Nucleation and growth on curved space

GOMEZ LR; GARCIA NA; DA VEGA

Córdoba

Workshop; XIII Latin American Workshop on Nonlinear Phenomena; 2013

Latin American Workshop on Nonlinear Phenomena

Nucleation and growth (NG) is by far the most common mechanism leading the dynamics of rstorder phase transitions. Between other examples, this process directs the formation of a crystalphase from an initial liquid (crystallization), and the dynamics of order-order phase transitionsin a huge variety of hard and soft condensed matter systems [P. G. Debenedetti, MetastableLiquids: Concepts and Principles (Princeton University Press, Princeton, NJ, 1998).].In its classical picture, NG starts with local structural uctuations of the initial phase whichlead to the formation of small nuclei of the new phase.the dynamical evolution of the phase transition. On one hand, the birth of a nucleus of the newphase produces an interphase, leading to an increase of free energy due to surface tension. Onthe other hand, there is a decrease in the total free energy due to the local formation of the lessenergetic phase. Here the competition of these surface and volume terms produce an activateddynamics, such that the only nuclei which can propagate are the ones whose size overpass acritical value.The aim of the present study is to provide a general physical description of NG in twodimensionalcrystalline systems lying on curved surfaces. Such curved crystals are not onlycommonly found in nature in systems like viral capsids, insect eyes, pollen grains, and radiolaria,but also can be grown in the laboratory by using colloidal particles, liquid crystals, blockcopolymers, and possibly other self-assembled condensed matter systems [V. Vitelli et. al,Proc. Natl Acad. Sci. USA 103, 12323 (2006); W. T. M. Irvine et. al, Nature (London) 468,947 (2010)]; [García et. al, Phys. Rev. E 88, 012306 (2013)].Here, by using theoretical calculations and simulations, we show how the curvature of thesubstrate aects the critical size of propagating nuclei and the minimum energy path towardsthe equilibrium crystal phase. The model is based on a coarse-grained Guinzburg-Landau freeenergy functional and a phase-eld evolution equation. This approach can be combined withpolar geodesic coordinates and conformal mapping to obtain analytical expressions for the sizeof the critical nuclei as a function of degree of undercooling and local substrate´s curvature.