Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 5

Fig. 1.3 Evaluation of con-
version from DSC curve

Similarly, if the concentration of a reactant is available, it can easily be converted
to the conversion. For example, if the value of C varies throughout the reaction from
the initial value C 0 to zero, the conversion is:

CC
C

0

α= .

(1.6)

0

Isolating C from Eq. 1.6 and substituting the resulting expression into Eq. 1.3 leads
to:

d
d

α

n

(1.7)

= ′ kT ()( 1 − α ) ,

t

where k' ( T ) = C 0 n − 1 k ( T ). Equation 1.7 is the basic equation of homogeneous ki-
netics. Comparing it against Eq. 1.1 suggests that homogeneous kinetics can be
described by a simple reaction model:

(1.8)

n

f () ( α =− 1 α ) .

that is called a reaction-order model.
Fitting the rate to the reaction models may provide some clues about the reaction
mechanism. Fitting homogeneous kinetics data to a reaction-order model (Eq. 1.8)
and determining that n equals 1 or 2 suggests that the reaction is, respectively,
monomolecular or bimolecular. In heterogeneous kinetics, the situation is not nearly
as simple. There are dozens of heterogeneous reaction models that have been de-
rived under various mechanistic assumptions [ 9 , 13 ]. Such multitude of the models
arises from the need to describe the multitude of ways by which the spatially local-
ized reaction zone propagates throughout the reactants. The mathematical equations
and names of some models are collected in Table 1.1 . Figure 1.4 displays the model
dependencies of f ( ʱ ) on ʱ .