Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

Abstract

We present results on polymorphism and perfection, as observed in the spontaneous crystallization of freely jointed polymers of hard spheres, obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration, after an initial dominance of the hexagonal closed packed (HCP) polymorph and a transitory random hexagonal close packed (rHCP) morphology, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal, compared to the amorphous state. In spite of the significant local re-arrangements, as reflected in the bending and torsion angle distributions, the average chain size remains unaltered during crystallization. Polymers in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

Local and Global Order in Dense Packings of Semi-flexible Polymers of Hard Spheres

“…Once crystallites of HCP and FCC characters start growing, at almost identical rates, the fraction of FIV-like sites decreases gradually until it practically disappears. The structural competition, observed here for all semi-flexible chain systems, between the FIV local symmetry and crystallization in the form of HCP and FCC sites is in perfect match with identical observations in simulations of fully flexible [37,[40][41][42][43][44][45] and monomeric HS systems [55,56], including bead-spring chains under quenching [61,105]. Once the population of FIV sites is eliminated, a trend manifestly valid for all simulated packings, the relative fractions of the HCP and FCC crystals undergo a sharp variation which is followed by the establishment of the final, stable ordered structures of crystalline (CRY) character.…”

“…This volume fraction is higher than the melting transition of freely-jointed hard-sphere chains as established in [37,[40][41][42]54]. An inspection of all panels shows clearly that the mechanism of phase transition, here in the form of crystallization, is very similar and rather independent of the equilibrium bending angle.…”

“…Just as for monomeric athermal hard spheres, off-lattice MC simulations have shown that random packings of fully flexible linear chains of tangent hard spheres are able to crystallize at high volume fractions through an entropy-driven mechanism, very similar to the one of monomeric analogs [37,[40][41][42]54]. Extremely long simulations [37] have shown the FCC polymorph to be the stable one for fully flexible chains of tangent hard spheres. In shorter simulations, an RHCP phase with a unique stacking direction [40][41][42] appears most often.…”

“…However, random hexagonal close packing (RHCP) is almost always observed due to the small free energy of stacking faults [35]. Thus, crystal perfection in the form of pure FCC crystals is rarely encountered in computer simulations [36,37].…”

“…The mechanism of crystallization of hard colloidal polymers [37][38][39][40][41][42][43][44][45] differs substantially from that of traditional polymers, the latter as revealed in x-ray scattering studies of short alkane chains [46][47][48], and in MD [49][50][51][52] or MC [39,53] simulations. Just as for monomeric athermal hard spheres, off-lattice MC simulations have shown that random packings of fully flexible linear chains of tangent hard spheres are able to crystallize at high volume fractions through an entropy-driven mechanism, very similar to the one of monomeric analogs [37,[40][41][42]54]. Extremely long simulations [37] have shown the FCC polymorph to be the stable one for fully flexible chains of tangent hard spheres.…”