Optimizing the Nematic Liquid Crystal Relaxation Speed by Magnetic Field

Transcription

1 Kent State University Digital Kent State University Libraries Chemical Physics Publications Department of Chemical Physics 2004 Optimizing the Nematic Liquid Crystal Relaxation Speed by Magnetic Field Bin Wang Xinghua Wang Philip J. Bos Kent State University - Kent Campus, pbos@kent.edu Follow this and additional works at: Part of the Physics Commons Recommended Citation Wang, Bin; Wang, Xinghua; and Bos, Philip J. (2004). Optimizing the Nematic Liquid Crystal Relaxation Speed by Magnetic Field. Journal of Applied Physics 96(4), Retrieved from This Article is brought to you for free and open access by the Department of Chemical Physics at Digital Kent State University Libraries. It has been accepted for inclusion in Chemical Physics Publications by an authorized administrator of Digital Kent State University Libraries. For more information, please contact digitalcommons@kent.edu.

2 JOURNAL OF APPLIED PHYSICS VOLUME 96, NUMBER 4 15 AUGUST 2004 Optimizing the nematic liquid crystal relaxation speed by magnetic field Bin Wang, Xinghua Wang, and Philip J. Bos a) Liquid Crystal Institute, Kent State University, Kent, Ohio (Received 2 September 2003; accepted 6 May 2004) Nematic liquid crystalline materials have been widely used in electro-optical control of visible light. However, when IR light is considered, the thickness of the liquid crystal layer must be increased which causes the relaxation time of the material to be slower than required for many applications. In this paper we use a magnetic field to increase the speed of thick nematic devices. We show that above a particular magnetic field strength, thicker cells relax more quickly than thinner ones. Also, we find that there exists an optimal voltage range for devices of a particular thickness and with a particular applied magnetic field. Devices that allow a half-wave modulation of 1.55 m light in less than 5 ms are shown to be possible with the use of a 2 T magnetic field American Institute of Physics. [DOI: / ] I. INTRODUCTION Liquid crystal technology has greatly influenced many areas of science and technology. One major application of liquid crystal technology is the liquid crystal display. Liquid crystals can also be used in many other areas, such as fiber optic telecommunications, optical imaging and recording, spatial light modulators, tunable wavelength filters, nondestructive mechanical testing of materials under stress, optical wave front correction, and so on. There are several advantages of using liquid crystal materials, such as low voltage driving, large optical birefringence, nonmechanical operation, and easy device fabrication. But a major disadvantage of using nematic liquid crystal materials is its slow relaxation speed. Because the relaxation time of a nematic liquid crystal with no field applied is proportional to the square of the device thickness, slow response is more of a problem when thick devices are required. In some nondisplay applications that require modulation of IR wavelengths, thick devices are required, and speeds in the range of milliseconds are needed. Many ways have been explored to increase nematic liquid crystal relaxation speed by means of choosing different liquid crystal materials, selecting optimized liquid crystal director configurations, operating liquid crystal device at elevated temperatures, and using dual frequency liquid crystal materials. In this paper we investigate increasing a nematic liquid crystal device relaxation speed by applying the magnetic field for a specific example which requires the liquid crystal device to provide a retardation swing of nm. The experimental and computer simulation results show that the relaxation speed of the liquid crystal device can be increased by applying the magnetic field, and under the optimized operating conditions the relaxation speed will reach a maximum value. II. EXPERIMENTAL SETUP The experimental setup for the nematic liquid crystal device switching speed measurement is shown in Fig. 1. A a) Electronic mail: pbos@kent.edu He-Ne laser serves as light source with a wavelength of nm. The liquid crystal cell gap is 11.7 m, and the alignment layer is polyimide 3510, which yields about 6 8 pretilt angle. The cell is antiparallel rubbed, which provides uniform alignment, and filled with Merck liquid crystal E44. The polarizer and analyzer are crossed to each other, and the cell rubbing directions are orientated at 45 with respect to polarizer and analyzer transmission axes. At room temperature, for the liquid crystal E44, the extraordinary and ordinary refractive indices n e and n o are and , the elastic constants for splay K 11 and bend K 33 are 15.5 pn and 28.0 pn, and the dielectric constants of // and are 22.0 and 5.2. The melting and clearing points of this liquid crystal material are 6 and 100 C, respectively. The experimental setup also provides a uniform tunable magnetic field that can be varied from 0.0 to 1.9 T. The magnetic field direction is parallel to the liquid crystal cell rubbing direction, which is orthogonal to the applied electric field direction shown in Fig. 1. A heating device and a thermal coupler are attached to the liquid crystal cell, so the switching speed measurement can also be performed in an elevated temperature. FIG. 1. Schematic experimental setup for the liquid crystal cell relaxation speed measurement with a magnetic B field. The direction of B field is perpendicular to the direction of electric E field, the polarizer and analyzer are crossed, and the liquid crystal cell rubbing direction is orientated at 45 with respect to the transmission axis of polarizer or analyzer /2004/96(4)/1785/5/$ American Institute of Physics

