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

Timur Shakirov

doi:10.3390/e21090856

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.

Highlights

Hard-sphere polymer models are easy in formulation and widely used for the investigation of the thermodynamic properties of polymeric systems
The entropy reduction does not affect the structure of the ordered state, both systems form a monomer-based mixture of face-centred cubic (FCC)
We considered a dense semi-flexible polymer system and analysed the effects of a weak square-well attraction as well as of square-shoulder repulsion on the thermodynamic properties of the dense semi-flexible polymer system

Summary

Introduction

Hard-sphere polymer models are easy in formulation and widely used for the investigation of the thermodynamic properties of polymeric systems. The entropy reduction does not affect the structure of the ordered state, both systems form a monomer-based mixture of face-centred cubic (FCC). The role of square-well attraction was investigated for single flexible hard-sphere chains theoretically (for short chains) [4] and numerically [5,6]. The type of the crystal structure, FCC, HCP, or body-centred cubic (BCC), depends on the chain length and interaction width of the square-well potential [6]. A geometrical stiffness, where the bead size is bigger than the bond length, induces the formation of complex non-crystalline single-chain structures depending on the bead size to the bond length ratio [14]

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Conclusion