# Nematic Liquid Crystal Composite Materials for DC and RF Switching
## 2 Electric-Field-Driven Conductivity Modulation in Pure Liquid Crystal Materials  
Liquid crystal is a state of matter having properties between solid crystal and conventional isotropic liquid. It can flow like liquids but still has a long-range orientation order and/or  
Figure 1: The types of nanoparticles commonly used as a dopant in liquid crystal matrices for altering electro-optical properties. various degrees of translational/positional molecular ordering. Like crystals, LCs show anisotropic characteristics in dielectric constant, refractive index, and magnetic susceptibilities which vary with directions. In a nematic phase, where the LC molecules do not have any long-range transitional order, they show a preferred orientational order. For this ordering, a liquid crystal shows dielectric anisotropy (\(\varepsilon_{\parallel}>\varepsilon_{\perp}\)) in a nematic phase. Both the parallel (\(\varepsilon_{\parallel}\)) and perpendicular (\(\varepsilon_{\perp}\)) components of dielectric constant have strong dependences on temperature and frequency [21; 22]. The typical behavior of a dielectric constant as the function of temperature and applied electric field frequencies is shown in Figure 2. An external perturbation can alter the macroscopic properties of the LC system. By applying mechanical, electrical, magnetic force, surface tension, or optical fields, we can rotate or modify the orientation order of the liquid. This, in turn, alters the LC sample properties [21; 22]. For example, liquid crystal molecules have an electrical dipole moment. When an electric or magnetic field is applied, the dipole rotates and aligns the director (denoted by n) along the field. Pure liquid crystals (LC) are dielectric materials, and therefore, an LC cell filled with pure liquid crystal acts like capacitors. Therefore, when an electric field is applied to this cell, there is only a displacement current but no conduction current. Considering this, the electrical conductance and capacitance of liquid crystal cells can be modeled for high-voltage and low-voltage regions using Equation (1) [23]  
\[C=\omega C_{o}\varepsilon^{\prime}_{\gamma}G=\omega C_{o}\varepsilon^{\prime \prime}_{\gamma}\gamma=\left\{ \begin{array}{l}\bot\text{for V}<\text{V}_{ \text{th}}\\ \|\text{for V}\gg\text{V}_{\text{th}}\end{array} \right. \tag{1}\]  
where \(\text{C}_{o}=\varepsilon_{o}\text{A}/\text{d}\) is called the geometric capacitance, A is the electrode area, d is the distance between the electrode, \(\text{V}_{\text{th}}\) is the threshold voltage of switching, and \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) are the real and the imaginary parts of the dielectric constant, respectively. Overall, the dielectric constant of a liquid crystal is given as  
\[E=\varepsilon_{\perp}cos^{2}\theta+\ \varepsilon_{\parallel}sin^{2}\theta \tag{2}\]  
For voltages \(<<\text{V}_{\text{th}}\), the dielectric constant of the cell is equal to \(\varepsilon_{\perp}\) as the LC director (n) is aligned parallel to the electrodes. On the other hand, for voltages \(>>\text{V}_{\text{th}}\), the dielectric constant of the cell is equal to \(\varepsilon_{\parallel}\) as \"n\" is aligned parallel to the direction of electric field. In pure liquid crystal materials, there is no free charge carrier or conductive path between electrodes. Therefore, the conductivity modulation from external stimuli (i.e., temperature, magnetic field, and electric field) is very low. [PERSON] et al. showed that the capacitance and conductance of pure LC materials is a function of the magnitudes and frequencies of applied voltage and field induced modulation is only a few times [23]. The authors examined three commercial LC materials: LC1348, LC 1001, and E49 with the cell area in a cm\({}^{2}\) scale and the cell separation in a micron scale. For all these materials, the capacitance values were in the nF range and LC1001 showed the lowest frequency dispersion.