Liquid crystals are condensed-matter systems that exhibit phases with orientational order of constituent anisotropic molecules while retaining partial fluidity characteristic of liquids. Depending on molecular organization and symmetry, they form distinct mesophases such as nematic, smectic, and cholesteric, each defined by specific order parameters and broken symmetries. Their physical behavior is governed by elastic continuum theories (e.g., Frank–Oseen) and coupling between director fields, flow, and external fields (electric, magnetic). Liquid crystals display anisotropic optical, dielectric, and rheological properties, enabling controllable phase transitions and defect structures that are central to both fundamental studies of soft matter and engineered photonic or electro-optic systems.
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