## 3 Results and Discussion
### Surface Properties of MPNTS  
Critical micelle concentration (CMC) is an important index to determine the properties of surfactants [28]. It represents the concentration at which the surfactant begins to form a large number of micelles. At the CMC of the surfactant aqueous solution, the hydrophobic groups of the surfactant molecules aggregate to form a hydrophobic region, while the hydrophilic groups outside the hydrophobic groups gather in the water to form  
Figure 3: \({}^{1}\)H MNR map of MPNTS (**a**) methylpropenyl polyether modified nonionic silicone surfactants, (**b**) methylpropenyl polyether, and (**c**) 1,1,3,5,5,5-heptamethyltrisiloxane. (The letters of the structural formula correspond to the characteristic peaks, representing H elements in different positions). a hydrophilic region. Such an arrangement forms a spherical-like structure known as a micelle. The appearance of micelles can vary, depending on their structure and composition. Generally speaking, the outer layer of micelles is the surface layer formed by hydrophilic groups, while the inner layer is the core region formed by the aggregation of hydrophobic groups. According to the morphology of the hydrophobic groups inside the micelles, the shape of the micelles can be spherical, rod-like, plate-like, or other shapes. The appearance and properties of micelles have a significant impact on their applications in various fields. For example, in biology, the structure of micelles is closely related to the formation and function of cell membranes; in the cosmetics industry, and micelles are widely used for skin cleaning and moisturizing purposes. When the solution reaches the critical micelle concentration, the surface tension of the solution decreases to the lowest value [29]. At this time, if the concentration of the surfactant is increased, the surface tension of the solution will no longer decrease, but a large number of micelles will be formed. In this case, the surface tension of the solution is the minimum surface tension that the surfactant can achieve. The smaller the CMC value, the lower the concentration needed for the surfactant to form micelles and the lower the concentration of saturated adsorption on the surface. Therefore, a lower concentration is required to modify surface properties to enable wetting, emulsification, compatibilization, foaming, and other functions. Additionally, the CMC is an important factor in determining the surfactant's application range. In this experiment, the surface tension method was adopted, and the CMC value of MPNTS was measured by the linear fitting method. It is considered the inflection point of surface tension with a change in concentration, which refers to the intersection points of the straight lines of surface tension under high and low concentrations. This method was simple, intuitive, and had little error. For NPNTS, it was observed that the surface tension dropped sharply when the concentration was from 1 mg/L to 60 mg/L, as well as when surface tension reduced from 64 mN/m to 20 mN/m. However, the surface tension remained almost unchanged after the concentration was 70 mg/L, and it finally stabilized at 18.68 mN/m (Figure 4). This is because increasing the concentration of the surfactant after the concentration exceeds the CMC can only lead to the formation of more micelles, while the actual surfactant composition in the water is only maintained at the CMC. In order to prove the reliability of the test data, some studies on the determination of CMC were compared. [PERSON] [30], [PERSON] [31] et al. used the surface tension method to accurately measure the CMC of surfactants. Based on this, we found, by linear fitting, that the intersection point of surface tension between high and low  
Figure 4: Effect of concentration of MPNTS on the surface tension of MPNTS aqueous solution. concentrations of MPNTS was located at 78 mg/L. So, we can confirm that the CMC value of MPNTS is 78 mg/L, and we found that the surface tension at this point was 18.68 mN/m.