Electroconvection standard

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). 

In this paper we have reviewed the structures appearing at onset of electro-convection in nematic liquid crystals. The influence of the relevant material parameters (ca and ao) and the role of the initial director alignment were explored. Our calculations using a linear stability analysis of the standard model of electroconvection (performed for zero frequency) revealed that four different scenarios characterized by different ranges of the wavenumber q can be identified (1) the Qf= 0 mode (a homogeneous deformation known as the Freedericksz transition) predicted and observed in cases C, D, E and H, which is... 

For the parameter combination o < 0 and <7a < 0, which can be found in some nematic compounds, electroconvection is definitely excluded within the standard model. Nevertheless, EC has surprisingly been observed in this case (for recent examples see, e.g. Kochowska et alP and Toth-Katona et al ). The theoretical analysis has proved that flexoelectricity is crucial for understanding this non-standard EC because in Eq. (4.7) the contribution V Pfi to Pel is dominant. It is interesting that the flexotorque on the director is determined by the difference (ei — 63) of the flexocoefScients while the sum (ei - - 63) governs the flexocharge and thus its contribution to the viscous torque. Further details will be sketched in Section 4.3.2. 

As already stated, electroconvection cannot be explained by the standard model for < 0 and Ca < 0. Surprisingly, EC has been observed also for this parameter combination in certain calamitic nematics.These EC patterns differ clearly from the standard EC patterns the rolls are dominantly parallel to the initial director alignment (see Fig. 4.6a). They are not observable using the common shadowgraph technique (single polarizer) but are by using crossed polarizers (plus sometimes an additional... 

Non-standard electroconvection Outer hair cell Polyvinylidene fluoride Pb-zirconate-titanate Self-assembled monolayer Small-angle X-ray scattering Standard electroconvection Scaiming electron microscopy Smectic A Smectic C... 

---