a wide range of electric fields With this assumption, the cell gap can be considered to be infinite, and the director angle (θ) for specific values of ξ E and b can be expressed as1  ( ) (z + b) π −1 θ (z) = − tan exp − , (1) ξE where θ is the rotation angle from the surface normal and z is the distance from the interface to the bulk Next, we considered the measurement of reflectance from the LC cell Along the lightpenetration path, the cell comprises a substrate, an alignment layer, the LC, an alignment layer, and a substrate [Figure 1(a)] As mentioned above, we focused on the interface between the LC and alignment layer with an infinite cell gap [Figure 1(b)] such that the cell can be thought to consist of a glass substrate, an alignment layer, and the LC Because the substrate is much thicker than the alignment layer and LC layer, the glass substrate does not factor into the measurement 097170-3 Baek, Kim, and Kim AIP Advances 5, 097170 (2015) FIG (a) Schematic of the LC cell used in the experiment The electric field is applied between two electrodes The size of the layer is exaggerated for a better understanding of the structure (b) Schematic of the measured region, which is primarily the depth-of-focus region near the interface between the alignment layer and LC of the top substrate Multilayer reflectance is well known and the reflection coefficient (r) is expressed as14 r=  A   C Ano + BnTno − C − DnT , Ano + BnTno + C + DnT B  = M = M1 M2 M3 · · · MN , D  (2) (3) where no is the refractive index of the medium of the incident wave and nT is the refractive index of the medium of the transmitted wave In the experiment, no was the refractive index of the glass substrate and nT was the refractive index of the extraordinary wave in the LC Mi is the transfer matrix of the ith layer and is expressed as  cos k i l i Mi =   −ini sin k i l i − i sin k i l i ni cos k i l i   ,   (4) where k i (= 2π/λ i = 2πni /λ o ) is the wave number, λ i is the wavelength, ni is the refractive index of ith layer, and λ is the wavelength of light in vacuum The measured reflectance is R = |r |2 The glass substrate and alignment layer have a constant refractive index However, the refractive index of the LC layer varies with the director orientation which varies with the electric field Therefore, in effect, we divided the LC layer into very thin uniform layers, and each layer had a different refractive index In the calculation, each layer was approximately 10-nm thick with a uniform refractive index The LC was homeotropically aligned without an electric field, and the light experiences the ordinary refractive index (no) In the presence of an electric field, the light polarized along the electric field was affected by the contribution of an extraordinary  refractive index (ne), and for a director tilted by θ, the refractive index is expressed as ne (θ) = none/ no2 sin2θ + ne2 cos2θ When the total number of layers was sufficient, the directors in the layer farthest from the interface aligned along the electric field The LC cell structure allows the application of a planar electric field to control the LC [Figure 1(a)] One substrate has two Cr electrodes approximately 40–130 µm apart, and the other substrate is glass and does not contain electrodes In the experiment, all the substrates were treated to induce homeotropic alignment The two substrates were fixed with a cell gap of 10–60 µm As the electric field is applied by the electrodes on one substrate, the electric field in the cell is not uniform; it is dependent on the distance from the electrode substrate and the position between the electrodes 097170-4 Baek, Kim, and Kim AIP Advances 5, 097170 (2015) However, as already mentioned, because the region of interest is near the electrode substrate, the non-uniformity and decrease in the electric-field strength can be ignored The LC was injected in the isotropic phase All the measurements were performed at room temperature The alignment materials used to induce homeotropic alignment were the polyimides AL-64168 and SE-5662 and lecithin The polyimides were spin-coated on the substrates at 2000 rpm for 30 s and then baked at ∼210 ◦C For lecithin, an ethanol solution with a small amount of dissolved lecithin was spread uniformly on the substrate and dried The substrate was cleaned to remove debris We used 4-cyano-4′-pentylbiphenyl (5CB; Merck) for the nematic LC The nematic phase of 5CB occurs in the range of 24–36 ◦C The elastic constants are K1 = 1.2 × 10−11 N and K3 = 1.6 × 10−11 N.15 To simplify the calculation, we adopted the one-constant approximation with K = 1.4 × 10−11 N because the combination of K1 and K3 causes complications as the director rotates along the electric field The error range should not be so large that the results are affected The dielectric anisotropy ε a is 11.5 (ε ∥ = 18.5, ε ⊥ = 7.0),16 and its refractive indices at 550 nm, which is the central wavelength of the measuring light, are ne = 1.72 and no = 1.54.17 We used a polarizing optical microscope (Eclipse E600, Nikon) to measure the reflectance To focus on the small area between the electrodes near the interface between the LC and the alignment layer, we used an objective lens of high magnification (CFI LU Plan Epi ELWD 100×, NA 0.8; Nikon) The depth of focus was 0.43 µm We inserted a green interference filter (GIF) to limit the wavelength at 550 ± 20 nm, and in the calculation, we used 550 nm as the reference wavelength Because the director rotates along the electric field, we adjusted the polarizer and analyzer axis along the electric field We measured the reflective intensity while controlling the electric field Because the intensity of reflected light is low, we accumulated light by increasing the exposure time and obtained the reflective intensity by averaging CCD images We used a sinusoidal wave at kHz with a function generator (33120A, Hewlett Packard) and amplifier (609E-6, Trek) In this report, all electric-field values mentioned are root-mean-square values Figure shows the change in the reflected light with the electric field The entire area in the images shows the aligned LC, and the electrodes are not visible, because the observable area was limited by the iris The reflective intensity increased with the electric field When the polarizer and analyzer were rotated by 90◦ and became perpendicular to the electric field, the reflective intensity did not change with the electric field for a constant refractive index (no), despite the director rotation In the calculation of the reflective intensity, the refractive index and thickness of the substrate, alignment layer, and LC are important The glass substrate had a refractive index of 1.53 and was several hundreds of micrometers