Modeling 3-D chiral nematic texture evolution under electric switching. Liquid Crystal Institute, Kent State University, Kent, OH 44242

Transcription

1 Modeling 3-D chiral nematic texture evolution under electric switching Vianney Gimenez-Pinto * and Robin L. B. Selinger Liquid Crystal Institute, Kent State University, Kent, OH Corresponding author: rselinge@kent.edu *Current Address: Department of Physics and Astronomy, University of Pennsylvania Abstract: Chiral nematic liquid crystals exhibit both a helical planar ground state with uniform twist and a metastable defect-rich focal conic texture, and can be switched between the two microstructures via application of transient voltage pulses. As both states are long-lived at room temperature and have sharply contrasting optical properties, these materials form the basis for bistable display applications. In this work, we model these electrically-induced texture transitions using finite difference methods to examine resulting microstructural evolution in three dimensions. We study planar to focal conic, focal conic to planar, and planar to planar transitions depending on voltage pulse amplitude. We investigate the special case of a cholesteric with matched twist and bend elastic constants, and demonstrate fast recovery of the planar ground state on switching without formation of a transient planar state. Our simulation method represents the evolving microstructure as a uniaxial director field, with relaxation dynamics calculated from a tensor representation so that half charge disclination defects are not suppressed. We evaluate both texture microstructural evolution as well as cell capacitance. We discuss potential application of this simplified approach for three-dimensional device design and optimization. Liquid crystals dielectric anisotropy makes it possible to control molecular orientation by applying an external electric field. In display devices, liquid crystals are enclosed between surfaces that impose anchoring forces on molecular orientation, and internal stresses also arise from the material s elastic response. Competition among these effects determines the resulting microstructural evolution of the liquid crystal s molecular orientation and resulting change of 1

2 optical properties under an applied electric field. While this mechanism serves as a common foundation for a wide variety of technological devices, the distinctive response properties of these materials to electric field allows further development and optimization of dynamical applications. For instance, polymer-dispersed liquid crystals (PDLC) [1] and polymer-stabilized cholesteric displays (PSCD) [2][3] are liquid-crystal/polymer composites in which geometry, confinement and anchoring conditions with the surrounding polymer produce a rich variety of mesophase textures. These switchable textures create states that produce scattering, transmission, and in the case of chiral nematic liquid crystals selective reflection of light with a characteristic wavelength. Recent experimental studies also report the potential development of micro-lenses based on chiral nematic films submerged in water [4]. Confinement of chiral nematic liquid crystals in micro-channels with different aspect ratios can produce either striped textures or an array of bubble defects [5]. Depending on geometry and anchoring conditions, chiral nematics confined in a spherical volume can exhibit complex textures including topological skyrmions [6] and defect lines varying from extended configurations to perfect three-fold knots [7]. While conventional liquid crystal displays require continuous applied AC electric fields to maintain an image, chiral nematic also known as cholesteric liquid crystals can undergo texture transitions under a finite voltage pulse. The cholesteric s ground state is a helical planar texture with a uniform twisted director field characterized by the pitch p, the length over which the director twists by 360. This pitch is a parameter of the material that depends on temperature o and may be adjusted by addition of chiral dopant. The planar texture shows selective reflection of light with a wavelength that depends on pitch. Cholesterics also exhibit a metastable defect-rich focal conic texture that produce scattering of light in all directions. Because both planar and focal conic textures are long-lived at room temperature and have sharply contrasting optical properties, these materials form the basis for bistable display devices that can maintain an image without expenditure of electric power [2]. Recent experimental studies of cholesteric liquid crystals with matched twist and bend elastic constants [8] have demonstrated a fast-switching mechanism between planar and focal 2

