Nonlinear nematic elasticity

2019

Phys. Rev. E

Ordinary nematic liquid crystals are characterized by having a uniform director field as ground state. In such a state, the director is the same everywhere and no distortion is to be seen at all. We give a definition of uniform distortion which makes precise the intuitive notion of seeing everywhere the same director landscape. We characterize all such distortions and prove that they fall into two families, each described by two scalar parameters. Uniform distortions exhaust R. Meyer's heliconical structures, which, as it has recently been recognized, include the ground state of twistbend nematics. The generalized elasticity of these new phases is treated with a simple free-energy density, which can be minimized by both uniform and non-uniform distortions, the latter injecting a germ of elastic frustration.

Section: B Compatibility Conditionsmentioning

confidence: 99%

Section: B Compatibility Conditionsmentioning

confidence: 99%

“…where c 1 and c 2 are as in (11) and the components of d in the frame (n 1 , n 2 , n) are to be given by (16). Clearly, the tensor in (20a) is already symmetric.…”

Section: B Compatibility Conditionsmentioning

confidence: 99%

Section: Fig 2: (Color Online)mentioning

confidence: 99%

See 2 more Smart Citations

Uniform distortions and generalized elasticity of liquid crystals

2019

Phys. Rev. E

“…where K 11 , K 22 , K 33 , and K 24 are the splay, twist, bend, and saddle-splay constants, respectively, each associated with a corresponding elastic mode. 1 The decomposition of F in independent elastic modes proposed in [10] is achieved through a new decomposition of ∇n.…”

Section: Introductionmentioning

confidence: 99%

Liquid crystal distortions revealed by an octupolar tensor

Pedrini

2020

Phys. Rev. E

The classical theory of liquid crystal elasticity as formulated by Oseen and Frank describes the (orientable) optic axis of these soft materials by a director n. The ground state is attained when n is uniform in space; all other states, which have a non-vanishing gradient ∇n, are distorted. This paper proposes an algebraic (and geometric) way to describe the local distortion of a liquid crystal by constructing from n and ∇n a third-rank, symmetric and traceless tensor A (the octupolar tensor). The (nonlinear) eigenvectors of A associated with the local maxima of its cubic form Φ on the unit sphere (its octupolar potential ) designate the directions of distortion concentration. The octupolar potential is illustrated geometrically and its symmetries are charted in the space of distortion characteristics, so as to educate the eye to capture the dominating elastic modes. Special distortions are studied, which have everywhere either the same octupolar potential or one with the same shape, but differently inflated. * andrea.pedrini@unipv.it † eg.virga@unipv.it arXiv:1911.03333v1 [cond-mat.soft]

An Elastic Quartic Twist Theory for Chromonic Liquid Crystals

Paparini

2023

J Elast

Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length "Equation missing" in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate "Equation missing".