# Phase Behavior and Rheological Properties of AES/CAPB/H\({}_{2}\)O Ternary System
## 3 Results and Discussion
### Small Angle X-ray Scattering Measurement  
Small angle X-ray scattering (SAXS) is an effective way to study the micro-structure of substances because it can obtain accurate structural information. Therefore, it is also widely \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **AES (70\%)** & **CAPB (38\%)** & **H\({}_{2}\)O** & \multirow{2}{*}{**Phase**} & **Viscosity** \\  & **(wt.\%)** & **(wt.\%)** & **(wt.\%)** & & **(Pa-s)** \\ \hline \(\alpha\) & 87.5 & 10 & 2.5 & L\(\alpha\) & 374.51 \\ \(\beta\) & 60 & 10 & 30 & H\({}_{1}\) & 753.48 \\ \(\gamma\) & 12 & 10 & 78 & L\({}_{1}\) & 0.02 \\ \(\delta\) & 12 & 20 & 68 & L\({}_{1}\) & 29.88 \\ \(\varepsilon\) & 30 & 50 & 20 & L\({}_{1}\)\(\rightarrow\) H\({}_{1}\) & 47.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Compositions, phases, and viscosity of representative samples in the AES/CAPB/H\({}_{2}\)O system. Figure 3: POM textures of representative samples with crossed polarizers at 25 \({}^{\circ}\)C: (**a**) sample \(\alpha\), (**b**) sample \(\beta\), (**c**) sample \(\delta\), and (**d**) sample \(\varepsilon\). used to identify the liquid crystalline phases of surfactant mixture systems [34; 35]. The ratio of spacings between allowed (reciprocal) lattice Bragg reflections varies with liquid crystalline phases: For the lamellar phase, the ratio of spacings is 1:2:3:4...; For hexagonal phase, the ratio of spacings is 1 : \(\sqrt{3}\) : \(\sqrt{4}\) : \(\sqrt{7}\)...; For cubic phases, the typical ratio of spacings is \(\sqrt{2}\) : \(\sqrt{4}\) : \(\sqrt{6}\) : \(\sqrt{8}\)... (\(\mathrm{I}_{1}\), \(\mathrm{V}_{1}\)) or \(\sqrt{6}\) : \(\sqrt{8}\) : \(\sqrt{14}\) : \(\sqrt{16}\)...(\(\mathrm{V}_{1}\)) [33]. As can be seen from Figure 4a, three Bragg peaks were observed for sample \(\alpha\) at \(q\) values of 0.1368 (\(q\)1), 0.2731 (\(q\)2), and 0.4099 (\(q\)3). The ratio of \(q\) values was calculated to be 1:2:3 (\(q\)1:\(q\)2:\(q\)3), which is the characteristic of the lamellar phase. For sample \(\beta\) (Figure 4b), the ratio of the observed three Bragg peak \(q\) values was 1:\(\sqrt{3}\) : \(\sqrt{4}\): (\(q\)1:\(q\)2:\(q\)3 = 0.1113:0.1921:0.2227), which is consistent with the characteristic of the hexagonal phase. Furthermore, well-defined scattering rings were observed in the two-dimensional SAXS patterns of sample \(\alpha\) and \(\beta\) (Figure S1a,b). With the results of POM and SAXS, sample \(\alpha\) and sample \(\beta\) could be identified as lamellar phase and hexagonal phase, respectively. The repeat distance (\(d\)) of the lamellar phase of sample \(\alpha\) calculated by Equation (1) [7] was 4.59 nm, while the distance from the center of one cylinder to another in the hexagonal phase (\(d_{H}\)) of sample \(\beta\) calculated by Equation (2) [7] was 6.52 nm. \[d=\frac{2\pi}{q1} \tag{1}\]  
\[d_{H}=\frac{4\pi}{\sqrt{3}\,q1} \tag{2}\]  
For sample \(\delta\), only a single broad peak was observed with extremely low intensity (about 0.05, Figure 4c) in its SAXS spectrum, which is completely inconsistent with the characteristics of cubic phases but consistent with the micellar phase [36]. Additionally, only a diffuse scattering ring was observed in the two-dimensional SAXS pattern of sample \(\delta\) (Figure S1c). Therefore, sample \(\delta\) can be identified as a micellar phase (\(\mathrm{L}_{1}\)). For sample \(\varepsilon\), the SAXS spectrum indicates that it is inconsistent with the characteristic of the hexagonal phase (Figure 4d). Compared with sample \(\delta\) (Figure 4c), besides the broad peak with very low intensity, a stronger peak was formed in sample \(\varepsilon\). The two-dimensional SAXS pattern of sample \(\varepsilon\) also showed a red scattering ring overlapping with a weak diffuse green scattering ring (Figure S1d). It indicates that as the concentration increases (sample \(\delta\rightarrow\varepsilon\)), the order of their mesoscopic structure is significantly enhanced, but the liquid crystal phase has not yet been completely formed.