thick The thickness was much greater than the depth of focus of the objective lens; therefore, we did not need to consider the entire substrate The polyimide alignment layers were approximately 250-nm thick The refractive index of SE-5662 is known as 1.54, which is similar to the value for glass.18 However, because the refractive index of AL-64168 is not known, we assumed it has a value similar to that of SE-5662 Therefore, we did not need to consider the reflection from the interface between the substrate and alignment layer As the lecithin layer is a one-molecule layer, its influence on the reflection can be disregarded To confirm the reliability of the technique, we obtained the anchoring coefficient by changing the cell gap for a given objective lens and given cell conditions (×100 magnification; 0.43-µm depth of focus; 80-µm distance between the electrodes; lecithin coating) When we varied the cell gap between 12 and 100 µm, the anchoring coefficients varied by ±10% However, when we changed the objective lens [magnifications (depths of focus) of ×100 (0.43 µm), ×50 (0.91 µm), and ×20 (2.24 µm)] with a given LC cell (100-µm cell gap; 80-µm distance between the electrodes; lecithin coating), the coefficient obtained at a high magnification (100×) was approximately 30% greater than that obtained at a low magnification (20×) The coefficients of the LC cell with a large distance (130 µm) between the electrodes were greater than that for a small distance (40 µm) These variations are supposed to be due to the boundary effect of the homemade electrode for a relatively large measuring area In conclusion, we obtained the appropriate anchoring coefficient when the distance between the electrodes of the LC cell was larger than 80 µm (this condition can be met by 097170-5 Baek, Kim, and Kim AIP Advances 5, 097170 (2015) FIG Change in the reflected light with applied electric field The electric field is (a) V/µm, (b) 5.0 V/µm, (c) 10.0 V/µm, (d) 12.5 V/µm, (e) 15.0 V/µm, (f) 17.5 V/µm respectively The central bright regions are the regions of interest A and P represent the analyzer and polarizer of the microscope The cell gap was 60 µm, the distance between the electrodes was 80 µm, and the alignment layer was SE-5662 For clarity, we adjusted the brightness and contrast of the images by the same amount minimizing the iris and irradiated area), cell gap was greater than 10 àm, and magnification of the objective lens was 100ì Figure shows the measured and calculated reflective intensity for the polyimides and lecithin The lower range of the electric coherence length (x-axis) is limited by the highest applied electric field, and the upper range is limited by the assumption that d >> ξ E The data were fitted as follows Given the extrapolation length and electric coherence length, we calculated the director rotation angle as a function of the distance from the substrate In addition, we divided the LC layer into very thin LC layers and calculated the refractive index of each layer and the overall reflectance of the interface and thin LC layers By varying the electric coherence length in a certain range, the reflectance calculation was repeated The calculated data were fitted to match the experimental data by adjusting the amplitude and offset The above process was repeated while adjusting the extrapolation length until the calculated and experimental data were well matched Regarding the fitting parameters, the amplitude matched the light intensity, and the offset value matched the light from the unimportant layers After several measurements, the extrapolation lengths were found to be 0.32 ± 0.08 µm for AL-64168, 0.23 ± 0.05 µm for SE-5662, and 0.31 ± 0.04 µm for lecithin There are several issues related to the experiment and calculation that need to be addressed In our experiment, the objective lens had a depth of focus of 0.42 µm, and most of the effective signal entered from the focal point within that range As the obtained extrapolation lengths were in the range of 0.2–0.3 µm and the electric coherence length was in the range of 0.1–0.6 µm, the range of electric coherence length in the experiment should not pose a problem for the measurement Next, the effect of reflection from outside the range of the depth of focus is considered In the experiment, the effective region of the director rotation is concentrated near the depth of focus; therefore, the reflection from outside the range of the depth of focus must be relatively small, and if 097170-6 Baek, Kim, and Kim AIP Advances 5, 097170 (2015) FIG Graphs showing the experimental and calculated results of the change in the reflected light with electric coherence length The fitted curves indicate the extrapolation length (a) AL-64168, b = 0.33 µm; (b) SE-5662, b = 0.24 µm; (c) Lecithin, b = 0.28 µm it exists, the reflected light diverges out of sight We confirmed that the extrapolation length remains stable with a varying LC-cell gap; the maximum deviation of the extrapolation length was only 10% The uncertainty of the refractive index and thickness of the alignment layer may induce an error in the calculation However, because the alignment layer is hundreds of nanometers thick and its refractive index is only slightly different from that of glass, the error caused by the alignment layer must be negligible When we apply the electric field, a disclination is induced in the region close to the interface between the electrodes; a faint image of the disclination is seen in Figures 3(b) and 3(c) However, an increase in the electric field removes the disclination In conclusion, we observed the reflection in an LC cell by using a polarizing optical microscope We focused on the interface of interest and applied an electric field in the planar direction For a given extrapolation length, we calculated the director orientation and reflectivity We repeated the comparison of the measured and calculated reflectivities by adjusting the extrapolation length Through this process, we obtained the anchoring coefficient of three alignment materials The extrapolation lengths were found to be 0.32 ± 0.08 µm, 0.23 ± 0.05 µm, and 0.31 ± 0.04 µm for AL-64168, SE-5662, and lecithin, respectively These values correspond to 4.4 × 10−5, 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reflective mode Sang -In Baek,... the anchoring coefficient of homeotropic alignment can be obtained rather easily Moreover, this technique can be applied using common tools available in the laboratory This study was financially... interface and thin LC layers By varying the electric coherence length in a certain range, the reflectance calculation was repeated The calculated data were fitted to match the experimental data by adjusting