peak temperature is taken as the melting pointTm. In principle, when the crystal and
the melt are at thermodynamic equilibrium,
Tc¼Tm (10.2)As illustrated by the crossover point of the curves in Fig.10.1b, the isobaric free
energy change of the polymer bulk system at the melting point appears as
DFm¼DHmTmDSm¼ 0 (10.3)Therefore,Tm¼DHm
DSm(10.4)
One can see that, as illustrated in Fig.10.1a, the practicalTcis always lower thanTm.
The volume-temperature curves for crystallization/melting are roughly the same
results. Such a hysteresis loop is an important feature of first-order phase transitions.
If we make a reference to the melting point ofinfinitely large crystals, we can define the
supercoolingas
DTTm^0 Tc (10.5)The occurrence of supercooling also reflects the nucleation and growth mecha-
nism of polymer crystallization. For the initiation of polymer crystallization,
DT can be as high as 20 30 K, much larger than that of common small
molecules. Such a large degree of supercooling for polymers is related to their
metastable chain-folding in the crystal nucleation.
Liquid crystalline polymers exhibit mesophases with various degrees of ordering
between the amorphous state and the crystalline state, i.e. the liquid crystalline
Fig. 10.1 Illustration of (a) DSC curves corresponding to crystallizationTcand meltingTmof
polymers upon cooling and heating processes, respectively; (b) free energy curves of amorphous
and crystalline states of polymers, with the equilibrium melting point given by the crossover of two
curves. Thearrowsindicate the phenomenon of supercooling
188 10 Polymer Crystallization