When a polymer melt is cooled toward low temperatures it solidifies either by forming crystals at the melting point or by undergoing a glass transition at the glass transition temperature Tg (which is below the melting point). Whether crystallization or vitrification occurs depends on the structural properties of the polymers. If the local structure is very regular (isotactic or syndiotatic orientations of side groups, for instance), the melt forms a crystal or at least a semicrystalline material provided it is cooled slowly enough. Faster cooling or a locally irregular structure (atatic polymers, for instance) can or does completely suppress crystallization. It is therefore much easier to supercool a polymer melt than it is for a simple fluid. While supercooling the melt stays in the liquid-like disordered state at all temperatures down to the glass transition. The transition occurs when the structural relaxation becomes of the order of 100 s or larger. It is preceded by a spectacular increase of the relaxation time by about 14 orders of magnitude in a narrow temperature interval. This behavior is not limited to polymer melts. It is typical of all glass forming systems. Thus, the challenging question is to understand how the dynamics can slow down so drastically while static properties remain almost unchanged.
Many groups, all over the world, are currently working on this problem. We try to contribute to this research by computer simulations of simple coarse-grained models for glass forming polymer melts.[1-4] Our current interest is focused on the following topics:
We studied by molecular-dynamics (MD) simulations the dynamics of nonentangled glass-forming polymer melts. The simulations are carried out at constant pressure with a bead-spring model where each chain contains N=10 monomers. The simulation results are quantitatively analyzed within the framework of an extension of idealized mode-coupling theory (MCT) to nonentangled polymer melts. Our analysis does not rely on fits, but is based on the following procedure: We determine from the simulation all static input quantities that the theory requires to predict the dynamics of the model. Predicted and simulated dynamics may then be compared.
The figure on the right shows an exemple of this comparison. It depicts the mean-square displacements (MSDs) of the monomers gM(t) and of chain's center of mass (CM) gC(t). Qualitatively, the MSDs display the following features: At short times, both the monomers and the CM move ballistically (~t2). The regime of ballistic motion is succeeded by a `plateau regime', where the MSDs increase only slowly with time. There, gM(t) is of the order of 10% of the monomer diameter. This reflects the temporary caging of a monomer by its neighbors. For longer times, gM(t) ~ tx with x=0.63, while gC(t) crosses over to final diffusion. The subdiffusive monomer-displacement can be attributed to chain connectivity; however, the value of the effective exponent x cannot be understood within the classical theory of polymer dynamics (i.e., the Rouse model). Chain connectivity dominates the monomer dynamics until the MSD becomes comparable to the chain size (Re is the chain's end-to-end distance). Then, final diffusion also sets in for the monomer motion, and we have gM(t) ~ gC(t) = 6 Dt, where D is the diffusion coefficient of a chain.
In the figure the data are plotted versus Dt. This representation forces agreement between theory and simulation at late times. So, a fair assessment of the quality of the comparison can only be made at intermediate times before the diffusive regime. Here, the comparison reveals the following strengths and weaknesses: We find good agreement for the monomer dynamics. In particular, the theory correctly describes the motion of the end monomer relative (g1) to the MSD of the central monomer (g5), see inset. Furthermore, it suggests that there should be deviations from pure Rouse behavior due to finite-N effects; this rationalizes the effective power law gM(t) ~ t0.63. On the other hand, the agreement with the CM motion is not so satisfactory. Careful examination reveals that the theoretical gC(t) enters the diffusive regime earlier than the simulated one. The origin of this discrepancy is not well understood.
J. Baschnagel (principal investigator), H. Meyer; S.-H. Chong (Okazaki, Japan), M. Fuchs (Konstanz, Germany); K. Binder, W. Paul (Mainz, Germany); S. C. Glotzer (Ann Arbor, USA)