## Wednesday, July 2, 2014

### Key concepts in glasses, I.

In 1995 a group of distinguished scientists were asked by Science magazine about outstanding problems that should receive attention in the following decade. The answers are compiled here, and ironically entitled, "Through a glass lightly". Phil Anderson said:
The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the next decade.
Although I know this remains an important problem it has been a bit of a mystery to me. However, my understanding has increased by hearing a couple of nice talks in Telluride by David Reichman. This has been solidified [pun intended!] by reading a very accessible (and short) review Supercooled liquids and the glass transition by Pablo Debenedetti and Frank Stillinger. I think I now have a crude/basic understanding of a few of the key ideas including
• defining the glass transition temperature
• strong versus fragile glasses
• dynamical heterogeneity
• violations of the Stokes-Einstein relation between viscosity and diffusion constant
• mode coupling theory
Hopefully, I will post about some of these. First, here is the "Angell plot" that distinguishes strong and fragile glasses. It shows the viscosity [on a logarithmic scale] of a supercooled liquid [i.e. a liquid that has been rapidly cooled to below its melting temperature] vs. Tg/T where T is temperature and Tg is the glass temperature. The latter can actually be defined as the temperature at which the viscosity becomes 10^13 poise. [For comparison the viscosity of water at room temperature and pressure is about  0.01 poise!].
In a normal liquid the temperature dependence of the viscosity is activated [eta ~ exp (A/T) and so this plot should give a straight line. (Arrhenius behaviour).

Angell made this plot in 1995 for a wide range of glasses and found they fell into two distinct categories, that he defined as strong and fragile.

The horizontal scale is from 0 to 1.
Note that the data on the vertical scale covers 15 orders of magnitude!

The strong glasses have a simple activated form for the temperature dependence of the viscosity. The fragile glasses have an activation energy that increases with decreasing temperature.
It is amazing that such chemically and structurally diverse systems exhibit such universal behaviour.