Theory and numerical simulation of field-induced director dynamics in confined nematics investigated by nuclear magnetic resonance

Abstract

We investigate the director reorientation in a nematic liquid crystal confined between two parallel plates and subjected to both a magnetic and an electric field. The permanent magnetic field is used first to align the director and, subsequently, to allow nuclear magnetic resonance (NMR) observation of the director response following the application of the electric field. For sufficiently strong electric fields, the director reorients and aligns parallel to the electric field. In this work we focus on the geometry where the electric and magnetic fields are orthogonal to each other. In this configuration the state of the system, immediately after applying the orthogonal electric field, is steady and unstable, at least in theory, since the director is assumed to be everywhere parallel to the magnetic field. In practice the real state of the system always deviates slightly from the perfect unstable steady state, which induces the start of the director reorientation toward the electric field. The nature and the characteristics of the initial deviation partially determine the reorientation process. In the classical approach, the small deviations from the ideal state are assumed to be due to thermal fluctuations, but this approach fails to account for some recent experimental results. For this reason we were led to investigate slightly non-uniform initial director configurations that are stable under the sole effect of the magnetic field but are sufficient to break the ideal unstable steady state created with the application of the orthogonal electric field. Such non-uniformities must be local or distributed over very small sample volumes, since their effects on the equilibrium NMR spectrum (before the application of the electric field) are not usually observed. In other words, we consider the presence of inversion walls in the bulk of the sample and local misalignments of the director on the boundary plates and investigate the effects of such non-uniformities on the response of the nematic to the application of the electric field, as observed by NMR. The model we propose, including such effects in parallel with thermal fluctuations, is able to account for the recently observed features of the field-induced director dynamics.

Keywords:

• nematic liquid crystal
• Leslie–Ericksen
• director reorientation
• progressive mode
• soliton mode

Acknowledgement

This work was partly supported by the European Union Science Program and “Fundação para a Ciência e a Tecnologia” (Portugal) through a post-doctoral research contract with A. Véron.

Notes

1. It results from the variation of the total free energy associated with an arbitrary parallel displacement of the director.

2. Due to the condition only the part of h normal to the director is effective, the part parallel to the director cancels with the term λn_i (in Equation (1)(21)).

3. The free energy density must be integrated over the volume of the cell. Since we use a two-dimensional model, the integration along the x ₃ axis reduces to a multiplication by the length of the cell along this axis assumed to be equal to L_, the length along the x ₂ axis (see Figure 1).

4. Note that with the notations used in this work the angle between the director and the magnetic field is π/2  −  θ.