Equilibrium of nematic vesicles

Napoli, Gaetano; Vergori, Luigi

doi:10.1088/1751-8113/43/44/445207

Cited by 30 publications

(50 citation statements)

References 39 publications

(69 reference statements)

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“…Using the new framework for nematic membranes, the emergence of topological forces between defects could be further analyzed beyond classical approaches [4,[23][24][25][26]. The geometric couplings pointed out configure a counterbalance between membrane elasticity and underlying nematic ordering, which gives rise to the distributions of membrane stresses in dependence with the relative contribution of each material interaction [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

2019

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An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are visualized on the sphere and on cylindrical surfaces.

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Section: Introductionmentioning

confidence: 99%

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

2019

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“…the proof of which is contained in Appendix A of [13]. As a consequence (38c), (40b), (49) and the symmetry of the extrinsic curvature tensor L, we have div s (Lt) = div s L · t + L · ∇ s t (50) = 2∇ s H · t − Ln · (∇ s α − ω).…”

Section: B Derivation Of the Equilibrium Equationsmentioning

confidence: 93%

Influence of the extrinsic curvature on two-dimensional nematic films

Napoli

Vergori

2018

Phys. Rev. E

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Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

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“…The nematic texture with defects determines how the stress is distributed along the membrane. The stress tensor has been calculated in several different ways: in [7] and using a variational principle the authors find it in the case of fluid membranes; in [8] and using an elegant and general geometric formalism, the authors find this tensor for very general schemes that can be applied to the relevant case of elastic membranes coated with nematic textures; in [9] the author finds the stress tensor of the bending energy, examining deformations respect to a flat membrane. Remarkably, in [10] the author finds this tensor in a novel way by using auxiliary variables, avoiding the tedious calculations of deforming the geometric objects involved.…”

Section: Introductionmentioning

confidence: 99%

Stresses in curved nematic membranes

Santiago

2018

Phys. Rev. E

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Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

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Equilibrium of nematic vesicles

Cited by 30 publications

References 39 publications

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints

Influence of the extrinsic curvature on two-dimensional nematic films

Stresses in curved nematic membranes

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