A polyethylene chain investigated with replica exchange molecular dynamics simulation: Equilibrium lamellar thickness and melting point, ordering and free energy

Folded alkane chains and the emergence of the lamellar crystal

The competition between chain stiffness and chain collapse gives rise to complex low temperature morphologies of single polymer chains, in our case alkanes. These structures are characterized by specific sequences of dihedral angles along the chain, i.e., dihedral angle correlations extending beyond local steric effects. To describe and classify these morphologies, one can transfer concepts from protein science, where this creation of dihedral angle correlations underlies the formation of α-helices and β-sheets. We show here by means of flat-histogram Monte Carlo simulations that, although lacking in primary structure being simple homopolymers, short alkane chains fold into non-trivial ground states (tertiary structure) consisting of chain segments of defined secondary structures. The folded lamellar crystal typical for polyethylene chains requires a minimum chain length to occur as the ground state folded structure, which we identify to be around 150 repeat units.

A Replica Exchange Molecular Dynamics Simulation of a Single Polyethylene Chain: Temperature Dependence of Structural Properties and Chain Conformational Study at the Equilibrium Melting Temperature

The conformational properties of a finite length polyethylene chain were explored over a wide range of temperatures using a replica exchange molecular dynamics simulation providing high quality simulation data representative for the equilibrium behavior of the chain molecule. The radial distribution function (RDF) and the structure factor S(q) of the chain as a function of temperature are analyzed in detail. The different characteristic peaks in the RDF and S(q) were assigned to specific distances in the chain and structural changes occurring with the temperature. In S(q), a peak characteristic for the order in the solid state was found and used to determine the equilibrium melting temperature. A detailed scaling analysis of the structure factor covering the full q range was performed according to the work of Hammouda. In the Θ region, a quantitative analysis of the full structure factor was done using the equivalent Kuhn chain, which enabled us to assign the Θ region of our chain and to demonstrate, in our particular case, the failure of the Gaussian chain approach. The chain conformational properties at the equilibrium melting temperature are discussed using conformational distribution functions, using the largest principal component of the radius of gyration and shape parameters as order parameters. We demonstrate that for the system studied here, the Landau free energy expression based on this conformational distribution information leads to erroneous conclusions concerning the thermodynamic transition behavior. Finally, we focus on the instantaneous conformational properties at the equilibrium melting temperature and give a detailed analysis of the conformational shapes using different shape parameters and a simulation snapshot. We show that the chain does not only take the lamellar rod-like and globular conformational shapes, typical of the solid and liquid states, but can also explore many other conformational states, including the toroidal conformational state. It is the first demonstration that a flexible molecule like PE can also take a toroidal conformational state, which is normally linked to stiffer chains.