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Abstract
A proper amount of 0.02wt.% multi-walled carbon nanotubes (MWCNTs) was added in the nematic liquid crystal (LC). Based on dipolar orientation polarization and space charge polarization conceptions, a simplified theoretical model of the charge transfer complex formed by LC and MWCNTs has been developed and utilized to analyze the dynamic behavior. The driven frequency range was 10Hz-10 KHz. Compared to the applied voltage driven method, focusing time has altered from 2.63 s to 0.096 s, and its response time has reduced to 0.4 s with frequency driven method. The doped LC lens under frequency driven has indicated a significant difference of the performances compared to the pure LC lens under applied voltage driven.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystal (LC) lens is an active electronically tunable device. Owing to its birefringence, LC lens can be tunable by external electric filed. It has some advantages, such as small, flexible, easy to assemble other optical devices. In recent years, LC lens has had a great development. Many different kinds of LC lens has been proposed to improve its performances [1,2]. Traditional lenses can be replaced by LC lens in some specific imaging applications [3,4]. However, slow response time is a challenge for fabricating high quality LC lens. The current methods are devising particular structure of LC lens [3,4]. In addition, the inclusion of nanoparticels in pure LC is another effective technique [5,6].
Because of their outstanding physical and electrical properties, carbon nanotubes (CNTs) have attracted a great number of attention during the past decays. CNT is one-dimensional carbon material with a rod-like structure. CNT can be divided into two categories, single walled carbon nanotubes (SWCNT), and multi walled carbon nanotubes (MWCNT). Compared with MWCNT, the size distribution of SWCNT is small, the defect is less, and the uniformity is much higher. The diameter of SWCNT is usually 0.6-2 nm, and the most inner layer of MWCNT is 0.4 nm. The maximum diameter can be up to hundreds of nanometers, but the diameter is about 2-100 nm. In SWCNT, the conductivity is usually semi-conductive, while in MWCNT it is always metallic. LC is easy to be induced by external electric field. It is very suit to be precursor, especially in doping field. Generally, CNT is as an additive, and it is doped in pure nematic LC. After doping, carbon-based nanostructured materials can be formed. In this mixture, CNT is parallel to the orientation of LC molecules. Based on the π-π stacking mechanism, the dielectric property of the mixture enhanced. At the same time, its viscoelastic force and viscosity also affected. In recent years, there have been many researches about LC doped with CNTs, especially in ionic effect [5–8]. Those current reports mainly discussed under the condition of the tunable amplitude of the external electric field [5–8]. The relevant studies under the condition of frequency driven is not enough [8,9]. In this study, the electro-optical dynamic behavior of doped LC lens under frequency driven has been presented.
2. Sample preparation and operating principle
2.1 Sample preparation
This study has chosen E7 LC from Merck Co. It is a well-known positive dielectric nematic mixture that has been widely used in fabrication several LC devices include LC lens. Its main features are a rotation-viscosity coefficient of 39 mm2/s at 20℃, an optical birefringence of 0.216 at 20℃and 589.3 nm (${n_e}$=1.7472,${n_o}$=1.5217), and its dielectric anisotropy of 14.1 at 20℃and 1KHz. The clear point of the material is at 58℃. CNTs in the experiments are MWCNTs from Shenzhen Nanotech Port Co. Ltd. It is > 90 wt.%. These MWCNTs, according to the data sheet, had a tube length of 1-2 µm and an outside diameter of 10 - 20 nm.
Preliminary experiments established the most intriguing range of MWCNTs concentrations of about 0.02wt.% in LC-MWCNTs mixture [10]. All the experiments have been realized at this concentration. Grinding has been used to reduce the length and size of MWCNTs. In addition, it also can reduce agglomeration. MWCNTs have grinded in two times for 30s each time. A number of MWCNTs dilution was carried out first in ethanol and later in the LC itself. In order to evaporate the remaining ethanol, the sample was heated over the LC isotropic transition and sonicated twice for 30mins each time to achiever homogeneous mixtures.
Two ITO glass-substrates were used. They formed an empty LC cell with spacers (glass microspheres, 100 µm diameter). The cell thickness of LC layer was 100 µm. The thickness has been more than the length of the MWCNTs. Thus, the situation that MWCNT can't rotate in the LC layer won't take place. A circular electrode pattern of 2.3 mm was fabricated through photolithography by removing the ITO electrode of the top ITO glass-substrate. The LC alignment configuration along x axis was with the LC director oriented parallel to the horizontal direction at the off-state. The polyimide (PI) layers were fabricated as the alignment layers in this LC cell. The horizontal LC alignment was induced by the rubbing-alignment. The mixture controlled at 80℃ to be isotropic had been filled into the empty LC cell by capillary. The classic sandwich structure of the LC lens is as shown in Fig. 1 (a). Figure 1 (b) shows the optical image and SEM image of the LC doped with dopant.
