Exploring nucleation and phase transition of crystalline phases confined on spherical surfaces via the Landau-Brazovskii model.

We numerically investigate the nucleation and phase transitions of crystalline structures confined on spherical surfaces by combining the spherical Landau-Brazovskii model and the high-index saddle dynamics. We report a size-dependent multi-step nucleation mechanism fundamentally distinct from the size-independent single-step nucleation mechanism in planar systems. Our numerical results show that the transition pathways connecting striped and spotted phases on spherical surfaces follow from a single-step to a multi-step nucleation process involving metastable intermediate mixed states as the sphere radius increases. Numerical experiments also demonstrate that the curvature modifies the critical nucleus size and transition paths towards the final states. Confined on a spherical surface, the nucleation is more likely to occur in the presence of topological defects. Furthermore, we reveal the emergence of spherical ordered structures by constructing the solution landscapes of the model system. These findings provide new insights into the modern nucleation theory for understanding the self-assembly in soft matter and biological systems.