This work describes an investigation of the static (or quasistatic) nuclear magnetic resonance (NMR) response in a nematic liquid crystal confined between two planar conducting plates and subject to a magnetic field and an electric field produced by a difference of voltage applied on the plates. Deuterium NMR spectroscopy of 4-pentyl-d${}_2$-4${}^{\prime }$-cyanobiphenyl (5CB-d${}_2$) under these conditions has revealed a voltage dependent inhomogeneous director distribution for a particular narrow range of voltages and for a fixed magnetic field (that of the spectrometer). In the ideal setup the two plates are assumed to be rigorously parallel, so that a difference of voltage applied on the plates leads to a constant electric field normal to them. When the magnetic field is parallel to the plates (orthogonal geometry) there exists a threshold value of the electric field for which the effect of both fields exactly compensate; moreover, for stronger electric field the director aligns with the electric field while for weaker electric field the director aligns with the magnetic field. If there is a lack of parallelism between the two plates, the electric field becomes inhomogeneous so that it may be larger than the threshold value in some region of the sample and smaller in the remaining part of the sample. In that case the director will adopt essentially two orientations within the sample, namely, parallel or perpendicular to the magnetic field, and the position of the frontier between the two domains depends on the voltage. This feature is clearly shown by deuterium NMR spectra that exhibit a transfer of intensity between two quadrupolar doublets with increase in the applied voltage. The coexistence of two director populations occurs for a range of voltages that depends on the degree of nonparallelism; accordingly, an estimation of this range by NMR yields an experimental estimation of the lack of parallelism. A tiny tilt of the magnetic field (nonorthogonal geometry) entrains a notably different behavior since a single doublet with voltage dependent splitting is observed in this case. In a first stage (simple model) of this work, the main features observed for the orthogonal and nonorthogonal geometries are interpreted within the framework of Leslie-Ericksen theory by employing the concept of a single effective field replacing the two real fields. However, the spectra reveal an additional director distribution, especially for the orthogonal geometry, that cannot be interpreted by this simple approach. In a second stage (advanced model), these less clear features have been investigated by numerical simulations of a two-dimensional model which includes the effects of inversion walls and of the high relative dielectric anisotropy of 5CB.

• Received 26 September 2012

DOI:https://doi.org/10.1103/PhysRevE.86.051708