Fig. 1. The LC lens doped with MWCNTs. (a) is schematic diagram of structure; (b) is optical image of the LC lens, optical image of the LC doped with MWCNTs after 3 days, and SEM of the LC doped with MWCNTs.
2.2 Operating principle
According to the above mentioned data, the adopted MWCNT has 1-2 µm length and an outside diameter of 10–20 nm. The LC, E7, has 10 nm length and 1 nm diameter. The diameter ratio of MWCNT and LC is about 10:1. The length ratio is about 100:1. The geometric structure formed by LC and MWCNTs is as shown in Fig. 2 (a). The sketch is not to scale. Experimental studies revealed that CNTs have a strong interaction with LC and align themselves parallel with the long axis of the nematic molecules [11–13]. Because of CNT's insolubility, there is no mutual adsorption between LC and MWCNTs. Under an external electric field, LC and MWCNTs could form charge transfer complex by electrostatic force. It can be verified by infrared spectroscopic data between pure LC and LC doped with MWCNTs, as show in built-in diagram in Fig. 2 (b). Compared with the infrared spectrum data of CNT in public report, a peak of 1702 has been obviously induced by the charge transfer complex. Because the difference of stacking density between LC and MWCNTs has been not very big, they have a linear relationship with the molecular size. Thus, the quality relationship between them can be regarded as the ratio of the molecular number.
Fig. 2. Schematic model of charge transfer complex, which is composed by nematic LC molecules and MWCNTs. CNTs are several orders of magnitude longer than LC molecules. (a) is a geometric schematic structure between LC and MWCNTs at initial state; (b) is a schematic principle of a gradient refractive index distribution in the LC lens doped with MWCNTs under the frequency driven. Real line means the last moment, and the dotted line represents the next moment.
The frequency of this study has been from low to medium frequency range. The charge transfer complex composed by LC and MWCNTs can be seen as a dipole, as shown in Fig. 2 (b). Under the external electric field, both positive and negative charges have been respectively distributed on the two sides of the charge transfer complex.
Based on the elastic continuum theory, a charger transfer complexes system consisting of LC and MWCNT in electric field has the total free energy density as [14]:
Where r is the charger transfer complex position, ${f_0}$ represents the free energy density of a uniform state, ${f_d}(r)$ denotes the elastic free energy density, ${f_e}(r)$ means the energy density contributed to external electric field and ${f_s}(r)$ is the anchoring free energy density.Nematics are uniaxial optically anisotropic liquids, so their effective refractive index depends on the angle $\theta$ deviating from the direction of light propagation [14],
Based on the geometrical optics and elastic continuum theory, the focal length equation of LC lens is as follows [1,2],
Where r means the radius of aperture, $\Delta n$ denotes the LC birefringence difference, and dLC is the thickness of the LC layer.3. Results and discussions
The experimental setup for measuring the dynamic electro-optical features of the proposed LC lens was as shown in Fig. 3. The sample was set on an electronic control translation stage. Then, the transmitted light was collected by a CCD (3 Megapixel, 1/2 inch, and 6.4mm×4.8 mm in size, from MindVision Co.). The rubbing direction of the LC lens has a 45 degree angle with a polarizer. The detected information was processed by a PC with USB-cable. Square wave signal of 2.9Vrms (root-mean-square, rms) was added up on the sample electrodes, then its frequency was varied from 10 Hz up to 10KHz. During the whole measurement, the LC lens was fixed without any mechanical movements.
Using the above experimental setup, the relationship between the focal length of the LC lens and the external electric field can be explored. A HeNe laser, 633 nm wavelength, was used to probe the LC lens. To measure the focal length of the LC lens, USAF 1951 was set in front of the CCD. A spatial frequency of 32.0lp/mm was chosen in the resolution chart in order to measure its image details. When the frequency has been changed, the distance between the LC lens and the imaging sensor has been immediately adjusted until the image of the resolution chart has been clear again. With this subjective judgment method, the focal length of the LC lens at different frequencies were recorded. The measured focal length of the LC lens as a function frequency has been presented in Fig. 4. It shows that when the frequency has been fixed and only if the voltage has altered, the focal length of the LC lens has been inversely proportional to the voltage value, $f \propto \frac{1}{V}$. As the voltage increases, the focal length declines. If the voltage of 2.9Vr.m.s, circled in Fig. 4, has been fixed and only the frequency has changed, the focal length of the LC lens has been proportional to the frequency value, $f \propto frequency$, as shown in built-in diagram. The focal length of the LC lens has increased with the frequency, $frequency \uparrow \to f \uparrow$. This is fully consistent with the above theoretical analysis. The focal length of the LC lens has been an inversely proportional relationship with the voltage. Because the corresponding refractive index has altered with the rotation angle of the charge transfer complex, ${n_{eff}}(r) \propto \frac{1}{{\theta (r)}}$. In this way, the focal length of the LC lens has decreased with the increase of voltage. The relationship between the focal length and the frequency has been proportional. Because the dielectric constant has decreased, the focal length has increased. Usually, the conventional LC lens operates at 1KHz frequency. In this study, as the frequency driven method has been adopted, the focal length range alters from 20-480 mm at 1KHz to 20-550 mm at 0.01-10KHz. The focal length range has significantly increased. Even if the frequency has reversed, the refractive index and the director of LC have no positive or negative values change. Frequency change is actually reversal of the electric field. Under the condition of reversing electric field, the charge transfer complex hold the same position, rotating around a fixed position. The direction of the electric field have reversed with the frequency. Those charge transfer complex has continued to hold the position, rotating around the same position. Nowadays, dual-frequency LC has been widely studied, which fabricate LC lens. However, it has some disadvantages for fabricating high quality LC lens, such as relatively high critical frequency (above 50KHz), the dielectric loss at high frequency and not long service life for devices. By comparison, LC doped with MWCNTs under frequency driven hasn’t had the above mentioned problems of dual-frequency LC. Therefore, it has a great potential in fabrication of high performance LC lens.
