Nematic Twist Cell: Strong Chirality Induced at the Surfaces

Nematic Twist Cell: Strong Chirality Induced at the Surfaces Tzu-Chieh Lin 1), Ian R. Nemitz 1), Joel S. Pendery 1), Christopher P.J. Schubert 2), Robert P. Lemieux 2), and Charles Rosenblatt 1,a) 1 Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106 USA 2 Department of Chemistry, Queen s University, Kingston, Ontario K7L 3N6 Canada A nematic twist cell, with easy axes forming an angle θ 0 = 20 and thickness d varying continuously across the cell, was filled with a mixture containing a configurationally achiral liquid crystal and a chiral dopant. A linear electrooptic effect, which requires a chiral environment, was observed on application of an ac electric field. This electroclinic effect varied monotonically with d, changing sign at d = d where the chiral dopant exactly 0 compensated the imposed pitch. The results indicate that a significant chiral electrooptic effect always exists near the surfaces of a nematic twist cell containing molecules that can be conformationally deracemized. Additionally, this approach can be used to measure the helical twisting power (HTP) of a chiral dopant in a liquid crystal. a. Author to whom correspondence should be addressed: Electronic mail: rosenblatt@case.edu

Chirality plays a ubiquitous role in nature, in areas ranging from optical phenomena in materials to the efficacy of pharmaceuticals to liquid crystals (s) [1]. For example, owing to both the orientational order and large optical anisotropy of s, one can observe an enormous optical rotatory power even in the isotropic phase that can vary strongly with temperature [2]. The so-called liquid crystal blue phases, which heretofore appeared only over a very small temperature range, have been modified to increase this range and are being explored for device applications [3]. Ferroelectric liquid crystals, which occur in a chiral smectic-c* phase [4], can be used as rapidly-switching light valves and even as an alignment layer for electricallycontrolled switching of the director orientation [5]. Recently our group demonstrated that an imposed torsional strain on an achiral liquid crystal, in which the easy axes of two rubbed substrates are rotated by an angle θ 0 with respect to each other, provides a strong chiral environment in the immediate vicinity likely within a few molecular diameters of the two substrates [6]. On applying an ac rms electric field E rms perpendicular to the liquid crystal director (i.e., parallel to the helical axis), we observed a modulation of the transmitted laser intensity I ac that was proportional to E rms, for which chirality is a necessary component. The rapid decrease of the electroclinic coefficient e c [ ( ) d I /4 I / de ac dc rms ] with increasing frequency f suggested that the electric field drives an in-plane rotation ϕ of the nematic director very close to the surfaces, which is transmitted slowly into the bulk too slowly for the bulk to follow at higher frequencies by the s elastic forces. We interpreted the results as a conformational deracemization of the liquid crystal caused by the high torsional strain within a few nanometers [7] of the surfaces. [However, one cannot exclude a deracemization of the orientational distributions of the chiral conformers [1,8] by the twist environment.] Thus, this

observation demonstrated top-down molecular-level chiral induction caused by a macroscopic torsional strain. But these results also suggest that such a chiral electrooptic effect should be present in all twist cells containing conformationally deracemizable molecules, including cells deployed in liquid crystal devices, and either needs to be treated as an unwanted artifact or can be exploited for advantage. The purpose of this paper is to report on experiments in nematic twist cells in which the liquid crystal is doped with a chiral agent to compensate approximately for the imposed twist θ 0. Our results demonstrate that: i) the chiral electrooptic effect is, indeed, localized very close to the two surfaces, ii) the electrooptic effect vanishes when the mixture s natural rotation θ across the cell gap equals the imposed cell twist θ 0, and iii) by determining the thickness of the cell at which θ = θ 0, one can determine accurately the helical twisting power of the dopant / liquid crystal combination. A pair of indium-tin-oxide (ITO) coated glass slides was used as substrates. After the ITO glass was cleaned in detergent, acetone, and ethanol, the planar-alignment material RN-1175 (Nissan Chemical Industries) was spin coated on the substrates. The coated substrates were prebaked at 80 for 5 min to form the polyamic acid, and then at 250 for 60 min to create the polyimide. The slides were then rubbed unidirectionally using a commercial rubbing cloth to create an easy axis on each substrate for alignment of the director. Two substrates were placed together: i) with their easy axes rotated by an angle θ 0 = (20 ± 1) with respect to each other (Figure 1) and ii) in the form of a wedge, in which the thickness d of the cell varied uniformly along the bisector of the easy axes, from approximately 3 µm at the left of Fig. 1 to approximately 8 µm at the right of Fig. 1. Here the thickness d corresponds to the thickness of the air gap between the two alignment layers, as measured by optical interferometry. We remark

