Next Article in Journal
Chlorophylls, Symmetry, Chirality, and Photosynthesis
Next Article in Special Issue
Polar Vector Property of the Stationary State of Condensed Molecular Matter
Previous Article in Journal
Recognition of Symmetric 3D Bodies
Previous Article in Special Issue
Non-Crystallographic Layer Lattice Restrictions in Order-Disorder (OD) Structures
Article Menu

Export Article

Open AccessArticle
Symmetry 2014, 6(3), 758-780;

Twinning of Polymer Crystals Suppressed by Entropy

Institute for Optoelectronics and Microsystems (ISOM), UPM, José Gutiérrez Abascal, 2, Madrid E-28006, Spain
Author to whom correspondence should be addressed.
Received: 31 May 2014 / Revised: 20 August 2014 / Accepted: 22 August 2014 / Published: 4 September 2014
(This article belongs to the Special Issue Crystal Symmetry and Structure)
PDF [961 KB, uploaded 4 September 2014]


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. View Full-Text
Keywords: twinning; polymer crystal; entropy; phase stability; cyclic twin; pentagonal symmetry; conformations twinning; polymer crystal; entropy; phase stability; cyclic twin; pentagonal symmetry; conformations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Karayiannis, N.C.; Foteinopoulou, K.; Laso, M. Twinning of Polymer Crystals Suppressed by Entropy. Symmetry 2014, 6, 758-780.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top