# Nematic Liquid Crystal Composite Materials for DC and RF Switching
## 3 Electrical Conductivity of Liquid Crystal and Carbon Nanotube Composites  
### Review on Conductivity Behavior of LC-CNT Dispersions  
As discussed above, a field-induced conductivity modulation is very low for pure LCs. This makes traditional LCs less preferable for DC and RF switching applications. One possible solution to increase the ON/OFF resistivity ratio is to add nanoparticle dopants. When liquid crystal molecules orient themselves in an electric field, they can also orient guest atoms along with them through an elastic interaction. [PERSON] et al. demonstrated that dye molecules can be aligned parallel to the electric field by LC molecules. For an LC cell of 12 \(\mu\)m thickness, switching occurs within 1-5 ms for an electric field of 4 \(\times\) 10\({}^{4}\) V/cm. After removing the electric field, the sample reverts to its initial condition in approximately 100 ms. [24]. There are several works reported on enhancement field-induced conductivity modulations using nanoparticles [6; 7; 8; 9; 10; 19; 20] Among all the nanoparticles, CNT might be the most suitable candidate for DC and RF switching as it is column is structured with a high aspect ratio and it has anisotropy in electrical conductivity. A small weight percentage of CNT does not change the composite's equilibrium (no external stimuli) conductivity much. Upon applying an electric field, various groups found a 2-4 order of magnitude change in the electrical conductivity [19; 20]. Although our main focus is on an LC-CNT composite, we discussed the electric-field-induced conductivity modulation in a metal-nanoparticle and an LC composite in Section 4 for comparison purposes as well. Carbon nanotubes received enormous attention over the last three decades due to their unique electrical, mechanical, and optical properties [25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. CNTs are capable of altering LC matrix chemistry, viscosity, dispersion quality, etc. In addition to that, CNT can also modify the physical properties of the composites [35]. For example, a faster electro-optic response, an altered dielectric anisotropy, and a local deformation in the nematic director are observed [36; 37; 38]. The electrical conductivity of the material system can be modified by external stimuli like surface interaction and electrical, magnetic, optical, and thermal excitations. In all the cases, external stimuli do not have a direct interaction with the CNTs. LC molecules respond to the stimuli, which in turn interact with CNTs by elastic force and molecular interactions. Studies revealed that the electrical conductivity of a LC-CNT mixture depends on the operational temperature, phase of LC, and CNT dopants concentration. [PERSON] et al. showed that the conductivity  
Figure 3: The cell capacitance and conductance for pure Liquid Crystal (LC) materials as function of the magnitude and frequency of applied voltage; (**a**) Capacitance modulation; (**b**) Conductance modulation [23]. behavior of p-ethoxy-benzylidene-p-n-butylaniline (EBBA)/Multiwalled Carbon Nanotube (MWCNT) composites is a function of CNT wt.% (Figure 4) [39; 40]. When the concentration exceeds a threshold concentration, which is also known as percolation threshold (which is 0.05-0.1% in the present case), the conductivity increased by several orders of magnitude. This is called percolation transition. A continuous conduction path is created by CNT clusters in the LC matrix. The ultrasmall critical concentration (< 0.1%) for insulation is due to the high aspect ratio of MWCNTs (100-1000). A similar behavior is also observed for a 5 CB/MWCNT mixer with a similar critical concentration C = 0.025 wt.% [40; 41]. Moreover, [PERSON] et al. showed that an EBBA/MWCT conductivity shows a positive temperature coefficient and heating-cooling hysteresis behavior (Figure 5a). Above the crystalline-to-nematic phase transition temperature (T\({}_{\text{SN}}\)), \(\sigma\) increases with temperature. There is no discontinuity near the nematic to isotropic phase transition temperature, T\({}_{\text{NI}}\) \(\sim\)351-353K.