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.

Through molecular simulations we investigate the dynamics of crystallization of hard spheres of uniform size from dense amorphous states and the role that hidden structures in an otherwise disordered medium might have on it. It is shown that short-range order in the form of sites with fivefold symmetry acts as a powerful inhibitor to crystal growth. Fivefold sites not only retard crystallization, but can self-assemble into organized structures that arrest crystallization at high densities or lead to the formation of defects in a crystal. The latter effect can be understood in terms of a random polyhedral model.

Crystal nucleation and growth of monodisperse hard-spheres as a function of packing density is studied by collision-driven molecular dynamics simulations. Short-range order in the form of fivefold local symmetry is identified and its dynamical and structural evolution is tracked as the originally amorphous assembly transits to the stable ordered phase. A cluster-based approach shows that hard-sphere configurations having initially a similar average fraction of fivefold and ordered sites can crystallize in completely different patterns both in terms of dynamics and morphology. It is found that at high volume fractions crystallization is significantly delayed in assemblies where sites with fivefold symmetry are abundant. Eventually, once the crystal phase is reached, fivefold symmetry either diminishes or arranges in specific geometric patterns. Such defects are spatially strongly correlated with twinning planes at crystalline boundaries. A detailed analysis is provided on the structural characteristics of the established crystal morphologies.

We present salient results of the analysis of the geometrical structure of a large fully equilibrated ensemble of nearly jammed packings of linear freely jointed chains of tangent hard spheres generated via extensive Monte Carlo simulations. In spite the expected differences due to chain connectivity, both the pair-correlation function and the contact network for chain packings are found to strongly resemble those in packings of monomeric hard spheres at the maximally random jammed (MRJ) state. A remarkable finding of the present work is the tendency of chains to form closed loops at the MRJ state as a consequence of chain collapse. Our simulations on disordered nearly jammed chain packings yield an average coordination number of 6, which fulfills the isostaticity condition and is in excellent agreement with the corresponding simulation [A. Donev, S. Torquato, and F. H. Stillinger, Phys. Rev. E 71, 011105 (2005)] and experimental [T. Aste, M. Saadatfar, and T. J. Senden, Phys. Rev. E 71, 061302 (2005)] findings for jammed packings of monatomic hard spheres. An exact correspondence between the statistical-mechanical ensembles of monomeric spheres and of hard-sphere chains offers insights regarding the structure and topology of the contact network of hard-sphere systems at the MRJ state.

We review recent results from extensive simulations of the crystallization of athermal polymer packings. It is shown that above a certain packing density, and for sufficiently long simulations, all random assemblies of freely-jointed chains of tangent hard spheres of uniform size show a spontaneous transition into a crystalline phase. These polymer crystals adopt predominantly random hexagonal close packed morphologies. An analysis of the local environment around monomers based on the shape and size of the Voronoi polyhedra clearly shows that Voronoi cells become more spherical and more symmetric as the system transits to the ordered state. The change in the local environment leads to an increase in the monomer translational contribution to the entropy of the system, which acts as the driving force for the phase transition. A comparison of the crystallization of hard-sphere polymers and monomers highlights similarities and differences resulting from the constraints imposed by chain connectivity.

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12–500 and at packing densities from dilute ones up to the maximally random jammed state.