Visual evaluation of surface anchoring strength by electrohydrodynamic convection of a nematic liquid crystal

Visual evaluation of the surface anchoring energies in a nematic liquid crystal (LC) cell is characterized by the direction of the convection roll pattern that appears in the low-frequency conduction regime. The convection roll pattern in a twisted nematic LC (TNLC) cell is oriented perpendicular to the midplane LC director dominating the direction of convection flow, and its direction is determined by the relative surface anchoring energy between two surface boundaries. Thus the direction of the roll pattern generated at the TNLC cell with asymmetric LC alignment layers can provide information on the surface anchoring energies at the two boundaries. We demonstrate a method for determining the two anchoring energies through a measured midplane LC director applied to the Ericksen-Leslie equation.

Figure 1

Microscopic images showing typical Williams convection roll patterns taken from an asymmetric asymmetric 90°-TNLC cell of 10 μm that has strong surface anchoring at the bottom boundary (PI) and weak surface anchoring at the top boundary (PVA), under voltage and frequency of (a) 10 V and 500 Hz, (b) 25 V and 1000 Hz, and (c) 35 V and 1500 Hz. The roll direction is not changed even under a strong electric field.

Figure 2

Simulated dynamics of the director at the midplane in 90°-TNLC cells of thicknesses of 10 (a) and 20 μm (b) under an electric field of 1.5 V/μm when $A_b={10}^{-4}\mathrm{N}/\mathrm{m}$, and $A_t={10}^{-5},{10}^{-6},5\times {10}^{-7}$, and ${10}^{-7}\mathrm{N}/\mathrm{m}$, showing clearly the thickness dependence of the director. The thicker the thickness is, the smaller the angle deviated from 45° is, as expected.

Figure 3

Microscopic images of the EHC taken for a 90°-TNLC cell of 10 μm cell thickness when PI was used for the bottom surface and PVA (a) and $\mathrm{Si}{\mathrm{O}}_2$ (b) were used for the top surfaces as homogeneous LC alignment layers. ${\varphi }_f$ was 21.5° for the combination of PVA/PI and 19.0° for the combination of $\mathrm{Si}{\mathrm{O}}_2/\mathrm{PI}$. When the azimuthal anchoring energy of PI, $A_b$, is known as $3.48\times {10}^{-5}\mathrm{N}/\mathrm{m}$, the anchoring energies of PVA and $\mathrm{Si}{\mathrm{O}}_2$ corresponding to the ${\varphi }_f$ are $3.72\times {10}^{-7}$ and $3\times {10}^{-7}\mathrm{N}/\mathrm{m}$, respectively, as shown in (c).

Figure 4

Microscopic images of EHC taken for 90°-TNLC cells, with PVA/PI (a) and $\mathrm{Si}{\mathrm{O}}_2/\mathrm{PI}$ (b) of 20 μm cell thickness and with PVA/PI (c) and $\mathrm{Si}{\mathrm{O}}_2/\mathrm{PI}$ (d) of 40 μm cell thickness. (e,f) show plotting of $A_t$ with $A_b$, obtained from Eq. (4) for PVA/PI and $\mathrm{Si}{\mathrm{O}}_2/\mathrm{PI}$, respectively, when ${\varphi }_f$ is given as 29.0°, 27.0°, 35.0°, and 34.0° by (a–d), respectively. The unknown two anchoring energies are determined by the cross pointing of the two curved lines.