Robust methods for the characterization of droplet behavior in molecular dynamics: from contact radius to contact angle

We present a comparative analysis of methodologies for studies of wetting behavior of liquid nano-droplets. Different droplet sizes were simulated using molecular dynamics (MD) under both complete and partial wetting conditions. The results show why conventional root mean square displacement (RMSD) metrics are inadequate for capturing finite system dynamics based on internal, center of mass, and coupling contributions to its value. The <i>z</i>-component of the center of mass is proposed as an alternative, accurate descriptor. A new equation for the contact radius of nano-droplets is derived using the radius of gyration (<i>R</i>_g) of interfacial molecules. In addition, a modified sinc kernel smoother is employed to develop a new method for calculating the dynamic contact angle. The accuracy and robustness of both the new and conventional methods were evaluated through calculations of physical properties, including apparent line tension and contact angle. The apparent line tension is positive only in highly hydrophilic systems and negative otherwise. Young's contact angle shows consistent results across methods for hydrophilic cases but varies in hydrophobic systems, signifying its dependence on the droplet shape analysis technique. The proposed methods yield physically meaningful results and are more reliable than standard circle fitting techniques.