“Polymorph Stability and Free Energy of Crystallization of Freely-Jointed Polymers of Hard Spheres”. Polymers 2023, 15(6), 1335.

AuthorsMiguel Herranz, Javier Benito, Katerina Foteinopoulou, Nikos Ch. Karayiannis.
Organisms: Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, Spain
Citation: Polymers 2023, 15(6), 1335; https://doi.org/10.3390/polym15061335
Link: https://www.mdpi.com/2073-4360/15/6/1335


The free energy of crystallization of monomeric hard spheres as well as their thermodynamically stable polymorph have been known for several decades. In this work, we present semianalytical calculations of the free energy of crystallization of freely-jointed polymers of hard spheres as well as of the free energy difference between the hexagonal closed packed (HCP) and face-centered cubic (FCC) polymorphs. The phase transition (crystallization) is driven by an increase in translational entropy that is larger than the loss of conformational entropy of chains in the crystal with respect to chains in the initial amorphous phase. The conformational entropic advantage of the HCP polymer crystal over the FCC one is found to be ΔschHCP−FCC≈0.331×10−5k “>ΔsHCPFCCch0.331×105k per monomer (expressed in terms of Boltzmann’s constant k). This slight conformational entropic advantage of the HCP crystal of chains is by far insufficient to compensate for the larger translational entropic advantage of the FCC crystal, which is predicted to be the stable one. The calculated overall thermodynamic advantage of the FCC over the HCP polymorph is supported by a recent Monte Carlo (MC) simulation on a very large system of 54 chains of 1000 hard sphere monomers. Semianalytical calculations using results from this MC simulation yield in addition a value of the total crystallization entropy for linear, fully flexible, athermal polymers of Δs≈0.93k “>Δs0.93k per monomer.