Volodymyr Borshch a, Sergij V. Shiyanovskii a & Oleg D. Lavrentovich a

Transcription

1 This article was downloaded by: [KSU Kent State University] On: 21 December 2014, At: 17:57 Publisher: Taylor & Francis Inorma Ltd Registered in England and Wales Registered Number: Registered oice: Mortimer House, Mortimer Street, London W1T 3JH, UK Molecular Crystals and Liquid Crystals Publication details, including instructions or authors and subscription inormation: Electric Field Induced Biaxial Order and Dierential Quenching o Uniaxial Fluctuations in a Nematic with Negative Dielectric Anisotropy Volodymyr Borshch a, Sergij V. Shiyanovskii a & Oleg D. Lavrentovich a a Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, USA Published online: 11 May To cite this article: Volodymyr Borshch, Sergij V. Shiyanovskii & Oleg D. Lavrentovich (2012) Electric Field Induced Biaxial Order and Dierential Quenching o Uniaxial Fluctuations in a Nematic with Negative Dielectric Anisotropy, Molecular Crystals and Liquid Crystals, 559:1, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every eort to ensure the accuracy o all the inormation (the Content ) contained in the publications on our platorm. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability or any purpose o the Content. Any opinions and views expressed in this publication are the opinions and views o the authors, and are not the views o or endorsed by Taylor & Francis. The accuracy o the Content should not be relied upon and should be independently veriied with primary sources o inormation. Taylor and Francis shall not be liable or any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out o the use o the Content. This article may be used or research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any orm to anyone is expressly orbidden. Terms & Conditions o access and use can be ound at

2 Mol. Cryst. Liq. Cryst., Vol. 559: pp , 2012 Copyright Taylor & Francis Group, LLC ISSN: print/ online DOI: / Electric Field Induced Biaxial Order and Dierential Quenching o Uniaxial Fluctuations in a Nematic with Negative Dielectric Anisotropy VOLODYMYR BORSHCH, SERGIJ V. SHIYANOVSKII, AND OLEG D. LAVRENTOVICH Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, USA We explore the response o a uniaxial nematic liquid crystal with a negative dielectric anisotropy to the electric ield applied normally to the director. The geometry causes two eects: ield-induced biaxiality order (FIBO) and dierential quenching o uniaxial luctuations (DQUF). We separate the two eects by tracing the ield-induced changes in optical response at the timescales o nanoseconds. The study paves the way to establish the possibility o ield-assisted ormation o the biaxial nematic phase and to explore the likelihood o the appearance o biaxial order in the ield-ree conditions. Keywords 1. Introduction Dynamics; ield-induced biaxiality; luctuations; nematic liquid crystal An electric ield applied to a dielectric can change the structural symmetry and thus the optical properties o the material. I the material is isotropic, the electric ield can induce an optically anisotropic uniaxial state; the eect is well known as the Kerr eect. I the isotropic dielectric represents a melted state o a liquid crystal (LC), then the Kerr eect becomes more pronounced as the temperature is reduced towards the transition point into the LC. When the material is already in the nematic LC state, the most evident eect o the applied electric ield is reorientation o the optic axis (the director) either along the ield (i the dielectric anisotropy is positive) or perpendicular to the ield i the dielectric anisotropy is negative. O especial interest is the situation when the electric ield does not cause macroscopic director reorientation o the uniaxial nematic LCs [1 4], or example, when the electric ield is applied perpendicularly to the director ˆn o a LC with negative dielectric anisotropy, ε = ε ε < 0. In this case, the applied electric ield can change the overall symmetry o the LC, inducing a secondary axis o molecular order that is perpendicular to ˆn so that the material in the ield becomes a biaxial nematic [5]. This eect can be called ield-induced biaxial order (FIBO). Development o bent-core LC materials and an intensive search or the biaxial nematic phase lead to a renewed interest to FIBO [6 8]. The challenge in characterizing the possible FIBO is that the ield can also modiy the luctuations o the main (uniaxial) director ˆn [1,9 13]. These changes in luctuations Address correspondence to Sergij Shiyanovskii, Liquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA. Tel: +1 (330) ; Fax: +1 (330) sshiyano@kent.edu 97

