Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 116

The observed difference can be rationalized by considering the difference in the
nature of the nucleation during crystallization and melting. If no foreign phase is
present, crystallization occurs by homogenous nucleation throughout the whole
melt phase. Melting, on the contrary, is a surface process [ 135 - 137 ]. The nuclei of
the melt phase are formed at the interface, i.e., heterogeneously. The difference in
the nature of homogeneous and heterogeneous nucleation entails significant ener-
getic differences. As discussed earlier (Sect. 3.5, Eq. 3.48), the free energy barrier
to heterogeneous nucleation, G * het is always smaller than that for the homogeneous
one by some geometrical factor, f ( ʘ ). For a cylindrical nucleus on a flat substrate,
the geometrical factor is as follows: [ 93 , 138 ]

− 2

f () (

Θ sin 2 Θ ) .

(3.76)

Θ =

π

Note that the value of A (Eq. 3.74) corresponds to the free energy of homogenous
nucleation. Thus, a small estimate of the A value unavoidably results in an unusu-
ally small value of ˃ (Eq. 3.75). On the other hand, if A is to be derived from the
free energy of heterogeneous nucleation, the right-hand side of Eq. 3.74 would have
to be multiplied by f ( ʘ ). Then, a small value of A determined experimentally can
be explained naturally by a small value of f ( ʘ ) without invoking any changes in ˃ .
According to Eq. 3.75, an order of magnitude decrease in ˃ would result from a two
orders of magnitude decrease in A . This would be equivalent to f ( ʘ ) being around
0.01. The respective contact angle estimated by Eq. 3.76 would be roughly 20 ﾰ. It
should be remarked that when liquid is in contact with solid of the same kind, the
contact angle can be as small as a few degrees [ 139 ]. Overall, it appears that the
polymer melting kinetics is consistent with the nucleation model, although it can be
improved further by treating the process as heterogeneous nucleation.

3.8 Solid-Solid Transitions

The nature of the universe loves nothing so much as to change the
things that are and to make new things like them. For everything
that exists is in a manner the seed of that which will be
Marcus Aurelius, Meditations

3.8.1 Background

The solid-solid transitions are quite common in ionic [ 6 , 7 ] and molecular [ 8 ] crys-
talline compounds. They represent transitions between different crystalline forms
(polymorphs) of the same compound. For example, on heating above ~ 125 ﾰC, am-
monium nitrate crystal is known to change its crystalline structure from tetragonal
to cubic lattice (Fig. 3.45 ) [ 140 ]. If in the cubic lattice, all three sides are perpen-