exponential is much more dependent on temperature than the other factors.
This is because a small change inTgives a relatively large change in (DT)^2.
Thus experimental results are often given as a constant ‘‘preexponential
factor’’ times an exponential factor involving (DT)^2.
It will be clear from the results that the nucleation rate depends very
strongly on temperature. This is further illustrated in Figure 14.3 for ice
nucleation. Near 408 C, the magnitude ofJhomincreases by a factor of 10
for a temperature decrease of about 0.5 K. Consequently, one often speaks
of the homogeneous nucleation temperature, meaning the temperature at
which nucleation becomes noticeable in practice. Rather arbitrarily, a value
TABLE14.2 Examples of Homogeneous Nucleation Rates
Observed for Different Systems
Freezing of water
Teq¼ 273 :15K DHV¼330 MJ?m^3 g¼ 23 :3mN?m^1
This results in Jhom¼ 1041 exp½45,000=ð 273 : 15 TÞ^2
A better fit to the experimental results is
Jhom¼ 1036 exp½82,000=ð 273 : 15 TÞ^2 m^3 ?s^1
Examples:
At 328 C:Jhom¼10 m^3 ?s^1 , i.e., 1 per liter per min
At 408 C:Jhom¼ 1014 m^3 ?s^1 , i.e., 1 per s in 10^4 mm^3
At 408 C,rcr¼1.85, i.e., a nucleus of*200 molecules.
Crystallization of sucrosefrom a saturated solution
Teq¼353 K DHV¼25 MJ?m^3 g¼5mN?m^1
This results in Jhom¼ 1039 exp½93,000=ð 353 TÞ^2
A better fit to the experimental results is
Jhom¼ 1032 exp½33,000=ð 353 TÞ^2 m^3 ?s^1
Examples:
At 58 8 C:Jhom¼250 m^3 ?s^1 , i.e., 15 per liter per min
At 52 8 C:Jhom¼ 1014 m^3 ?s^1
At 52 8 C,rcr¼2.4 nm, i.e., a nucleus of*160 molecules.
Crystallization of tristearatefrom paraffin oil
Teq¼317 K DHV¼150 MJ?m^3 g¼10 mN?m^1
This results in Jhom¼ 1038 exp½19,000=ð 317 TÞ^2
A better fit to the experimental results is
Jhom¼ 4? 1025 exp½18,000=ð 317 TÞ^2 m^3 ?s^1
Examples:
At 25 8 C:Jhom¼ 104 m^3 ?s^1 , i.e., 10 per liter per s
At 18 8 C:Jhom¼ 1014 m^3 ?s^1
At 18 8 C,rcr¼1.7 nm, i.e., a nucleus of*14 molecules.
The results are quite approximate and meant to illustrate trends.