## 4 Properties of GR
### Electronic Transport Properties  
G shows the best carrier mobility at 10\({}^{5}\) cm\({}^{2}\)/Vs [142]. It is suggested that, from theoretical studies, because of extrinsic carrier mobility, GR has some advantage over G from the view of electronic properties. It can be seen that from Table 2, in y-direction 6,6,12-graphyne shows the highest values against all the other structures. By utilizing the Boltzmann transportation equation, with deformation potential theory and relaxation time approximation, Shuai et al. studied the electronic properties of the material [142; 143]. This method provides the information that because electron-acoustic phonon coupling at the lower level of energy can cause high carrier mobility, and this mobility is considered as an upper limit of the system. From a device application view, the structure that consists of delocalized electronic states shows an approximated calculation of carrier mobility at 3 \(\times\) 10\({}^{5}\) cm\({}^{2}\)/Vs with this method for G [142].  
From Table 3, it can be observed that all mentioned structures have considerable carrier mobility in the range of 10\({}^{4}\) cm\({}^{2}\)/Vs to 10\({}^{5}\) cm\({}^{2}\)/Vs. Due to the rectangular symmetry, \(\gamma\)-graphyne has obvious anisotropy [142]. The \(\gamma\)-graphyne shows higher carrier mobility in one direction as compared to G, and it shows mobility values of electrons and holes in the range of 5.41 \(\times\) 10\({}^{5}\) cm\({}^{2}\)/Vs and 4.29 \(\times\) 10\({}^{5}\) cm\({}^{2}\)/Vs, respectively. Because of two Dirac cones in the Brillouin zone with weak electron-phonon coupling can be a cause of this higher mobility [142].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Property** & **Graphene** & **\(\alpha\)-Graphyne** & **\(\beta\)-Graphyne** & **\(\gamma\)-Graphyne** & **Graphdiyne** \\ \hline Carbon Hybridization & sp\({}^{2}\) & sp + sp\({}^{2}\)[113] & sp + sp\({}^{2}\)[113] & sp + sp\({}^{2}\)[113] & sp + sp\({}^{2}\)[70] \\ \hline Lattice Structure & Hexagonal & Hexagonal [105] & Hexagonal [105] & Hexagonal [105] & Hexagonal [105] & Hexagonal [54] \\ \hline Acetylenic Linkage \% & 0\% & 100\% [70] & 66.67\% [70] & 33.33\% [70] & Varied (more than \(\gamma\)) [54] \\ \hline Band Gap & 0 eV & \(\sim\)0.44 eV [106] & \(\sim\)0.52 eV [106] & \(\sim\)0.47 eV [106] & 0.5–1.1 eV [54; 121] \\ \hline Carrier Mobility (cm\({}^{2}\)/V-s) & \(\sim\)10\({}^{5}\)[128] & High, anisotropic [128] & High [128] & High (5 \(\times\) 10\({}^{5}\)) & Moderate–High [129] \\ \hline Thermal Conductivity & \(\sim\)500 W/m\(\cdot\)K [132] & Lower than graphene [140] & Lower [140] & Lower (\(\sim\)50 W/m\(\cdot\)K) [140] & \
\begin{tabular}{c} Much lower \\ (\(\sim\)10–20 W/m\(\cdot\)K) \\ [140] \\ \end{tabular} \\ \hline Mechanical Strength & \(\sim\)1 TPa [47] & Moderate [78] & Moderate [78] & Moderate [78] & Lower than graphene [106] \\ \hline Synthesis Status & Scalable [9] & Theoretical [70] & Theoretical [141] &
\begin{tabular}{c} Synthesised \\ [94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 123; 124; 125; 126; 127; 128; 129; 130; 131; 132; 133; 134;