Diffusion-Wetting: a universal molecular relation

Quantifying wettability at the nanoscale remains challenging because apparent macroscopic contact angles average over multiple surface-specific effects such as roughness, chemical heterogeneity, and defect/pinning, thereby obscuring the underlying microscopic hydrophilic or hydrophobic response. We derive an analytical relation linking the microscopic water contact angle to the lateral diffusion of interfacial molecules, establishing a quantitative connection between water dynamics and the wetting behavior. Molecular dynamics simulations confirm that the ratio of interfacial to bulk diffusion uniquely determines the contact angle across the full hydrophilic-hydrophobic spectrum. This diffusion-based formulation eliminates the need for droplet geometries or free-energy sampling, enabling quantitative assessment of wetting directly from equilibrium molecular dynamics trajectories, which for simple interfaces can be remarkably short. The approach provides a universal and efficient route to evaluate surface affinity in reactive, defective, or confined environments.