# Nematic Liquid Crystal Composite Materials for DC and RF Switching
## 3 Electrical Conductivity of Liquid Crystal and Carbon Nanotube Composites
### Dual Frequency Switching  
Nematic liquid crystals (NLC) and their composites are widely used in various electro-optical devices. One of the main drawbacks of such devices is, they have long switching off time. It refers to the time required by the system to get back to its equilibrium state after turning off the field. When the field is taken away, the relaxation of the LC molecule is only driven by elastic torque. The elastic torque depends on the viscosity of the LC matrix, and it is a slow process, which makes the off time very long. Research are going on to cut down the switching off time. For example, [PERSON] et al. doped NLCs with a small amount of CNT to achieve a faster field-induced switching [71]. [PERSON] et al. and  
Figure 14: (**a**) In-plane gold electrodes having a 1-mm width and separated by 50 \(\upmu\)m in a glass wafer; (**b**) two pairs of electrodes in a cross configuration to inspect the conductivity in mutually perpendicular directions. The inset shows the gap in between the electrodes. [PERSON] et al. used SWCNT to improve the alignment layer to shorten the off time [72; 73]. An alternative and effective way of faster switching is to use dual frequency nematic liquid crystals [74; 75; 76]. Dual frequency Nematic liquid crystals (DFNLCs, also abbreviated as DFLC) show a positive dielectric anisotropy at a lower frequency and a negative dielectric anisotropy at a high frequency. The frequency at which the sign changes is called the crossover frequency. For this frequency-driven reversible change in \(\Delta\varepsilon\), it is possible to switch the LC director's orientation perpendicular or parallel to the applied field. This makes the switching very fast as the driving torque is very large (proportional to \(\Delta\varepsilon\)) compared to traditional NLC. Dual frequency NLCs are applied in fast-operating phase modulators, optical shutters, tunable polarization filters, etc. [77; 78; 79]. On the other hand, some drawbacks of DFNLCs are the temperature dependence of a crossover frequency, the negative dielectric anisotropy is much bigger than that of positive one, etc. [80; 81]. Another big concern is that, at high frequencies, power consumption is very high which also shifts the crossover frequency. Thus, it is desirable to operate the device in a moderate frequency range (for example, below 50 kHz) and to use those DFNLCs as the switching material, which have a low crossover frequency (i.e., 1 kHz) [82]. Usually DFNLCs are prepared by mixing two or more LC compounds from two categories of NLC. One category shows a positive \(\Delta\varepsilon\) at a low frequency, which decreases as the operating frequency increases. Another category shows a negative \(\Delta\varepsilon\) and shows very little frequency dependence up to the MHz frequency range. For the second category, a negative \(\Delta\varepsilon\) is achieved by neighboring a fluoro substitution on the phenyl ring of LC molecules [83]. From the molecular point of view, positive LCs consist of large and long molecules with a longitudinal dipole moment (\(\varepsilon_{\parallel}\)), whereas negative LCs consist of small molecules with a transverse dipole moment as shown in Figure 15a. [PERSON] et al. demonstrated a frequency-driven conductivity switching in an LC-CNT composite. For their experiment, they used PCPBB (4-pentylphenyl 2-chloro-4-(4-pentylbenzoyloxy) benzoate) as a host material, which shows a nematic phase for the temperature range 0 \({}^{\circ}\)C to 121.8 \({}^{\circ}\)C [84]. They doped the host material with a 3.6 \(\times\) 10\({}^{-4}\) volume fraction of SWCNT of peak length 500 nm and used a conventional ITO(Indium Tin oxide) -coated glass cell with a cell gap of 25-30 \(\upmu\)m and an electrode sheet resistance of 10 \(\Omega\)/square. The equilibrium (no field applied) conductivity of LC's increased by two orders of magnitude upon doping with CNTs. Beside this, the conductivity became more temperature-dependent than the pure LCs.