Pattern Formation in Electrohydrodynamic Convection

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Abstract
One hundred years after their discovery, we meet liquid crystals everywhere in our daily life. Their most widely known application is the liquid crystal displays (LCDs) in watches, pocket calculators, or gasoline pumps. Applications aside, liquid crystals show many exciting properties, making them highly interesting for fundamental research. For example, electrohydrodynamic convection (EHC) in nematic liquid crystals, which is studied in cells of a configuration similar to liquid crystal displays, serves with its characteristic properties as a model System for investigating central questions of pattern formation and chaos.Today's liquid crystal displays work on the principle described in 1971 by Martin Schadt and Wolfgang Helfrich (Figure 1). In nematic liquid crystals, organic molecules orient on average along a macroscopic direction, described by the director field n(r), that has neither head nor tail (n = −n). Nematics are therefore anisotropic and for energetic reasons, n(r) orients parallel (perpendicular) to an electric field when the dielectric permittivity (ε∥) along n is larger (smaller) than the perpendicular (ε⊦ one. For positive εa = ε∥ − ε⊦, when an electric field is applied perpendicular to the direction of n, a reorientation of n takes place together with a corresponding change in the optical property of the cell. The controlled change by an electric field in the optic axis (orientation) in well-defined areas of the display then allows the representation of numbers, etc.