Unwinding of a cholesteric liquid crystal and bidirectional surface anchoring

Abstract

We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transitions between metastable states occur as a series of pitchjumps as the helix expels quarter or half-turn twists, depending on the relative sizes of the strength of the surface potential and the bidirectional anchoring. We show that secondary easy axis directions can play a significant role in the unwinding of the cholesteric in its transition towards a nematic, especially when the surface anchoring strength is large.

Capillary and winding transitions in a confined cholesteric liquid crystal

“…These variations can be induced by temperature or by an electric field. Previous and more recent works have analysed the problem using simple elastic models [17][18][19][20][21][22][23][24]. There are various experimental works that deal with these problems [25][26][27][28][29][30][31][32][33].…”

Steady state solutions in a model of a cholesteric liquid crystal sample

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Motivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [3,4,16,18], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter.

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“…The theoretical investigation in [8] has more recently been extended by a number of authors (cf. [2,12,16,20,24]) through the use of different boundary conditions and analysis methods. The most relevant previous work for the present situation is probably that of Kiselev and Slucking [13] and McKay [16] both of whom consider cholesteric unwinding in finite regions and with weak anchoring, which in the case of [13] is different at the two boundaries.…”

“…[2,12,16,20,24]) through the use of different boundary conditions and analysis methods. The most relevant previous work for the present situation is probably that of Kiselev and Slucking [13] and McKay [16] both of whom consider cholesteric unwinding in finite regions and with weak anchoring, which in the case of [13] is different at the two boundaries. In our situation the boundaries exhibit infinite anchoring (the Dirichlet condition at x 3 = 0) and zero anchoring (the natural, or Neumann condition at x 3 = d) but as we show below, we see both preferred alignment angles and an increase in the pitch of the helix due to the magnetic field as in previous work.…”

“…We then perturb this (segment of) orbit and investigate how the time it takes a solution to travel from one boundary condition to the other changes relative to T * . This time is measured by appropriately defined time maps, whose definition arises naturally from the phase plane portrait and the first integral (16) (see, e.g. [14,22]).…”