3 98 V. Borshch et al. o ˆn are anisotropic. Imagine, or example, a planar LC slab cell with ˆn = (1, 0, 0) and ε = ε ε < 0 under the action o the applied electric ield, E = (0, 0,E). The applied electric ield supresses the luctuations o ˆn in the vertical (x,z) plane but hardly aects the luctuations in the horizontal (x,y) plane. The eect can be called a dierential quenching o uniaxial luctuations (DQUF) [12a]. Dunmur and Paly-Muhoray [14] provided a theoretical description o how the FIBO and DQUF eects modiy the optical properties o a uniaxial nematic. Experimental separation o FIBO rom DQUF represents a ormidable challenge, as qualitatively described below. The DQUF induces changes o the eective bireringence o the sample that are linearly proportional to the amplitude o the applied ield (page 148 o [1]), δ n E. The ield-induced change in the eective bireringence measured in the (x,y) plane and caused by FIBO eect, should be quadratic in the applied ield (δ n E 2 ), thanks to the nonpolar character o the nematic and molecular dielectric biaxiality (individual molecules are not axially symmetric). One thus expects the DQUF eect to dominate FIBO at relatively low ields. To separate the two, we propose to use the dierence in characteristic relaxation times. The FIBO eect is expected to be ast, because it results rom molecular orientational order. For example, the ield-induced changes in the uniaxial scalar order parameter occur at the timescale o less than 100 ns [15]. On the other hand, the DQUF is expected to be slower, as described by the ieldinduced director reorientation with characteristic time τ ON γ/( ε ε 0 E 2 ), which results in an estimate τ ON 20 µs ore = 10 7 Vm 1, with the typical values o the rotational viscosity γ = 0.1Pa s, and dielectric anisotropy ε = 6. In this work, we explore the nanosecond dynamics o ield-induced optical bireringence changes in a dielectrically negative uniaxial nematic, with the goal o experimental separation o FIBO and DQUF. Section 2 describes the experiments. Section 3 presents the theoretical model. Section 4 discusses the results. 2. Experimental Technique We use a single component nematic 4 -butyl-4-heptyl-bicyclohexyl-4-carbonitrile (abbreviated as CCN-47) provided by Nematel GmbH (Fig. 1), with negative dielectric anisotropy ε = 6. CCN-47 is illed into a planar cell o a thickness d = 7.9 µm. The inner suraces o the cell s bounding plates are coated with a polyimide layer PI-2555 (Nissan Chemicals) and rubbed in the antiparallel directions. All the measurements were perormed in the nematic phase o the material at 35 C. The temperature is stabilized by Linkam LTS350 hotstage. Figure 1. Structure o a molecule o CCN-47. Negative dielectric anisotropy is due to the transverse cyano-group dipole. The other name is ZLI CAS number