3 conic textures. Under a high enough voltage pulse, such materials relax directly to a defect-free planar texture with uniformly oriented helical structure. If elastic constants are not matched, switching is significantly slower because the material first forms a transient planar state with pitch p =(K 33 /K 22 ) p, where K 33 is the bend elastic constant and K 22 is the twist elastic constant. The planar ground state eventually forms via nucleation and growth from the transient planar state, often creating oily streak defects. To examine the novel switching mechanism proposed in [8], here we perform simulation studies of this bi-stable switching mechanism in cholesteric liquid crystals in the special case of matched elastic constants, comparing their relaxation behavior after applied pulses of different voltages. We examine planar to focal conic; focal conic to planar; and planar to planar transitions as a function of voltage pulse amplitude. Our findings demonstrate and confirm the mechanism proposed to explain experimental observations in [8]: when the applied voltage exceeds a threshold, the focal conic relaxes directly from an untwisted state to the helical planar ground state. These simulations demonstrate that the transient planar state is absent for the case of matched elastic constants. In addition, we observe the emergence of disordered focal conic textures with defects and undulations in the helical axis along a wide range of voltages. These results are in qualitative agreement with observed bistable switching behavior in chiral nematics. These simulation studies show nucleation and growth of perfect planar textures from the anchoring surfaces, while disordered states appear due to defects that nucleate in the bulk after switching. To carry out these studies, we use a finite difference approach for modeling textures of cholesteric liquid crystals including their co-evolving electric field response. The same technique can be used for achiral nematic liquid crystals. Numerical relaxation methods based on the discretization of the continuum Frank free energy are invaluable tools in the study of liquid crystalline textures. Due to the inversion symmetry associated with the nematic director field n, it is necessary to implement a free energy representation based on the Q ij nematic order parameter tensor as well-documented in the literature by Yang [1] and Zumer [9] in order to avoid suppressing half-charge disclination defects. The Frank free energy may be written as 3

4 f = 1 ( 12 K K 22 + K 33 )G ( 2 K 11 K 22 )G ( 4 K 11 + K 33 )G 6 q 0 K 22 G K 22 ( n n + n n) (0) where K11, K22 and K33 are the elastic constants corresponding with splay, twist and bend deformations of the nematic director and the terms G i are G 1 = Q jk,l Q jk,l = 2 n G 2 = Q jk,k Q jl,l = n ( ) 2 + ( n n ) 2 + ( n n ) 2 ( ) ( ) 2 + ( n n ) 2 G 4 = e jkl Q jm Q km,l = n n n n + n n (0) G 6 = Q jk Q lm, j Q lm,k = 2 ( n n ) G 1 While Eq. 1 and 2 represent an accurate continuum model, their solution is computationally intensive when applied to large three-dimensional systems, particularly when combined with a simultaneous solution of the material s dielectric response to a time-varying applied voltage. To model time evolution of the director field, we implement a relaxation method based on a simplified free energy functional derived from the Qij tensor formalism described in Eq. 1 and 2. This approach has the distinctive advantage that it is consistent with the inversion symmetry of nematics and can be used for computation of large three-dimensional systems. In the aim to develop a method for modeling devices at the laboratory scale, spatial discretization for finite difference calculations will by necessity be large compared to the defect core size, of order 10 nm. As we will thus not resolve the variation of the scalar order parameter within the core of defects, to reduce the computational complexity of the problem we assume that the scalar order parameter is spatially uniform. Likewise as a simplifying approximation, we neglect biaxiality in molecular ordering. These approximations reduce the number of degrees of freedom for the symmetric, traceless Q ij tensor from five to two at each point in space, thus allowing the state of nematic ordering to be described simply as a three-dimensional director field. To model the liquid crystal bulk, we define a cubic lattice with nearest neighbor spacing c and use the symmetries of the lattice to simplify the Qij tensor free energy functional. If we assume a single elastic constant approximation, making the model similar to the Lebwohl-Lasher 4

