*2.4. NR Data Modeling*

The data analysis was performed using AuroreNR software (v5.0) [42]. A two-layer model was used to fit the data, dividing surface-active molecules between polar heads and aliphatic tails (Figure 1). It has been recently demonstrated that using this model results in a better fit of the experimental curves [27]. The fixed parameters used in the fitting procedure (Table 1) are molecular volumes of DPPC heads (*V*m\_heads) and tails (*V*m\_tails) [43,44] and the total scattering length of DPPC heads (Σ*b*heads) and tails (Σ*b*tails). Heads-layer thickness (*t*heads) was calculated from the *V*m\_heads, and finally, the roughness (*r*) of the three interfaces (i.e., air/tails-layer, tails-layer/heads-layer, and heads-layer/subphase) was assumed identical following the approach reported by Campbell et al. [27]. Besides, its value was consistent with the presence of capillary waves [45]. A real interface is characterized by a finite roughness, whose minimum value depends on the capillary waves of the subphase [45,46]. Therefore, the change in SLD along the *z*-axis of a real interface is described here by the SLD profile of the ideal interface modulated by an error function, ERF [47]:

$$\text{ERF}\left(\frac{z-z\_0}{\sigma/\sqrt{2}}\right) = \frac{2}{\sqrt{\pi}} \int\_0^{\frac{z-z\_0}{\sigma/\sqrt{2}}} \text{e}^{-t^2} \text{dt} \tag{2}$$

where *z*<sup>0</sup> and σ indicate the position and the roughness (respectively) of the interface between the layers.

**Table 1.** Fixed parameters used for data modeling. The molecular volumes of h-DPPC, cm-DPPC, and d62-DPPC are equal; the only difference between the sample parameters is the value of the total scattering length of the tails Σ*b*tail. One can calculate the scattering length density (SLD) values shown considering *b* and *V*<sup>m</sup> (SLD = Σ*b*/*V*m).


Experimental data of h-DPPC, cm-DPPC and d62-DPPC were fitted together. Thus, the ambiguity in the interpretation of the sample structure, which may arise from the different sensitivity that the curves exhibit with respect to the different sample components, is significantly reduced. Using this approach, the variables determined through the fitting procedure were solely the surface roughness (*r*), the thickness of the tails-layer (*t*tails), and the heads volume fraction (*f* heads), whose value was constrained to ensure the same surface excess (Γ) of tails Γtails and heads Γhead, calculated as follows:

$$
\Gamma\_i = \frac{\text{SLD}\_i t\_i f\_i}{\Sigma b\_i \text{N}\_\Lambda} \tag{3}
$$

where Σ*bi* and *fi* are the total scattering length and the volume fraction of the *i*-th component (tails or heads), respectively, and NA is the Avogadro's number. While the tails volume fraction *f* tails was fixed to unity (i.e., 100%), for the determination of *f* heads the solvation of the polar headgroups was taken into account. This yields the following equation:

$$f\_{\text{heads}} = \frac{t\_{\text{tails}} V\_{\text{m\\_heads}}}{t\_{\text{heads}} V\_{\text{m\\_tails}}} \tag{4}$$

#### *2.5. Ellipsometry*

Ellipsometry experiments were performed on a Picometer Light ellipsometer (Beaglehole Instruments, Kelburn, New Zealand) using a He-Ne laser with λ = 632 nm. The Langmuir trough used to record the isotherm was coupled with the ellipsometer to measure and control the surface pressure of the lipid monolayer during the measurements of the ellipsometric angles. We studied a DPPC monolayer at the air/buffer interface by measuring the ellipsometric angles as a function of the angle of incidence, AOI, at <sup>Π</sup> <sup>=</sup> 30 mN·m<sup>−</sup>1. The range of AOI was 45◦–70◦ with a step of 0.5◦.

