Carr-Helfrich mechanism

Although the dominant means to create a space-charge field within the interference pattern in liquid crystals is given by Eq. (2), it has been shown that there are other mechanisms to create a space-charge field. One is derived from the conductivity anisotropy and is known as the Carr-Helfrich effect [43,49] ... 

Electrically driven convection in nematic liquid crystals [6,7,16] represents an alternative system with particular features listed in the Introduction. At onset, EC represents typically a regular array of convection rolls associated with a spatially periodic modulation of the director and the space charge distribution. Depending on the experimental conditions, the nature of the roll patterns changes, which is particularly reflected in the wide range of possible wavelengths A found. In many cases A scales with the thickness d of the nematic layer, and therefore, it is convenient to introduce a dimensionless wavenumber as q = that will be used throughout the paper. Most of the patterns can be understood in terms of the Carr-Helfrich (CH) mechanism [17, 18] to be discussed below, from which the standard model (SM) has been derived... 

Table 1. Eight different combinations (labelled A to H) of initial director alignments and the sign of anisotropies a, ffa- The EC pattern species are characterized in the last column CH stands for patterns, which are compatible with the Carr-Helfrich mechanism, in contrast to the remaining, nonstandard ones (ns-EC).

References [59] investigate the static and dynamic behavior of the electrohydrodynamic instability in fireely suspended layers of nematic liquid crystals. The existence of a domain mode was shown, which consists of adjacent elongated domains with a spatial period proportional to the thickness of the layer. This mode occurs only if the thickness of the layer exceeds a critical value 7 /x), and can be understood in terms of the same anisotropic mechanism as the Carr-Helfrich-type, as in the case of the Kapustin-WiUiams modulated structure. 

Thus, to date we have three theoretically predicted modes for a high-frequency instability caused by the Carr-Helfrich anisotropic mechanism. They are the conductance and dielectric regimes and the inertia mode. Two of these (the conducting regime and the inertia mode) correspond to the steady-state motion of the liquid and the stationary deviations of the... 

A distinguishing feature of this model is the absence of a positive feedback between the magnitude of the space charge and the orientation of the director, which is required for the Carr-Helfrich mechanism. These physical parameters are independent of each other here. 

At high frequencies, with a reduction in temperature, the threshold field of the normal prechevron domains increases smoothly, not displaying any peculiarity when the temperature is T, where the anisotropy of the electrical conductivity disappears. Without doubt, the high-frequency electrohydrodynamic mode is caused by the isotropic mechanism of destabilization, since when cr /crx = 1, the Carr-Helfrich model does not hold. Analysis shows [123] that the new low-frequency mode (longitudinal domains) is also caused by the isotropic mechanism. 

The basic mechanism for electric field induced instabilities is now very well understood in terms of the Carr-Helfrich model based on field induced space charges due to conductivity and dielectric anisotropies [16, 31], Helfrich [16] made derivations for only DC fields, which were further extended to AC fields by Dubois-Violette and co-... 

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