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

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