Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range

Abstract

A melt of short semi-flexible polymers with hard-sphere-type non-bonded interaction undergoes a first-order crystallisation transition at lower density than a melt of hard-sphere monomers or a flexible hard-sphere chain. In contrast to the flexible hard-sphere chains, the semi-flexible ones have an intrinsic stiffness energy scale, which determines the natural temperature scale of the system. In this paper, we investigate the effect of weak additional non-bonded interaction on the phase transition temperature. We study the system using the stochastic approximation Monte Carlo (SAMC) method to estimate the micro-canonical entropy of the system. Since the density of states in the purely hard-sphere non-bonded interaction case already covers 5600 orders of magnitude, we consider the effect of weak interactions as a perturbation. In this case, the system undergoes the same ordering transition with a temperature shift non-uniformly depending on the additional interaction. Short-range attractions impede ordering of the melt of semi-flexible polymers and decrease the transition temperature, whereas relatively long-range attractions assist ordering and shift the transition temperature to higher values, whereas weak repulsive interactions demonstrate an opposite effect on the transition temperature.

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

“…In spite of the granular, colloidal, or droplet polymers being significantly less well explored than the “traditional” ones, over the years, there have been significant advances in their synthesis and characterization [ 61 , 62 , 63 , 64 , 65 ]. From the perspective of theory and simulation [ 66 , 67 ], emphasis is placed on the phase transition of semi-flexible [ 68 , 69 , 70 ] or flexible [ 71 , 72 ] chains of hard spheres, while recently, it was demonstrated that the use of block copolymers leads to HCP stable phases [ 73 , 74 , 75 ]. The stabilization of HCP colloidal structures has been investigated through the insertion of polymers [ 76 , 77 ].…”

Entropy-Driven Heterogeneous Crystallization of Hard-Sphere Chains under Unidimensional Confinement

“…These alternating layers possess a unique stacking direction and are free of twin defects, as the latter are incompatible with the entropic barriers imposed by chain connectivity [ 15 ]. The critical phase transition of hard-sphere chains is heavily affected by factors, such as bond gaps [ 16 , 17 ] and/or chain stiffness [ 18 ].…”

“…The crystallization or solidification of hard-sphere chains in the bulk has been reported in the literature, considering as the influence of chain length, backbone stiffness, and bond geometry [ 14 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ], and highlighting similarities and differences with respect to the crystal nucleation and growth of monomeric analogs [ 13 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. The jamming or phase transition of athermal, initially random packings, both of monomers and of chains, under confinement have not been studied as extensively as the bulk case, but independent works have provided significant insights over the years [ 3 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ].…”

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

“…Theoretical and modeling works are of major importance in the study of crystallization of hard sphere chains [68,69]. From the perspective of simulation, emphasis is placed on the phase transition of semi-flexible [70][71][72] or flexible [73,74] chains of hard spheres, while recently it was demonstrated that the use of block copolymers leads to HCP stable phases [75][76][77]. The stabilization of HCP colloidal structures has been investigated through insertion of polymers [78,79].…”