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This paper presents the calculated and experimental interference colors of liquid crystal (LC) films due to the optical retardation of two orthogonal electromagnetic components at different surface anchoring conditions and applied voltages. We simulate the deformation of LC director using finite element method and convert the calculated colors into sRGB parameters. A gold micro-structure is fabricated and used to control the optical retardation. Polarizing micrographs were collected and compared with the calculated colors.
©2011 Optical Society of America
1. Introduction
It has been known that the slight changes in the birefringence of mineral grains result in a big changes of interference colors between crossed polarizers. The interference colors with a help of the Michel-Lévy interference chart have been used for the identification of minerals for more than one century [1]. A colorimetric analysis of the color of the light passed through a birefringent crystal between two polarizers was discussed theoretically [2,3], in which the phenomenon is also called “chromatic polarization.” Recently, liquid crystals (LCs) have many applications in low cost, portable, highly sensitive and selective chemical and biological sensors [4–7], and the interference colors of liquid crystal films have been used to determine the birefringence, the thickness of a LC film and the orientation of LC directors by comparing the observed colors to the colors on the Michel-Lévy chart [8–11]. However, the colors from different versions of the chart are described in the pictures, which are not precise descriptions of the actual colors under a certain condition.
In this article, we calculate the perceived colors of LC films for different applied voltages and surface anchoring conditions. The perceived colors are converted into sRGB values such that the corresponding colors can be displayed on a color computer monitor and printed out on a color printer [12]. The calculation method can be used to generate the colors for different structures of LC films. These generated colors can show the transitions due to the small changes of the applied voltages and surface anchoring conditions. In the experiment, the micrographs of a LC film formed in a microelectroplated Au structure were collected and compared with the calculated colors. These results provide a useful tool to the applications of LC-based sensors and a way to improve the performance of LC-based optical sensors.
2. Interference colors
Consider the light perpendicularly passes through a thin film of LCs between crossed polarizer and analyzer denoted by P and A respectively, and the two polarization directions of the light are denoted by the X and Y axes. As shown in Fig. 1(a) , the angle between P and X is 45 degree, and the angle between X and A is also 45 degree. Assuming the intensity of light after the polarizer as unit, the intensity of transmitted light is:
where is the effective birefringence of LC films, d is the thickness of LC films and λ is the wavelength of the incident light. is the optical retardation of light through the LC film. Thus, the intensity of transmitted light depends on the wavelength of the incident light and the LC film displays beautiful colors.
Fig. 1 (a)Schematic illustration (not scaled) of the polarization directions and the LC directors. (b)Vertical aligned LC directors deform in transverse electric field with a weak bottom anchoring. A top substrate (not shown) can be added.
The perceived colors can be calculated using CIE (International Commission on Illumination) XYZ color space. When the spectral intensity distribution of light resource is known, the tristimulus values can be calculated by the formula,
where and are the tristimulus values of the spectrum. By normalizing them, we only need two coordinates (X′, Y′) to describe the chromaticity, which can be plotted on a CIE chromaticity diagram. The tristimulus values are converted into sRGB values such that the corresponding color can be displayed on a color computer monitor or printed out on a color printer [13].3. Results
3.1 Birefringence of LC films
The birefringence of a LC film comes from the orientation of anisotropic LC molecules with respect to the polarization direction of the incident light. In the case of a homeotropically aligned LC [Fig. 1(a)], no light can go through the crossed polarizer because there is no birefringence. After applying a suitable voltage, the LC molecules will be tilted [Fig. 1(b)], which makes different polarized light in the X and Y direction propagate at different speeds. This birefringence results in the wavelength-dependent transmitted intensity according to Eq. (1). Then, Eq. (2) is used to calculate the perceived colors. The unit vector called LC director describes the mean molecular alignment at a point (x, y, z) in a given sample volume V. LC director distributions in the transverse electric field from Au electrodes are simulated using the vector model of LCs by the method of the Finite Element Method [14–16]. The LC director distributions at different applied voltages and a strong anchoring for a ~7.5 μm thick and ~20 μm wide E7 LC film are shown in Fig. 2(a) (the director distribution in the middle is assumed to be uniform in X and Y directions). The E7 LC director distributions at different bottom surface anchoring energies and a 5 V applied voltage for a ~3 μm thick and ~20 μm wide LC film are shown in Fig. 2(b). From these LC director distributions, the effective birefringence can be calculated using Eq. (3) and used to calculate the interference color.
