Polymers are good glass formers because, very often, the chains are atactic, and the crystal form is automatically forbidden.
In the polymer community, the dominant view point is that polymer melts are “fragile liquids” in the sens of Angell. Upon cooling, their viscosity (η) increases faster than an Arrhenius factor, and follows the Williams-Landel-Ferry law:
where T is the temperature, and T* is typically 50° below the glass transition point Tg, which we find in handbooks. The behavior near T* is not easily observable because the rates are too slow in this region. T* is a “ghost” transition.
A simple interpretation of T* came early from Cohen and Turnbull; it is based on a free volume v(T) (the difference of the atomic volume extrapolated from the hot melt and atomic volume in the fully formed glass). The basic assumption is that a local jump frequency ν scales like
where Ω is the cavity volume required to make a jump with the smallest plausible clump of atoms. Upon cooling, v(T) collapses fast (fragile liquids) and ν drops very fast. Eq 2 also allowed Kovacs and others to predict many history dependent properties in glass formation.
However, in the present days, the free volume model is not fashionable for two reasons:
- aIt does not seem to agree with observed effects of external pressures.
- bOther microscopic approaches have shown up the following three main streams of thoughts:
- iOne based on density fluctuations, with some nonlinearity in the corresponding energies. This is called “mode mode coupling,” and it has had a significant success in explaining properties above Tg. In this picture, there is no large scale structure showing up near T*.
- iiOne based on similarities with spin glasses, magnetic alloys where the spin couplings are a mixture of ferromagnetic pairs and antiferromagnetic pairs. Here, there are no density effects. The major feature is “frustration”: all the interactions cannot be optimized simultaneously. Frustration can exist in polymer glasses and even with simple spherical balls (each ball would prefer to be surrounded by 13 neighbors rather than 12, but we cannot achieve this on all the sample). Frustration is ignored in mode-mode coupling. One weakness of the spin glass analogy is that most of our knowledge comes from a very special model, where each spin is coupled to all the others (no neighborhood effect).
- iiiA number of simulations are performed in the fast region (at relatively high T). They show that certain fluctuations are partly quenched, and if we want to assign them an effective temperature, it differs from the bulk temperature. But the spatial size of these fluctuations is unclear, and may be too small to lead to the very universal properties.
These theoretical advances are important but obscure. On the experimental side, the major finding (in my belief) is granularity: the glass cannot be considered as uniform. For instance, rotational relaxation monitored by fluorescence depolarization on a single dye molecule, indicates a commutation of the dye (from one diffusion regime to another and the reverse). A glass is a mosaic structure.
Shall we, ultimately, arrive at a universal picture for Tg in fragile liquids? I am not sure. In 2000, I produced a theoretical dream: (a) near Tg the glass is assumed to contain clusters slightly more compact than the matrix. They cannot grow more because of frustration effects, as noted by Kivelson and others; (b) the jumps are by one cluster rather than by one molecule. The required cavity space Ω for a jump is not empty, but filled with the more fluid matrix (the criticism against free volume based on pressure effects is thus removed).
This picture may be totally inadequate. But, we probably need some thoughts on that level if we want to explain the glass transitions in simple terms to our students…