Threshold electroconvection

Abstract A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation. 

Figure 1. Schematic morphological phase diagram in the f/ — / plane. Solid lines correspond to the threshold voltage of standard electroconvection, the dashed line denotes the threshold of the prewavy patterns or wide domains (see later). For details see [16].

The dashed line in Fig. 1 is the experimental threshold curve for prewavy patterns or wide domains (A 4 — lOd) that also represent electroconvecting structures though not captured by the standard model (see later in Section 2.2.). 

Case G planar alignment, 6 < 0 o-q < 0. Standard EC (based on the CH mechanism) cannot occur for the material parameter combination e < 0, da < 0 [2] except the a induced" pattern type. Nevertheless, convection associated with roll formation has been observed in ac electric field in the homologous series of N-(p-n-alkoxybenzylidene)-n-alkylanilines, di-n-4-4 -alkyloxyazoxybenzenes and 4-n-alkyloxy-phenyl-4-n alkyloxy-benzoates [52-54]. The characteristics of the patterns the orientation of the rolls, contrast, frequency dependence of the wavevector and the threshold, director variation in space and time etc. - are substantially different from those observed in the standard EC. Since this roll formation process falls outside of the frame of the standard model, it has been called nonstandard electroconvection (ns-EC). 

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