Physical Chemistry of Foods

thecritical radius for nucleation rcris obtained:

rcr¼


2 g

DHVð 1 
T=TeqÞ

ð 14 : 6 Þ

Inserting this into Eq. (14.5) we obtain for themaximum ofDG

DGmax¼

16 pg^3

3 ½DHVð 1 
T=Teqފ^2

¼

4

3

pr^2 crg ð 14 : 7 Þ

It may be noted that the value ofDGmaxequals 1/3 of the interfacial term in
Eq. (14.5) forr¼rcr.
It follows that the lower the temperature, the smaller will bercr,asis
illustrated in Figure 14.2. This can also be reasoned by use of theKelvin

FIGURE14.2 The excess free energyDGembof a spherical embryo of a new phase
as a function of embryo radiusr, calculated by use of Eq. (14.5) for two cases:
undercooling by 10 or 20 K.