*4.3. Combining Neutron Reflectometry and Ellipsometry Experiments*

Here, we considered that performing NR and ellipsometry experiments to study lipid monolayers at the air/water interface is convenient due to their complementarity. On one side, the thickness of aliphatic chains as well as the degree of hydration of the polar headgroups can be obtained by NR whilst ellipsometry is more sensitive to the orientation of the aliphatic chains and, therefore, to the physical state of the monolayer. Despite ellipsometry being a very versatile technique, overcoming its limitations in obtaining the refractive index and thickness of monolayers at the air/water interface has required to date complex mathematical calculations (see, for example [34,61]), and/or the parallel use of another technique such as NR. However, we show here an alternative approach to overcome those limitations and the possibility to study optically anisotropic interfacial systems such as phospholipid monolayers in the LC phase (e.g., DPPC). Besides, we report a method to derive the surface excess of the monolayer by the simultaneous modeling of Δ and Ψ as a function of the angle of incidence (Figure 4) that yields a similar value than the one obtained by NR.

## **5. Conclusions**

We firstly reported the Π-*A* isotherm of DPPC at the air/buffer interface. The Π-*A* isotherm presented in this work shows an expansion towards higher molecular areas and a less pronounced phase transition than that using pure water as the subphase. We attributed these differences to the presence of cations (especially Mg2<sup>+</sup>) and HEPES in the subphase, interacting with the lipid molecules at the interface. We have also shown how, combining NR and ellipsometry, we could get a complete characterization of DPPC monolayers. All of the results obtained in this work are consistent with each other, and can be rationalized due to the presence of the HKM buffer when comparing with the literature data on DPPC thickness, molecular area, and refractive index. Therefore, the use of NR in combination with ellipsometry is proposed as an effective and accurate method for studying the optical properties including the anisotropy in the refractive index and the structure of lipid monolayers in the liquid condensed phase at the air/water interface.

**Author Contributions:** Conceptualization, methodology, data curation and writing the manuscript by all the authors: J.C.-T., A.S., D.P., and A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We thank the ILL for the provision of neutron beam time on FIGARO instrument (10.5291/ILL-DATA.TEST-3104), and the Partnership for Soft and Condensed Matter, PSCM, for the use of the ellipsometer and the Langmuir trough. AS and JC acknowledge a PhD contract from the ILL. The authors are grateful to Richard Campbell for a critical review of this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
