Order reconstruction in frustrated nematic twist cells

Abstract

Within the Landau-de Gennes theory of liquid crystals, we study the equilibrium configurations of a nematic cell with twist boundary conditions. Under the assumption that the order tensor Q be uniaxial on both bounding plates, we find three separate classes of solutions, one of which contains the absolute energy minimizer, a twistlike solution that exists for all values of the distance d between the plates. The solutions in the remaining two classes exist only if d exceeds a critical value d(c). One class consists of metastable, twistlike solutions, while the other consists of unstable, exchangelike solutions, where the eigenvalues of Q are exchanged across the cell. When d=d(c), the metastable solution relaxes back to the absolute energy minimizer, undergoing an order reconstruction somewhere within the cell. The critical distance d(c) equals, in general, a few biaxial coherence lengths. This scenario applies to all the values of the boundary twist but pi/2, which thus appears as a very special case, though it is the one more studied in the literature. In fact, when the directors prescribed on the two plates are at right angles, two symmetric twistlike solutions merge continuously into an exchangelike solution at the critical value of d where the latter becomes unstable. Our analysis shows how the classical bifurcation associated with this phenomenon is unfolded by perturbing the boundary conditions.

Order reconstruction patterns in nematic liquid crystal wells

“…We adopt the following three-dimensional parametrization of the Q-tensor order parameter, as given in [13,22]:…”

“…For example, we carry out illustrative simulations with τ = 4. The same temperature was chosen in [22], where the authors study OR patterns in 'classical' hybrid planar cells. In dimensional terms, this would correspond to a well with R ∼ 120-150 nm [19].…”

Liquid Crystals and Their Defects

“…The director n is subjected to antagonistic boundary conditions n(x 1 , x 2 , 0) = ±e 1 , n(x 1 , x 2 , δ) = ±e 3 on the plates, and periodic boundary conditions n(0, x 2 , x 3 ) = n(l 1 , x 2 , x 3 ), n(x 1 , 0, x 3 ) = n(x 1 , l 2 , x 3 ) on the other faces. Similar problems have been considered by many authors using a variety of models (see, for example, [2,13,14,23,30,61,76]). In [6] it is explained how using a Landau -de Gennes model, or molecular dynamics simulations [77], leads for sufficiently small plate separation δ to a jump in the director (defined as in Section 3.2 as the eigenvector of Q corresponding to it largest eigenvalue).…”

Flow and Nematic Director Profiles in a Microfluidic Channel: The Interplay of Nematic Material Constants and Backflow

“…The order-reconstruction or discontinuous solution exists for all values of L * , for our choice of symmetric Dirichlet conditions, with no flow. It is the unique solution for suitably large L * and unstable for suitably small L * [18]. However, the instability only manifests in certain directions, so that, for an appropriate choice of initial condition, we can recover the discontinuous solution for smaller values of L * .…”