Bifurcation properties of nematic liquid crystals exposed to an electric field: Switchability, bistability, and multistability

Abstract

Bistable liquid crystal displays (LCDs) offer the potential for considerable power savings compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically distinct means that contrast can be maintained in a display without an externally applied electric field. An applied field is required only to switch the device from one state to the other, as needed. In this paper we examine the basic physical principles involved in generating multiple stable states and the switching between these states. We consider a two-dimensional geometry in which variable surface anchoring conditions are used to control the steady-state solutions and explore how different anchoring conditions can influence the number and type of solutions and whether or not switching is possible between the states. We find a wide range of possible behaviors, including bistability, tristability, and tetrastability, and investigate how the solution landscape changes as the boundary conditions are tuned.

Electric-field variations within a nematic-liquid-crystal layer

“…The full time-dependent model would be extremely complicated, not to mention computationally intensive. Even with the uniform field assumption, many works [1][2][3][4]17] instead use a gradient flow model, which assumes that the system evolves always in the direction that minimizes its total free energy. In this simpler case [bulk and surface energy densities given by Eqs.…”

“…In this simpler case [bulk and surface energy densities given by Eqs. 5and 8, with φ ≡ z], this process leads to [2][3][4]17] θ t + δW δθ…”

“…Boundary conditions analogous to those specified by Eqs. (13) and 14can also be written (see [2][3][4]17]), and an initial condition θ (z,0) closes the model. With coupling to the electric field, matters are considerably more complicated.…”

“…Robust and accurate mathematical models for prototype LCDs allow simulations of hypothetical devices to be made quickly and at low cost, and this in turn can lead to new and potentially improved designs being identified. An example of this is the use of mathematical models to identify so-called bistable LCD designs [1][2][3][4][5][6]: such designs offer the potential for substantially lower power consumption as compared to traditional LCDs, with implications for battery lifetimes and portability, and possibly allowing LCD-based devices to compete with the "e-ink" technology [7] used in many e-readers.…”

Gaining Control through Frustration: Two-Fold Approach for Liquid Crystal Three-Dimensional Command Layers

“…The success of LCDs might indicate that nowadays a thorough understanding has been reached. Though this is certainly true for near-surface LC ordering on flat substrates, − a comprehensive description of the anchoring process on nanopatterned surfaces where both topography and chemistry play a competing role, such as in the new zenithal bistable displays (ZBDs), − appears still a complicated matter.…”