1,721,072 research outputs found
New variational problems in the statics of liquid crystals
No full textVirga, Epifanio G.. (1990). New variational problems in the statics of liquid crystals. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1476
Uniform distortions and generalized elasticity of liquid crystals
No full textOrdinary 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 twist-bend nematics. The generalized elasticity of these new phases is treated with a simple free-energy density, which can be minimized by both uniform and nonuniform distortions, the latter injecting a germ of elastic frustration
Relieving nematic geometric frustration in the plane
Full text linkFrustration in nematic-ordered media (endowed with a director field) is
treated in a purely geometric fashion in a flat, two-dimensional space. We
recall the definition of quasi-uniform distortions and envision these as viable
ways to relieve director fields prescribed on either a straight line or the
unit circle. We prove that using a planar spiral is the only way to fill the
whole plane with a quasi-uniform distortion. Apart from that, all relieving
quasi-uniform distortions can at most be defined in a half-plane; however, in a
generic sense, they are all asymptotically spirals
Ericksen’s Secret Influence
No full textSometimes, even a cursory remark at the end of a lecture, if growing out of deep intelligence and directed to a sensitive mind, can have momentous consequences. This was the case in the episode recounted here, which linked Ericksen and de Gennes, albeit indirectly
Axis-symmetric boundary-value problems for nematic liquid crystals with variable degree of orientation
No full textTortorelli, Vincenzo M.; Virga, Epifanio G.. (1991). Axis-symmetric boundary-value problems for nematic liquid crystals with variable degree of orientation. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1548
Ridge approximation for thin nematic polymer networks
No full textNematic polymer networks (NPNs) are nematic elastomers within which the nematic director is enslaved to the elastic deformation. The elastic free energy of a NPN sheet of thickness h has both stretching and bending components (the former scaling like h, the latter scaling like h3). NPN sheets bear a director field m imprinted in them (usually, uniformly throughout their thickness); they can be activated by changing the nematic order (e.g., by illumination or heating). This paper illustrates an attempt to compute the bending energy of a NPN sheet and to show which role it can play in determining the activated shape. Our approach is approximate: the activated surface consists of flat sectors connected by ridges, where the unit normal jumps and the bending energy is concentrated. By increasing the number of ridges, we should get closer to the real situation, where the activated surface is smooth and the bending energy is distributed on it. The method is applied to a disk with imprinted a spiraling planar hedgehog. It is shown that upon activation the disk, like a tiny hand, is able to grab a rigid lamina
Nematic tactoid population
No full textTactoids are pointed, spindlelike droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a special class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primarily among them). We show how the prevalence of a shape is affected by a dimensionless measure α of the drop’s volume and the ratios k24 and k3 of the saddle-splay constant K24 and the bending constant K33 of the material to the splay constant K11. Tactoids, in particular, prevail for α < 16.2 + 0.3k3 − (14.9 − 0.1k3 )k24 . Our class of shapes (and director fields) is sufficiently different from those employed so far to unveil a rather different role of K24
A review on octupolar tensors
No full textIn its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential, a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review
Paradoxes for Chromonic Liquid Crystal Droplets
No full textChromonic liquid crystals constitute a novel lyotropic phase, whose elastic
properties have so far been modeled within the classical Oseen-Frank theory,
provided that the twist constant is assumed to be considerably smaller than the
saddle-splay constant, in violation of one Ericksen inequality. This paper
shows that paradoxical consequences follow from such a violation for droplets
of these materials surrounded by an isotropic fluid. For example, tactoids with
a degenerate planar anchoring simply disintegrate indefinitely in myriads of
smaller ones
Instability of toroidal nematics
No full textToroidal nematics are nematic liquid crystals confined within a circular torus and subject to planar degenerate anchoring on the boundary of the torus. They may be droplets floating in an isotropic environment or cavities carved out of a solid substrate. A universal solution of Frank’s elastic free energy is an equilibrium configuration for the nematic director field, irrespective of the values of the elastic constants, whose vector lines are the coaxial parallels of the torus. We explore the local stability of this configuration and identify a range of parameters where the main drive towards instability does not come from the surface-like elastic constant K24 being large, but from the ratio K2/K3 of the twist to bend elastic constants being small, which also makes our study relevant to chromonic liquid crystals
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