3 1786 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Wang, Wang, and Bos III. COMPARISONS OF THE EXPERIMENTAL AND COMPUTER SIMULATION RESULTS Due to the complexity of the electro-optical response of liquid crystal materials, it is impossible to find a simple analytical solution to describe the performance of a liquid crystal device. Therefore, computer simulations are used. A. Simulation method selection Generally speaking, computer simulation of a liquid crystal device involves a liquid crystal director calculation and an optical calculation. Assuming liquid crystal director has a strong anchoring energy at the top and bottom substrates, the free energy density for a liquid crystal material in an electric and magnetic field, based on the Frank-Oseen strain free energy density, 1 is given by Eq. (1), f g = 1 2 K 11 n K 22 n n + q K 33 n n + q 0 2 f ext with f ext = 1 2 n E n H 2, where n is a unit vector, which represents the liquid crystal director orientation, K 11, K 22, and K 33 are liquid crystal splay, twist, and bend elastic constants, q 0 is a chiral wave number =2 / p and p is the intrinsic chiral pitch of the liquid crystal, E and H are the electric and magnetic fields, and and are liquid crystal dielectric and diamagnetic anisotropies. In Eq. (1), the first three terms represent the liquid crystal elastic free energy, and the electric and magnetic energy are represented by the expression f ext. Notice from Fig. 1, the directions of electric field E and magnetic field H are perpendicular to each other. Since the liquid crystal director configuration will assume the lowest free energy state, when electric field E is turned off, the liquid crystal director tends to align along the magnetic field H direction and liquid crystal relaxation speed from electric field applied to no electric field applied is going to be increased because of this magnetic field. The detailed procedure of calculating the liquid crystal director configuration can be found in the Appendix. To obtain a one-dimensional optical simulation, the 2 2 Jones Matrix 2 and 4 4 Berreman 3 methods are frequently used. In our experimental setup, only the normally incident transmissive case is considered, so the 2 2 Jones Matrix method is sufficient to simulate the output light transmission and state of the polarized light for different external fields. The detailed derivation of the 2 2 Jones Matrix method can be found in Ref. 2. B. Comparison of experimental and simulation results at room temperature with external E and B fields Plugging all the known parameters of the cell and liquid crystal material into the director and optical simulation program, the normalized transmission versus voltage curve (TV curve) for the experimental and simulation results at room temperature for B=0.0 T is shown in Fig. 2. It indicates the 1 FIG. 2. Comparisons of the experimental and simulation results of light transmission vs voltage for the liquid crystal cell at room temperature with a magnetic field B=0.0 T, cell thickness d=11.7 m, and wavelength =543.5 nm. simulation result agrees with the experimental result very well. In order to simulate the switching speed influenced by the B field, liquid crystal diamagnetic anisotropy and rotational viscosity need to be estimated by fitting the simulation results with the experiment results. To obtain, we measure the liquid crystal TV curve at different B fields, then try plugging different values into the simulation program until the simulation results approximately agree with the experimental results. With this method, the estimated value obtained is about (SI unit). The liquid crystal rotational viscosity is a crucial parameter to simulate the device switching speed. By plugging different value into the simulation program to fit the experimental result at B = 0.0 T, the approximate rotational viscosity obtained at room temperature is mpa S. The experimental and simulation results of the device relaxation speed from 5.0 V to 0.0 V are shown in Fig. 3(a). With the estimated and values used in the simulation program, the device relaxation speed from 5.0 V to 0.0 V at room temperature with different magnetic fields can be obtained. To save space, only the experimental and simulation results for the B field of 1.0 T and 1.9 T are shown in Figs. 3(b) and 3(c). For a retardation swing of nm, the relaxation speeds at magnetic fields of 0.0 T, 1.0 T, and 1.9 T are 58.5 ms, 46.8 ms, and 29.8 ms, respectively. C. Comparison of experimental and simulation results at elevated temperature with external E and B fields Since we are ultimately interested in a high-speed liquid crystal device, here the B field combined with the effect of temperature on the liquid crystal switching speed will be considered. It is known that optical and electrical parameters of a liquid crystal materials change when at elevated temperatures. 4 In the Appendix the relationship of liquid crystal parameters to temperature is given. Using the procedure discussed above, the estimated rotation viscosity at 65 C is about 43.0 mpa S and the value