Ellipsometry is a non-destructive optical technique widely used for the study of surfaces and thin films [28,48]. It is based on the determination of the polarization changes that light undergoes when it is reflected at an interface. The reflection coefficients parallel and perpendicular to the plane of incidence, *r*<sup>p</sup> and *r*<sup>s</sup> respectively, are related to the ellipsometric angles Δ, and Ψ. This relationship is known as ellipticity, ρ, and is defined by the following equation:

$$\rho = \frac{r\_{\text{P}}}{r\_{\text{S}}} = \tan \Psi \mathbf{e}^{i\Delta} \tag{5}$$

where ρ is the ellipticity that depends on the AOI, the wavelength of the light and both the thickness and the dielectrical properties of the material on which the reflection of the light beam occurs.

Although the ellipsometric angles are experimentally easily accessible, they do not provide direct access to the refractive index and the thickness of the lipid monolayer. Thus, it is necessary to model the experimental sets of Δ and Ψ vs. AOI to determine *d*<sup>F</sup> and *n*F. For the data analysis, we constructed a slab model considering the profile of refractive indices perpendicular to the surface. In contrast to NR, ellipsometry cannot distinguish between heads and tails of lipid molecules, and the different layers are considered as one homogenous layer with negligible roughness (see Figure 1**)**. Therefore, the model used in this work consisted of one slab formed by the lipid monolayer characterized by *n*<sup>F</sup> and *d*F.

Once constructed the model, we fitted the data of Δ and Ψ vs. AOI using a numeric nonlinear minimization procedure, specifically, a trust-region reflective algorithm [49]. This method is based on the determination of the ellipsometric angles of the model that minimizes the differences with those experimentally obtained (a more detailed explanation can be found in references [49–51]). For the calculation of Δ and Ψ of the model, we used a power series expansion to the first order of the relative film thickness (2π*d*F/λ) that allows us to relate ρ, i.e., Δ and Ψ, with *n*<sup>F</sup> and *d*<sup>F</sup> as follows:

$$
\rho \approx \rho\_0 + i\rho' \frac{2\pi d\_{\rm F}}{\lambda} \tag{6}
$$

where ρ<sup>0</sup> is the ellipsometric ratio of the ambient/substrate interface and ρ' (Equation (7)) is a linear coefficient defined by the refractive indices of the air and the subphase, *n*<sup>1</sup> and *n*2, respectively, and the incident and transmission angles, αinc and αtra, respectively.

$$\rho' = -2\frac{n\_1}{n\_2^2 - n\_1^2} \frac{\sin^2(\alpha\_{\rm inc})\cos(\alpha\_{\rm inc})}{\cos^2(\alpha\_{\rm inc} - \alpha\_{\rm tra})} \frac{\left(n\_\rm F^2 - n\_1^2\right)\left(n\_\rm F^2 - n\_2^2\right)}{n\_\rm F} \tag{7}$$

Drude reported this approximation for the first time based on the fact that the terms of a higher order than the first are negligible when the thickness of the film is very small [34,52]. Therefore, the Equations (5)–(7) provide the values of Δ and Ψ for given values of *n*<sup>F</sup> and *d*F. Finally, the variation of *n*<sup>F</sup> and *d*<sup>F</sup> allows one to obtain the real parameters of the film as those that minimizes the differences between the calculated ellipsometric angles and those experimentally obtained. The function minimized and used to determine the quality of a given solution is the squared deviation (χ2) between measured and calculated ellipsometric angles and it is defined by:

$$\chi^2 = \frac{1}{N - M} \sum\_{i=1}^{N} \left[ \left( \frac{\Delta\_{(i)\exp} - \Delta\_{(i)\text{model}}}{\delta\_{(i)\Delta}} \right)^2 + \left( \frac{\Psi\_{(i)\exp} - \Psi\_{(i)\text{model}}}{\delta\_{(i)\Psi}} \right)^2 \right] \tag{8}$$

where *N* is the number of points, *M* is the number of parameters determined (i.e., two parameters, *d*<sup>F</sup> and *n*F), Δexp and Δmodel correspond to the ellipsometric angle Δ experimentally obtained and the calculated for the model, respectively, and δ<sup>Δ</sup> the uncertainty of the i-th experimental Δ or Ψ value.
