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

Abstract

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 η can increase from about η=1 Poise at the melting transition to η≈1013 Poise at the glass transition temperature Tg), 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 T0<Tg) – the mode coupling theory attributes the transition to a (smeared out) dynamical transition (from ergodic to nonergodic behavior) at a critical temperature Tc>Tg. 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>Tc 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 Tc 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.