5 approach, the system s free energy (Eq. 1) can be written as f = K 1 4 G q G K n n + n n ( ) (0) Neglecting the surface integral, we use a finite difference technique to express the G i terms as a function of cross and dot products of the nematic director on nearest neighbor lattice sites. The quantity F 1 = a,b Q b a ( jk Q jk ) Q b a jk Q jk ( ) is a lattice approximant to G 1 more details of this calculation can be found in [10] thus the achiral term of the free energy can be written ( ) Q b a ( jk Q jk ) F achiral = K 4 d 3 rg 1 ( r ) = K 4 c Q b a jk Q jk (0) a,b F 4 = a,b In a similar way, using the lattice approximation to G 4 Q a b ε jm + Q jm jkl r b a ( l r l )Q b a km Q km we can write the chiral part of the free energy as 2 F chiral = Kq 0 d 3 rg 4 ( r Q a b ) = Kq 0 c ε jm + Q jm jkl 2 r b a ( l r l ) Q b a ( km Q km ) (0) a,b Re-expressing the nematic tensor as Q jk = n j n k 1 3δ jk we obtain a free energy functional simplified by considering interaction with only the nearest neighbors in the lattice: F = K 2 c 1 ( n a n b ) <a,b>( ) 2 Kq 0 c n a n b ( )( ) (0) <a,b> n a n b r ab This discretized version of the free energy functional is explicitly independent of director sign, and allows topological defects with fractional charge m = -½, + ½. Like the Lebwohl-Lasher model, this approach includes the single elastic constant approximation and lattice discretization. We calculate time evolution of the director field by solving for the dynamics of the director rotation in the overdamped limit, rather than by a Monte Carlo approach. Similar studies on Lebwohl-Lasher Molecular Dynamics have been recently implemented to model the nematic-isotropic phase transition [11][12]. The torque τ acting on the director located at the 5

6 lattice site a produced by nearest-neighbors interactions is calculated asτ l = e lki n k a F n i a. So the torque acting on site a is given by τ = Kc n a n b +q 0 n a n b b ( )( ) b n a n b ( )+ n a n b ( ) r ab ( n a n b ) ( )( r ab n a ) n b r ab ( n a n b ) 2 This model only allows director rotation and neglects backflow effects. The local director at each site updates according to n t = n t 1 + ω n ( t 1 )Δt, where ω is the angular velocity. Next, we renormalize the director at each lattice site. This approach assumes over-damped dynamics, with angular velocity proportional to torque by a factor ξ, which is inversely proportional to the liquid crystal s rotational viscosity γ 1. The single elastic constant, rotational viscosity and dielectric constant parameters are set to values corresponding with a commonly used commercial liquid (0) crystal compound: K = 13.0 x N, γ 1 = Pa s, ε =22.0 and ε = 5.2. Simulation lattice spacing was set to c = µm and system size was set to Nx = Ny = Nz = 30 a.u, approximating a cube of side 10.0 µm. We consider a cholesteric liquid crystal with pitch p = 3.33 µm; so that the parameter q 0 in the chiral free energy term is q 0= 6π/10 µm -1. An external electrical field is applied by imposing a voltage between the two surfaces in the x-direction. The external applied voltage is adjusted as a function of time for the desired pulse magnitude and duration. Liquid crystal devices are normally switched using an AC field to prevent charged ionic species from aggregating at the electrodes. As a simplifying assumption, we calculate response to a DC field, and use material dielectric properties matched to the AC frequency of interest; ion motion effects are not included in the model. More details in the AC and DC dielectric response of liquid crystals have been reported in experimental studies [18][19]. We include an extra term in the free energy given by F electric = D E where D = ε 0 ε ij E is the electric displacement vector, and ε ij is the anisotropic dielectric tensor for the liquid crystal [13][14]. The local dielectric tensor in the liquid crystalline bulk is 6