Fig. 2 (a)Schematic illustration (not scaled) of the LC director distribution a ~7.5 μm thick and ~20 μm wide LC film at different applied voltages. (b) Schematic illustration (not scaled) of the LC director distribution a ~3 μm thick and ~20 μm wide LC film at different bottom surface anchoring energies. (the director distribution in the middle between the electrodes is assumed to be uniform in (X) and (Y) directions)
3.2 Interference colors of LC films at different applied voltages
In the calculation of the perceived colors, we use the standard illuminant A (incandescent lighting) and CIE 1931 tristimulus values. The LC is E7. The sRGB colors are displayed using Matlab. Figure 3 shows the CIE chromaticity diagram of the colors of a ~7.5 μm thick and ~20 μm wide LC film with the apparent colors at different applied voltages under different bottom surface anchoring conditions. The upper interface has a strong anchoring. The chromaticity sensitivity decreases as the applied voltage increases. The weaker surface anchoring, the wider color gamut, because the optical retardation is larger under the weaker anchoring condition at the same applied voltage. Figure 4(a) shows the calculated optical retardation with the apparent colors that depend on the applied voltages at different bottom surface anchoring coefficients.
Fig. 3 CIE chromaticity diagram of the colors of a ~7.5 μm thick and ~20 μm wide LC film with the apparent colors at different applied voltages under different bottom surface anchoring conditions.
Fig. 4 (a) Optical retardations depend on the applied voltage in a ~7.5 μm thick and ~20 μm wide LC film with the apparent colors at different bottom surface anchoring conditions. (b) Scanning electron microscope pictures of the gold interdigitated structure.
In order to compare the calculated colors to the experimental ones, an electroplated ~7.5 μm high, ~10 μm wide and ~20 μm spacing interdigitated finger structure was used in this work [Fig. 4(b)] and the birefringence was altered by applying a voltage (Fig. 1). A glass wafer was used as a substrate. A 3 nm of chromium and a 40 nm of gold were deposited on the glass substrate using a sputter as a seed layer for later micro-electroplating. SPR220-7.0 photoresist with an around 7.5 μm thickness was used to pattern the interdigitated finger structure in a common photolithography process, which is used as a mold. In order to yield a thick structure, a micro-electroplating process in a pulse mode with 99.99% high-purity of gold was used. After electroplating, the photoresist was washed out. The seed layers of Au and Cr were etched by wet etching and dry etching, respectively.
The surface alignment layers were formed by spin coating a 4 mM copper perchlorate solution in ethanol on the structure and baked in an oven at 90 °C for 5 minutes. The E7 LC was filled at an isotropic state. An upper glass substrate with the same alignment layer is used to maintain the thickness, so the thickness of the LC film is ~7.5 μm decided by the thickness of the Au electrodes.. The strong anchoring at the upper and bottom surface dominates the anchoring at the Au electrodes because the width is about 20 μm in the X direction. So the LC orientation in the middle of the electrodes has a good homeotropic alignment [Fig. 1(a)]. The images captured by polarization microscope (12 Watt incandescent lighting) are shown in Fig. 5 . Three orders of the interference colors can be seen, which are identified by the triple appearances of the red color. The first order colors have a much shorter range (from ~2.0 V to ~2.2 V) of the applied voltages than the higher order colors (from ~2.2 V to ~3.0 V for the second order). These experimental results agree with the calculated results for the strong anchoring case in Fig. 4(a).
