## 4 Discussion  
There was a small difference in the surface roughness between the air-toluene-\(h_{\text{B}}\) and air-toluene-\(d_{\text{S}}\) samples. As mentioned above, this was probably owing to the isotopic effects of toluene-\(h_{\text{B}}\) and toluene-\(d_{\text{S}}\). From previous reports related to the roughness of a thermally perturbed interface [24; 25], the mean square roughness of the liquid-vapor interface can be expressed as  
\[\sigma^{2}=\sigma_{0}{}^{2}+\tfrac{k_{\text{B}}T}{2\pi\gamma}\ln\left(\tfrac{2 Q_{\text{max}}}{Q\Delta\beta}\right) \tag{1}\]  
where \(\sigma_{0}\) is the intrinsic width of the interface, \(k_{\text{B}}\) is the Boltzmann constant, \(T\) is the temperature, \(\gamma\) is the interfacial tension of the liquid-vapor interface, \(Q_{\text{max}}\) (\(\cong\pi/\alpha\), where a is the molecular diameter) is the short wavelength cutoff of the capillary waves and \(\Delta\beta\) is the angular acceptance of the detector. H\({}_{2}\)O/D\({}_{2}\)O and other-\(h/d\) molecules have slightly different molecular size and chemical/kinetic properties [26; 27; 28; 29; 30]. In particular, deuteration of toluene results in a change in molar volume and surface tension from 106.28 (mL/mol) and 28.51 (mN/m) to 105.98 (mL/mol) and 28.4 (mN/m). Thus, it is reasonable to suppose that the interfacial tension and molecular sizes are slightly different between hydrogenated and deuterated toluene. Since the interfacial tension and molecular size of deuterated toluene are smaller than those of the hydrogenated toluene, the surface roughness of the air-toluene-\(d_{\text{S}}\) sample decreased owing to their synergistic effect. Figure 4: **(A)** NR profiles obtained from the toluene-\(d_{\text{S}}\)-D\({}_{2}\)O and toluene-\(d_{\text{S}}\)-D\({}_{2}\)O-SDS samples. The NR profiles of the toluene-\(d_{\text{S}}\)-D\({}_{2}\)O sample are vertically shifted to show the NR profiles more clearly. **(B)** The SLD profiles of the air-D\({}_{2}\)O-SDS and toluene-\(d_{\text{S}}\)-D\({}_{2}\)O-SDS samples. 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 S4. In the results of the SDS adsorption structure studies, there were small differences in the SDS adsorption layer structure on the air-D\({}_{2}\)O and toluene-\(d_{8}\)-D\({}_{2}\)O interfaces. Figure 4B shows the SLD profiles that led to the modeled reflectivity curves. Since the SLD is related to the volume fraction (\(\varphi\)), assuming that the SDS layer only contains the alkyl-chain moiety of adsorbing SDS, the determined SLD value can be used to deduce \(\varphi\) as follows [13]:  
\[\varphi_{s}=(\rho-\rho_{w})/(\rho_{s}-\rho_{w}) \tag{2}\]  
where \(\varphi_{s}\) is the volume fraction of SDS, \(\rho_{w}\) is the SLD value of water (D\({}_{2}\)O) and \(\rho_{s}\) is the SLD value of the SDS. The surface excess (in mol/area) of an SDS species, \(\Gamma_{S}\), is given by [13; 31; 32; 33]  
\[\Gamma_{S}=\rho_{s}t\varphi_{s}/b_{s}N_{A} \tag{3}\]  
where \(b_{s}\) is the scattering length of the SDS molecule and \(N_{A}\) is Avogadro's number. The obtained surface excess values were 4.75 (\(\mu\)mol/m\({}^{2}\)) for the air-D\({}_{2}\)O-SDS sample; this result is consistent with the reference [13]. Therefore, it can be suggested that an SDS alkyl-chain exists in an extended conformation at the surface of water. On the other hand, recent interface structure studies of the SDS molecule suggested that the SDS headgroup is surrounded by water molecules, the SDS tail group does not interact strongly with \(n\)-hexadecane molecules and the SDS alkyl tail is in a disordered state and partially in contact with water [21]. In addition, in both experimental and simulation studies, similar phenomena were observed at the water-CCl\({}_{4}\)-SDS sample interface [22; 23] and the average length of the SDS molecule at the water-CCl\({}_{4}\) interface based on these findings was 1.33 nm.