Coarsening dynamics of biaxial nematic liquid crystals

Nikolai V. Priezjev and Robert A. Pelcovits, Phys. Rev. E 66, 051705 (2002)

Coarsening dynamics of biaxial nematic liquid crystals is very interesting and unusual because of the nature of the topological line defects. There are four topologically distinct classes of line defects in biaxial nematics, which are disclination lines distinguished by the rotation of the long and short axes of the rectangular building particles about the core of the line. Three of these classes (which we denote as Cu, Cv and Cw) correspond to 180 degree rotations of two of the three molecular axes (see picture below), while the fourth class corresponds to a 360 degree rotation. The fundamental homotopy group of biaxial nematics is non-Abelian leading to a number of interesting consequences, e.g., the merging of two defects will depend on the path they follow, and two 180 degrees disclinations of different types will be connected by a 360 degrees "umbilical" cord after crossing each other. The latter fact is known to result in obstruction to crossing of the lines and might lead to slow kinetics of biaxial nematics. We have studied biaxial nematics using Langevin molecular dynamics on a lattice model. 

As discussed in greater detail in our paper, we carried out simulations of quenches from a completely disordered state (where many defects are present) to the zero temperature ordered state (no defects). Three distinct coarsening sequences are possible depending on the parameters of the model, which in turn determine the energies of the different types of defects. In the animation below, we consider a parameterization which favors the classes Cu  (blue lines) and Cw  (green lines) over Cv  (red lines). Note that red lines decay very rapidly and blue and green loops coarsen independently at later times. The system size is 403 and periodic boundary conditions are used so all the segments are connected to form loops. 

The most interesting and novel coarsening sequence occurs when all three elastic constants associated with the axis rotations are equal. In the animation below, we show the equilibration process for a system of size 403. Note the formation of a network of nearly equal populations of all three types of defects, which meet at a ''junction'' points. Neighboring junction points pinch together as the system coarsens, leading to the creation of nonintersecting loops which then shrink. 

It is also possible to have a coarsening sequence where only one class of defects survives until late times. In the following animation, one can see a rather quick equilibration of Cv  (red lines) and Cw  (green lines) defects, while the Cu  (blue lines) remain for a long time. 

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