# Synergistic Effect and Phase Behavior of SCG-CAPB-H\({}_{2}\)O
## 3 Results and Discussion  
### Synergistic Effect of SCG/CAPB Ternary Compound System  
#### 3.1.1 CMC of SCG/CAPB System  
It is widely recognized that surfactants possess a crucial attribute in reducing the surface tension of water. As the concentration of surfactants increases, surface adsorption within the solution gradually intensifies. The hydrophobic segment of the surfactant aligns towards the surface, disrupting the hydrogen bonding network within water molecules, consequently leading to a gradual decline in surface tension. Upon reaching the critical micelle concentration (CMC), micelle formation initiates. Further escalation of surfactant concentration beyond this threshold elicits minimal alterations in surface tension. Using the surface tension method, we determined the critical micelle concentrations (CMC) and additional surface properties of individual surfactants SCG and CAPB, as well as their binary SCG/CAPB system (where \(X_{1}=C_{SCG}/(C_{SCG}+C_{CAPB})\). Figure 2 illustrates the correlation between surface tension (\(\gamma\)) and the logarithm of concentration (logC). The surface tension decreases rapidly with increasing surfactant concentration, eventually reaching a plateau. Linear regression was employed to fit the trend lines of both segments, and their intersection indicated the critical micelle concentration (CMC). At this point, the corresponding surface tension represents the minimum achievable surface tension of the solution, donated as \(\gamma_{CMC}\). Table 1 provides the critical micelle concentrations and minimum surface tensions for individual surfactants as well as their mixed systems. The critical micelle concentration (CMC) of sodium cocoyl glycinate is determined to be 3.013 mmol/L, which corresponds to approximately 0.84 g/L by mass concentration. This value is slightly higher than the reported value of 0.57 g/L in the literature [31]. This difference is likely attributed to variations in the content of sodium chloride in the raw materials [46]. It is noteworthy that the reported CMC values of sodium cocoyl glycinate in the literature [47, 48] range from 0.21 to 33.8 mmol/L, which is also likely due to differences in the sodium chloride content in the raw materials used in different studies. Similarly, the CMC value of cocamidopropyl betaine was determined to be 0.974 mmol/L, which is slightly higher than the reported value of 0.881 mmol/L in the literature [49]. Considering the inevitable presence of sodium chloride impurities in the raw materials of cocamidopropyl betaine [50], this also contributes to the observed discrepancies in the CMC values reported in different studies [51, 52, 33, 53, 54, 55, 34]. The results demonstrate that the addition of a small amount of CAPB significantly reduces both the CMC and \(\gamma_{CMC}\) of the SCG/CAPB mixed system compared to the SCG system alone. This reduction indicates enhanced surface activity in the mixed system. Figure 2: The correlation between surface tension (\(\gamma\)) and the logarithm of concentration (logC) over different ratios \((X_{1})\) of the binary SCG/CAPB system. To investigate whether mixed micelles exhibit ideal or non-ideal behavior, we employed a pseudo-phase separation model to analyze their properties. [57; 58]. In this model, micelles are considered equilibrium macroscopic phases containing respective monomer solutions. The ideal critical micelle concentration (CMC*) for binary surfactant can be determined using Equation (2). \[\frac{1}{CMC^{*}}=\frac{X_{1}}{CMC_{1}}+\frac{1-X_{1}}{CMC_{2}} \tag{2}\]  
In Equation (2), \(CMC_{1}\) and \(CMC_{2}\) represent the critical micelle concentrations (CMC) of SCG and CAPB, respectively. The calculation results of CMC* for the SCG/CAPB system is displayed in Table 1.  
In Table 1, the experimental critical micelle concentration (CMC) value is one order of magnitude lower than CMC*. This indicates that the SCG/CAPB mixture deviates from ideal behavior, suggesting a strong synergistic interaction between SCG and CAPB.