An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter
Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor order parameter Q , and shown to decompose as a dyad involving the tangent vector to the disclination line and the rotation vector. Further, we derive a kinematic law for the velocity of disclination lines by connecting this tensor to a topological charge density as in the Halperin-Mazenko description of defects in vector models. Using this framework, analytical predictions for the velocity of interacting line disclinations and of self-annihilating disclination loops are given and confirmed through numerical computation.
more »
« less
- Award ID(s):
- 1838977
- NSF-PAR ID:
- 10380829
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 18
- Issue:
- 11
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 2234 to 2244
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for , analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity. -
null (Ed.)In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble +1/2 or −1/2 defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach–Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.more » « less
-
We study numerically the reconfiguration process of colliding m=1/2 strength disclinations in an achiral nematic liquid crystal (NLC). A Landau–de Gennes approach in terms of tensor nematic-order parameters is used. Initially, different pairs m1,m2 of parallel wedge disclination lines connecting opposite substrates confining the NLC in a plane-parallel cell of a thickness h are imposed: {1/2,1/2}, {−1/2,−1/2} and {−1/2,1/2}. The collisions are imposed by the relative rotation of the azimuthal angle θ of the substrates that strongly pin the defect end points. Pairs {1/2,1/2} and {−1/2,−1/2} “rewire” at the critical angle θc1=3π4 in all cases studied. On the other hand, two qualitatively different scenarios are observed for {−1/2,1/2}. In the thinner film regime hmore » « less
-
A substrate was patterned with two pairs of half-integer strength topological defects, (+½, +½) and (+½, −½). In a sufficiently thick cell, a disclination line runs in an arch above the substrate connecting the two half integer defects within each pair. The director around the disclination line for the like-sign pair must rotate in 3D, whereas for the opposite-sign defect pair the director lies in the xy-plane parallel to the substrate. For a negative dielectric anisotropy nematic, an electric field applied normal to the substrate drives the director into the xy-plane, forcing the arch of the disclination line of the like-sign pair to become extended along the z-axis. For sufficiently large field the arch splits, resulting in two nearly parallel disclination lines traversing the cell from one substrate to the other. The opposite-sign defect pair is largely unaffected by the electric field as the director already already lies in the xy-plane. Experimental results are presented, which are consistent with numerical simulations.more » « less
-
An escaped radial director profile in a nematic liquid crystal cell can be transformed into a pair of strength m = +1/2 surface defects (and their associated disclination lines) at a threshold electric field. Analogously, a half-integer defect pair can be transformed at a threshold electric field into a director profile that escapes into the third dimension. These transitions were demonstrated experimentally and numerically, and are discussed in terms of topologically discontinuous and continuous pathways that connect the two states. Additionally, we note that the pair of disclination lines associated with the m = +1/2 surface defects were observed to co-rotate around a common point for a sufficiently large electric field at a sufficiently low frequency.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D1SM01584B
