The characteristics of heterogeneous nucleation on concave surfaces and implications for directed nucleation or surface activity by surface nanopatterning

Abstract

The characteristics of heterogeneous nucleation on concave spherical surfaces were analysed using a novel analytical approach and compared with nucleation on both convex and planar surfaces. The complex expressions of ∂ΔG/∂r (ΔG: free energy change and r: embryo radius) for nucleation on concave spherical surfaces can be reduced to the simple form for nucleation on planar surfaces by introducing an appropriate pseudo-contact angle, providing a new fundamental link. The advantages of heterogeneous nucleation on a concave spherical surface of radius R over a planar surface occur primarily when 2R<10r⁎ (r*: nucleus radius) and diminish rapidly when 2R>10r*. This is similar to nucleation on convex spherical surfaces, where the disadvantages of nucleation over a planar surface occur primarily when 2R<10r* and diminish rapidly when 2R>10r*. The substrate size 10r* thus provides an approximate borderline that distinguishes between curved and planar surfaces for nucleation. The advantages or disadvantages of nucleation over a planar surface are most outstanding when the concave (advantageous) or convex (disadvantageous) surface shows a specific contact angle with the nucleus. The nanoscale nature of the threshold size 10r* presents a clear fundamental support to surface nanopatterning for directed nucleation. A minimum depth is required for a nanoscale crater to be a favourable nucleation site.