CONICET | Buscador de Institutos y Recursos Humanos

Nucleation and growth is by far the most common mechanism leading the dynamics of phase transitions [P. G. Debenedetti, 1998; P. M. Chaikin et. al, 1995]. In two-dimensional flat systems this mechanism has been applied to a variety of topics ranging from condensation and crystallization in condensed matter, to problems in statistical mechanics or chemical reactions. In the other hand, different phases of regular curved structures [V. Vitelli et al., 2006] are not only commonly found in nature in systems like viral capsids, pollen grains, and radiolaria, but also can be grown in the laboratory in the form of crystals or liquid crystals phases by using colloidal particles [A. R. Bausch et al., 2003; W. T. M. Irvine et al., 2010;], block copolymers [A. Hexemer, 2006; D. A. Vega et al., 2013], liquid crystals [T. Lopez-Leon et al., 2011; E. Pairam et al., 2013], and possibly other self-assembled systems. In this work we present a simple description of nucleation and growth of two-dimensional phases lying on arbitrarily curved backgrounds. Our model is based on a coarse-grained Ginzburg-Landau description taking into account the main energetic contributions valid a large variety of physical systems and substrate's geometries. We found how curvature modifies the critical size of propagating nuclei and the minimum energy path towards the equilibrium phase. In general this mechanism will be faster on regions of positive curvature, where height of barriers for nucleation are smaller due to geometrical reasons. Substrates of varying curvature can originate complexities in the energy landscape for nucleation, inducing the formation of local barriers where initially propagating nuclei may become stabilized and trapped by the underlying curvature. Such process gives rise to the formation of local pinning forces in the case of nucleation and growth on rough substrates.