Soft Report - Dipartimento di Fisica - Sapienza

Packing vs. Temperature Effects in PolymersThe pioneering studies of Williams [1] and, morerecently, by Schug et al [2] and Paluch et al [3]pointed out that a deeper insight into the dynamicsof glass-forming liquids and amorphous polymers isgained by the knowledge of the relaxation times as afunction of both temperature and pressure. In fact,the possibility to reach the glassy state by twoalternative paths, i.e., by cooling or compressing,enables a more stringent test of several theories,which usually predict a Vogel–Fulcher kind ofbehavior for the temperature dependence of therelaxation time but different pressure dependencies.We have performed a molecular dynamics simulationFig. 1: The pressure-temperature dependence ofthe segmental relaxation time for a linear polymermodel. The inset shows the pressure dependence ofthe ratio between the isobaric and isochronicexpansivities.of a melt of unentangled polymers [4]. Thetranslational motion, the large-scale and the localreorientation processes of the chains, as well as theirrelations with the so-called ‘‘normal’’ and‘‘segmental’’ dielectric relaxation modes arethoroughly investigated in wide temperature andpressure ranges (Figure 1). The study addresses theissue whether the temperature or the density is adominant control parameter of the dynamics or thetwo quantities give rise to comparable effects. Byexamining the ratio between the isochronic andisobaric expansivities, one finds that the temperatureis dominant when the dynamics is fast. If therelaxation slows down, the fluctuations of the freevolume increase their role and become comparableto those of the thermal energy.The role of packing effects has been alsoinvestigated by addressing the issue of the finitelength of polymer chains which affects both the staticand the relaxation properties of the density of themelt state [5]. These have been investigated bymolecular-dynamics simulations of a Lennard-Jonesmodel with fixed bond length. Under isothermal–isobaric conditions the density increases with themolecular weight. A suitable Voronoi tessellationreveals the extra free volume around the chain endsand shows that it is strongly localized within the firstend monomer (Figure 2). Simple arguments aregiven for interpreting the main changes of themonomer radial distribution function and thecorresponding static structure factor when the chainlength is increased. As to the relaxationaspects of the density, it is found that the structuralrelaxation time increases with the molecular weight,which is interpreted as a signature of the well-knowncorresponding increase of the glass transitiontemperature.References[1] G. Williams, Trans. Faraday Soc. 60, 1548(1964).[2] K. U. Schug, H. E. King, R. Böhmer, J. Chem.Phys. 109, 1472 (1998).[3] M. Paluch, A. Patkowski, E. Fischer, Phys. Rev.Lett. 85, 2140 (2000).[4] A.Barbieri, S.Capaccioli, E.Campani and D.Leporini, J.Chem.Phys., 120, 437 ( 2004 ).[5] A Barbieri, D.Prevosto, M.Lucchesi and DLeporini,J. Phys.: Condens. Matter, 16, 6609 (2004).Fig. 2: The average volume of the Voronoipolyhedra around the monomers located at the nposition along the chain with length M. Note thelarger volume of the polyhedra surrounding thechain-ends ( n = 1).AuthorsA. Barbieri(a), E. Campani(a,b), S. Capaccioli(a,b),D. Leporini(a,b), M.Lucchesi (a,c)(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.55SOFT Scientific Report 2004-06