Towards understanding of shape formation mechanism of mesoporous silica particles

Growth of even simple crystals is a rather hard problem to describe because of the non-equilibrium nature of the process. Meso(nano)porous silica particles, which are self-assembled in a sol-gel template synthesis, demonstrate an example of shapes of high complexity, similar to those observed in the biological world. Despite such complexity, here we present the evidence that at least a part of the formation of these shapes is an equilibrium process. We demonstrate it for an example of mesoporous fibers, one of the abundant shapes. We present a quantitative proof that the fiber free energy is described by the Boltzmann distribution, which is predicted by the equilibrium thermodynamics. This finding may open up new ground for a quantitative description of the morphogenesis of complex self-assembled shapes, including biological hierarchy.