Selective nucleation in porous media

Geometrical arguments suggest that pore-mediated nucleation happens in general in a two-step fashion, the first step being nucleation within the pore, the second being nucleation from the filled pore into solution [Page & Sear, Phys. Rev. Lett. 97, 65701 (2006)]. The free energy barriers controlling the two steps of this process show opposite dependencies on pore size, implying that for given thermodynamic conditions there exists a pore size for which nucleation happens fastest. Here we show, within the two- and three-dimensional Ising lattice gas, that this preferred pore size tracks the size of the bulk critical nucleus, up to a numerical prefactor. This observation suggests a simple prescription for directing nucleation to certain locations within heterogeneous porous media.