Understanding the glass transition and the amorphous state of matter: can computer simulation solve the challenge?

The glass transition of supercooled fluids is one of the big puzzles of condensed matter physics, because there occurs a dramatic slowing down (the viscosity eta can increase from about eta = 1 Poise at the melting transition to eta approximate to 10(13) Poise at the glass transition temperature T-g), but one hardly sees any accompanying change in the static structure. Theoretical concepts are very controversial - e.g., the Gibbs-di Marzio theory attributes glassy freezing to an underlying "entropy catastrophe" (the entropy of the supercooled fluid would fall below the crystal entropy at the Kauzmann temperature T-0 < T-g) - the mode coupling theory attributes the transition to a (smeared out) dynamical transition (from ergodic to nonergodic behavior) at a critical temperature T-c > T-g. Computer simulations offer the advantage that atomistically detailed information on structure and dynamics of well-defined models can readily be obtained, including quantities that are not accessible in experiments. But they have the disadvantage that a limited range of relaxation times (typically about 6 to 7 decades only) is accessible, and thus it is mostly the regime T > T-c that can be studied. Using coarse-grained models for short polymer chains, such as the bond-fluctuation model on the lattice or a beadspring model in the continuum, nevertheless useful information has been obtained: e.g., it could be shown that the configurational entropy S stays nonvanishing, although the strong decrease of S that does occur can account for the increase of the relaxation time in accord with the Gibbs-Adam theory. Also the mode coupling theory is compatible with the relaxation, although difficulties remain. These difficulties are traced to the limited range of T where idealized mode coupling theory applies (rounding of singularities very close to T-c is not fully understood). Finally, molecular dynamics simulations for a realistic model of fluid SiO2 are presented to show that simulations can contribute to a better understanding of the properties of real amorphous materials. (C) 1999 Elsevier Science B.V. All rights reserved.