Refinement of boundary conditions for nematic liquid crystals in the one-constant approximation

2017 ◽  
Vol 72 (6) ◽  
pp. 150-152
Author(s):  
A. G. Kalugin
Crystals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 138 ◽  
Author(s):  
Jordi Ignés-Mullol ◽  
Marc Mora ◽  
Berta Martínez-Prat ◽  
Ignasi Vélez-Cerón ◽  
R. Santiago Herrera ◽  
...  

Spherical confinement of nematic liquid crystals leads to the formation of equilibrium director field configurations that include point and line defects. Driving these materials with flows or dynamic fields often results in the formation of alternative metastable states. In this article, we study the effect of magnetic field alignment, both under static and dynamic conditions, of nematic gems (nematic droplets in coexistence with the isotropic phase) and emulsified nematic droplets of a lyotropic chromonic liquid crystal. We use a custom polarizing optical microscopy assembly that incorporates a permanent magnet whose strength and orientation can be dynamically changed. By comparing simulated optical patterns with microscopy images, we measure an equilibrium twisted bipolar pattern within nematic gems that is only marginally different from the one reported for emulsified droplets. Both systems evolve to concentric configurations upon application of a static magnetic field, but behave very differently when the field is rotated. While the concentric texture within the emulsified droplets is preserved and only displays asynchronous oscillations for high rotating speeds, the nematic gems transform into a metastable untwisted bipolar configuration that is memorized by the system when the field is removed. Our results demonstrate the importance of boundary conditions in determining the dynamic behavior of confined liquid crystals even for configurations that share similar equilibrium bulk structures.


2010 ◽  
Vol 20 (09) ◽  
pp. 2937-2942 ◽  
Author(s):  
B. CLIMENT-EZQUERRA ◽  
F. GUILLÉN-GONZÁLEZ ◽  
M. A. RODRÍGUEZ-BELLIDO

We study a nematic crystal model that appeared in [Liu et al., 2007], modeling stretching effects depending on the different shapes of the microscopic molecules of the material, under periodic boundary conditions. The aim of the present article is two-fold: to extend the results given in [Sun & Liu, 2009], to a model with more complete stretching terms and to obtain some stability and asymptotic stability properties for this model.


2019 ◽  
Vol 12 (4) ◽  
pp. 363-392
Author(s):  
Stuart Day ◽  
Arghir Dani Zarnescu

AbstractWe consider an energy functional motivated by the celebrated {K_{13}} problem in the Oseen–Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional surface term. It is known that this energy is unbounded from below and our aim has been to study the local minimisers. We show that even having a critical point in a suitable energy space imposes severe restrictions on the boundary conditions. Having suitable boundary conditions makes the energy functional bounded and in this case we study the partial regularity of the global minimisers.


2003 ◽  
Vol 14 (1) ◽  
pp. 39-59 ◽  
Author(s):  
PAOLO BISCARI ◽  
TIMOTHY J. SLUCKIN

We study the interactions between a nematic liquid crystal disclination and the surface of the half-space which bounds it. When strong anchoring conditions are applied on the boundary, the biaxial core of the disclination affects the repulsive force that tends to drive the disclination away from the surface. If we replace the strong boundary conditions with an anchoring potential, the surface-disclination interaction depends on the surface extrapolation length. In particular, the nematic may expel the disclination if the anchoring strength is below a critical value.


Author(s):  
C Atkinson ◽  
P.J.S Pereira

Orientational director effects in nematic liquid crystals with small Ericksen number are investigated. The director field is disturbed by a semi-infinite plate on y =0 and and moving with a constant velocity U . Strong anchoring conditions at the plate are assumed. The resulting equations are a system of nonlinear partial differential equations for a nematic in the one elastic constant approximation. These equations are reduced to a coupled set of nonlinear ordinary differential equations by a suitable transformation. No such transformation seems possible for the many elastic constant case. The resulting equations are solved using analytical methods and strict bounding solutions obtained. These strict analytical solutions are compared with Picard iterated solutions.


1992 ◽  
Vol 47 (12) ◽  
pp. 1235-1240 ◽  
Author(s):  
A. L. Alexe-Ionescu ◽  
R. Barberi ◽  
G. Barbero ◽  
T. Beica ◽  
R. Moldovan

The surface energy of nematic liquid crystals is deduced from a phenomenological point of view. The idea of an easy surface tensor order parameter is proposed. An expression similar to a Landau expansion for the free energy of a system characterized by two order parameters is deduced and analysed. An interpretation similar to the one usually accepted for magnetic materials is given. The possibility of surface transitions induced by temperature is discussed.


1994 ◽  
Vol 4 (2) ◽  
pp. 239-252 ◽  
Author(s):  
A. Hertrich ◽  
A. P. Krekhov ◽  
O. A. Scaldin

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