Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityA Manifestation of the Ostwald Step Rule: The Free-EnergyLandscape of Single-Molecule Polyethylene CrystalsFolded states of chainlike macromolecules includingproteins [1] and crystalline polymers [2] are undercurrent intense study. In spite of the largedifferences between homopolymers and proteins,interesting correspondences between the structuraltransitions of isolated, single homopolymer chainsand the protein folding have been noted by bothnumerical simulations and experiments. One keyissue is if the morphologies of folded states arethermodynamically or kinetically controlled. Kineticfactors are believed to set the growth rate ofpolymer crystals [2] as well as the thickening offolded macromolecules. While this is a safeconclusion for long chains (polymers) , where largeFig. 1: (left) Snapshots of the crystallization of asingle PE chain with N=500 monomers. Note thepresence of initial distinct nucleation sites mergingat later times. (right) Final crystal structure withselected cross-sections.entropic barriers hamper the conformation changesleading to structures which are, e.g., partiallycrystalline, it may be questioned for shorter chains(oligomers) which are less impeded.Extensive molecular-dynamics simulations of thecrystallization process of a single polyethylene chain( PE ) with N=500 monomers have been performed[4-6]. The development of the ordered structure isseen to proceed along different routes involvingeither the global reorganization of the chain or,alternatively, well-separated connected nuclei(Figure 1). No dependence on the thermal historywas observed at the late stages of the crystallization.The folding process involves several intermediateordered metastable states, in strong analogy withthe experiments, and ends up in a well-defined longlivedlamella with ten stems of approximately equallength, arranged into a regular, hexagonal pattern(Figure 1). This behavior may be seen as amanifestation of the Ostwald step rule [3]. Both themetastable states and the long-lived one areevidenced as the local minima and the global one ofthe free-energy landscape (FEL), respectively (Figure2) [4,5]. The study of the microscopic organizationof the lamella evidenced that the two caps are ratherflat, i.e., the loops connecting the stems are short.Interestingly, annealing the chain through thedifferent metastable states leaves the averagenumber of monomers per loop nearly unchanged [6].It is also seen that the chain ends, the so-called cilia,are localized on the surface of the lamella, inagreement with the experiments, and that structuralfluctuations take place on the lamella surface.References[1] M. Gruebele, Annu. Rev. Phys. Chem., 50, 485(1999).[2] G. Ungar, J. Stejny, A. Keller, I. Bidd, and M. C.Whiting, Science 229, 386 (1985).[3] W. Ostwald, Z. Phys. Chem., Stoechiom.Verwandtschaftsl. 22, 289 (1897).[4] L Larini, A Barbieri, D Prevosto, P A Rolla and DLeporini, J. Phys.: Condens. Matter, 17, L199(2005).[5] L Larini, D Leporini, J.Chem.Phys., 123, 144907( 2005 ).[6] L Larini, A Barbieri D Leporini, in press onPhysica A ( doi:10.1016/j.physa.2005.08.048 )Fig. 2: (left) Free-energy landscape ( FEL ) of thePE single-molecule crystals. (right) FEL at differenttemperatures as a function of the largest momentof inertia of the chain. The labels indicate thenumber of stems of the ordered structurescorresponding to the minima.AuthorsA.Barbieri(a), D.Prevosto (a), L.Larini (a,b),D.Leporini (a,b), P.A.Rolla (a)(a) Dipartimento di Fisica ‘‘Enrico Fermi,’’ Universita`di Pisa, via F. Buonarroti 2, I-56127 Pisa, Italy (b)CRS-SOFT (c) Dip. Fisica “E. Fermi” Univ. Pisa andCNR-INFM Polylab Largo B. Pontecorvo 3, Pisa.SOFT Scientific Report 2004-0656