7 ε ij = ε + ( ε ε )n i n j [1], and accordingly it varies as a function of position and time as the director field relaxes. Thus we have a dielectric tensor that depends on the nematic director, while at the same time there is an electric torque affecting the orientation of the nematic director. D = 0 We calculate the electrostatic potential, electric field and dielectric tensor by solving at the beginning of each time step before updating the nematic director. For this electrostatic calculation we use a successive over-relaxation iterative solution approach [15] with convergence criterion Δϕ < In the first time step after the applied voltage changes, the electrostatic calculation requires of order 25,000 iterations to converge. In subsequent time steps, we use the solution from the previous time step as an initial guess and achieve convergence in about 300 iterations. Once we have solved for the electrical field we proceed to apply an electrical torque on the liquid crystal director τ electric = D E = ( ε 0 ε ij E ) E [14] and integrate the director relaxation forward in time. To monitor evolution of the liquid crystal texture, we also calculate the capacitance of the cell C = D ˆxda s V at each time step using the induced surface charge on one substrate under a voltage V. After the voltage pulse is removed, we apply a small test voltage V1 = 1V small enough so it does not affect the final cholesteric texture but allows us to calculate capacitance. Surface anchoring terms are added to the free energy to describe interaction of the liquid crystal with the confining substrates. We impose weak azimuthal and polar anchoring conditions at both substrates. Thus, the free energy of the system has an additional term describing its anisotropic interfacial energy as ϑ s = f s ds + f + s ds +. The interfacial energy density is f s = W ς n ς ( ) 2 +W η ( n η ) 2 ς, η, ι ( ) ι where is an orthonormal triplet and is the easy axis of orientation [17]. An additional torque is applied to the director given surface weak anchoring τ s = 2c 2 W ς ( n ς )( n ς )+W η ( n η)( n η). We implemented unidirectional anchoring with 7

8 easy axis ι = y, thus τ s = 2c 2 W a ( n x)( n x)+w p ( n z)( n z), where W a and W p are the azimuthal and polar anchoring strengths respectively (Wa = Wp = ~10-6 N/m). This modeling approach builds on previous work by Anderson, et al. [16] who carried out studies of bulk material response of cholesteric liquid crystals under a voltage pulse using a two-dimensional model. They demonstrated the feasibility of modeling this system at the mesoscopic level, inspiring our extension to three dimensions for better modeling of real devices. And as nucleation and growth behave differently in two vs. three dimensions, a full three-dimensional description is needed. Figure 1 (Color online) Planar-to-planar transition after a 10V pulse is applied to an initial perfect-planar texture. a) Microstructural evolution of the 3-D nematic director during the planar-to-planar switching. b) Capacitance of the liquid crystal cell. c) Elastic, electric and total energy of the system. 8

9 Planar-to-planar, planar-to-focal conic, and focal conic-to-planar transitions: Using the simulation approach described above, we modeled the electrical switching of chiral nematic textures in a bulk of liquid crystal material. First we consider a planar initial state with a defect-free helical texture with the helical axis along the x-direction. We apply a voltage pulse of magnitude V0 ranging from 4V - 60V during time steps, corresponding to 500ms, after which the sample relaxes to an equilibrium texture. For a small applied voltage pulse V0 = 10V, we observe planar-to-planar switching behavior, as shown in Fig. 1. The applied voltage initially unwinds the helix, and after the voltage drops, the planar texture reforms via nucleation from one of the substrates. The total energy and capacitance measurement show that the system is fully relaxed and stable after switching. We note that the pitch in the final state is slightly longer than in the initial state. This final texture state is a consequence of competition among all elastic (K) free energy terms, incorporating also the contribution from anchoring (W) energy. On the other hand, the initial state in the simulation was parameterized to match the q 0 parameter, which only appears in the chiral term of the free energy functional. For applied voltage smaller than 10V, the field is not strong enough to unwind the helix and the planar texture persists. For an intermediate applied voltage V 0 = 15 to 40V, when the voltage is removed, the planar texture is not recovered and we observe a defect-rich focal conic texture with the local helical axis oriented in many different directions. Figure 2 show the microstructural evolution of the planar-to-focal conic transition with an applied voltage pulse of 15V. These disordered textures still show some periodicity while coexisting with defects and undulations of the helical axis. 9

