The Role of Geometry on the Ease of Solidification Inside and Out of Cylindrical Nanopores

We investigated the role of a nanoporous particle on the formation of macroscopic solid in the framework of equilibrium thermodynamics and from the free-energy perspective. The model particle has cylindrical pores with equidistant circular openings on the particle surface. We focused on two potentially limiting steps: (i) the solid nucleation from liquid inside a single pore and (ii) the bridging of multiple pores on the particle surface. We examined the nucleation near the liquid-vapor meniscus inside a pore by considering different solid-vapor and solid-pore wall contact angles, as well as the liquid-vapor meniscus angles. For bridging, we quantified the effects of the proximity of neighboring pores and the number of participating pores where we considered two or three pores, placed two different distances apart, and three contact angles of the solid with the particle surface. Except in special cases where an analytical solution could be developed, we determined the equilibrium nucleus and bridge shapes numerically using the Surface Evolver code. The geometry of these equilibrium shapes was the key for correctly calculating the energy barriers. Our results indicate that the meniscus angle can be an important factor in reducing the barrier for nucleation if the internal angles of the solid nucleus satisfy a certain criterion. For the solid growth out of the pores, we found that the barriers were significantly lower in the presence of multiple, closely packed pores compared to the growth from a single pore. This paper is deliberately written with no reference to material properties or a specific process to highlight the generality of geometry-controlled barriers. A direct application where our findings can be particularly valuable is the ice formation in clouds, which is the subject of intensive research in atmospheric sciences for its role in influencing precipitation patterns and hence the climate.