Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 16

(1.20)

− 1 − −

=+

1 1 ,

k k k

ef D

where k ef , k, and k D , respectively, are the effective, reaction, and diffusion rate con-
stants. Assuming that k and k d obey the Arrhenius temperature dependence, we can
derive the effective activation energy of the overall process as follows

ER k
T

d
d

ln Ek Ek

kk

+
+

=−

=

ef D D

,

(1.21)

ef

− 1

D

where E and E D are the activation energies of the reaction and diffusion. In Eq. 1.21,
E D can be reasonably well approximated by the activation energy of viscous flow
[ 37 ]. Because both k and k D vary with temperature, E ef should generally vary with
temperature taking the values between E and E D . Figure 1.11 displays the respec-
tive temperature dependence of E ef estimated under assumption that E D is typically
smaller than E . Equation 1.21 also suggests that E ef can be constant in two special
cases. First, when diffusion is much faster than the reaction ( k D >> k ) the process
is said to occur in the reaction regime, and the value of E ef = E . Second, when the
process occurs in the diffusion regime ( k >> k D ) then E ef = E D . The effect of diffu-
sion is equally important for reactions of solids such as decomposition or oxidation
when escape of a gaseous product or delivery of gaseous reactant can be controlled
by diffusion through a solid product formed on the surface of a solid reagent [ 38 ].
All in all, we should recognize that strong intermolecular interactions encoun-
tered in condensed-phase media generally affect a single reaction step to such extent
that its kinetics depends on the reaction medium properties and the energy barrier
varies as these properties change with conversion and/or temperature. Furthermore,
a single reaction step can be complicated by additional steps such as diffusion.
Then the kinetics of the overall process that involves a reaction and diffusion step
becomes driven by two energy barriers. The temperature dependence of such pro-

Fig. 1.11 Temperature varia-
tion of the effective activation
energy of a process, whose
overall rate is determined by
the rate of both diffusion and
reaction (Eq. 1.20)

E ef = E

E = E D

T