Crystallization of Flexible Chains of Tangent Hard Spheres under Full Confinement

Abstract

We present results from extensive Monte Carlo simulations on the crystallization of athermal polymers under full confinement. Polymers are represented as freely jointed chains of tangent hard spheres of uniform size. Confinement is applied through the presence of flat, parallel, and impenetrable walls in all dimensions. We analyze crystallization as the summation of two contributions: one that occurs in the bulk volume of the system (bulk crystallization), and one on the wall surfaces (surface crystallization). Depending on volume fraction initially amorphous (disordered) hard-sphere chain packings transit to the stable crystal phase. The established ordered morphologies consist primarily of hexagonal close-packed (HCP) crystals in the bulk volume and of triangular (TRI) crystals on the surface. As in the case of athermal packings in the bulk (without confinement), a structural competition is observed between the 5-fold local symmetry and the formation of close-packed crystallites. Effectively, the full confinement inside a cube favors the growth of the HCP crystal, as the FCC one is quite incompatible with the imposed spatial constraints. Consequently, we observe the formation of noncompact ordered motifs which grow from the surface to the inner volume of the simulation cell. We further compare the 2D and 3D crystals formed by monomeric hard spheres under the same simulation conditions. Significant differences are observed at low densities that tend to diminish as concentration increases.

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

“…In spite of these difficulties, a wide variety of increasingly more efficient MC methods have been developed over the last few decades [ 78 , 79 , 82 , 83 , 84 , 85 , 86 , 87 , 88 ]. The work to be reported in this manuscript is based on a powerful suite of advanced MC moves [ 89 ], which in the past has enabled us to observe the entropy-driven athermal polymer crystallization for the first time [ 71 ], and to identify and analyze the factors that affect the phenomenon, including chain length and its distribution [ 71 , 90 ], the presence of bond gaps or tangency [ 91 ], and confinement in one [ 92 ] or all three [ 93 ] dimensions.…”

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

“…Site i is identified as an X-type crystal when the calculated CCE norm is lower than a critical threshold, ≤ . In past studies, an empirical threshold of 0.245 was determined for packings of non-overlapping spheres [41,95,96] in the bulk [40][41][42][43]55,56] and under confinement [44,45]. Due to the strict concept behind the descriptor, the CCE norm is highly discriminatory, so the value of a site cannot be simultaneously very low for two different reference crystals.…”

“…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].…”

“…However, both the FCC or RHCP crystals of tangent hard-sphere chains are usually free of twin defects due to a conformational entropic barrier [57]. It has been established that the phase transition and the ordered morphologies of hard-sphere chains are affected insignificantly by chain length, but are sensitive to factors such as gaps in bond lengths [43,58], the presence of surfaces/confinement [44,59,60] and chain stiffness [61][62][63][64].…”

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

“…In spite of these difficulties, a wide variety of increasingly more efficient MC methods have been developed over the last decades [80,81,[84][85][86][87][88][89][90]. The work to be reported in this manuscript is based on a powerful suite of advanced MC moves [91] which has enabled us in the past to observe the entropy-driven athermal polymer crystallization for the first time [73] and to identify and analyze the factors that affect the phenomenon, including chain length and its distribution [73,92], the presence of bond gaps or tangency [93] and confinement in one [94] or all three [95] dimensions.…”