The characterization of wettability of substrates by liquid nanodrops

TL;DR

This paper reevaluates the applicability of Derjaguin's formula for liquid nanodrops' wettability, proposing a modified formula to accurately determine contact angles on various substrates at the nanoscale.

Contribution

It introduces a new formula for calculating nanodroplet contact angles, extending the applicability of wettability characterization to nanoscales and different substrate wetting properties.

Findings

Derjaguin's formula is valid for large droplets on incompletely-wettable substrates.

The formula cannot be applied to nanodroplets, especially on completely-wettable substrates.

A new formula is proposed for nanodroplets influenced by disjoining pressure.

Abstract

Wettability of a substrates is characterized by a contact angle. Applicability of the simple formula developed by Derjaguin, which relates to the contact angle and disjoining pressure to nano-scale liquid droplets is reconsidered within the framework of the theory of the first-order wetting transition of volatile liquids. It is concluded that his formula is generally correct for large droplets on an incompletely-wettable substrate. But it can not be applied to nanodroplets, in particular, on a completely-wettable substrate. An effective contact angle can be defined even for the nanaodroplet. A formula similar to the Derjaguin formula is proposed by which we can calculate the contact angle of nanodorplets on both an incompletely- and a completely-wettable substrate for which the whole volume of the droplet is under the influence of the disjoining pressure.