## 3 Results
### Measurements of Neutron Reflection from Air-Liquid Interfaces  
Initially, to confirm the measurement accuracy of the sample cell system, NR profiles were obtained from the air-organic and air-D\({}_{2}\)O solution interfaces.  
Figure 2: The transmittance dependence on the wavelength of the incident neutrons. The red circles are the transmittance of the sample cell and the blue circles are the transmittance of the toluene-\(d_{8}\) including the sample cell. The dashed lines are the calculated transmittance values for each sample.  
Figure 3A shows the NR profiles at the air-organic and air-D\({}_{2}\)O interfaces. All NR data showed a definite critical \(Q_{c}\) point. However, the air-toluene-\(l_{8}\) reflectivity exhibited a quite rounded critical edge. It is possible that the data shape at the 0.006-0.008 A\({}^{-1}\) region may not become smooth because the neutron beam intensity dropped dramatically in the endpoint region. Since the critical \(Q_{c}\) for total external reflection, defined as \((16\pi\rho)^{1/2}\), is sensitive to the SLD difference between the upper and lower layer, the measurement accuracy of the neutron reflection from the liquid interfaces can be evaluated by determining the SLD values of organic and aqueous liquids from the obtained \(Q_{c}\) points. Table S2 shows the parameters used to fit the measured NR profiles from the air-organic and air-D\({}_{2}\)O solution interfaces. The obtained SLD and roughness values of three liquid samples, air-D\({}_{2}\)O, air-toluene-\(l_{8}\) and toluene-\(d_{8}\), were 6.28 \(\times\) 10\({}^{-6}\) and 4.1 A, 0.93 \(\times\) 10\({}^{-6}\) and 10.7 A and 5.60 \(\times\) 10\({}^{-6}\) A\({}^{-2}\) and 9.8 A, respectively. As expected, the obtained SLD values agree with the predicted values (6.30 \(\times\) 10\({}^{-6}\), 0.93 \(\times\) 10\({}^{-6}\) and 5.60 \(\times\) 10\({}^{-6}\) A\({}^{-2}\)). Therefore, it can be concluded that the sample cell system used in these experiments is suitable for measuring NR from aqueous and organic liquid surfaces. The obtained roughness value of the toluene-\(l_{8}\) sample was bigger than that of the air-toluene-\(d_{8}\) sample. This is probably owing to the isotopic effects of toluene-\(l_{8}\) and toluene-\(d_{8}\). Note that the background level of the air-toluene-\(l_{8}\) sample was higher than that of the air-toluene-\(d_{8}\) sample and the background level was in the order of 4 \(\times\) 10\({}^{-6}\). Thus, it can be suggested that the solvent for air-liquid interface reflection measurements must use deuterated solvents to provide low-background NR data.  
In addition, we investigated the adsorption structures of SDS molecules on the air-D\({}_{2}\)O surface using the sample cell system. Since SDS is a well-known surfactant and its adsorption structure at the air-water interface has been studied using the NR technique [23], it is suitable for exploratory experiments of air-liquid interface structure studies. Figure 3B shows the NR profiles obtained from the air-D\({}_{2}\)O-SDS (10 mM) sample. The NR result is consistent with the assumption of an SDS layer with a thickness of 1.8 nm. Table S3 lists the parameters used to fit the measured NR profiles from the air-D\({}_{2}\)O-SDS solution interface. The thickness, SLD and roughness values obtained from the NR analysis were 1.78 nm, 2.26 \(\times\) 10\({}^{-6}\) A\({}^{-2}\) and 10.1 A, respectively. Because the length of an SDS molecule is \(\sim\)1.7 nm, this result indicates that an SDS monolayer was formed on the surface of the D\({}_{2}\)O solution. This result is consistent with previous findings [23].  
Figure 3: (**A**) NR profiles obtained from the air-organic and air-D\({}_{2}\)O interfaces. (**B**) NR profiles obtained from the air-D\({}_{2}\)O-SDS sample. \(RQ_{z}\)\({}^{4}\) vs. \(Q_{z}\) profiles are shown in Figure S2, and the fitting curves and the SLD profiles of the air-D\({}_{2}\)O-SDS sample obtained by different models (Tables S3 and S5) are given in Figure S3.