Reassessment of DLVO theory at sub-nanometric scale: Application to Na-smectite

The nearly century-old DLVO (Derjaguin, Landau, Verview, and Overbeek) theory decomposes the interaction forces between solid surfaces separated by a fluid into attractive and repulsive components. In its standard version, it applies beyond solid surface separation distances of around 1 nm. For sub-nanometer distances, additional so-called hydration forces were widely invoked to explain the discrepancy between theory and measurements. Alternatively to this semi-empirical approach, either the validity of the theoretical expression for the electrostatic component of the disjoining pressure, or the adaptation of the Boltzmann distribution usually considered in the application of DLVO theory are questioned. Here, it is suggested that the introduction of a hydration component whose parameters cannot be predetermined but are a matter of calibration is unnecessary. Hydration effects, introduced in the calculation of ionic concentrations, directly influence ions distributions and therefore the repulsion of adjacent electric double layers. This effect is thus part of the electrostatic component of the disjoining pressure. An analytical expression extending DLVO theory to small surface separation distances together with a simplified electrical model, both proposed here, enable reproducing data for Na-smectite. Results are also in good agreement with thermodynamic and molecular dynamics calculations. It is confirmed that the discrepancy between theory and observations is mainly due to the underestimation of counterions concentration at the mid-plane identified using an inappropriate electrical model. For ions with radii around 0.1 nm, commonly found in natural media, the standard DLVO expression can still be used, but with mid-plane concentrations calculated using an appropriate electrical model