*3.3. Ellipsometry*

We performed ellipsometry measurements by exploring the variation of the ellipsometric angles Δ and Ψ as a function of the AOI. In Figure 4a,b, we show the variation of Δ and Ψ for the air/water interface, as a reference measurement, the air/buffer interface, and the h-DPPC monolayer (<sup>Π</sup> <sup>=</sup> 30 mN·m<sup>−</sup>1) spread on the HKM buffer. Firstly, both interfaces air/water and air/buffer yield similar results, which allows us to consider that the refractive index of the buffer does not change to that of water. Nevertheless, the DPPC monolayer at the air/buffer interface shows different values of Δ with respect to the ones obtained for the HKM buffer and water, particularly at values of the angle of incidence close to the Brewster angle. This is the consequence of the change in the state of polarization of the light beam when it interacts with the lipid molecules instead of the bare air/buffer interface. To explain the experimental data, we consider a one-layer optically anisotropic model for the DPPC monolayer (as described in the methods section) with an average refractive index *n*<sup>F</sup> = <sup>1</sup> <sup>3</sup>*nz* <sup>+</sup> <sup>2</sup> <sup>3</sup>*nx*. Considering the DPPC monolayer in LC as an optically uniaxial system (uniaxially birefringent), the anisotropy can be defined as Δ*n* = *n*<sup>z</sup> − *n*x, being *n*<sup>x</sup> and *n*<sup>z</sup> the refractive indexes of the layer parallel and perpendicular to the interface, respectively [35]. In our first approach, we simultaneously get the values of *n*<sup>F</sup> and *d*<sup>F</sup> that better fit the experimental data thus yielding the lowest χ<sup>2</sup> value. In detail, we simultaneously fit the variation of Δ and Ψ with AOI shown in Figure 4a,b with different *n*<sup>F</sup> − *d*<sup>F</sup> initial values covering a wide range of *n*<sup>F</sup> (from 1.33, corresponding to the bulk phase, to 1.60) and *d*<sup>F</sup> (from 0 to 30 Å). Concretely, the combination of 300 values of both parameters resulted in 9 <sup>×</sup> <sup>10</sup><sup>5</sup> *<sup>n</sup>*<sup>F</sup> <sup>−</sup> *<sup>d</sup>*<sup>F</sup> pairs of solutions with a given χ2. This approach allowed us to build a matrix shown as a color-map in Figure 4c. This map

presents a clear dark blue area in the region defined by *n*<sup>F</sup> ∈ [1.44, 1.60] and *d*<sup>F</sup> ∈ [10*A*, 30Å] that correspond to values of <sup>χ</sup><sup>2</sup> <sup>≈</sup> 1. A priori, it is difficult to select a single pair of values in this area with the minimum χ2. In the following, we show how we can extract the surface excess and the optical anisotropy of the DPPC monolayer from further analysis of the results shown in Figure 4c and compare with the ones obtained by neutron reflectometry.

**Figure 4.** (**a**) Δ and (**b**) Ψ vs. AOI of H2O (blue diamonds), HKM buffer (red circles), and DPPC (green circles). The green line corresponds to the ellipsometric angles values obtained from the fit that minimizes the χ2. (**c**) Colormap of the squared deviation χ<sup>2</sup> between measured and calculated Δ and Ψ of a DPPC monolayer at the air/buffer interface at <sup>Π</sup> <sup>=</sup> 30 mN·m<sup>−</sup>1. Each pixel of the figure represents a value of χ<sup>2</sup> obtained from the fit of Δ and Ψ vs. AOI using the correspondent values of *d*<sup>F</sup> and *n*F. (**d**) Normal distribution of Γ values correspondent to the region of lowest χ2.

