Free energy barrier to melting of single-chain polymer crystallite

Abstract

We report Monte Carlo simulations of the melting of a single-polymer crystallite. We find that, unlike most atomic and molecular crystals, such crystallites can be heated appreciably above their melting temperature before they transform to the disordered ''coil'' state. The surface of the superheated crystallite is found to be disordered. The thickness of the disordered layer increases with super-heating. However, the order-disorder transition is not gradual but sudden. Free-energy calculations reveal the presence of a large free-energy barrier to melting. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1553980͔It is easy to supercool liquids but difficult to superheat solids. The reason is that the free surface of a crystallite can melt at a temperature that is well below the bulk melting temperature.1,2 As a consequence, solids usually melt from the surface inward without significant superheating. There exist experimental studies that show superheating of solids, but in these experiments the crystals are either confined in a nonmelting matrix 3,4 or the experiments reveal superheating of one particular crystal surface only. 5,6The melting of a single-chain polymer system is expected to be different. The reason is that all the polymer units are restricted by the strong covalent bonds along the chain. This implies that, when a single polymer partially melts ͑or dissolves͒, the molten units cannot escape from the surroundings of the crystallite. Rather, they stay around as a ''corona'' and can, in this way, affect the remainder of the melting process. The simulations presented below show that these features make the melting of polymer crystallites qualitatively different from that of atomic or molecular crystals.Lattice models provide a highly simplified picture of freezing and melting. Nevertheless, it has been shown that such models are sufficiently flexible to account for the phenomenon of surface melting in simple ''atomic'' systems. 7 We used a polymer lattice model described in Ref. 8 to study the melting of a single-chain crystallite. In this model, polymers live on a simple cubic lattice, but the monomermonomer bonds on the chain can be directed both along main axes of the lattice and along the face and body diagonals: 6ϩ12ϩ8ϭ26 directions in all. The polymers can be semi-flexible and have attractive nearest-neighbor interactions. For each bond-bond connection along the chain, all noncollinear bonds are assumed to have the same energetic cost defined as E c . The attractive interactions can be anisotropic: Parallel polymer bonds attract more strongly than nonparallel bonds ͑their difference is defined as E p ), or isotropic: the site-site energy change ͑defined as B͒ when forming one polymer-solvent contact from polymer-polymer and solvent-solvent contacts. By varying E c , B and E p , we can ''tune'' the ''phase-diagram'' of a single polymer. A flexible (E c ϭ0) polymer with a large B but small E p undergoes a coil-globule transition.9 In contrast, a flexible polymer with a large E p but small B wi...

Effect of the Coil−Globule Transition on the Free-Energy Barrier for Intrachain Crystal Nucleation

“…15 In the present study, we investigate how this barrier is changed as the chain-freezing transition crosses the coil-globule transition. Of course, such a comparison is only meaningful if, in all cases, the driving force for crystallization is the same.…”

Intramolecular Nucleation Model for Polymer Crystallization

“…Recently, we have shown that it is possible to compute the free energy barrier separating the solid and the "liquid" state of a singlechain molecule. 24 In the present paper, we exploit this approach to study the chain-length dependence of single-chain crystal nucleation. Below we show that our simulations allow us to understand why the free energy barriers, for both primary and secondary nucleations, hardly depend on polymer chain length.…”

“…The figure demonstrates that, indeed, the barrier for crystallization is chain-length-insensitive while the barrier for melting depends strongly on chain length. 24 The dashed line is calculated from eq 3 with σ ) 15Ep and the fitted equilibrium melting temperature 3.2657Ep/kB. …”

Polymer Crystallization Driven by Anisotropic Interactions

“…However, under suitable conditions, crystallization can even occur in a single-chain system. Using a combination of biased sampling, multihistogram techniques, and parallel tempering [125], we can directly compute the [52] free-energy barrier (if any) that separates the crystalline state of the single chain from the disordered "coil" state [126]. Technical details can be found in Sect.…”