10 Figure 2 (Color online) Planar-to-focal conic transition, under a transient voltage pulse of V 1=15V applied to an initial planar texture. a) Microstructural evolution of the 3-D nematic director. b) Capacitance of the liquid crystal cell. c) Elastic, electric and total energy of the system. For voltage pulse or magnitude between 15V and 40V we observe this planar to focal conic texture transition. With an applied voltage pulse V0 = 60V, the simulation again shows a planar-to-planar transition, as shown in Figure 3. The final state is a perfect defect-free planar texture, that is, the helical axis is uniformly oriented perpendicular to the sample substrates and no defects are present. The observation of these planar-to-planar transitions at small and large voltages and planar-to-focal conic transitions at intermediate voltages agrees with the bistable switching behavior of cholesteric liquid crystal textures widely reported in the literature [1][9]. 10

11 Figure 3 (Color online) Final state after a transient voltage pulse is applied to a cholesteric liquid crystal initially in the planar state. Lowest and highest magnitude voltage pulses both produce a planar-to-planar transition, while a range of intermediate magnitude voltage pulses produce a planar-to-focal conic texture transition. Next we model focal conic-to-planar transitions. We take as our initial state a defect texture obtained after full relaxation of the planar-to-focal conic under a voltage pulse of size 15V as shown in Figure 3. Figure 4 shows the focal conic-to-planar transition with a high applied voltage pulse of 60V. The strong electric field effectively erases the defect-rich focal conic state, allowing the system to relax back to the defect-free planar state. By contrast, small and intermediate applied voltage are insufficient to erase the focal conic state. Snapshots of the relaxed textures after electrical switching with voltage pulses from 4-60V are shown in Figure 5. For pulses 40V, the final disordered textures exhibit defects in the helix periodicity as well as undulations in the overall helical axis of the texture. Observed defect structures vary with the strength of the applied voltage; details are shown in supplementary material. This transition behavior and sequence is in close qualitative agreement with experimentally observed texture switching and bistability in cholesteric liquid crystals. 11

12 (a) Initial State 60V pulse ON Relaxation after pulse Final State (b) (c) C (pf) t (a.u) Top substrate Bottom substrate E (a.u) t (a.u) E total E elastic E electric Figure 4 (Color online) Disordered helical-to-planar transition when a voltage pulse of 60V is applied to the disordered helical texture. a) Microstructural evolution of the 3-D nematic director. b) Capacitance of the liquid crystal cell. c) Elastic, electric and total energy of the system. Figure 5 (Color online) Summary of disordered helical (focal conic) - planar texture sequence relaxed after voltage pulse is applied to a disordered helical focal conic texture in simulations with weak anchoring conditions. 12

13 While the bistable switching behavior in chiral nematics has been widely reported in the literature [1][9], this model presents for the first time a 3-D simulation of the emerging perfect-planar and defect-rich focal conic textures at different voltages from both planar and disordered helical states. These simulations capture different morphologies from rounded and elongated enclosed morphologies to undulated stripes in the periodicity of the disordered focal conic states. Figure 6 shows simulation data for capacitance vs. time and applied external electric field. Fig. 6(a) shows data for simulations with a planar initial state, corresponding to the microstructures shown in Fig. 3. Here we observe that the restoration of the helix to perfect planar obtained with V0 = 10V and 60V has faster relaxations than disordered helical textures at intermediate voltages. However, the initial helix unwinding shown by an initial jump in cell capacitance - is faster when applying a 60V pulse than with a 10V pulse. This suggests that a complete planar-vertical-planar sequence for texture switching could be achieved in shorter time periods with larger voltages. Figure 6(b) shows a similar capacitance measurement when switching from an initially defect-rich focal conic texture, corresponding to microstructures shown in Fig. 5. At 60V, the perfect planar texture relaxes and reaches stability faster than any disordered helical textures observed in the simulation run. This result shows a qualitative agreement with the fast switching behavior observed experimentally in systems with matched elastic constants. The transient planar state was never observed as expected for the case of matched twist and bend elastic constants. As discussed above, our simulation model is based on the assumption of a single elastic constant, the use of a structured cubic lattice, and a finite difference scheme taking into account nearest neighbors interactions within the lattice. However, model can easily be extended to a case with different elastic constants. This would result in a more complex form with higher order terms involving a double sum with two nearest neighbors at the time. E.g. a more accurate description that includes K = K 11 = K 22 K 33 would have a free energy functional given by 13

