Effect of surface viscosity, anchoring energy, and cell gap on the response time of nematic liquid crystals

• The relaxation of nematic liquid crystals is calculated by taking the surface viscosity into account.
• An analytical expression for the relaxation time depending on surface viscosity, anchoring strength and cell gap is obtained.
• The results are numerically verified.
• Surface viscosity is crucial for thin and weak anchored cells.
• The effect on optical time and pretilt angle is also studied.

An analytical expression for the relaxation time of a nematic liquid crystal is obtained for the first time by considering the influence of surface viscosity, anchoring energy strength and cell gap, validated numerically by using the so-called relaxation method. This general equation for the molecular response time (τ0τ0) was derived for a vertical aligned cell and by solving an eigenvalue equation coming from the usual balance of torque equation in the Derzhanskii and Petrov formulation, recovering the usual equations in the appropriate limit. The results show that τ∼dbτ∼db, where b=2b=2 is observed only for strongly anchored cells, while for moderate to weak anchored cells, the exponent lies between 1 and 2, depending on both, surface viscosity and anchoring strength. We found that the surface viscosity is important when calculating the response time, specially for thin cells, critical for liquid crystal devices. The surface viscosity’s effect on the optical response time with pretilt is also explored. Our results bring new insights about the role of surface viscosity and its effects in applied physics.