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In this work, we study the nematic-isotropic phase transition based on thedynamics of the Landau--De Gennes theory of liquid crystals. At the criticaltemperature, the Landau--De Gennes bulk potential favors the isotropic phaseand nematic phase equally. When the elastic coefficient is much smaller thanthat of the bulk potential, a scaling limit can be derived by formal asymptoticexpansions: the solution gradient concentrates on a closed surface evolving bymean curvature flow. Moreover, on one side of the surface the solution tends tothe nematic phase which is governed by the harmonic map heat flow into thesphere while on the other side, it tends to the isotropic phase. To rigorouslyjustify such a scaling limit, we prove a convergence result by combining weakconvergence methods and the modulated energy method. Our proof applies as longas the limiting mean curvature flow remains smooth.

Nematic-Isotropic phase transition in Liquid crystals: a variational derivation of effective geometric motions