4 Electric Field Induced Biaxial Order and Fluctuations Quenching 99 Figure 2. The experimental setup. Adding additional phase dierence o π/2 by the Babinet-Soleil compensator (B-S) allows to separate optical phase retardation part o the signal rom other eects (change o light scattering or other parasitic eects). The ield induced bireringence dynamics is monitored by measuring the intensity I = I 0 sin 2 πl (L = nd is the retardance, n is the eective bireringence, and d is λ the cell thickness) o laser beam (He-Ne, λ = 633 nm) passing through the cell and two crossed linear polarizers (Fig. 2). The rubbing direction o the cell is at 45 with respect to the polarizers. The Babinet-Soleil compensator introduces a controllable retardance, that is chosen to set the linear regime in which I L (L (k +1/2)λ, k integer), where small changes in retardance lead to pronounced modulation o the transmitted light intensity. Because we trace the dynamics o optical changes at the scale o nanoseconds, it is important to keep the RC delay time o the cell as small as possible. Small RC time ensures short time o charging the cell, thus minimizing the delay time when the electric ield is applied to the LC inside this cell. For this purpose we use low-resistance ITO electrodes (10 /square) and make the electrode area small (around 2 mm 2 ). The measured capacitance o the cell illed with CCN-47 is 41 pf at 35 C. Applying a rectangular pulse and measuring the current through the cell, we conirm that RC time is about 1 2 ns. The driving voltage pulse with a sharp ront (5 ns rise time) is produced by a generator DEI HV1000 (Direct Energy). Voltage pulses o dierent amplitude and o duration t p = µs are applied to the LC cell, and the optical response is measured using a ast photodetector TIA-500S-TS (Terahertz Technologies) with the response time <1 ns (Fig. 3). The voltage pulses and photodetector signals are measured with 1 GS/s digital oscilloscope TDS2014 (Tektronix). Because the rise time o the voltage pulses and the RC-time o the cell are short as compared to the relaxation times o the optical response, the ront and back edges o the voltage pulses are considered to be instantaneous. The voltage amplitude achieved immediately ater the ront edge, however, is not a constant and shows a slow decrease with time. This slow decrease is well modelled by the unction U(t) = U 0 e νt, where U 0 and ν are the itting parameters (Fig. 3(a)). The time dependence o the electric ield E(t) = U(t)/d is then: E(t) = U 0 d e νt. (1) Figure 3b represents the main experimental result o this work. It shows the dynamics o an increase (ield ON) and decrease (ield OFF) o the ield-induced optical retardance

5 100 V. Borshch et al. Figure 3. Typical voltage pulses (a) applied to the CCN-47 cell, and the corresponding optical responses (b) as detected by the ast photodetector. or ive dierent amplitudes o voltage applied to the CCN-47 cell. Below we present our model to it this dynamics and to separate the contributions o FIBO and DQUF. 3. Model To analyse the experimental data we consider the total change o the retardance, caused by the applied electric ield, L(t) = L(t) L(0) = L b (t) + L (t), as a sum o the contributions rom FIBO eect, L b (t), and DQUF eect, L (t). Both eects are small, thus we can neglect the terms describing the coupling o these two. We assume that the dynamics o the system is controlled by the linear response and ascribe a single relaxation time τ b to the FIBO process: τ b d L b (t) dt = L b (t) L b (t), (2)

6 Electric Field Induced Biaxial Order and Fluctuations Quenching 101 where L b (t) = c b E 2 (t)d is an equilibrium contribution corresponding to the instantaneous value o the electric ield E(t) at the moment o time t and c b is the susceptibility parameter o the LC. The solution o Eq. (2), when E(t) turns on at t = 0, is t L b (t ) L b (t) = e (t t )/τ b dt. (3) 0 τ b Substituting (1) in (3), we obtain the solutions or the ON and OFF processes: L ON c b U0 2 b (0 <t t p ) = d(1 2ντ b ) (e 2νt e t/τ b ) and (4) L OFF b (t >t p ) = L ON b (t p )exp( (t t p )/τ b ), (5) where t p is the duration o the applied voltage pulse. The analysis o L (t) is more complicated because L (t) = q L (q,t) contains contributions rom the entire spectrum o luctuations with dierent wavevectors q. We describe each L (q,t) by a linear response equation, similar to (2): τ(q,t) d L (q,t) = L (q,t) L (q,t), (6) dt where the relaxation time τ(q,t) and quasi-equilibrium value L (q,t) depend on q and current ield E(t). In one-constant approximation or the elastic moduli, K 11 = K 22 = K 33 = K, γ e τ(q,t) = Kq 2 + ε ε 0 E 2 (t), L ε ε 0 E 2 (t) (q,t) Kq 2 (Kq 2 + ε ε 0 E 2 (t)), (7) where γ e is the eective rotational viscosity and ε 0 is the dielectric permittivity o ree space. During the ON process, the main contribution to the optical phase retardation is provided by the luctuations with q<q E = E ε ε 0 /K (or E 10 7 Vm 1, q E 10 7 m 1 ), that have approximately the same characteristic time τ ON = γ e d 2 / ε ε 0 U 2 0. (8) Thus or the ON process o DQUF, one may write an equation similar to (2): τ ON d L ON (t) dt = L (t) L ON (t), (9) where L (t) = q L (q,t) = c E(t) d [7], and c is the LC material parameter. Using (1), we ind a solution o Eq. (9): L ON (0 <t t p) = c U 0 1 ντ ON ( e νt ) e t/τon. (10) To model L OFF (t >t p ), when the electric ield is turned o and each luctuation relaxes with its own characteristic time τ(q) = γ/kq 2, we split the luctuations into two

