Growth of even simple crystals is a rather hard problem to describe because of the non-equilibrium, kinetic nature of the process. Recently a synthesis of extraordinary curved nanoporous silica colloidal shapes, such as rods, discoids, spheres, tubes and hollow helicoids has been reported. These particles demonstrate an example of shapes of high complexity, similar to one observed in the biological world. Furthermore, these structures are the natural examples of the assembly of nanostructures into larger scale objects, which is one of the most important tasks of modern nanotechnology. In this respect, the ability to control curved shapes portends a variety of applications and new technologies where nanostructure and geometry determine function (for example, slow drug release, encapsulation of fluorescent molecules, lab-on-a-particle, etc.). The understanding of fundamentals of the shaping mechanism can also shed light on the formation of various shapes in biological world (what is called morphogenesis).
In this talk, the physical principles that stand behind the shape formation of these particles will be described. I will demonstrate that at least a part of the formation of these shapes is an equilibrium process driven by the minimization of energy. Apart from visual resembling between the result of simulations and the observed shapes, a quantitative proof will be presented. In particular, we found that the distribution of the free energy obeys the Boltzmann distribution, which is predicted by the equilibrium thermodynamics.