Fig. 5 The polarization micrographs (10 × 5 μm middle area between electrodes) of a ~7.5 μm thick and ~20 μm wide LC film at different the applied voltages. Three orders of interference colors appear.
3.3 Interference colors of LC films at different anchoring conditions
The LC orientation is very sensitive to the surface boundary condition, which has many applications in LC based chemical and biological sensors [4–7]. Here, the sensitivity of the interference colors to the surface anchoring condition is demonstrated. In this study, the bottom surface of the same structure is functionalized to specifically bind the targeted analytes, which means bottom surface anchoring energy can be weakened [Fig. 1(b)]. The presence of the weakened surface anchoring under a suitable bias electric field influences the LC tilted angles on the bottom surface and the LC director distribution in the bulk of the cell [Fig. 2(b)]. The initial alignment is homeotropic and strong anchoring is assumed on the upper interface between LC and air [5]. Dimethyl methylphosphonate (DMMP), a simulant of nerve agent Sarin, was used as the targeted analyte [5] to weaken the surface anchoring. After the surfaces were functionalized by spin coating a 4 mM copper perchlorate solution in ethanol on the structure and baked in an oven at 90 °C for 5 minutes, the space between two electrodes was filled with E7 LC at an isotropic state. The sample was spun to obtain a ~3 μm thick LC cell at 3200 rpm. This thickness was estimated by comparing the measured Fredericks threshold voltage to the simulation one. Initially the functionalized surfaces and air-LC interface made LC homeotropically aligned. A cleanroom swab with DMMP put in a small glass chamber was used to produce the DMMP vapor. The saturated DMMP vapor is at a ~parts per thousand concentration.
The optical polarization images were captured by a digital camera. The polarization microscope images in Fig. 6 show the process of the orientational transition from homeotropic to unidirectional tilted at the bottom glass substrate, after the surface anchoring driven orientational transition induced by DMMP binding to Cu2+ began at a 5 V bias voltage (below Fredericks voltage), which corresponds to the process of LC director reorientation [Fig. 2(b)]. The transition was accompanied by a continuous change in the color of the LC film as shown in Fig. 6. As the DMMP vapor was diffused through LCs and bound at the functionalized bottom surface, the surface anchoring became weaker and weaker. With the help of the applied electric field, the LC molecules reoriented more and more. Thus, the increased optical retardation as a result of increased birefringence changed the interference colors. The progression of colors are pure white, yellowish-white, light yellow, bright yellow, reddish-orange, red and purple corresponding to the optical retardation 0.259 μm, 0.267 μm, 0.306 μm, 0.332 μm, 0.505 μm, 0.536 μm and 0.565 μm approximately. The colors observed in these images agree well with the calculated sRGB colors of a 3.5 μm thick LC film shown in Fig. 7 . The reason that the calculated results of the 3.5 μm thick LC film match better with the experimental results than the ones of the 3 μm thick LC film may be attributed to the measurement error of the thickness, the fabrication error and the simulation error.
Fig. 6 The polarization microscope images after the surface anchoring driven orientational transition induced by DMMP began at a 5 V bias voltage (below Fredericks voltage). The pictures show the process of the orientational transition from homeotropic to unidirectional tilted at the bottom glass substrate. White arrows show the directions of crossed polarizers.
Fig. 7 Optical retardations depend on surface anchoring energy in different thick LC films with the apparent colors at a 5 V bias voltage.
4. Summary
The results obtained in this paper on the interference colors are directly applicable to the LC based optical sensors. The color change with respect to the change of birefringence due to the orientational change of LCs is very sensitive. The sensitivity of the interference colors is different at different ranges of the optical retardation resulted from different applied voltages or different surface anchoring energies.
Acknowledgments
This work was supported by the NASA EPSCOR program under grant number NNX07AT55A, and NSF EPSCOR program under grant number SUB-2008-EPS-0814103-CIDEN-UAH.
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