stronger upon approachingTg, where a sharp bend in the curve occurs.
Notice thatZais given on a log scale. The decrease when going fromTgto
Tgþ10 K is, for example, by a factor of 300, whereas in most pure liquids
(above the melting point) a 10 K temperature change causes a change in
viscosity by a factor between 1.2 and 2.
Changes in enthalpy of the system follow the same pattern as the
changes in specific volume given in Figure 16.2a. Frame (c) gives thefirst
derivatives of the enthalpy curves. The sharp discontinuity in the enthalpy
curve for crystallization or melting atTm is seen in frame (c) as an
(endothermic) peak. (Actually, the melting peak will be much narrower and
far higher than drawn.) This is characteristic for a first-order transition
(Section 14.1). At the glass transition,Tg, the enthalpy curve is continuous,
but the first derivative shows a sudden step. The second derivative will show
a peak. We then speak of a second-order transition, which is thus
characteristic for a glass.
It may be added that formation or disappearance of a glass is not a
thermodynamic phase transition, since a glass does not represent an
equilibrium state; nor is the value ofTgprecisely constant. At equilibrium,
crystals will form upon cooling. A glass is only obtained at very fast cooling
rates, over 10^5 K?s^1 in highly fluid liquids like water. By the same token,
heating a glass aboveTgwill lead to the formation of crystals (showing up in
an exothermic peak), unless heating is extremely fast.
Like melting points,glass transition temperaturesvary greatly among
pure substances. Examples are given in Table 16.1, and it is seen that the
differenceTmTgdoes not vary greatly. (The values forTg^0 are discussed in
Section 16.2.)
Polymers. As mentioned, the formation of a glass from a ‘‘simple’’
liquid, which means a liquid consisting of small molecules, is very difficult.
However, polymer glasses can form readily. As mentioned in Section 6.6.1
for starch, several polymer melts, as well as highly concentrated polymer
solutions, can form crystallites—i.e., microcrystalline regions—below a
certain temperature. Further cooling then does not lead to a greater
proportion of crystalline material: as the crystalline fraction increases, it
becomes ever more difficult for a (part of a) polymer chain to become
incorporated in a crystallite, because its conformational freedom becomes
ever more constrained. See also Figure 6.22. In practice, the crystalline
portion will often be of the order of one-third. Still further cooling will then
lead to a glass transition. BelowTg, part of the material will thus be
crystalline, the remainder being glassy.
Starchis a common polymer in foods. In its native state it contains
crystallites, and it shows a melting transition during gelatinization. After