## 3 Results and Discussion
### Dependence of Extraction on Temperature  
In spite of a variety of studies on metal extraction thermodynamics [34], to the best of our knowledge, the thermodynamics for the extraction of Cs(I) and Sr(II) with SC4A have seldom been reported. They are important for understanding the nature of the extraction process and predicting the extraction rate. The extraction of Cs(I) and Sr(II) with SC4A was examined at different temperatures between 288 and 308 K. A plot of \(\ln\)\(D\) versus \(1/T\) was constructed, as shown in Figure 6.  
As can be seen in Figure 6, increasing the extraction temperature resulted in an obvious decrease in \(D_{\text{Cs}}\) and \(D_{\text{Sr}}\), indicating that the extraction reaction is exothermic. Therefore, increasing the operation temperature in the experimental conditions adversely affected the extraction.  
It could be determined from Figures 3-5 that the extracted species of Cs(I) and Sr(II) with SC4A are Cs- SC4A and Sr-2 SC4A, respectively, the extraction equilibrium of Sr(II) is similar to that reported in the literature [35], and can be expressed as follows:  
\[\text{Sr}^{2+}{}_{(\text{a})}+2\text{H}_{4}\text{L}_{(\text{o})} \rightleftharpoons\text{Sr}\cdot 2\text{H}_{3}\text{L}_{(\text{o})}+2\text{H}^{+}{}_{( \text{a})} \tag{4}\]  
where H\({}_{4}\)L and Sr\(\cdot\)2H\({}_{3}\)L are free SC4A and Sr-SC4A complex.  
The conditional extraction equilibrium constant, \(K_{\rm ex1}\), in Reaction (4) is described as:  
\[K_{\rm ex}=\left[\rm Sr\cdot 2H_{3}L\right]_{(o)}\left[H^{+}\right]^{2}_{(a)}/( \left[\rm Sr^{2+}\right]_{(a)}\left[H_{4}L\right]^{2}_{(o)}) \tag{5}\]  
The distribution coefficient \(D_{\rm Cs}\) is defined as:  
\[D_{\rm Sr}=\left[\rm Sr\cdot 2H_{3}L\right]_{(o)}/\left[\rm Sr^{2+}\right]_{(a)} \tag{6}\]  
According to Equations (5) and (6), the relationship between the distribution ratio and the extraction constant can be described as:  
\[\ln D_{\rm Sr}=\ln\,K_{\rm ex}+2\ln\,[H_{4}L]_{(o)}-2\ln\,[H^{+}]_{(a)} \tag{7}\]  
Thus, the change in the enthalpy (\(\Delta H^{\circ}\)), entropy (\(\Delta S^{\circ}\)) and Gibbs free energy (\(\Delta G^{\circ}\)) during the extraction procedure can be calculated using the Arrhenius law and the Gibbs-Helmholtz equation:  
\[\rm d\,\ln\,K_{\rm ex}/dT=\Delta H^{\circ}/(RT^{2}) \tag{8}\]  
\[\Delta G^{\circ}=\Delta H^{\circ}-T\Delta S^{\circ} \tag{9}\]  
Then, \(\ln\,D_{\rm Cs}\) can be calculated using the following equation:  
\[\ln\,D_{\rm Sr}=-\Delta H^{\circ}/(RT)-2\ln[H^{+}]_{(a)}+2\ln\,[H_{4}L]_{(o)}+ \Delta S^{\circ}/R \tag{10}\]  
Similar to the calculation of \(\ln\,D_{\rm Sr}\), \(\ln\,D_{\rm Cs}\) can be expressed as (the calculation of \(\ln\,D_{\rm Cs}\) in Supplementary Materials):  
\[\ln\,D_{\rm Cs}=-\Delta H^{\circ}/(RT)-\ln[H^{+}]_{(a)}\,\,+\ln\,[H_{4}L]_{(o) }+\Delta S^{\circ}/R \tag{11}\]  
The values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) were determined from the slope and intercept respectively as shown in Figure 6. The values of \(\Delta H^{\circ}\), \(\Delta S^{\circ}\) and \(\Delta G^{\circ}\) of the system were summarized in Table 2. The \(\Delta H^{\circ}\) was negative indicating that the extraction of Cs(I) or Sr(II) with SC4A was an exothermic process. The negative values of \(\Delta S^{\circ}\) suggested a decrease in degree of freedom of the system as the metal ions are restricted by complex formation. \(\Delta G^{\circ}\) was negative, indicating that the reaction is spontaneous.