Ph.D. thesis (pdf) - dirac

Chapter 2
Slow and fast dynamics
2.1 The glass transition
By cooling a liquid at sufficiently high rates it is possible to avoid crystallization and
to form a supercooled liquid; a thermodynamical metastable equilibrium state with
a higher free energy than the crystal. We will in general refer to the supercooled
liquid as the equilibrium liquid, even if it is metastable, because the important point
is that all properties are unique functions of the state point, for example defined by
the temperature and the pressure.
The volume (and enthalpy) of a given liquid in general decreases with decreasing
temperature, meaning that whenever the temperature is decreased by some amount,
the volume will decrease by some amount given by the expansivity. However, the
volume does not reach its new equilibrium value instantaneously, rather the liquid
equilibrates in some way over time. This process is called structural relaxation and
the associated characteristic time is the structural relaxation time or the alpha relaxation
time. The alpha relaxation is what we refer to as the slow dynamics of the
system. The alpha relaxation time is closely related to the viscosity of the liquid,
and as the viscosity grows upon cooling so does the time required to reach equilibrium.
The increase of relaxation time and viscosity, the viscous slowing down, is a
dramatic phenomenon at low temperatures because changes of the temperature by
a few percent leads to changes in the relaxation time by several orders of magnitude.
The viscous slowing down has the consequence that there is a temperature, the glass
transition temperature T g , at which the volume can no longer reach its equilibrium
value within the time scale of a given cooling experiment. At lower temperatures
the liquid will no longer be an equilibrium liquid because the structural relaxation
of the liquid is frozen in. The non-equilibrium solid formed in this way is called a
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