Order reconstruction in frustrated nematic twist cells

Area of Science:

• Condensed Matter Physics
• Soft Matter Physics
• Materials Science

Background:

• Liquid crystals exhibit complex equilibrium configurations influenced by boundary conditions.
• The Landau-de Gennes theory provides a framework for understanding liquid crystal behavior, particularly order tensor dynamics.

Purpose of the Study:

• To investigate equilibrium configurations of nematic liquid crystal cells with twist boundary conditions.
• To identify and classify different solution classes within the Landau-de Gennes theory.
• To analyze the stability and energy minimization properties of these configurations.

Main Methods:

• Application of the Landau-de Gennes theory to a nematic cell model.
• Mathematical analysis of equilibrium equations under uniaxial boundary conditions.
• Identification of critical distances and stability analysis of different solution branches.

Main Results:

• Three distinct classes of solutions were identified: a globally energy-minimizing twistlike solution, metastable twistlike solutions, and unstable exchangelike solutions.
• The twistlike solution exists for all cell distances, while the other two emerge above a critical distance d(c).
• The special case of a pi/2 boundary twist leads to a continuous transition from twistlike to exchangelike solutions at d(c).

Conclusions:

• The study reveals a rich phase diagram of nematic liquid crystal configurations dependent on cell thickness and boundary twist.
• The critical distance d(c) is related to biaxial coherence lengths, indicating the importance of biaxiality in these transitions.
• Perturbing boundary conditions can unfold classical bifurcations, offering insights into controlling liquid crystal behavior.