Crystallization Regime. This has been discussed in the previous
section. It should be realized that properties of the crystal primarily
determine which regime applies. This concerns (a) the magnitude of the
various bond energies between the molecules in the crystal and (b) the
concentration and the nature of dislocations present, screw dislocations in
particular. The latter greatly depends on the impurities present. The density
of screw dislocations tends to vary between crystal faces.
Fitting Difficulty. When argon crystallizes (say, at 2008 C), there
is no difficulty of incorporating the perfectly spherical atoms in the crystal
lattice. If an atom arrives at a vacant site it will always fit. For most
molecular crystals the situation is quite different. Consider a sugar molecule,
say a disaccharide. If it arrives at a vacant site on a crystal, it has to be in a
specificorientation to become incorporated; otherwise it will probably
diffuse away. This will markedly slow down the growth rate. Another
property of many, especially large, organic molecules is that they can
assume variousconformations, and only one of these will fit in a vacant site.
This phenomenon also decreases growth rate.
A clear example of fitting difficulty is given bytriglyceridemolecules,
which can assume many conformations. The loss in entropy upon
crystallization is thus very large. Figure 15.9 gives data on the growth and
the dissolution rates of (a face of) a trilaurin crystal. Dissolution does not
involve any fitting difficulty. If the same were true for growth, the growth
curve would just be an extrapolation of the dissolution curve, but it clearly is
not. For small values ofjlnbj, the difference in slope is by about three
orders of magnitude.
Note At lnb ¼ 0, the rates at which molecules become
incorporated into and dissolve from a crystal face is equal and
opposite. This means that the curve must exhibit a gradual change
in slope near the origin. The accuracy of the experiment is not
nearly good enough to check this.
Most likely, triglyceride molecules do not have to be in an exactly
correct conformation to become attached to the crystal: that would take too
long. Presumably, they become at first partly attached and then adsorb
further segment by segment. Comparison of theory and experiment leads to
the conclusion that about 80% of a molecule needs be in the correct
conformation before it is permanently attached (at least if lnb>0.4).
This also means that the molecule does not have to arrive in a perfect
orientation, although some orientation is certainly needed. Long-chain
molecules in solution near a crystal surface tend to be oriented more or less
parallel to this surface. If they have to become incorporated in a direction