Quantifying surfactant adsorption at fluid interfaces by combining X-ray reflectivity and simulations
Adsorption of surfactants to fluid interfaces occurs in numerous daily-life and technological contexts. The surfactant surface coverage $\Gamma$ governs interface characteristics like tension $\gamma$, viscoelastic properties, and the stability of thin foam films. Directly measuring $\Gamma$ as a function of the bulk concentration $c$ is highly desirable but challenging, particularly for non-ionic surfactants that lack easily detectable labels. Neutron reflectometry is currently the only generally applicable method, but it is not available for routine experiments. Here, we propose a simulation-assisted approach to deduce the adsorption isotherm $\Gamma(c)$ from X-ray reflectivity data: As a first step, we use atomistic molecular dynamics simulations of surfactant-loaded air/water interfaces with prespecified $\Gamma$ to obtain interfacial electron density profiles. From these profiles, we compute theoretical X-ray reflectivity curves and compare them with experimental measurements to determine the matching bulk concentration. We focus on two non-ionic surfactants (C$_{12}$EO$_6$ and $\beta$-C$_{12}$G$_2$}) with previously established force fields to illustrate how this combined approach of experiments and simulations can determine the adsorption isotherm. Additional insights are gained through comparison with the measured surface tension isotherms $\gamma(c)$, based on the equation of state $\gamma(\Gamma)$ from simulations.