Size dependence of shape and stiffness of single sessile oil nanodroplets as measured by atomic force microscopy.

This article presents results and guidelines on the quantitative analysis of size, shape, and stiffness of single sessile oil droplets in air and in water. Atomic force microscopy (AFM) facilitates the analysis of micro- and nanoscale droplets which are of growing importance for agrochemicals, cosmetics, or foodstuffs containing emulsions with nanoscale compartments or droplets. Measurement of droplet shape and stiffness provides information on the contact angle with the support surface as well as the interfacial tension of the liquid-liquid interface. In this study, micro- and nanoscale droplets were imaged both in amplitude modulation (AM) and force mapping modes. The effects of the AM mode set point ratio on the measured droplet shape are discussed, and a modified spherical cap model is suggested to extract the droplet-substrate contact angle. This model was applied to a population of different sized oil droplets imaged in water and led to the finding that the contact angle with the solid support varies with the droplet size. Force mapping was undertaken to measure the droplet stiffness as a function of the droplet size. Smaller droplets were found to be stiffer, in reasonable agreement with the Attard-Miklavcic model [Langmuir 2001, 17, 8217-8223] which describes the deformation of a sessile droplet in the nonwetting regime, i.e., by partial wrapping of the droplet around the probe surface. The model limitations are discussed in terms of the diverging droplet stiffness predicted for droplet radii similar to the probe radius as well as the error propagation associated with the droplet shape function.