‘Nemator’ Model of Orientational Distortions in Liquid Crystals with Defects*

The Oseen-Frank (OF) and Landau-de Gennes (LdG) models of liquid crystals (LCs) are classical tools for analysis and simulations of static and dynamic orientational distortions.
In this work, we present a model of distortions in uniaxial nematic LCs, which unites the advantages of OF and LdG models. We define the distortion field by the vector N, which we call ‘nemator’. Nemator N=s^1/2n brings together the features of director n and uniaxial order parameter s. We derive the free energy density f_N=f_u(s)+f_g(S_ij,S_ij,k) as a function of the dyadic tensor S_ij=N_iN_j and its spatial derivatives S_ij,k=∂S_ij/∂x_k. The uniform term f_u(s) depends on the invariant TrS=N^.N=s and the gradient term f_g(S_ij,S_ij,k) contains a complete set of nine elastic terms with the corresponding elastic moduli M_α(s). We obtain the relations between M_α(s) and the OF (K_β) and LdG (L_γ) moduli.
Advancing the OF model, the nemator model considers the spatial inhomogeneity of s and does not create a singularity when N flips, N→-N, allowing simulations of semi-integer disclinations and other defects. And the nemator free energy is valid in the entire temperature range of nematic phase, because it is not a polynomial expansion like the LdG model.