7 102 V. Borshch et al. types: ast luctuations described by phenomenological relaxation time τ OFF, and slow ones that provide a constant contribution during the time o experiment (several microseconds): L OFF (t >t p ) = L ON (t p) [ (1 r 0 ) exp ( (t t p )/τ OFF ) ] + r0, (11) where r 0 is the relative contribution o slow luctuations. To summarize our model, L(t) = L b (t) + L (t) is described by equations (4), (5), (10), and (11), with six itting parameters: material parameters c b, c, relaxation times τ b, τ ON, and τ OFF, and the relative contribution o slow luctuations r 0. The parameters U 0 and ν are ound rom the independent itting o the voltage pulse with (1). 4. Results and Discussion Figure 4 shows how the experimental data on dynamics o optical response are itted with the model or a pulse with U 0 = 557 V. The unctions describing FIBO by Equations (4), (5) and DQUB by (10), (11) it the data well, never deviating beyond the experimental noise. The itting parameters or this voltage pulse are: τ b = 44 ns, τ ON = 194 ns, τ OFF = 292 ns, r 0 = 0.31, c b = m 2 V 2, c = mv 1. Based on these values, we separate FIBO (dotted line on Fig. 4) and DQUF components o the optical response. The same approach is used in analysing the data or other voltages. The itting o the experimental data supports the basic predictions o the model Figs 5, 6. First, the susceptibility parameters c b and c are practically voltage-independent, Fig. 5. Second, the biaxial time τ b does not depend on the electric ield, Fig. 6. We perormed an additional itting with two independent values o τ b, one or the ON branch, Eq. (4), and another or the OFF branch, Eq. (5). This itting resulted in two values o τ b that Figure 4. The experimental points o the optical response (light blue dots) are itted with the equations (4), (5) (rising blue line), and (10), (11) (decaying blue line). The itting parameters are: τ b = 44 ns, τ ON = 194 ns, τ OFF = 292 ns, r 0 = 0.31, c b = m 2 V 2, c = mv 1.The dashed blue line corresponds to BIF component o the optical retardance expressions (4) and (5). The pink dots are the experimental measurement o the applied voltage described by equation (1) (red line) with itting parameters U 0 = 557 V and ν = s 1.

8 Electric Field Induced Biaxial Order and Fluctuations Quenching 103 Figure 5. The dependence o the biaxial c b (blue circles) and luctuational c (red squares) susceptibilities on the maximum applied voltage U 0. According to our model they should not depend on the applied electric ield. dier by less than 10%, supporting the idea that τ b is a single parameter or both processes. Third, τ ON decreases at higher voltages. The model, Eq. (8), does predict such a decrease, but with a rate τ ON U 2 that is somewhat higher than the experimental trend τ ON U 1. The reason or this discrepancy is rooted in the act that the model approximates the collective behaviour o all luctuations with a single time constant and thus anticipates a steeper voltage dependency. Finally, note that the phenomenological time constant τ OFF and the relative contribution r 0 o the slow luctuations in DQUF show a weak decrease with the applied voltage, Figs 6, 7. Figure 6. The dependence o the characteristic times τ b (solid blue circles), τ ON (solid red rectangulars), and τ OFF (open red rectangulars) on the maximum applied voltage U 0. According to our model the biaxial time τ b has to be constant. The behaviour o τ OFF its well with U 1 0 unction (red curve).

