Volume Dependence of Contact Angle in Nanodroplets: Interface Layering Contributions beyond the Standard Line Tension

The volume dependence of the contact angle (VDCA) of a droplet at the nanoscale is primarily ascribed to the standard line tension. Researchers have identified additional volume-dependent sources that arise from the liquid layering structure within the three-phase contact zone (TPZ). These sources introduce systematic errors in the analysis of wettability and the measurement of standard line tension in nanodroplets. Therefore, this study examines the effect of the liquid layering structure on the VDCA and contrasts it with the standard line tension. The mechanism is elucidated through a thermodynamic theoretical analysis of the liquid at the adsorbed layer in cylindrical droplets: the liquid layering structure influences the contact angle by altering the liquid density distribution and the corresponding Gibbs adsorption. The validity of the theoretical analysis is confirmed through molecular dynamics simulations of parallel liquid films and cylindrical droplets. This study analyzes the effects of sources associated with liquid layering, including normal solid capillary force and Laplace pressure. The findings demonstrate that the influence of the liquid layering structure on the VDCA is first order in relation to the contact curvature, comparable to the contribution from the standard line. Furthermore, this study examines how the layering liquid structure influences the wettability of nanodroplets, offering a new thermodynamic perspective for understanding the origins of line tension in experimental contexts.