Derivation of the refractive index of lipid monolayers at an air-water interface

We demonstrate by means of a simple thought experiment on lipid films dispersed over an air-water interface that a core refractive index of the system approaches root 2, a very significant value for the lipid (DPPC or DPPE) monolayers. The thought experiment consists of balancing two principal types of acting pressures: the vertical and the horizontal/lateral ones, both taken at a thermodynamic equilibrium. The horizontal pressure of (modified) van der Waals type comes from the minimalistic application of the (movable) lateral barrier, as can be expected to occur in Langmuir experiments, provided that the application of pressure is very weak. On the other hand, after relaxing the system when the barrier goes back, one expects to arrive at another scenario. This is when the vertical pressure of the air-water quasi-planar system of hydrophobic propensity applies, provided that an idealized assumption of the equally distributed pressurizing energy is true. This is in accord with a Kubo evaluation for a certain number of charged point-like objects immersed in water spherical shells and surrounded by air for which the Kelvin (J.J. Thomson) law prevails. At the horizontal vs. vertical pressure conditions one may uncover, by employing simple analytic means the basic dielectric and optical properties of the domain-wise, pairwise-interaction involving lipid film. It turns out that a simple Gladstone-Dale scenario, pointing to splitting the core refractive index into root 2 approximate to 1 + 0.41 overwhelms, with the fractional value of ca. 0.41 attributed to a molecular contribution of the charged lipid-water (dipolar) local system, affecting the overall pressure-addressing scenario. (By the value of refractive index centering at one, the vacuum conditions are to be addressed.) One may argue, however, that the fractional part of the refractive index seems to be a bit outside the contemporary experimental reach. On the other hand, it can be rationalized by the Casimir critical soft-matter fluctuational effect.