Entropy-Driven Crystallization in Dense Systems of Athermal Chain Molecules

We describe the direct observation of entropy-driven crystallization in simulations of dense packings of linear hard-sphere chains. Crystal nuclei form spontaneously in the phase coexistence region independently of chain length. Incipient nuclei consistently develop well defined, stack-faulted layered morphologies with a single stacking direction. These morphologies deviate markedly from those of monomeric analogs. The ordering transition is driven by the increase in translational entropy: ordered sites exhibit enhanced mobility as their local free volume becomes more spherical and symmetric.

Figure 1

Evolution of degree of crystallinity ${\tau }_c$ with MC steps for systems characterized by uniform (for average chain lengths $N=12$ and 24) and most probable chain length distributions at various packing densities $\phi$.

Figure 2

System configurations ($\phi =0.61$), at (a) early stage of simulation (amorphous packing) and (b) late stage where the majority of sites possess a highly ordered local environment (${\tau }_c\simeq 0.83$). Grey and black spheres correspond to sites with hcp-like and fcc-like local order, respectively. Sites with high CCE norms are shown as parts of a mesh cloud. (c) and (d) Same as in (a) and (b) but all sites colored according to the parent chain. Image created with VMD software [31].

Figure 3

Evolution of degree of crystallinity ${\tau }_c$, average asphericity of the Voronoi polyhedra $b$, and fraction of flippers $v_{\mathrm{flip}}$ of amplitude $d\varphi =1°$ as a function of MC steps ($N=12$, $\phi =0.61$).