## 2 Microwave Liquid Crystal Technology
### Performance Metric of Microwave Liquid Crystals
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**LC** & \(\epsilon_{r,\perp}\) & **tan\(\delta_{\perp}\)** & \(\epsilon_{r,\perp}\) & **tan\(\delta_{\parallel}\)** & \(\Delta\epsilon\) & \(\frac{\tau_{LC}}{\tau_{0}}\) & \(\tau_{LC}\) & \(\mathbf{\mu_{LC}}\) & \(\mathbf{K}_{11}\) **(pN)** & \(\mathbf{K}_{22}\) **(pN)** & \(\mathbf{K}_{33}\) **(pN)** & \(\mathbf{Y_{rot}}\) & \(\mathbf{\Delta_{E11\,MHz}}\) & \(\mathbf{T_{c}}\) **(c)** & **Ref.** \\ \hline K15 (5 CB) & 2.7 & 0.0273 & 3.1 & 0.0132 & 0.4 & 12.9 & 4.7 & 7.0 & 4.2 & 13.5 & 0.126 & 14.4 & 38.0 & [56] \\ \hline E7 & 2.53 & 0.022 & 2.98 & 0.009 & 0.45 & 15.1 & 6.86 & 10.8 & & & 0.254 & 14.3 & 58.0 & [59] \\ \hline BL006 & 2.58 & 0.0191 & 3.16 & 0.0069 & 0.58 & 18.4 & 9.6 & 16.0 & & & 0.569 & 17.1 & 118.5 & [59] \\ \hline MDA-03-2838 & 2.55 & 0.026 & 3.68 & 0.008 & 1.13 & 30.7 & 11.8 & & & & & & & [186] \\ \hline MDA-03-2844 & 2.4 & 0.021 & 3.4 & 0.007 & 1.0 & 29.4 & 14.0 & & & & & & & [186] \\ \hline GT3-23001 & 2.41 & 0.0141 & 3.18 & 0.0037 & 0.77 & 24.2 & 17.2 & 24.0 & 14.0 & 34.5 & 0.727 & 4.0 & 173.5 & [59] \\ \hline GT5-26001 & 2.39 & 0.007 & 3.27 & 0.0022 & 0.88 & 26.9 & 38.4 & 12.0 & & 41.9 & 1.958 & 1.0 & 146.0 & [75] \\ \hline GTS-28004 & 2.40 & 0.0043 & 3.32 & 0.0014 & 0.92 & 27.7 & 64.4 & 11.8 & & 52.9 & 5.953 & 0.8 & 151.0 & [75] \\ \hline TUD-566 & 2.41 & 0.006 & 3.34 & 0.0027 & 0.93 & 27.8 & 46.4 & 13.0 & 8.0 & 48.0 & 2.100 & 1.0 & 105.5 & [75] \\ \hline GT7-29001 & 2.46 & 0.0116 & 3.53 & 0.0064 & 1.07 & 30.3 & 26.1 & 14.5 & & 18.0 & 0.307 & 22.1 & 124.0 & [59] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dielectric and elastic properties of different LC mixtures at room temperature. The values for \(K_{11}\), \(K_{22}\), and \(K_{33}\) are constants for splay, twist, and bend deformations according to [191, 192, 195], \(\gamma_{rot}\) is the rotational viscosity, \(\Delta\epsilon_{r,1\mathrm{kHz}}\) the anisotropy at low frequency, typically at 1 kHz, and \(\tau_{LC}\) and \(\eta_{LC}\) are the material’s tunability and figure-of-merit, respectively. Microwave parameters are measured at 19 GHz, except for MDA-03-2838 and MDA-03-2844, which are characterized at 9 GHz. Figure 7: Resonator cavity with coupling iris, where the empty or LC-filled quartz tube is placed in the center (**left**). A dual-mode resonator is shown for both TE\({}_{111}\) and TM\({}_{010}\) mode to measure the LC characteristics parallel and perpendicular to the Radio Frequency (RF) field in a single step only (**middle**), where an example of \(S_{21}\) measurements for empty and filled tubes is illustrated below. An industrial-scale temperature-controlled LC-characterization setup with permanent magnets (**right**). performance parameters are directly derived from the measured electromagnetic quantities, the anisotropy and tunability in relative permittivity, as well as the material's figure-of-merit:  
\[\Delta\varepsilon=\varepsilon_{r,\parallel}-\varepsilon_{r,\perp} \tag{1}\]  
\[\tau_{LC}=\frac{\Delta\varepsilon}{\varepsilon_{r,\parallel}} \tag{2}\]  
\[\eta_{LC}=\frac{\tau_{LC}}{\tan\delta_{max}} \tag{3}\]  
Compared to standard display mixtures K15, E7, and BL006, Merck's first-generation LC compounds such as the GT3 series, having a long conjugation body with biphenyl or terphenyl structure, exhibit already much higher anisotropy, tunability, and figure-of-merit of the materials. This has even been improved by Merck's second-generation LC mixtures such as the GT5 series and TUD-566, which use single classes, including bistolane and other novel components with triple bonding in between. With these LC's, tunability \(\tau_{LC}\) is more than doubled and the material's figure-of-merit \(\eta_{LC}\) is increased by factor 9 to 13 compared to standard LC K15, where to the author's knowledge, \(\eta_{LC}\) of 46 to 64 are the highest values reported so far at microwaves. However, the tuning speed or response time are much slower than for K15 and the first-generation LCs, as can be seen from Figure 8.