Accounting for Nanofilm Contributions in Interfacial Free Energy Calculations Using Classical Density Functional Theory

Abstract

Fluid nanofilms play a fundamental role in nanoscale interfacial thermodynamics, yet their treatment in classical density functional theory (cDFT) remains incomplete. We investigate nanofilm interfacial properties using a cDFT framework built upon the perturbed-chain statistical associating fluid theory (PC-SAFT) for both fluid-fluid and fluid-solid interfacial systems. Comparison with molecular simulations shows that the long-standing numerical discrepancies regarding free-standing nanofilms persist in the PC-SAFT functional predictions, supporting the view that they stem from thermal capillary-wave fluctuations rather than deficiencies of the density functional itself, as such fluctuations are inherently neglected in the mean-field approximation adopted by standard cDFT. Importantly, we establish a thermodynamically consistent framework for interfacial free energy (IFE) calculation, which explicitly incorporates nanofilm thermodynamic contributions and redefines the effective fluid volume by excluding the solid-phase region. The proposed method exhibits excellent consistency with another method based on the relationship between IFE and disjoining pressure for fluid systems, while both fluid-fluid and fluid-solid IFEs differ substantially from those predicted by the conventional method. We find that neglecting nanofilm contributions induces prominent size-dependent variations in the IFE and contact angle of hemicylindrical droplets, which is inconsistent with the extensive literature. Different methods also lead to opposite signs of the line tension for a hemispherical argon nanodroplet on a strongly lyophobic surface. The proposed framework provides a unified molecular-level basis for understanding interfacial processes involving nanofilms, including wetting, nucleation, adsorption, and other phenomena that rely on the accurate evaluation of IFEs.