Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 96

Fig. 3.30 Free energy of
nucleation as a function of
nucleus radius. (Adapted
from Vyazovkin [ 91 ] with
permission of Elsevier)

∆ G S

∆ G*

0

r*

∆ G V

r

Inserting this value into Eq. 3.34 allows one to determine the height of free energy
barrier as:

3

16 πσ

*

∆ G = . (3.36)

2

3 ( ∆ G )

V

The Δ G * can be linked to supercooling through the temperature dependence of Δ G V :

∆∆ ∆ GHTS

V

= − .

(3.37)

V V

Assuming that Δ H V and Δ S V do not depend much on temperature, Δ S V in Eq. 3.37
can be replaced with its value at equilibrium (i.e., when T = T m and Δ G V = 0):

∆∆ ∆ ∆∆

H
T

= −

HT
T

V f

m

GHT = − , (3.38)

V V

m

where Δ T = T m − T is the supercooling and Δ H f = − Δ H V is the enthalpy of fusion per
unit volume. Substitution of Eq. 3.38 into Eq. 3.36 gives:

32

16 T

HT

πσ

*

m

(3.39)

∆ G = ,

2 2

3 ( ∆∆ ) ()

f

where Δ H is the heat of fusion per unit volume. Similarly, substitution of Eq. 3.38
into 3.35 reveals a dependence of the critical nucleus size on supercooling:

2σ m
∆∆

T
HT

*

r = .

(3.40)