Fig. 4. The frequency, the voltage and the focal length function relationship of the LC lens doped with MWCNTs. Black dots have meant the frequency of 10 Hz, red dots have presented the frequency of 100 Hz, blue dots have been the frequency of 1KHz and the green dots have donated the frequency of 10KHz. Focal length has been measured several times. Built-in diagram is about the relationship between frequency of the external electric field and focal length of LC lens, and the voltage of the external electric field is at 2.9Vrms.
In order to present the detailed electro-optical information of the fabricated LC lens, another experiment has been presented as follows. In this experiment, the above experimental setup has been still utilized. But the two polarizers have been removed, while a light stop and a beam expander have been added. A HeNe laser, 633 nm wavelength, has been still chosen as a light source to probe the LC lens. The laser has been firstly expanded, and a parallel light source can be obtained. Then, the light stop has been used to irradiate at the aperture of LC lens. The condition of the experiment was at 2.9Vrms with different frequencies. The variant frequencies was 10 Hz, 100 Hz, 1KHz and 10KHz, respectively. Every time PSF has been measured at the corresponding focal length place. The final results were as shown in Fig. 5. From those results, the LC lens can operate normally without affection of doping MWCNTs. The minimum scales in Fig. 5 are all 500 µm.
Fig. 5. Point spread functions (PSFs) of the fabricated LC lens with different frequencies of the external electric field have been measured at focal length places. The condition of the external electric field was at 2.9Vrms with different frequency from 10 Hz to 10KHz. (a) is 10 Hz at focal length of 60 mm; (b) is 100 Hz at focal length of 75 mm; (c) is 1KHz at focal length of 173 mm; (d) is 10KHz at focal length of 257 mm.
The charge transfer complex has been formed by LC and MWCNTs under the external electric field. The polarization behavior has happened at different frequencies. Generally, the space charge in the charge transfer complex will produce different polarization behavior with the frequency of the external electric field. There are four types of general polarization, such as electronic polarization, ionic polarization, dipolar orientation polarization and space charge polarization. The first two kinds of polarization have all generated at high frequency. In this study, these two kinds of polarization have been regarded as constants without considering their affections. In the charge transfer complex, the main roles are respectively dipole orientation polarization and space charge polarization. It is well-known from previous studies that the response time of LC lens closely relates to the dielectric constant [10,11]. The dielectric constant has decreased with the increase of frequency, $frequency \uparrow \to {\varepsilon _{xy}} \downarrow$. The charge transfer complex has a different dielectric constant compared with the pure LC [10,11]. The charge transfer complex has much bigger volume than the pure LC molecules. Under the same condition of the external electric field, the charge transfer complex have been rotated by a little moment of force induced by the external electric field. In macroscopic scale, the response time of the charge transfer complex has been much faster than that of pure LC. The focusing time of the LC lens under different situations have been measured, as shown in Table 1. In order to present the features of the frequency driven method, several samples have been taken into consideration. There have been three samples, the LC lens doped with 0.02wt.% MWCNTs under 100 Hz (sample A), the LC lens doped with 0.02wt.% MWCNTs under 10 KHz (sample B), and the conventional LC lens under 1 KHz (sample C), respectively. In those samples, the LC lenses have the same structure, 2.3 mm diameter top electrode circular, and 100 µm thickness LC layer, as shown in Fig. 1 (a). The experiment has been measured by a response time measuring instrument EOT-01 by Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Science. The focusing time of the LC lens has been greatly enhanced under the frequency driven method. In Tabl.1, those data clearly present. Compared with three samples, the focusing time alters from 2.63s to 0.096s. The improvement has been about 96%. The response time was measured as follows. A function generator provided an AC electric field (square wave, frequency from 1KHz to 10KHz, voltage of 2.9 Vrms) across the cell thickness. The threshold voltage and the driving voltage have been defined as the voltages at which the transmitted light power is increased to 10% and 90% of the initial value at a null voltage, respectively. In Fig. 6, the curve of the optical transmittance-time for LC lens has been shown. The range of τon was about 0.22 s. On the other hand, the τoff was about 0.18 s. The response time (τon + τoff) was about 0.4 s. Compared with the pure LC lens, the response time is improved dramatically.
