ofJhom¼ 1014 m^3 ?s^1 (e.g., corresponding to about 1 in 10mm^3 during
15 min) is often taken. ThenThomwould equal about 408 C for water. At
T¼Thom, we may putrcr¼rhom, the radius of nuclei characteristic for
homogeneous nucleation.
It is also seen that there are great differences between systems, both in
the preexponential factor—which primarily affects the overall level of the
nucleation rate—and in the exponential factor—which primarily determines
the steepness of the curve with respect to temperature. The differenceTeq
Thomroughly equals 40 K for ice, 28 K for sucrose, and 26 K for tristearate
in paraffin oil. In natural fats, where triglycerides crystallize from a
triglyceride oil, the temperature difference is only about 20 K, presumably
because the interfacial tension between oil and crystal is far smaller (about 4
rather than 10 mN?m^1 ).
Complications. It is also seen in Table 14.2 that large differences
are observed between theoretical and experimental results, in both the
preexponential and the exponential factor. For highly polar materials, such
FIGURE14.3 Rate of homogeneous nucleationJhomfor the formation of ice in
pure water at ambient pressure as a function of the undercoolingDT. The broken line
is a rough estimate. The dotted lines indicate the ‘‘homogeneous nucleation point.’’