*3.1.* Π*-A Isotherm*

Figure 2a shows the Π-*A* isotherm for DPPC in the HKM buffer. DPPC shows a liquid expanded (LE) phase at a very low surface pressure, followed by a minor liquid expanded–liquid condensed (LE–LC) coexistence region at <sup>Π</sup> <sup>≈</sup> 5 mN·m<sup>−</sup>1. Further compression yields a LC phase, characterized by a long range molecular order, until it reaches the collapse at <sup>Π</sup> <sup>≈</sup> 54 mN·m<sup>−</sup>1. The <sup>Π</sup>-*<sup>A</sup>* isotherm does not show a well-defined LE–LC coexistence region as DPPC on water, characterized by a well-defined plateau of coexistence [27,38]. In Figure 2b, we report the corresponding compressional elastic modulus *C*s <sup>−</sup>1, calculated from the surface pressure isotherm following

$$\text{C}\_{s}\text{ $^{-1}$ } = -A \left(\frac{\partial \Pi}{\partial A}\right) \tag{9}$$

where Π represents the surface pressure and *A* the surface area. The Π-*A* isotherm shown in Figure 2a is quite similar to those previously reported in the literature for DPPC in water, consequently, we interpret them in a similar way [27]. At increasing Π, DPPC molecules are pushed closer and the compressional elastic modulus increases until it reaches a maximum. The low Π region is commonly assigned to a 2D liquid expanded state (LE). A minimum in the compression modulus at <sup>Π</sup> <sup>≈</sup> 5 mN·m<sup>−</sup>1, is commonly attributed to the existence of a LE–LC phase transition, which can be more clearly observed than the slight pseudo plateau in the isotherm (Figure 2a). The global maximum value of *C*s <sup>−</sup><sup>1</sup> is 130 mN·m<sup>−</sup>1, which corresponds to the LC phase. The values of *C*<sup>s</sup> <sup>−</sup><sup>1</sup> in this LC phase are smaller than the ones observed for DPPC at the air/water interface, which present a maximum at *C*<sup>s</sup> <sup>−</sup><sup>1</sup> <sup>≈</sup> 230 mN·m−<sup>1</sup> [27], indicating a less condensed monolayer. Importantly, Figure 2 shows that a DPPC monolayer in the presence of buffer containing divalent salts exhibits more lateral compressibility due to a less acyl chain compaction, and, therefore, is more permeable [53].

**Figure 2.** (**a**) Π-*A* isotherm of a DPPC monolayer at the air/buffer interface and (**b**) corresponding *C*<sup>s</sup> −1 as a function of Π.

#### *3.2. NR Results*

Neutron reflectometry measurements were performed to study the structure of DPPC monolayers in the LC phase. In particular, we selected a sample with a surface pressure value of 30 mN·m−<sup>1</sup> corresponding to an area per molecule of 53.8 Å2, well above the LE–LC coexistence phase. This guarantees a laterally homogeneous interface on the length scale of the in-plane neutron coherence length, on the order of several microns, and implies that the measured NR can be correlated

with the SLD depth profile averaged across the interfacial area delimited by this coherence length. The reflectivity profiles were recorded over the whole Q-range accessible in three isotopic contrasts: h-DPPC, cm-DPPC, and d62-DPPC in ACMW as shown in Figure 3a. As a reference, the measurement of the bare air/D2O interface is shown also in Figure 3a, including a fit to the data that corresponds to a roughness, *r*0, of 2.8 ± 0.1 Å in agreement with the theoretical value expected for thermally excited capillary waves (<sup>∼</sup> *k*B*T*/γ0), with γ<sup>0</sup> being the interfacial tension of the bare D2O interface [45,46].

