Hybrid Cassie-Wenzel model for droplets on surfaces with nanoscale roughness

Several models have been developed to predict the contact angle of a droplet sitting on a roughened surface; however, no such model has been developed for substrates with nanoscale surface structures. In this paper we propose a hybrid Cassie-Wenzel model, which considers two factors attributed to the breakdown of macroscopic predictions, including the width of the wall-fluid depletion region and the coexistence of Cassie and Wenzel states in cases where the wall-fluid interface presents nanoscale structures. At the molecular scale, the parameter of surface roughness can be corrected by treating the wall-fluid interface as a hybrid Cassie-Wenzel state in which the fraction in the Wenzel state depends on fluid density within the cavities. A more general model developed using data fitted to fluid density is able to account for deviating tendencies induced by nanoscale surface features. A comparison of predicted results obtained in this study with those from previous works demonstrates that the proposed hybrid Cassie-Wenzel model is applicable to the evaluation of wettability in a wide range of substrates with nanoscale surface structures, corresponding to a Cassie state, a Wenzel state, and a mixed state. More importantly, the present work provides a quantitative approach to the estimation of wettability even amidst nanoscale effects, which can have a significant influence in cases with surface features at the molecular scale.