14 ( ) <a,b>( ) 2 F = 1 ( 6 2K + K 33)c 1 n a n b ( ) n b n c c K 33 K a b c Kq 0 c n a n b ( )( ) <a,b> n a n b r ab r ab r ac ( ) 2 ( n a r ab )( n a r ac ) 1 ( ) 3 (0) where the two sums on b and c are over the nearest neighbors of site a. (a) Switching from planar state (b) Switching from disordered state C (pf) C 4V C 4V C 10V C 10V C 15V C 15V C 20V C 20V C 40V C 40V C 60V C 60V C (pf) C 4V C 4V C 10V C 10V C 15V C 15V C 20V C 20V C 40V C 40V C 60V C 60V time steps (a.u) time steps (a.u) Figure 6 (Color online) Capacitance as a function of time in the liquid crystal cell during switching at different voltages V 0. a) Initial perfect planar state; b) Initial disordered focal conic state. C and C correspond with the cell capacitance calculated with the induced charge in the top and bottom substrates respectively. Vertical line shows the time step when the voltage pulse V 0 is removed. Extensions to include surface terms depending on K24 (saddle-splay) and K13 (splay-bend) elastic constants, can be implemented to accurately describe a richer behavior in liquid crystalline systems and provide insight into the design and engineering of new devices. This type of modeling approach presents the capability to set the liquid crystalline bulk in any form; spherical, cubical, oblate or prolate, allowing the study of different confined geometries with suitable application in devices as displays, sensors, among others. These numerical methods show to be a valuable tool for further design, engineering and development of optimized liquid crystalline devices. 14

15 In summary, we introduced a simplified method to model 3D microstructural evolution in chiral nematic liquid crystals confined between anchoring substrates under a transient applied voltage pulse. This approach allows efficient computation of microstructural evolution in three dimensions. We modeled texture evolution in chiral nematic liquid crystals by solving for the dynamics of the director field in the presence of electric field. We studied the switching process and electrical response that drives the transition between perfect planar and focal conic textures in samples with equal elastic constants. Results show agreement with the fast switching behavior at large voltages recently reported in experimental studies [8]. Acknowledgments: We thank S.Y. Lu, S. Afghah and A. Konya for insightful conversations and tests on this simulation approach. We acknowledge J. V. Selinger for his help on the initial developing of this model. This work was funded by NSF DMR , NSF DMR , the Wright Center of Innovation for Advanced Data Management and Analysis, and by the Ohio Board of Regents. Computing resources provided by the Ohio Supercomputer Center (V.G.-P., R.S). References [1] S.-T. Wu and D.-K. Yang, Fundamentals of Liquid Crystal Devices (Wiley Series in Display Technology). Wiley, [2] J. W. Doane, A. A. Khan, I. Shiyanovskaya, and A. Green, United States Patent: [Online]. Available: [Accessed: 03-Feb-2014]. [3] J. W. Doane and A. Khan, Flexible Flat Panel Displays (Wiley Series in Display Technology) Chapter 17. Wiley, [4] P. Popov, L. W. Honaker, M. Mirheydari, E. K. Mann, and A. Jákli, Chiral nematic liquid crystal microlenses, Sci. Rep., vol. 7, no. 1, p. 1603, Dec [5] Y. Guo, S. Afghah, J. Xiang, O. D. Lavrentovich, R. L. B. Selinger, and Q.-H. Wei, Cholesteric liquid crystals in rectangular microchannels: skyrmions and stripes, Soft Matter, vol. 12, no. 29, pp ,