**Figure 3.** (**a**) Neutron reflectivity data of pure D2O interface (black circle), h-DPPC (red squares), cm-DPPC (blue triangles), and d62-DPPC (magenta diamonds) monolayers at <sup>Π</sup> = 30 mN·m−<sup>1</sup> in HKM-ACMW. The fitting curves of the bare D2O interface (orange curve), h-DPPC (red), cm-DPPC (blue), and d62-DPPC (magenta) monolayers are shown. The χ<sup>2</sup> value is 2. The figure is displayed on an *R*(Qz)Qz <sup>4</sup> scale to highlight the quality of the fits at high Qz values. (**b**) SLD profiles normal to the interface of monolayers of h-DPPC (red), cm-DPPC (blue), and d62-DPPC (magenta) monolayers at <sup>Π</sup> = 30 mN·m<sup>−</sup>1. (**c**) Volume fraction profiles normal to the interface of monolayers to highlight the distribution of tails (violet) and heads (green). (**d**) Cross-sectional area profiles normal to the interface of monolayers to highlight the distribution of tails (violet) and heads (green). Note that the area of the head-groups here does not consider the hydration.

The neutron reflectivity profiles were fitted according to a two-layer model, based on the model recently reported by Campbell et al. [27]. In detail, the model consists of a first layer containing the lipid aliphatic tails in contact with air and, a second one, containing the polar headgroups submerged in the aqueous subphase (see Figure 1a). All parameters used to describe both layers (such as the values of Σ*b* and molecular volumes) are included in Table 1. The best fit of the reflectivity profiles measured is also included in Figure 3a as solid lines. The resulting SLD profiles across the interface are plotted in Figure 3b.

The structural parameters obtained from the fits are summarized in Table 2. The roughness of the three interfaces (air/tails-layer, tails-layer/heads-layer, and heads-layer/subphase) was constrained to be equal. The value obtained from the fitting is 3.0 ± 0.5 Å, which is perfectly consistent with the presence of capillary waves due to thermal fluctuations (usually estimated through the relation: *r* ≈ *r*<sup>0</sup> γ0/(γ<sup>0</sup> − Π) [54,55]). The value of the thickness of DPPC monolayer is 23.5 Å, with 15.0 Å corresponding to the aliphatic tails in contact with air. Using the parameters from Tables 1 and 2, the variation of the volume fraction, *f* DPPC(*z*), with the distance to the interface, was calculated using the difference of two error functions as follows

$$f\_{\text{DPPC}}(z) = \begin{cases} \frac{1}{2} f\_{\text{tails}} \left[ \text{ERF} \left( \frac{z}{\sqrt{\gamma\_2}} \right) - \text{ERF} \left( \frac{z - t\_{\text{tails}}}{\gamma/\sqrt{2}} \right) \right], & 0 \le z \le t\_{\text{tails}}\\\frac{1}{2} f\_{\text{hads}} \left[ \text{ERF} \left( \frac{z}{\gamma/\sqrt{2}} \right) - \text{ERF} \left( \frac{z - t\_{\text{today}}}{\gamma/\sqrt{2}} \right) \right], & t\_{\text{tails}} \le z \le t\_{\text{tails}} + t\_{\text{heads}} \end{cases} \tag{10}$$

The structural information elucidated by NR on DPPC monolayers can be better interpreted, therefore, by the volume fraction profiles and the corresponding cross-sectional area profiles as a function of the distance from the interface, which are shown in Figure 3c,d, respectively. Such as the volume fraction, the cross-sectional area profile is modulated by the same error function and it is calculated as follows:

$$A\_{\rm DPPC}(z) = \begin{cases} \frac{V\_{\rm m, t \rm tils}}{2 \int\_{t \rm tils/t\_{\rm tils}} \left[ \rm{ERF} \left( \frac{z}{r/\sqrt{2}} \right) - \rm{ERF} \left( \frac{z - t\_{\rm tils}}{r/\sqrt{2}} \right) \right], & 0 \le z \le t\_{\rm tils} \\\frac{V\_{\rm m, b\rm bads}}{2 \int\_{t \rm bends} \int\_{b\rm bads} \left[ \rm{ERF} \left( \frac{z}{r/\sqrt{2}} \right) - \rm{ERF} \left( \frac{z - t\_{\rm bends}}{r/\sqrt{2}} \right) \right], & t\_{\rm tils} \le z \le t\_{\rm tils} + t\_{\rm bends} \end{cases} \tag{11}$$

The values used to calculate the cross-sectional area from Equation (11) are collected from Tables 1 and 2.

**Table 2.** Parameters resulting from the data modeling. \* The hydration degree of the headgroups are considered here.

