Physical Chemistry of Foods

14.2 NUCLEATION THEORY

Nucleation theory is presently in a state of confusion, and quantitative
predictions of nucleation rate cannot generally be given. Nevertheless, the
basic principles are enlightening, and trends can be well predicted.
Experimental determination of the nucleation rate is discussed in Section
14.3.

14.2.1 Homogeneous Nucleation

In a homogeneous system, i.e., in the absence of phase boundaries,
nucleation is said to be homogeneous. A new phasebcan form if conditions
(temperature, pressure, or solute concentration) are such that its chemical
potential is smaller than that of phasea. It will then frequently happen that
a cluster of molecules in phaseaorient themselves by chance as they would
be in phaseb. If the new phase is a liquid, the solute (or vapor) molecules
have merely to associate to form such an embryo; if the new phase is a solid,
the molecules also have to attain a mutual orientation as in the crystals to be
formed.

Embryos. The excess free energy of a spherical embryo of radiusr
over that of the same volume of phaseais given by

DGemb¼

4

3

pr^3 DGVþ 4 pr^2 DGS ð 14 : 4 Þ

whereDGVis the free energy change of the material as given by Eq. (14.3)
expressed per unit volume.DGSis the interfacial free energy per unit surface
area between the two phases; it equals the interfacial tensiong. Assumingg
to be independent of temperature, which is not too far from reality for a
small temperature difference, we obtain

DGemb¼

4

3

pr^3 DHV 1 

T

Teq



þ 4 pr^2 g ð 14 : 5 Þ

Examples of the relation betweenDGemband the embryo radiusrare given
in Figure 14.2. As long asr<rcr, the embryo tends to dissolve, since that
gives a decrease in free energy. Whenr>rcr, the embryo will spontaneously
grow and hence become a nucleus. By differentiating Eq. (14.5) and putting
the result equal to zero, which corresponds toDGemb¼DGmax, the value of