Quantifying surfactant adsorption at fluid interfaces by combining X-ray reflection and simulation

TL;DR

The paper addresses the challenge of quantifying the adsorption isotherm $Γ(c)$ for non-ionic surfactants at fluid interfaces. It introduces a workflow that couples X-ray reflectivity (XRR) and GIXOS experiments with atomistic molecular dynamics to generate interfacial electron density profiles for fixed $Γ$, enabling the calculation of theoretical reflectivity curves that are matched to measurements to infer $Γ(c)$, and then reconstructs $γ(c)$ via the MD-derived equation of state $γ(Γ)$. The approach is demonstrated on $C_{12}EO_6$ and $β$-$C_{12}G_2$: for $C_{12}EO_6$, the MD-assisted analysis yields an adsorption isotherm that reproduces the measured surface-tension isotherm; for $β$-$C_{12}G_2$, cross-validation with GIXOS and XRR reveals broadly consistent $Γ(c)$ and uncovers a hump in $γ(Γ)$ indicative of metastable two-phase behavior. Overall, the method enables routine, lab-based quantification of surfactant adsorption and provides a robust route to force-field validation and thermodynamic interpretation of interfacial tensions.

Abstract

Adsorption of surfactants to fluid interfaces occurs in daily-life and technological contexts like dish washing and oil spill remediation. The surfactant surface coverage $Γ$ governs interface characteristics like tension $γ$, viscoelastic properties, and the stability of thin foam films. Directly measuring $Γ$ as a function of the bulk concentration $c$ is highly desirable but challenging, particularly for non-ionic surfactants that lack easily detectable labels. Here, we propose a generic approach to deduce the adsorption isotherm $Γ(c)$: As a first step, we use atomistic molecular dynamics simulations of surfactant-loaded air/water interfaces with known $Γ$ to obtain interfacial electron density profiles. From these profiles, we then compute theoretical X-ray reflectivity curves, which we compare with experimental measurements to find the matching $c$. We focus on two non-ionic surfactants (C$_{12}$EO$_6$} and $β$-C$_{12}$G$_2$}) with previously verified force fields to demonstrate how this combined approach of experiments and simulations can determine the adsorption isotherm. By using the equation of state $γ(Γ)$ from simulations, our results replicate the measured surface tension isotherms $γ(c)$.

Figures (10)

• Figure 1: Chemical structures of the surfactants investigated.
• Figure 2: XRR curves $R(q_z)$ of the surfaces of aqueous C12EO6 solutions with bulk concentrations ranging from 0.530 M, all below the CMC. For clarity, the curves are plotted as $R\cdot q_z^4$ on a logarithmic scale as a function of $q_z$.
• Figure 3: (A) Simulation snapshot of a water layer with 48.0 C12EO6 surfactants on each surface, corresponding to $\Gamma=\qty{2.0}{\per\nano\meter\squared}$. CH2 groups and CH3 groups (both represented as united atoms) are shown in light blue, oxygen atoms in red, and polar hydrogen atoms in white. The periodic simulation box is indicated with a rectangle. (B) Associated electron density profile $\rho_{\text{e}}(z)$ in the direction perpendicular to the interfaces.
• Figure 4: (A) One-sided electron density profiles from simulations with various surface coverages of C12EO6 surfactants (see legend in panel B). (B) Associated XRR curves. For clarity, the curves are plotted as $R\cdot q_z^4$ on a logarithmic scale as a function of $q_z$.
• Figure 5: Experimental XRR curve for C12EO6 at $c=\qty{10}{\micro M}$ (symbols) together with theoretical XRR curves (lines) corresponding to simulations with three different surface coverages. For clarity, the curves are plotted as $R\cdot q_z^4$ on a logarithmic scale as a function of $q_z$. Only $\Gamma=\qty{2.0}{\per\nano\meter\squared}$ leads to good agreement with the experimental reflectivity data.