that the ITO near to the narrow end of the wedge was etched off to avoid contact between electrodes on the two substrates. The cell was filled in the isotropic phase with a c = (0.00144 ± 0.00005) weight-fraction mixture of the right-handed chiral dopant CB15 in the liquid crystal 9OO4 [Fig. 1, inset, having a phase sequence Iso 83 o N 70 o Sm-A 62 o Sm-C 50 o Sm-B 35 o Cryst]. The optical arrangement, which is based on a modification of the classical electroclinic geometry [9] that corrects for the imposed director twist in the cell, is described in detail elsewhere [6]. Briefly, an ac voltage at frequency f was applied across the cell, and the detector output was fed into both a dc voltmeter and a lock-in amplifier that was referenced to the driving frequency f. Four frequencies were examined: f = 31, 100, 310 and 1000 Hz. The ac optical intensity I ac, its phase relative to the applied voltage V rms, and the dc optical intensity I dc were computer recorded as the voltage was ramped upward over a time of 150 s. Figure 2 shows a typical set of data I ac / 4I dc this is proportional to the field-induced director rotation ϕ immediately at the substrates [6] vs. the applied rms voltage V rms at f = 1000 Hz for different values of the liquid crystal thickness d. Because the thickness d PI of each of the two polyimide alignment layers was ~ 0.16 to 0.18 µm, which is only one order of magnitude smaller than the liquid crystal thickness d, we needed to correct the data to account for the voltage drop across the two polyimide layers [10]. At the frequencies used, the cell behaved as capacitors in series rather than resistors in series, where the total capacitance ( ) 1 C = ε0a 2 dpi / εpi + dtest / εtest. Here ε 0 is the permittivity of free space, A the area of the capacitor, ε PI the dielectric constant ( ~ 3.0 [Ref. 11]) of the polyimide, and ε test is the dielectric constant of the test material (air or ) filling the gap d test between the polyimide layers. Thus, we constructed an empty test cell of uniform thickness d test = 5.2 µm

and having an ITO overlap area A = 75 mm 2. We then measured the capacitance of the empty cell at temperature T = 77 o C this is the temperature for all data presented in this work using an Andeen-Hagerling 2500 capacitance bridge, finding C = 125 pf, and thus 2d PI / ε PI = (0.10 ± 0.01) µm. We then filled the cell with 9OO4 in the planar alignment and obtained C = 550 pf, from which we deduced ε εtest = 4.7, i.e., the dielectric constant of the 9OO4 perpendicular to the director. Having these values, it is easy to determine the rms voltage d across only the (of thickness d) in our experimental cell: ( ) 1 PI ε V V rms = V 2 + 1. Thus rms rms εpi d V rms was smaller than the applied V rms by approximately 14% in the thinnest regions of the wedged cell, and about 6% in the thickest regions. Figure 3 shows the electroclinic coefficients e c vs. cell spacing d at the four frequencies, corresponding to the slopes ( ) d I /4 I / dv in Fig. 2 multiplied by the thickness d and finally ac dc rms corrected for the voltage drop across the only, as described above, i.e. ( ) e = d I /4 I / de. Figures 2 and 3 clearly show that the electroclinic response changes c ac dc rms sign at a cell thickness d = d 0 = (4.8 ± 0.1) µm, which was obtained by averaging the zero crossings of e c for the four sets of frequency data. In our previous work [Ref. 6] we proposed a simple model in which the 9OO4 partially deracemizes conformationally so as to relax the energy cost of the imposed twist; this deracemization, in turn, has an entropic energy cost. The result was a small enantiomer excess in the bulk nematic, but which was insufficient to produce the e c magnitudes observed. However, because of the competition between the twist elasticity, which promotes a uniform director profile through the cell, and the surface anchoring energy, which promotes a surface orientation along the easy axes, there is an equilibrium deviation θ of the director at the surfaces from the two easy axes. In a pure (undoped) achiral

, this results in a very sharp twist, i.e., a very tight effective helical pitch, within a few molecular widths of the surface. It is this tight pitch that causes a much larger deracemization in the vicinity of the surface, sufficient to give rise to the observed electroclinic response. But if the is doped with an appropriate concentration of chiral agent, as is the case presented herein, θ would be smaller, zero, or even change sign, the latter resulting in a sign change of the electroclinic effect. From Ref. 6 one can show that the form of the electroclinic coefficient due to deracemization at the surface for a chirally-doped cell of thickness d ~ d 0 becomes c ( θ 2 π / ) /( 2 ) e d P K + Wd, (1) 0 22 where K 22 is the twist elastic constant, P is the pitch of the doped liquid crystal, and W is the azimuthal anchoring strength coefficient. Thus, in the thin regions of the cell (d < d 0 ), our chiral dopant was insufficient to completely compensate the imposed rotation angle θ 0 between the easy axes, as shown schematically in Fig. 1a. Here there remain moderately sharp twists very close to the two surfaces, having the same handedness as the bulk twist. This surface twist is smaller than in an undoped cell, and thus the observed electroclinic effect is smaller than that in Ref. 6. Then, from Eq. 1, we see that the dopant-induced bulk pitch P exactly matches the imposed pitch at one particular thickness d0 = θ0 P/2π, and no sharp twist occurs at the surfaces; see Fig. 1b. To be sure, the bulk remains twisted and, in principle, causes an electroclinic effect, but e c is too small to measure because of this long bulk pitch. In thicker regions of the cell (d > d 0 ) the bulk pitch P remains unchanged, but the director overshoots the easy axes, as shown in Fig. 1c As a result θ changes sign, with a tight surface twist having a handedness opposite that of the bulk. Thus the electroclinic effect also changes sign and increases in magnitude with increasing d (Eq. 1). Overall, two important results arise from Figs. 2 and 3. First, the observed electroclinic effect clearly must be a surface phenomenon. As noted

