Models for Transport and Relaxation in Glass Forming and Complex Fluids: Universality?

Abstract

The question whether most properties of glasses and the glass transition phenomenon behave with universal features or not has been disputed for many years. The use of the technical term “universality” for glasses is, however, to be understood in a different way compared to the case of phase transitions in statistical mechanics, for instance. In this latter field the physical situation is simple: Most of the scaling properties of critical quantities, such as the order parameter, the correlation length etc. and all the critical exponents depend on the order parameter dimension and the spatial dimension of the Euclidian space rather than on the details of the materials or the precise form of the interaction energy [1, 2]. It is well known, for example, that the critical properties, i.e. the behavior of the material near a critical point, of the (ferromagnetic) Ising model are identical to those of the lattice gas, the binary mixture, or the binary polymer blend. What is of course different in all cases and depends strongly on all details of the material is the critical temperature itself. The precise value of the critical point for the Ising model depends on the lattice type and is, in general, not known exactly for three dimensions [2, 3]. However, this critical point will be different from that of the binary mixture (at the critical composition, which corresponds to the zero field Ising model) or the polymer blend. In the latter case, the coupling constant even depends on the length of the polymers and all non-universal properties will also be molecular-weight dependent.