Fig. 6. Electro-optical response of the LC lens by applying a 2.9Vrms with alternate frequency of 1KHz and 10KHz.
Table 1. Comparison results among three samples.
In this experiment, a scene with three building blocks has been chosen, as shown in Fig. 7. Those objects were set from far to near in this scene. The intervals along vertical direction abbreviated as V in Fig. 7 were 5 cm, and the left and right intervals along horizontal direction abbreviated as H in Fig. 7 were 4 cm. The building blocks were just three to five centimeters in size. The voltage of the electric field has kept at 2.9Vrms, then the frequency has altered from 10 Hz to 10KHz. During the whole measurement, the distance between the CCD and the LC lens was fixed. Figure 7 shows the optical result of the CCD under the above mentioned conditions. There have been three states of the LC lens, frequency at 10 Hz, frequency at 1KHz and frequency at 10KHz, respectively. The solid line means the result of frequency at 10 Hz. At this time, those converging light has fallen on the focal plane. There has been a clear focus of object “1” on the image. Obviously, this state of the LC lens has been just in-focus. Double line is under the condition of frequency at 1KHz. With the increase of the frequency, the focal length of the LC lens has increased. That means a clear focus of object “2” on the image. At this time, those converging light has fallen on the focal plane 1. In contrast, the images of objects “1” and “3” have been blurry, because the objects have been out-of-focus. Then, dash line presents the case of frequency at 10KHz. While the frequency of LC lens has continued to rise, the focal length of the LC lens has also increased. The measured optical images has been a clear focus of object “3” on the image. At this time, those converging light has fallen on the focal plane 2.The LC lens can be refocused by altering frequency.
Fig. 7. The optical results of CCD at three positions under the condition of different frequencies. During the whole measurement, the distance between the object scene and the LC lens was fixed.
As the grinding method has been utilized to improve solubility of MWCNT, the distribution of MWCNT has been relatively uniformity in LC. In Fig. 1 (b), those measurements are under the condition of 3 days. The aim of the measurement is to present the good distribution by the proposed method. As is well-known, the ultrasonic vibration method could be utilized to disperse nano-material into a solution in a very short time. But the dispersed mixture will not be kept for a long time by the ultrasonic vibration method. After 3 days, the normal time is chosen to distinguish this factor. The effect of the method of grinding has been proved. It is very helpful for good dispersion, then it is also a relatively simple way to achieve the goal of good dispersion. Many times grinding could effectively reduce MWCNT surface areas. In this way, MWCNT couldn't easily react with other substances. However, the proposed method is not chemical synthesize, which means that the situation of the good dispersion is not very stable compared to those chemical synthesize. Thus, the mixture still has a CNTs agglomeration problem after more than one month. After many tests, the life time of the LC lens is about 1-2 months. The most important reason is that the LC lens is generally fabricated by handwork. The package of LC lens is not as good as mechanical package. There are always some leakages at seal. Therefore, the life time of LC lens is no very long. Correspondingly, the life time of the proposed grinding method is around 1 month, which will not influence the use of the LC lens. These factors such as fabrication, cost, and performance should be taken into account because the conclusion that the grinding method will be a proper for fabricating high quality LC lens can be made from the above experiments. The proposed method for fabricating LC lens is appropriate in improving LC lens performances.
4. Conclusion
When the frequency of the external electric field has been below 10 Hz, the LC lens hasn’t been operate at normal state. When the operation frequency has been above 50KHz, the polarization behavior has been so complicated beyond the scope of this study. In this study, the LC lens can operate under the range of 0.01-10KHz. The principle of the LC lens driven by frequency has been discussed by the charge transfer complex model at details. This study further perceives the physical characteristics of the LC lens. The charge transfer complex model is proposed to explain the LC-MWCNTs mixture under frequency driven. This method can effectively reduce the operation voltage and response time of the LC lens. However, the charge transfer complex has been still so complicated that many particular phenomenons deserve further research and explore.
Funding
National Natural Science Foundation of China (NSFC) (51703071, 61771353); Education Bureau of Hubei Province China (D20171504); China Postdoctoral Science Foundation (2014M562017); Hubei Provincial Key Laboratory of Intelligent Robot (HBIR201805).
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