Explain homeotropic anchoring for negative anisotropic elasticity

Explain why the homeotropic anchoring condition is favored at the isotropic–nematic interface in the Landau–de Gennes Q-tensor model when the anisotropic elastic constant L_2 is negative.

Background

The paper compares the Landau–de Gennes Q-tensor theory with vectorial models of the isotropic–nematic interface. In vectorial theories, the order-parameter and director modes can often be separated, and interfacial terms involving the normal or tangential components of the director directly yield homeotropic or tangential anchoring conditions.

For the Landau–de Gennes theory, biaxiality near the phase-transition interface prevents an equally direct reduction. Although the paper introduces a div–curl decomposition and proves the asymptotic surface tension and homeotropic boundary condition for L_2<0, the authors explicitly identify the underlying mechanism producing this anchoring preference as unclear.