Entropy-Driven Crystallization in Dense Systems of Athermal Chain Molecules

Abstract

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.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

“…As explained in detail in Karayiannis et al (2010Karayiannis et al ( , 2009c, as the originally disordered packing transits to the ordered state, the local environment becomes more spherical and more symmetric. To quantify the structural transition we first identify the enclosing polyhedron around each site as determined from Voronoi tessellation.…”

“…Consequently, the proposed metric is highly discriminating between different crystal structures. This feature renders the CCE norm a robust descriptor to accurately identify crystal nucleation and growth in general atomic and particulate systems (Hoy and Karayiannis, 2013;Karayiannis et al, 2009bKarayiannis et al, , 2009cKarayiannis et al, ,2011Karayiannis et al, , 2012Karayiannis et al, , 2013aKarayiannis et al, , 2013bWu et al, 2014). The mathematical formulation of the CCE descriptor along with details on the algorithmic implementation can be found elsewhere (Karayiannis et al, 2010;Karayiannis et al, 2009bKarayiannis et al, , 2013b.…”

Twinning of Polymer Crystals Suppressed by Entropy

“…This difficulty is caused by chain entanglements, which slow system dynamics down into practical unobservability. For the time being, it is only through the use of advanced Monte Carlo (MC) techniques that crystallization of freely-jointed chains of tangent hard spheres can be achieved [18,19]. In these simulations, only layered structures of varying degrees of perfection were obtained (Figure 2).…”

“…The latter assumption seems to be in contradiction with the freely jointed nature of our hard-sphere chains, in which the bond angle is free to vary except for the geometrical constraints imposed by monomer overlaps. Our use of the RIS relies on the representation of the freely jointed chains by RIS chains with fixed bond angles and a discrete set of rotational isomeric states that accurately reproduce the known bond angle fbond (θ) and bond torsion ftors (φ) distributions, both of which have been accurately measured [18,19,43,44]. The bending angle distribution in the crystal fbond (θ) (Figure 1 in Ref.…”

“…On the other hand, systems of freely-jointed chains of strictly tangent hard spheres have also been found to crystallize, although only in simulations with advanced Monte Carlo (MC) methods, and at much higher computational cost [18,19]. The only, but by no means minor, structural difference between chain packings and monomeric analogs is the connectivity between individual spheres: in the simplest chain model, individual hard spheres (monomers) are strictly tangent and are arranged in linear strings.…”