diffractogram of crystalline sugar shows many sharp peaks, that of
amorphous sugar none. The glass transition phenomenon will be
explained for a pure substance (a monomolecular liquid) with reference to
Figure 16.2.
Assume that a liquid is slowly cooled, so that the system remains in
equilibrium. In Figure 16.2a we see that thespecific volume(1/r) gradually
decreases until the melting pointTmis reached, where 1/rsharply decreases
because the material crystallizes. In the crystalline state the value further
decreases with decreasing temperature, though at a slower rate. However, if
cooling proceeds extremely fast, crystallization may not occur—since it
takes time to get started—and then 1/rkeeps decreasing as depicted, until its
value approaches that of the crystalline solid. At this temperature,Tg,a
glassis said to be formed. The specific volume curve shows a sharp bend,
and its value now remains close to, though somewhat larger than, that of a
crystal. The excess of specific volume over that in the crystalline state can be
seen as a measure of the extent to which molecules can show free
translational and rotational motion. In the glassy state such freedom is
nearly zero, as in a crystal.
The change from a liquid with great freedom of motion to the state at
Tgwhere molecular motion is arrested is not a sharp one. Since the amount
of molecular motion varies inversely with theviscosity, this can be illustrated
by the change in viscosity, as in Figure 16.2b. Its value increases ever
FIGURE16.1 Molecule densityrM, or the probability of finding the center of
gravity of a molecule as a function of the distance from a central moleculein a given
direction, for a crystalline and an amorphous solid consisting of the same (small)
molecules. Highly simplified.