Crystallization in melts of semi-flexible hard polymer chains: An interplay of entropies and dimensions

T. Shakirov, W. Paul

Institut für Physik, Martin Luther Universität Halle-Wittenberg, 06099 Halle 

Stochastic Approximation Monte Carlo simulations [1] are employed to obtain the complete thermodynamic equilibrium information for a melt of short, semi-flexible polymer chains with purely repulsive intermolecular interactions. Thermodynamics is obtained based on the density of states of our simple coarse-grained model, which varies by up to 5000 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density [2]. The lyotropic three-dimensional orientational ordering transition drives the crystallization and is accompanied by a two-dimensional hexagonal ordering transition in the plane perpendicular to the chains. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition is similar to the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. The tilt of the chain axis with respect to the lamella surface makes this a rotator II phase.

[1] B. Werlich, T. Shakirov, M. P. Taylor, W. Paul, Comput. Phys. Commun. 186, 65, (2015) (link)
[2] T. Shakirov, W. Paul, preprint