Modeling of crystal nucleation and growth in athermal polymers: self-assembly of layered nano-morphologies

We describe the salient characteristics and analyze the entropic origins of the spontaneous crystal nucleation and growth as observed in extensive Monte Carlo simulations of dense packings of athermal polymers of freely-jointed chains of tangent hard spheres of uniform size (N. Karayiannis, K. Foteinopoulou and M. Laso, Phys. Rev. Lett., 2009 (103), 045703). Self-assembly of well-defined nano-patterns, in the form of randomly alternating layers of hexagonal close packing (hcp) or face centered cubic (fcc) character with a single stacking direction, is realized spontaneously at volume fractions (packing densities) of 0.58 and above independently of the average chain length and the shape of the applied molecular weight distribution. Finally, the entropic origins of the crystallization are revealed: throughout the ordering transition, while the free volume around each monomer site remains unaltered in size, its shape becomes more spherical and more symmetric. In turn, spheres along the chains are able to explore more efficiently their accessible volume in the ordered (crystalline) state increasing the translational entropy of the system.