Topological defects in liquid crystals (LCs) have been paid much attention both in basic science and technological applications. They are the structural singular points of the LC alignment, and there are a variety of defect types, which are categorized according to the topological charge. These topological defects can be spontaneously formed when LCs are put into a glass cell without an alignment layer. Due to the high elastic energy at these defect positions, they are thermodynamically intermediate states and will disappear for some duration of time.
These days, the molecular alignment of LCs can be controlled by various techniques, and topological defects can be intentionally generated by the patterning of an alignment layer. 1–3 Many types of thin optics with topological defects using the LC patterns were demonstrated using a photo-alignment layer.4–6 Topological defects also could be formed by stabilizing the alignment by a polymer pattern without a photo-alignment layer.7 Many interesting phenomena relevant to the topological defects were reported in biology, too. The self-propelled bacteria's motion was controlled by the LC patterns, including topological defects formed on a photo-alignment layer.8 It was reported that the cell growth and the collective motion were controlled by the topological defects formed by the biological cells aligned like LC molecules, and the fate of the cells was determined by the type of the topological defects,9,10 and predesigned cell culture on a photoaligned LC elastomer was demonstrated.11 Those studies indicate that the collective motion of objects and molecules is dominated by topological defects, and the underlying principle should be studied.
On the other hand, we have investigated the photo-induced behavior of LCs including photo-responsive molecules. We prepared an LC-made double emulsions, and the photo-induced phase transition was observed, and the molecular orientation changed from the center of a topological defect.12 Also, we demonstrated the photo-induced rolling motion of an LC droplet in a surfactant solution, and found that the topological defect was oriented toward the light source.13 In the previous paper, we studied the molecular orientation change around topological defects by using the polarization/phase microscopy and found that the molecular orientation changes and the ordering occurred step-by-step, instead of changing them at the same time.14 These studies indicate that the molecular orientation change around topological defects seems more complicated than believed.
This study introduced the neural network (NN) prediction of the orientation conditions of LC (orientation angle and order parameter). There were several applications using NN for LCs; it was utilized for temperature estimation by using the color information of LCs;15 convolutional NN was used for detection of topological defects, and the topological dynamics were studied;16 several physical properties such as the order parameter, temperature and pitch length of cholesteric LCs were predicted from the patterns of LCs.17,18 In this study, by training the NN function by using the color information for different orientation angles and temperatures in a planer cell in advance, we could predict the molecular orientation angle and the order parameter from the local color information. By inducing a perturbation on the LCs by photo-irradiation, the change of the molecular orientation/ordering change around the topological defects was observed. We could clarify the complicated processes of the molecular alignment change from the time sequence of the molecular orientation angle and the order parameter.
Microscopic observation and neural network prediction
The color difference of LCs observed by a microscope is used to obtain different orientation angles and ordering conditions by the distinction of the LC conditions using a pre-trained NN function. We used a microscope with a combination of the polarized and phase-contrast functions to have a color difference for different orientation angles and ordering conditions. The polarization microscope is usually used to observe the LC orientation angle, where the LC orientation angle at 45 degrees to the polarizer and analyzer shows the highest transmission. However, the polarized microscope cannot distinguish the molecular orientation angles parallel or perpendicular to the polarizer/analyzer. When we use the phase-contrast microscope to observe LCs, we could distinguish a different angle and ordering conditions from different color regions because the extraordinary and ordinary refractive indexes contribute, but the information on the orientation direction is unclear. The color depends both on the orientation direction and the ordering of LCs by a combination of polarization and phase-contrast microscopy. The ratio of the transmittance for the extraordinary and ordinary directions is varied by a change in the orientation angle. As a result, the final color depends on the angle. Furthermore, the molecular ordering change causes the refractive index change both in the extraordinary and ordinary directions, and the final color also depends on it.
Although the final transmittance can be theoretically predicted based on optics theory,14 (Appendix in Supporting Information (SI)) the absolute transmittance is necessary, and it needs a careful procedure to calibrate the light intensities of transmittance. This procedure was troublesome for LCs with a transmittance spectrum, including oscillation due to the light interference for a thin LC layer, which is easily affected by the variation of LC cells. However, we could obtain only three observables, RGB values detected with a color camera. This is why the NN function was introduced for the empirical estimation of the orientation angle and ordering.
An optical configuration of the device is the same as before14 (Figure S1 and its description in Supporting Information (SI)). Briefly, the microscope consisted of a phase microscope with a polarization-dependent detection. A sample was illuminated by the UV-LED, and the photo-induced change was observed by a CMOS camera using a white light illumination. A sample is subject to photo-isomerization by the UV light, causing the molecular orientation change. The UV light was illuminated to the sample for 200 ms and turned off. The image sequence was obtained at an interval of 20 or 30 ms.
Next, the NN prediction procedure for the orientation angle and the order parameter is described in Fig.1. An LC in an alignment cell was measured under various temperatures and angle conditions and obtain the color information for each condition. This information was used for the training of a NN function. The alignment cell was rotated at every 5 degrees, and the temperature was changed from 25 to 50 degrees at an interval of 2 or 5 degrees, and the color was measured for each condition. The NN function was trained to predict the orientation angle and the temperature from the color information (RGB values). We used 96 combinations of the temperatures and angles dataset. The correlation plot for the temperature and the orientation angle is shown in Fig.2. The correlation coefficients were sufficiently high to predict the orientation angle and temperature as long as the angles and temperatures range in the training data. At each local position of a microscopic image, the RGB information could be converted into the orientation angle and the temperature, as shown in Fig.1(c).
The difference in the predicted temperatures at local positions in an image does not mean that the temperature is varied at different positions in the same sample, but indicating that the ordering condition is different. Around the topological defects, the ordering conditions were different at each local position. We assume that the local LC ordering is represented by the ordering condition at different temperatures for an LC in the alignment cell. The NN function then corresponds the color at each local position to the LC conditions in the alignment cell at a specific temperature and orientation angle. To make a correlation between the order parameter and the temperature for an LC in an alignment cell, the temperature dependence of the order parameter (P) was obtained using the polarized absorption measurement.
N-(4-methoxybenzylidene)-4-butylaniline (MBBA, Tokyo Kasei) was used as purchased. The sample was put into an LC cell (E.H.C) with a sample thickness of 3 mm. An alignment planar cell was used to collect the training data for the NN function, and the color images were obtained at different angles of the alignment direction to the polarizer and at the temperatures from 25.0 to 50.0 °C. We used an LC cell with non-rubbed polyimide layers inside for observation of topological defects, to make the same cell conditions as the training data acquisition, and the temperature was set at 30.0 °C. The pump light was UV-LED (SOLIS-365C, Thorlabs; wavelength: 365 nm, intensity: 0.625 mW/cm2) and the illumination light was white LED (SOLIS-3C, Thorlabs; intensity: 0.098 mW/cm2). A color CMOS camera (VCXU-23C, Baumer) was used for measurements, and a color image sequence was obtained. The temperature was controlled by a temperature controller for microscopes (TP-CHS-C, Tokai Hit). The intensity of the pump light was adjusted to prevent the phase transition.