4 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Wang, Wang, and Bos 1787 FIG. 3. Comparisons of the experimental and simulation results of the switching speed of the liquid crystal cell at room temperature with different magnetic fields B. The cell thickness d=11.7 m, wavelength =543.5 nm, driving voltage is from 5.0 V to 0.0 V. (a) B=0.0 T, (b) B =1.0 T, (c) B=1.9 T. E in Eq. (A5) at this temperature is about ev. For a retardation swing of nm, plugging the liquid crystal material parameters at this elevated temperature into the simulation program, the relaxation speeds at different magnetic fields are obtained. Figures 4(a) 4(c) show the simulation and experimental results of the liquid crystal cell relaxation speed from 5.0 V to 0.0 V at 65 C with magnetic FIG. 4. Comparisons of the experimental and simulation results of the switching speed of the liquid crystal cell at 65 C with different magnetic fields B. The cell thickness d=11.7 m, wavelength =543.5 nm, driving voltage is from 5.0 V to 0.0 V. (a) B=0.0 T, (b) B=1.0 T, (c) B=1.9 T. fields of 0.0 T, 1.0 T, and 1.9 T. The relaxation speeds are about 18.0 ms, 11.0 ms, and 6.3 ms, respectively. On comparison of the device switching speed at room temperature without B field, which is 58.5 ms, the combined effect of a B field and elevated temperature can increase the relaxation speed by almost ten times. On comparison of Figs. 3 and 4, one will notice that there is a lost order in Fig. 4, which is due to the liquid crystal material anisotropy n decrease at elevated temperature.

5 1788 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Wang, Wang, and Bos FIG. 5. The simulation results of the liquid crystal cell relaxation speed. The driving voltage is from 5.0 V to 0.0 V with the temperature of 65 C with different cell gaps d and magnetic fields B. IV. RELAXATION SPEED OPTIMIZATION BY COMPUTER SIMULATIONS Once the simulation program has been proven to agree with the experimental results, it can be used to predict or optimize the device performance. It is known that the liquid crystal relaxation speed for driving voltage from off to on and on to off is different. The former usually is faster than the latter, especially when driving voltage is high. Therefore, in the following discussion we focus our attention only on increasing liquid crystal relaxation speed from on to off under the external fields. Figure 5 shows the simulated liquid crystal device relaxation time for retardation swing of nm and driving voltage from 5.0 V to 0.0 V at 65 C with different magnetic fields and cell gaps. An interesting fact shown in Fig. 5 is that the magnetic field has greater influence on increasing relaxation speed for a thick cell than that for a thin one, especially when the magnetic field is large. It is known that without B field, a liquid crystal device relaxation speed will decrease as its cell gap increases. However, this conclusion cannot be applied to the case in which B field is nonzero. The liquid crystal device relaxation speed is mostly determined by the directors in the cell middle layer, since they have the smallest restoration torque for directors return to their original equilibrium positions. When no B field is applied, the restoration torque of the middle layer directors mainly comes from the top and bottom substrates. Therefore, a thin gap liquid crystal device has larger elastic torque and faster relaxation speed than the thick one. When a B field is applied, the middle layer directors not only experience magnetic torque but also the elastic restoration torque, which results in an accelerated relaxation speed. From Eq. (1), it can be seen that the magnetic torque will reach its maximum when the polar angle between director and magnetic field B is 45 and minimum when this angle is 0 or 90. In order to obtain nm retardation swing, the liquid crystal directors polar angle in the middle layer of a thin cell is close to 90 with respect to B field direction, therefore, the restoration torque mainly comes from the cell boundaries, whereas FIG. 6. The simulation results of a 20.0 m thickness liquid crystal cell at a temperature of 65 C with a magnetic field B=1.0 T. (a) Liquid crystal director configurations at different driving voltages. From top to bottom, the plots correspond to 4.0, 3.5, 3.0, 2.75, 2.5, 2.25, and 2.0 V. (b) Liquid crystal relaxation speeds for a retardation swing of nm. for the same retardation swing, the middle layer director polar angle for a thick cell is close to 45 with respect to B field direction, thus the restoration torque mainly comes from magnetic torque. In other words, for the thin gap case, the middle layer directors need a large rotation angle to reach nm retardation swing, but for the thick gap case, a small director rotation angle can produce same retardation change, which may yield a high relaxation speed. Figure 5 indicates that after certain thickness at B=1.5 T, the relaxation speed for the thicker cell exceeds the thinner ones. It is also known that for a fixed cell gap when no magnetic field is applied, a higher driving voltage will yield a faster relaxation speed than a low driving voltage, since the higher voltage will create larger elastic restoration torque, which comes from the cell boundaries. But it will not hold for the case B 0. Figures 6(a) and 6(b) show the simulated liquid crystal cell director configuration and relaxation speed for retardation swing of nm at a temperature of 65 C under conditions B=1.0 T and d=20.0 m from a particular driving voltage to 0.0 V. Figure 6(b) clearly shows that when a magnetic field is applied, there exists an optimized driving voltage for a fast relaxation speed, and the optimized driving voltage is not the highest.

