Dielectric relaxation and memory effects in nematic liquid crystals

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Liquid crystals are fluids with anisotropic dielectric properties. Since the 1930s, when dielectric anisotropy was shown by Frederiks and Tsvetkov to cause director reorientation in an applied electric field, deepening our understanding of this property has been a leading theme in the development of liquid crystal science that culminated in the modern liquid crystal displays revolution. Saupe contributed greatly to the field by first co-authoring the molecular statistical theory of the nematic order, and then using it to explain how the nematic order affects dielectric relaxation in liquid crystals, i.e., how the components of the dielectric tensor depend on the frequency of the applied electric field. We review recent developments in the field associated with the finite rate of the dielectric relaxation, which results in a time lag of the electric displacement as compared with the instantaneous value of the electric field. This time lag causes profound effects on director reorientation when the characteristic time of the field change is close to (or smaller than) the dielectric relaxation time. We review recent experimental and theoretical works that link dielectric relaxation in nematic liquid crystals to the dynamics of the director and dielectric heating, and illustrate how the dielectric memory effect features in electro-optics of these materials.