Approach 1: Calculation of the surface excess of DPPC monolayer using de Feitjer's equation. We first used the sets of values (*n*F, *<sup>d</sup>*F) that yields <sup>χ</sup><sup>2</sup> <sup>≈</sup> 1 in Figure 4c to calculate the surface excess of DPPC monolayers (Γ) by using de Feitjer's equation [56]:

$$
\Gamma = \frac{d\_{\rm F}(n\_{\rm F} - n\_{\rm bulk})}{\rm dn/dc} \tag{12}
$$

Here d*n*/d*<sup>c</sup>* is the refractive index increment. In detail, we used a value of 0.138 mL·g−<sup>1</sup> obtained from reference [22]. *n*bulk is the refractive index of the bulk phase, here we used a value of 1.335 that corresponds to water taking into account that the presence of buffer does not change the ellipsometry angles as shown in Figure 4a,b. Figure 4d reports the distribution of Γ calculated for the different pairs of (*n*F, *d*F) values yielding the lowest χ2. Concretely, we have used all the values that satisfies <sup>χ</sup><sup>2</sup> <sup>≤</sup> 1.5χ<sup>2</sup> min, where χ<sup>2</sup> min accounts for the best value. The tendency shown by Γ can be modelled by a normal distribution (red line in Figure 4d) obtaining <sup>Γ</sup> <sup>=</sup> 3.0 <sup>±</sup> 0.2 <sup>μ</sup>mol·m<sup>−</sup>2. This result is in further agreement with the values of Γtails, and Γheads obtained by NR.

Approach 2: A new method to calculate the anisotropy of the refractive index *n*F. We present here for the first time a novel approach to calculate the anisotropy parameter Δ*n* as well as *nx* and *nz*, which are the refractive indices corresponding to the aliphatic tails parallel and normal to the surface, respectively. Let us first consider here that the hydrophilic heads-layer has a refractive index close to that of the bulk due to the high level of head group hydration, 32% according to the NR data (see Table 2) and previously demonstrated in references [23,35]. We, therefore, assumed that only the hydrophobic aliphatic chains can be precisely detected by ellipsometry. In this context, using the values of *n*<sup>F</sup> = 1.547 <sup>±</sup> 0.005 and *d*<sup>F</sup> = 13.7 <sup>±</sup> 0.3 Å that yields the best <sup>χ</sup><sup>2</sup> (=1.71, according to data plotted in Figure 4c) together with a value of dΔ = Δ − Δbulk for a single angle of incidence close to the Brewster conditions, we could calculate the values of *nx* and *nz* using

$$\begin{split} \text{d}\Lambda(\text{AOI}) &= -\frac{4\pi d\_{\text{F}}}{\lambda} \frac{n\_{\text{air}} \sin(\text{AOI}) \tan(\text{AOI})}{1 - \frac{n\_{\text{air}}^{2}}{n\_{\text{water}} 2} \tan^{2}(\text{AOI})} \\ &\frac{1}{n\_{\text{air}}^{2} - n\_{\text{water}} 2} \Big( n\_{\text{x}}^{2} - n\_{\text{air}}^{2} - n\_{\text{water}}^{2} + \frac{n\_{\text{air}}^{2} n\_{\text{water}} 2}{n\_{\text{z}}^{2}} \right) \end{split} \tag{13}$$

which comes from the separation of the real and imaginary parts in Equation (5) according to the Drude approximation [52], and the definition of the average refractive index

$$m\_{\rm F} = \frac{1}{3}(2n\_{\rm x} + n\_{\rm z})\tag{14}$$

In particular, we used a value of dΔ = 0.1375 rad that comes from the difference between the value of Δ of the lipid monolayer (188.48◦) and the one correspondent to the buffer (180.60◦) at an angle of incidence of 52◦, for which we had the highest sensitivity as it was close to the Brewster angle (see Figure 4a). Using the values of *n*F, *d*<sup>F</sup> and dΔ in Equations (13) and (14), we obtained *nx* = 1.537 and *nz* = 1.566 yielding an anisotropy value, Δ*n*, of 0.029.

#### **4. Discussion**
