14.3 NUCLEATION IN A FINELY DISPERSED
MATERIAL
When a bulk material contains about one catalytic impurity per mm^3 at a
given supersaturation, nucleation will generally be fast enough to ensure a
rapid phase transition, say crystallization. If the material is divided into
emulsion droplets of 100mm^3 , only about 1 in 10^7 droplets will contain an
impurity that can induce crystallization, which is a negligible amount. The
emulsified material thus needs a far greater supersaturation, possibly
corresponding to homogeneous nucleation, before most of it can crystallize
(cf. Figure 14.4). This is because a phase transition in one drop cannot
induce a transition in another drop (see further on for an exception). A
material in a finely dispersed state thus can be undercooled far deeper than a
bulk material, and its nucleation rate will generally be much slower.
Moreover, the amount crystallized will depend on the temperature history.
This is of practical significance in several oil-in-water emulsions. It is
especially important in natural foods, where most of the water is in cells:
most cells do not contain effective catalytic impurities. Consequences will be
discussed in Section 16.3.
Figure 14.9a gives a few examples. A highly purified emulsified
tristearate can be cooled to almost thehomogeneousnucleation temperature
before crystallization occurs (curve 1); it thus contains virtually no catalytic
impurities. Upon heating the cold emulsion, it shows no sign of melting until
it almost reaches the equilibrium temperature (curve 3). There is thus a large
hysteresis between cooling and melting, about 28 K in this case. A
nonpurified sample shows less undercooling, and the cooling curve (2) is
far less steep. Here, nucleation must have been almost completely
heterogeneous. The catalytic impurities for triglycerides must be for the
most part composed of monoglycerides (inverse micelles?), since Ncat
correlates well with the concentration of these substances.
Kinetics. Emulsions have long been used to determine crystal
nucleation kinetics, i.e., to find values ofNcatand ofJhetor Jhomas a
function of supersaturation or other conditions. The material is emulsified
in a suitable medium, e.g., water in silicone oil or oil in water, with a suitable
surfactant, and the droplet size distribution is determined. To obtain useful
results, a series of emulsions differing in average droplet size should be
made. The emulsions are cooled to various temperaturesTcbelowTeq, and
after a given time the amount of crystalline material is determined, e.g., by a
change in density, or from the heat of fusion, or by means of some
spectroscopic method. The same method is applied to the bulk material
starting atTc, and from the ratio of the results the valueyis calculated,