A nematic liquid crystal

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Order, broken symmetry and collective behaviour · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Nematic order and the isotropic-nematic transition

Problem

A nematic liquid crystal, compound X, clears to the isotropic phase at TNI=320.0 KT_{\rm NI} = 320.0\,\mathrm{K}. Just above TNIT_{\rm NI} the isotropic liquid still shows magnetically induced (Cotton-Mouton) birefringence Δn\Delta n, which the Landau-de Gennes quadratic term predicts should follow Δn=k/(T−T∗)\Delta n = k/(T - T^*) for some constant kk and supercooling limit T∗T^*. Measurements give Δn=2.50×10−5\Delta n = 2.50\times10^{-5} at T=321.0 KT = 321.0\,\mathrm{K} and Δn=1.25×10−5\Delta n = 1.25\times10^{-5} at T=323.0 KT = 323.0\,\mathrm{K}. ((a)) Find T∗T^*. ((b)) Predict Δn\Delta n at T=322.0 KT = 322.0\,\mathrm{K}.

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