16 [6] A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film, Nat. Phys., p. nphys4245, Aug [7] D. Seč, S. Čopar, and S. Žumer, Topological zoo of free-standing knots in confined chiral nematic fluids, Nat. Commun., vol. 5, p. ncomms4057, Jan [8] M. Yu, X. Zhou, J. Jiang, H. Yang, and D.-K. Yang, Matched elastic constants for a perfect helical planar state and a fast switching time in chiral nematic liquid crystals, Soft Matter, vol. 12, no. 19, pp , [9] S. Žumer and G. P. Crawford, Liquid Crystals In Complex Geometries: Formed by Polymer And Porous Networks. Taylor & Francis, [10] V. K. Gimenez Pinto, Modeling Liquid Crystal Polymeric Devices, Kent State University, [11] S. Chakrabarty, D. Chakrabarti, and B. Bagchi, Power law relaxation and glassy dynamics in Lebwohl-Lasher model near the isotropic-nematic phase transition, Phys. Rev. E, vol. 73, no. 6, p , Jun [12] A. Varghese and P. Ilg, Time correlation functions in the Lebwohl-Lasher model of liquid crystals, Phys. Rev. E, vol. 96, no. 3, p , Sep [13] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (International Series of Monographs on Physics). Oxford University Press, USA, [14] A. Jakli and A. Saupe, One- and Two-Dimensional Fluids: Properties of Smectic, Lamellar and Columnar Liquid Crystals (Condensed Matter Physics). Taylor & Francis, [15] J. D. Jackson, Classical Electrodynamics Third Edition. Wiley, [16] J. Anderson, P. Watson, T. Ernst, and P. Bos, Computer simulation evidence of the transient planar state during the homeotropic to focal conic transition in cholesteric liquid crystals, Phys. Rev. E, vol. 61, no. 4, pp , Apr [17] W. Zhao, C.-X. Wu, and M. Iwamoto, Analysis of weak-anchoring effect in nematic liquid crystals, Phys. Rev. E, vol. 62, no. 2, pp. R1481 R1484, Aug [18] G. H. Heilmeier, A NEW ELECTRIC-FIELD-CONTROLLED REFLECTIVE OPTICAL STORAGE EFFECT IN MIXED-LIQUID CRYSTAL SYSTEMS, Appl. Phys. Lett., vol. 13, no. 4, p. 132, Aug [19] G. H. Heilmeier and J. E. Goldmacher, A new electric field controlled reflective optical 16

17 storage effect in mixed liquid crystal systems, Proc. IEEE, vol. 57, no. 1, pp ,

18 Supplementary Information for: Modeling 3-D chiral nematic texture evolution under electric switching Vianney Gimenez-Pinto * and Robin L. B. Selinger Liquid Crystal Institute, Kent State University, Kent, OH Corresponding author: rselinge@kent.edu *Current Address: Department of Physics and Astronomy, University of Pennsylvania Textures transitions from an initial planar state Videos 1-7 show the microstructural evolution of the chiral nematic textures when switching from an initial perfect (defect-free) planar state: Supplementary video 1: V 0 = 4 V Supplementary video 2: V 0 = 8 V Supplementary video 3: V 0 = 10 V Supplementary video 4: V 0 = 15 V Supplementary video 5: V 0 = 20 V Supplementary video 6: V 0 = 40 V Supplementary video 7: V 0 = 60 V Texture transitions from an initial focal conic state Voltage pulses of different magnitude V 0 are applied to a texture state with disordered helical axis. When V 0 12V, the defect textures exhibit different enclosed morphologies: for a voltage of 4V helical periodicity shows a rounded circle-like morphology while the 10V texture presents elongated enclosed shapes in its periodicity see Figure 5 and supplementary videos For 15V < V0 < 40V, fully enclosed shapes are not longer seen. Disordered textures show up as undulated stripes with a few defects in the helix periodicity. The perfect planar texture, with characteristic uniform helical axis parallel to the substrate normal is recovered with the application of a large voltage V0 = 60V. Videos 8-16 show the microstructural evolution when switching with applying different V 0 voltages to an initial focal conic state. 18

19 Supplementary video 8: V 0 = 4 V Supplementary video 9: V 0 = 6 V Supplementary video 10: V 0 = 8 V Supplementary video 11: V 0 = 10 V Supplementary video 12: V 0 = 12 V Supplementary video 13: V 0 = 15 V Supplementary video 14: V 0 = 20 V Supplementary video 15: V 0 = 40 V Supplementary video 16: V 0 = 60 V 19