‘Nemator’ Model of Orientational Distortions in Liquid Crystals with Defects
ORAL
Abstract
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=s1/2n brings together the features of director n and uniaxial order parameter s. We derive the free energy density fN=fu(s)+fg(Sij,Sij,k) as a function of the dyadic tensor Sij=NiNj and its spatial derivatives Sij,k=∂Sij/∂xk. The uniform term fu(s) depends on the invariant TrS=N.N=s and the gradient term fg(Sij,Sij,k) contains a complete set of nine elastic terms with the corresponding elastic moduli Mα(s). We obtain the relations between Mα(s) and the OF (Kβ) and LdG (Lγ) 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.
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=s1/2n brings together the features of director n and uniaxial order parameter s. We derive the free energy density fN=fu(s)+fg(Sij,Sij,k) as a function of the dyadic tensor Sij=NiNj and its spatial derivatives Sij,k=∂Sij/∂xk. The uniform term fu(s) depends on the invariant TrS=N.N=s and the gradient term fg(Sij,Sij,k) contains a complete set of nine elastic terms with the corresponding elastic moduli Mα(s). We obtain the relations between Mα(s) and the OF (Kβ) and LdG (Lγ) 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.
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Presenters
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Sergij Shiyanovskii
Liquid Crystal Insitute, Kent State University
Authors
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Natalie Aryasova
Institute of Physics NASU
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Sergij Shiyanovskii
Liquid Crystal Insitute, Kent State University