## 3 Results and Discussion  
We used [PERSON]'s method to produce GOs but introduced an intercalation step using co-acids to obtain larger-sized GO (L-GO) flakes. Graphite was immersed in the co-acid solution of H\({}_{2}\)SO\({}_{4}\) and H\({}_{3}\)PO\({}_{4}\), which resulted in an interaction of H\({}_{2}\)SO\({}_{4}\) and HSO\({}_{4}\)\({}^{-}\) with graphenes in HOPG. This acid-based intercalation\(-\)oxidation chemistry of graphite is well known: H\({}_{3}\)PO\({}_{4}\) can be intercalated effectively between graphenes, and H\({}_{2}\)SO\({}_{4}\) predominantly causes the oxidation of graphenes [19; 20]. In addition, co-acid molecules form hydrogen bonds between them, which increases the intercalation distance between graphite layers. As a result, it was reported that the interlayer spacing of graphite (3.35 A) increases significantly over \(\sim\)8 A [19], thereby decreasing the interlayer interactions between graphenes, as schematically shown in Figure 1a. After preparation of GOs with (and without) the intercalation step using co-acids, and their subsequent exfoliation in waters, the lateral size of L-GO flakes was \(150\pm 29\) um (measured by 51 flakes), whereas that of GO flakes was \(28\pm 24\) um (measuredby 65 flakes; Figure 1b), although both exfoliations were performed using the same procedure (see experimental section). Liquid crystal behaviors of GO suspensions with different sizes have been systematically studied by changing their concentrations. In general, as the GO concentration increases, overlap of excluded volumes of GO flakes occurs; therefore, random movement of GO flakes in the suspension is limited. As a result, the arrangement of GO flakes in the suspension changes from random isotropic phase to ordered nematic phase [21]. This liquid crystal phase transition is known to be strongly affected by the size of colloidal particles. According to [PERSON]'s theory [22], the empirical value of the critical concentration has the relationship per the following equation:  
\[\Phi\approx 4\text{T/W}, \tag{1}\]  
where \(\Phi\) is the volume fraction of colloidal particles in the suspension, and T and W are the thickness and lateral width of the circular particles, respectively. GOs are also colloidal disks in a suspension; so, as the lateral size of the GO flakes increases, the critical concentration for the formation of liquid crystals decreases. To track the liquid crystal behaviors of GO and L-GO suspensions, we employed polarized optical microscopy (POM). Observation of the birefringent domains in the POM image can reveal the ordering of the GO flakes in the suspension [12]. Figure 2a,b show POM images of the GO and L-GO suspensions with increasing concentrations. For the GO suspension, as the concentration increased, we observed the appearance of isotropic circular domains at the concentration of 12 mg/mL and ordered lamellar domains at 20 mg/mL. This is a common characteristic of lyotropic liquid crystal materials: as the concentration of colloidal particles increases, a more ordered liquid crystal phase is formed [23; 24]. In contrast, for the L-GO suspension, ordered lamellar domains began to appear at the concentration of 4 mg/mL. Compared to the GO suspension, the critical concentration for the ordered lamellar liquid was four times lower for the L-GO suspension. To further investigate the liquid crystal behavior of GO and L-GO suspension, we examined the shear rate dependencies of the viscosity for these suspensions at different concentrations. The GO suspensions showed almost constant viscosity over a wide range of shear rates when their concentrations were 4 and 12 mg/mL. However, when the concentration increased to 20 mg/mL, the viscosity decreased as the shear rate increased.