Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 149

After some rearrangements, Eq. 3.96 converts to Eq. 3.97:

K
K

(3.97)

x =

1 (

− x ).

U D

+

Considering that by its meaning x D is the extent of conversion of the native to dena-
tured state, we can replace it by customarily used ʱ . Then substitution of Eq. 3.97
into 3.94 gives:

d
d

α kK

K

(3.98)

=

1 (

− α ).

t +

Equation 3.98 can now be used to derive the effective activation energy as follows:

0

ER t
T

∂ ln( dd α / ) ∆ H

K

=+ +

=− E , (3.99)

ef

− 1

1

∂

α

where E is the activation of the irreversible step (U ₒ D) and Δ H 0 is the enthalpy of
the reversible step (N ⃔ U). The effective activation energy obviously depends on
temperature because the equilibrium constant in Eq. 3.99 is temperature dependent.
The general trend of this dependence is depicted in Fig. 3.75 . It suggests that in
the low temperature limit, i.e., just above equilibrium, the temperature dependence
of the denaturation rate should demonstrate the effective activation energy close
to the sum of the activation of the irreversible step and the enthalpy of the revers-
ible step. Note that denaturation is an endothermic process, i.e., Δ H 0 > 0. However,
as the process temperature shifts further from the equilibrium value, the effective
activation energy should asymptotically approach the activation energy of the ir-
reversible step.

Fig. 3.75 Theoretical tem-
perature dependence of the
effective activation energy
as derived from the Lumry-
Eyring model (Eq. 3.99)

E ef =E + ∆ H 0

E ef =E

T