9 104 V. Borshch et al. Figure 7. The dependence o relative amplitude r 0 o the slow luctuations on the maximum applied voltage U 0. The pulse duration t p, slightly higher than 1 µs, turns out to be suiciently large as compared to the time constants ound rom the itting o data. Thereore, the experimentally measured optical retardance at the end o the applied pulse should be close to the values that correspond to the stationary values (under the constant electric ield), or both FIBO and DQUF. We use the itting parameters to calculate the values o L ON b (t p ) and L ON (t p)at the end o the applied pulse and to extract their dependence on the applied voltage, Fig. 8. As expected, the FIBO contribution is quadratic in the ield, while the DQUF contribution is linear with the ield, Fig. 8. Figure 8. Reconstructed FIBO (obtained rom Eq. (10)) and DQUF (Eq. (4)) components o retardance at time t p as unction o the maximum applied voltage U 0.

10 Conclusions Electric Field Induced Biaxial Order and Fluctuations Quenching 105 We have explored the response o a uniaxial nematic liquid crystal with a negative dielectric anisotropy to the electric ield applied normally to the director. We used the idea o dierent relaxation times to separate the eects associated with the ield-induced biaxial order (FIBO) and with dierential quenching o uniaxial luctuations (DQUF). The experimental data suggest that the dynamics o optical response does indeed allows one to extract the eect o FIBO at the background o DQUF despite the act that the studied material CCN- 47 shows no signs o the biaxial nematic order in the ield-ree state. This approach will be used in urther studies o ield-induced biaxial order in uniaxial nematic liquid crystals as well as in the search o the materials in which the biaxial nematic order can appear even without the applied ield. Acknowledgments This work was supported by DOE Grant #DE-FG02-06ER The authors thank R. Eidenschink (Nematel GmbH) or providing us with CCN-47 or the experiment. Reerences [1] de Gennes, P. G., & Prost, J. (1995). The Physics o Liquid Crystals, 2nd edition, Oxord University Press: Oxord. [2] Fan, Ch.-P., & Stephen, M. J. (1970). Phys. Rev. Lett., 25, 500. [3] Lelidis, I., & Durand, G. (1998). In: P. E. Cladis & P. Paly-Muhoray (Eds.), Dynamics and Deects in Liquid Crystals, Chapter Thermal Entropic Eect at the Electric Field Induced Isotropic-Nematic Transition, Gordon and Breach Science Publishers: Amsterdam, p. 61. [4] Lelidis, I., Nobili, M., & Durand, G. (1993). Phys.Rev.E, 48, [5] (a) Paly-Muhoray, P., & Dunmur, D. A. (1982). Phys. Lett., 91A, 121; (b) Paly-Muhoray, P., & Dunmur, D. A. (1983). Mol. Cryst. Liq. Cryst., 97, 337. [6] Olivares, J. A., Stojadinovic, S., Dingemans, T., Sprunt, S., & Jákli, A. (2003). Phys. Rev. E, 68, [7] Mamatha Nagaraj, Panarin, Y. P., Manna, U., Vij, J. K., Keith, C., & Tschierske, C. (2010). Appl. Phys. Lett., 96, [8] Stannarius, R., Eremin, A., Tamba, M.-G., Pelzl, G., & Weisslog, W. (2007). Phys.Rev.E, 76, [9] de Gennes, P. G. (1968). C.R. Acad. Sci., Paris, 266B, 15. [10] Poggi, Y., & Filippini, J. C. (1977). Phys. Rev. Lett., 39, 150. [11] Dunmur, D. A., Waterworth, T. F., & Paly-Muhoray, P. (1985). Mol. Cryst. Liq. Cryst., 124, 73. [12] (a) Dunmur, D. A., Szumilin, K., & Waterworth, T. F. (1987). Mol. Cryst. Liq. Cryst., 149, 385; (b) Dunmur, D. A., & Szumilin, K. (1989). Liq. Cryst., 6, 449. [13] Martinand, J. L., & Durand, G. (1972). Solid State Comm., 10, 815. [14] Dunmur, D. A., & Paly-Muhoray, P. (1988). J. Phys. Chem., 92, [15] Gu, M., Shiyanovskii, S. V., & Lavrentovich, O. D. (2008). Phys. Rev. E, 78, (R).