Thermodynamic Investigation of the Barrier for Heterogeneous Nucleation on a Fluid Surface in Comparison with a Rigid Surface

When a vapor phase is in contact with a solid or nonvolatile fluid, under conditions where the vapor is thermodynamically metastable to condensation, a droplet may nucleate from the vapor either homogenously within the vapor phase, or heterogeneously at the solid or fluid substrate interface. The case where the droplet is thermodynamically favored to nucleate heterogeneously is the subject of this article. The heterogeneous nucleation of a sessile drop on a soft surface has been studied many times experimentally and theoretically. It has been observed experimentally that heterogeneous nucleation happens faster on a soft surface in comparison with a rigid surface. Here we use Gibbsian surface thermodynamics to provide a physical understanding for this observation. Due to the difficulties of considering soft-elastic surfaces, we demonstrate that by considering only the fluidity of a surface (i.e., by considering a fluid surface as an infinitely soft material and comparing a fluid surface with a rigid surface), thermodynamics will predict that heterogeneous nucleation is easier on soft surfaces compared with rigid surfaces. We first investigate the effect of contact angle on the barrier for heterogeneous nucleation on rigid substrates at constant vapor phase pressure. Then we find a lower energy barrier for heterogeneous nucleation at a fluid surface in comparison with heterogeneous nucleation at a rigid surface which explains the faster nucleation on soft surfaces compared with rigid surfaces. Finally we inspect the role of each contribution to the energy barrier.