Twinning of Polymer Crystals Suppressed by Entropy

Nikos Karayiannis,Katerina Foteinopoulou,Manuel Laso

doi:10.3390/sym6030758

Abstract

We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.

Highlights

Twins are regular aggregates consisting of individual crystals of the same species joined together in definite and specific mutual orientations
For these reasons we have focused our work on dense systems of chains of strictly tangent hard spheres, in which entropy differences between twinned and untwinned phases can only be of conformational origin
Twinned structures observed in molecular dynamics (MD) simulations are a consequence of kinetic trapping of the algorithm, which is unable to surmount the free energy barrier that separates the single and the twinned crystals

Summary

Introduction

Twins are regular aggregates consisting of individual crystals of the same species joined together in definite and specific mutual orientations. Whereas twinning in crystals of low molecular weight substances, both organic and inorganic, is comparatively frequent (see [1,2,3,4,5,6,7,8] and references therein), twinning in polymers is rather an exceptional phenomenon: the first widely accepted observation of twinning in polymer crystals [7] was reported as late as 1963 (in the following, the term “polymer” refers primarily to synthetic macromolecules made up of one or a few repeat units, lacking the very specific monomeric succession and interactions found in biological macromolecules such as proteins; coordination and purely inorganic polymers are excluded from the present work). These freely-jointed chains of tangent hard spheres crystallize in layered structures of mixed hcp (hexagonal closed packed) and fcc (face centered cubic) character (Figure 2, to be described in more detail below), but twinned structures have not been observed to date

Enthalpic versus Entropic Effects on Polymer Twinning

Morphology of Twins in Systems of Monoatomic Hard Spheres

Calculation of Entropic Loss Caused by Twinning

Calculation of Entropic Loss by Exhaustive Enumeration

Chain Entropy Loss and Calculation of Phase Stability

Conclusions