Impact of Negative Line Tension on the Shape of Nanometer-Size Sessile Droplets

Abstract

The sign and value of the line tension has been measured from the size dependence of the contact angle of nanometer-size sessile fullerene (C60) droplets on the planar SiO2 interface, measured with atomic force microscopy (AFM). Analysis according to the modified Young's equation indicates a negative line tension, with a magnitude between -10{-11} and -10{-10} N/m, in good agreement with theoretical predictions. The experiments also indicate that droplets with contact area radii below 10 nm are in fact two-dimensional round terraces.

Adsorption energy as a metric for wettability at the nanoscale

“…4(a), for the spherical caps matches the adsorption energy derived from the shapes of measured droplets, for which line tension is not included. Note that the value of line tension used here agrees with theoretical expectations891920.…”

“…Line tension is applied only to the extrapolated macroscale drops (see Fig. 4), where to match α calculated from actual droplet shapes, we need λ DNG  = 4.1 × 10 −10  N. This value of line tension is within the range of magnitudes predicted theoretically891920. The numerical value depends on the details of our model, which we created specifically to be calibrated and then to depend only on droplet topography.…”

“…In this regime droplets’ shapes are strongly influenced by effects such as line tension5, Tolman lengths6, and precursor film formation7. Though nanoscale droplets have non-trivial shapes, earlier studies have approximated them by spherical caps89, thus extending the contact angle framework from the macroscale to the nanoscale where a suitable metric for wettability is lacking. Creating, isolating, and measuring nanoscale droplets is challenging10, however, and purely geometrical figures of merit may suffer from inherent uncertainties associated with nanoscale measurements, see e.g.…”

“…ref. 9. A scalable metric for quantifying wettability is needed, especially given the emergence of technologies exploiting liquid-solid interactions at the nanoscale111213141516.…”

Droplet spreading and pinning on heterogeneous substrates

“…Equation (1) has to be supplemented by a correction term involving the line tension τ , related to κ, the curvature of the contact line [17,18] cos θ = cos θ eq + τ γ κ.…”