6 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Wang, Wang, and Bos 1789 Figure 6(a) shows when the driving voltage is below 2.0 V, the magnetic torque pushes the middle layer liquid crystal directors down almost to 0, but at the substrates boundaries strong anchoring condition still remains at the pretilt angle of 8. Driving voltage of 2.25 V makes the directors aligning close to pretilt angle through the cell thickness; the calculation shows that when driving voltage is below 2.5 V, liquid crystal cell still cannot generate enough retardation swing to reach nm; when driving voltage is above 2.75 V the device can create retardation swing larger than nm. The relaxation speed versus driving voltage is plotted in Fig. 6(b) and shows that the optimized driving voltage is around 3.0 V. Since the cell gap is quite thick, the relaxation speed mostly depends on the magnetic torque. When driving voltage is around 3.0 V, the middle layer director polar angle is close to 45 shown in Fig. 6(a), which experiences the larger magnetic torque, therefore the maximum switching speed is obtained. When driving voltage is 4.0 V, the middle layer director polar angle is close to 90, the magnetic torque becomes smaller and relaxation speed is slower than the driving voltage of 3.0 V case. The optimized switching time for this case is about 6.9 ms. For the case of B=1.9 T, we obtain the optimized driving voltage around 4.9 V and the corresponding switching time is about 2.0 ms. V. CONCLUSIONS The relaxation speed of a uniformly aligned liquid crystal cell under elevated temperature and an applied magnetic field is studied by experimental and computer simulation methods. The experimental and simulation results show that by heating and applying the magnetic field the nematic liquid crystal relaxation speed can be increased greatly, and fast response can be obtained for thick devices required for IR electro-optical applications. Computer simulations also show that under certain magnetic fields, thicker liquid crystal cells can yield faster relaxation speeds than thinner ones, and there exists an optimal driving voltage to reach the maximum relaxation speed. ACKNOWLEDGMENTS This research are funded by DARPA THOR project. The authors would like to acknowledge the helpful comments of Dr. Paul McManamon and Dr. Edward Watson of the AFRL. APPENDIX Liquid Crystal Director Calculation To obtain liquid crystal director configurations with an external field, Eq. (1) in the paper can be rewritten in the polar coordinates in terms of and, where is the director polar angle and is director twist angle. 5 For uniformly aligned liquid crystal device always equals 0. In the equilibrium state, the total free energy is minimized by Euler- Lagrange equation shown in Eq. (A1). f g f g dz d f g z =0, A1 where z is the cell normal direction. The dynamic equation of the liquid crystal director between the external field torques and viscosity torque is given by Eq. (A2), t = f g, A2 then using relaxation method, the director updated formula can be obtained, new = old t f g, A3 and the final director field distribution can be found. If liquid crystal rotational viscosity is known, the device switching speed can also be obtained by Eq. (A3). Liquid Crystal Parameters Variation with Temperature The following expressions represent how liquid crystal parameters vary with temperature: 4 n = n S; // = // S, = S, = S; = S; K 11 = K 11 S 2,K 22 = K 11 S 2,K 33 = K 33 S 2 ; where the parameters with prime sign indicate they are at elevated temperature and without prime sign indicate they are at room temperature. S is the liquid crystal order parameter, which is given by Eq. (A4), S = TV2 T NI V NI , A4 where T NI is the liquid crystal material clearing temperatures, T is the elevated temperature, and V and V NI are the liquid crystal molar volume at elevated and clearing temperatures. In our simulation, we assume V/V NI =1. The rotation viscosity at elevated temperature is given by Eq. (A5), Se E/k B T, A5 where S is liquid crystal order parameter governed by Eq. (A4), E is an activation energy, k B is Boltzmann constant, and T is the temperature. 1 P. G. De Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University Press, Oxford, 1995), Chap. 3p P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, New York, 1999), Chap. 4 p D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972). 4 W. H. de Jeu, Physical Properties of Liquid Crystalline Materials (Gordon and Breach Science, New York, 1980). 5 J. E. Anderson, P. E. Watson, and P. J. Bos, LC3D: Liquid Crystal Display 3D Director Simulator Software and Technology Guide (Artech House, Norwood, 2001), Chap. 3, p. 33.