^{1,a)}, V. T. Tondiglia

^{1}, L. V. Natarajan

^{1}, R. Bricker

^{2}, Y. Cui

^{3}, D. K. Yang

^{3}and T. J. Bunning

^{2}

### Abstract

Recent work on negative dielectricanisotropy cholesteric liquid crystals (CLCs) showed that externally applied dc voltages resulted in blue tuning of the reflection band position up to 20% of its original position. These results also showed that the observed shift in reflection band position was not caused by a direct interaction between the CLC and the applied voltage, but indirectly through electromechanical stresses that deformed the conductive glass substrates, in turn deforming the liquid crystal. In this work, the goal is to clarify that the major limiting factors on the tuning range limit result from the magnitude of the surface anchoring energy and surface induced hysteresis effects. An analytic solution for the tuning range limit and its dependence on the surface and bulk properties is derived that agrees well with the experimental data. Using this model, it was shown that tuning range limits in excess of 35% of the notch position should be expected with typically available alignment materials, and that with proper CLC/surface optimizations, values in the range of 75% are possible.

Special thanks are extended for financial support to the Air Force Office of Scientific Research (AFOSR) and the National Research Council (NRC).

I. INTRODUCTION

II. MATERIALS AND METHODS

A. Anchoring energy measurements

B. Tuning range limit experiments

III. EXPERIMENTAL RESULTS

IV. DISCUSSION

A. Theoretical description of surface anchoring energy on the tuning limit

### Key Topics

- Liquid crystals
- 8.0
- Anisotropy
- 7.0
- Dielectric thin films
- 7.0
- Elasticity
- 7.0
- Free energy
- 7.0

##### C09K19/00

## Figures

(Color online) (a) The typical cell configuration for electromechanical tuning of −Δɛ CLC including the following important parameters such as the cell gap thickness (g), the unglued region spacing (L), the rubbing direction, and the tuning region (dashed circle) where the maximum tuning occurs. The director configuration for a CLC confined between anti-parallel rubbed Elvamide with rubbing directions along the dashed arrows. Due to the finite surface energy the orientation of the director may differ from that of the rubbing direction by (± θ/2). (b) The electromechanical tuning mechanism shown near the tuning region where distortions of g occur under applied voltages resulting in distortions of the pitch.

(Color online) (a) The typical cell configuration for electromechanical tuning of −Δɛ CLC including the following important parameters such as the cell gap thickness (g), the unglued region spacing (L), the rubbing direction, and the tuning region (dashed circle) where the maximum tuning occurs. The director configuration for a CLC confined between anti-parallel rubbed Elvamide with rubbing directions along the dashed arrows. Due to the finite surface energy the orientation of the director may differ from that of the rubbing direction by (± θ/2). (b) The electromechanical tuning mechanism shown near the tuning region where distortions of g occur under applied voltages resulting in distortions of the pitch.

(Color online) (a) The experimental setup used to measure the twist angle, θ, in a long pitch cholesteric sample. (b) Numerical calculations for the transmitted intensity for a cholesteric with a twist angle θ = 30° at various retardation values Г = 2πΔnd/λ as a function of the analyzer angle α. (c) A graph of the minimum intensity (I_{min}) vs the analyzer angle at the minimum (α_{min}) for different values of Г along with a parabolic fit.

(Color online) (a) The experimental setup used to measure the twist angle, θ, in a long pitch cholesteric sample. (b) Numerical calculations for the transmitted intensity for a cholesteric with a twist angle θ = 30° at various retardation values Г = 2πΔnd/λ as a function of the analyzer angle α. (c) A graph of the minimum intensity (I_{min}) vs the analyzer angle at the minimum (α_{min}) for different values of Г along with a parabolic fit.

(Color online) (a) Example transmission spectra for a CLC at 0 V with a rubbing number of 13 along with the locations of their band edges (vertical lines) as determined by the analysis software. (b) A plot of the band edges identified as the high energy (short wavelength) and low energy (long wavelength), and their average (notch position) as a function of applied voltage. The dashed vertical line in this graph identifies the tuning limit. (c) The voltage dependence on the notch position as the voltage is cycled from 0-190 V (blue), then 190-(−190 V) (red), and finally from (−190)-190 V (black).

(Color online) (a) Example transmission spectra for a CLC at 0 V with a rubbing number of 13 along with the locations of their band edges (vertical lines) as determined by the analysis software. (b) A plot of the band edges identified as the high energy (short wavelength) and low energy (long wavelength), and their average (notch position) as a function of applied voltage. The dashed vertical line in this graph identifies the tuning limit. (c) The voltage dependence on the notch position as the voltage is cycled from 0-190 V (blue), then 190-(−190 V) (red), and finally from (−190)-190 V (black).

(Color online) Experimentally obtained tuning range limit vs notch position for multiple 5 *μ*m cells. Using the tuning range limit model to fit the tuning range limit data (solid curve), an extrapolation length L_{e} = 0.76 ± 0.05 μm was obtained resulting in an anchoring energy W_{θ} = 13 *μ*J/m^{2} assuming that K_{22} = 10 pN. Also shown are curves having different anchoring strengths with values of 50 μJ/m^{2} (dotted) and 330 μJ/m^{2} (dashed-dotted), along their predicted tuning range limits at 1500 nm that shows significant increases with higher anchoring energy.

(Color online) Experimentally obtained tuning range limit vs notch position for multiple 5 *μ*m cells. Using the tuning range limit model to fit the tuning range limit data (solid curve), an extrapolation length L_{e} = 0.76 ± 0.05 μm was obtained resulting in an anchoring energy W_{θ} = 13 *μ*J/m^{2} assuming that K_{22} = 10 pN. Also shown are curves having different anchoring strengths with values of 50 μJ/m^{2} (dotted) and 330 μJ/m^{2} (dashed-dotted), along their predicted tuning range limits at 1500 nm that shows significant increases with higher anchoring energy.

(Color online) The measured anchoring energy W_{θ} between E44 and Elvamide (circles–left axis) and the measured tuning range limit for ZLI-4788 with Elvamide (squares–right axis) as a function of the rubbing number. The solid curve is a guide to show the general trend of the data and is not theoretically determined. For the tuning experiments, the notch position λ_{n} ranged between 620 and 623 nm.

(Color online) The measured anchoring energy W_{θ} between E44 and Elvamide (circles–left axis) and the measured tuning range limit for ZLI-4788 with Elvamide (squares–right axis) as a function of the rubbing number. The solid curve is a guide to show the general trend of the data and is not theoretically determined. For the tuning experiments, the notch position λ_{n} ranged between 620 and 623 nm.

(Color online) (a) A graphical interpretation of the free energy per area and possible solutions to the free energy for weak and strong anchoring. (b) The maximum strain (u_{max}) as a function of the number of half pitches for a cholesteric using the analytic model for various values of πL_{e}/g. (c) A comparison of the analytical model to numerical results obtained for the same equation for a 10 *μ*m cell, K_{22} = 10 pN, and the anchoring energies described in the legend.

(Color online) (a) A graphical interpretation of the free energy per area and possible solutions to the free energy for weak and strong anchoring. (b) The maximum strain (u_{max}) as a function of the number of half pitches for a cholesteric using the analytic model for various values of πL_{e}/g. (c) A comparison of the analytical model to numerical results obtained for the same equation for a 10 *μ*m cell, K_{22} = 10 pN, and the anchoring energies described in the legend.

## Tables

Experimental results from the anchoring strength measurements using Elvamide.

Experimental results from the anchoring strength measurements using Elvamide.

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