This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous results in liquid-crystal physics, including: (1) free energy balance between cholesteric and blue phases, (2) director deformations in hybrid-aligned nematic cells, (3) spontaneous twist of achiral liquid crystals confined in a torus or cylinder, and (4) curvature of smectic layers.
Liquid Crystals Reviews
Taylor and Francis
Selinger, J. (2018). Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals. Liquid Crystals Reviews. https://doi.org/10.1080/21680396.2019.1581103
Selinger, Jonathan. 2018. “Interpretation of Saddle-Splay and the Oseen-Frank Free Energy in Liquid Crystals”. Liquid Crystals Reviews. https://doi.org/10.1080/21680396.2019.1581103.
Selinger, J. Interpretation of Saddle-Splay and the Oseen-Frank Free Energy in Liquid Crystals. Liquid Crystals Reviews, 2018, doi:10.1080/21680396.2019.1581103.