Line pinning effect reshapes nucleation at surface edges: A generalized theory for nanopore activation

Heterogeneous nucleation at surface edges is pervasive across nature and industry, yet the role of line pinning effect, arising from asymmetric capillary interactions at geometric singularities, remains poorly understood. Herein, we develop a generalized nucleation theory that explicitly incorporates edge pinning energy, thereby extending classical frameworks to account for nanoscale confinement and interfacial asymmetry. Through analytical treatment of droplet formation within geometrically defined nanopores, we derive a closed-form expression for the line pinning energy as a function of Laplace pressure, pore geometry, and wettability. This formulation reveals that line pinning effect can significantly reshape the nucleation energy landscape, introducing nontrivial dependencies on contact angle and pore morphology. Our results uncover a tunable, geometry-mediated mechanism for controlling nucleation barriers, offering predictive insight into phase transitions in confined environments and suggesting strategies for design in applications ranging from nanofluidics to crystallization control.