in Ref. 6 and as seen in Fig. 3, the rapid decrease of e c with increasing frequency suggests that the electric field drives the electroclinic behavior at the surface, and the surface director rotation propagates slowly into the bulk via elastic effects. That e c changes sign in the doped sample as the thickness passes d 0 conclusively demonstrates that the observed electrooptic effect is due to a tight twist localized near the surface for d d 0. But perhaps more importantly, these results show that a significant chiral electrooptic signature should exist in every nematic twist cell that is not completely pitch compensated. Although the bulk exhibits chiral symmetry in all twist cells, the bulk twist generally is insufficient to produce an observable effect; the sharp twist at the surface, however, is easily observable. The observed electrooptic response, which may be an unwanted artifact in certain situations, has a silver lining: It can be exploited as a method to extract the helical twisting power of a chiral dopant in a liquid crystal, especially negative dielectric anisotropy liquid crystals. Here the HTP is defined as (Pc) -1. The average thickness d 0 for which e c = 0 corresponds to an average pitch P = 2 πd0 / θ0 = (86 ± 2) µm for our sample, from which we obtain HTP = (8.1 ± 0.4) µm -1. We compared this result to an alternative approach for measuring the helical pitch proposed by Raynes [12]. We prepared a 90 o planar twist cell using 10 µm spacer beads and filled the cell with a c = (0.00031 ± 0.00002) CB15 mixture in 9OO4. Both left and right-handed twist domains appeared in the cell, with domain walls terminating at the spacer beads (Fig. 4). Because the right-handed domains are favored due to the CB15 additive, the domain walls have curvature radius R. Raynes showed that the pitch P = 2R within the context of a single elastic constant and the neglect of pretilt [12]. Using polarized photomicrographs (Fig. 4) we obtained R = (174 ± 8) µm, corresponding to a pitch P = (348 ± 16) µm and an HTP = (9.3 ± 1.1) µm -1. This is in reasonable agreement with our value of HTP

obtained above, but without the approximations needed by Raynes approach. As an aside, we note that the measurement of the HTP via the surface electroclinic effect requires only a measurement of the gap d between the alignment layers, without having to account for the voltage drop across these layers. The magnitudes of e c would be slightly in error, but their zero crossings would still occur at d 0, if one were not to use a correction for the voltage drop due to the alignment layers. To summarize, we have shown that the electroclinic effect in a nematic twist cell is due to the highly twisted environment very close to the surfaces and that this measurable electrooptic effect should occur in all non-pitch-compensated twist cells containing molecules that can be conformationally deracemized. Finally, what might be considered an unwanted artifact in some contexts can be used as an accurate method to determine the helical twisting power of a chiral dopant. Acknowledgments: We thank Alberta Ferrarini, Rajratan Basu, and Hiroshi Yokoyama for useful discussions. The data collection and analysis were supported by the U.S. Department of Energy s Materials Chemistry Program under Grant No. DE-FG02-01ER45934, the experimental construction, computer interfacing, and software development by the National Science Foundation s Condensed Matter Physics and Solid State and Materials Chemistry Programs under grant DMR-1065491, and the chemical synthesis by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.

Figures 1. Schematic representation of experiment. The easy axes are rotated by θ 0 = 20 o respect to each other. For d < d 0 (panel a) the chirally doped liquid crystal rotates through the bulk of the cell (solid blue molecules ), but there is a sharp right-handed twist by angle θ over a very narrow region of a few molecules (orange, with stripes) near the surfaces. For d = d 0 (panel b) the bulk helical rotation is equal to θ 0 and therefore θ = 0. For d > d 0 (panel c) the bulk helical rotation overshoots the easy axes, and there is a sharp lefthanded twist by angle θ over a few molecules (green, with stripes) near the surfaces. 2. I ac / 4I dc measured at seven different gap thicknesses d, vs. the rms voltage at f = 1000 Hz applied across the entire cell. 3. The electroclinic coefficient e c vs. the cell gap d at four different frequencies. The horizontal line corresponds to the zero crossing of e c. Typical error bars are shown. 4. Polarized micrograph of disclination lines running between the 10 µm spacers in a 90 o nematic twist cell of 9OO4 doped with c = 0.00031 weight-fraction CB15.

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Easy axis θ 0 d < d 0 θ d > d 0 a Rotate Right b c Rotate Left

1.0 0.5 7.6 m 6.4 m 5.8 m I ac / 4I dc 0.0-0.5-1.0 5.0 m 4.2 m 3.7 m 3.3 m -1.5 0 1 2 3 4 5 6 V rms

30 e c (rad m V-1 ) 20 10 0-10 31 Hz 100 Hz 310 Hz 1000 Hz -20 3 4 5 6 7 8 Cell width d ( m)