Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 11

d
d

α d

d

α

= β .

(1.14)

t T

α α

Equation 1.14 is derived by substitution of the derivatives in accord with Eq. 1.9.
The isoconversional rates are also obtainable from DSC data that would have to be
converted to ʱ versus T curves (Eq. 1.5, Fig. 1.3 ) to estimate the values of T ʱ . The
isoconversional rate is then estimated from the experimentally measured flow rate
at T ʱ as follows:

d
d

α 1 d

d

H
t

=

.

(1.15)

t ∆ H

α tot T

α

Once the temperature dependence of the isoconversional rate is determined from a
series of temperature programs, e.g., several heating rates or several temperatures,
it can be parameterized through a combination of Eqs. 1.1 and 1.2 as:

E
RT

d
d

α

α
α

ln = ln[ Af ( α )] − ,

(1.16)

α

t

α , i , i

where the subscript i represents the number of the temperature program. This equa-
tion is the base of the differential isoconversional method by Friedman [ 24 ]. A plot
on the left-hand side of Eq. 1.16 against the reciprocal temperature gives a straight
line whose slope yields the isoconversional value of the effective activation energy,
E ʱ , without any assumptions about the process model. The two other parameters of
the kinetic triplet (preexponent and reaction model) are encrypted in the intercept
but they can be evaluated by using several simple techniques discussed in Chap. 2.
Repeating the calculations (Eq. 1.16) for every value of ʱ results in evaluating
a dependence of the effective activation energy on the extent of conversion. Ob-
taining such dependence is the major outcome of the application of the Friedman
method as well as of any other isoconversional method. An overview of the meth-
ods is provided in Chap. 2. For now, we need to point out the effective nature of the
activation energy estimated. The term “effective” as well as “overall,” or “global,”
or “apparent” is used to emphasize that the activation energy estimated from experi-
mental kinetic data does not necessarily have a simple meaning signified by Eq. 1.1.
This equation is an equation of a single-step process that means that all the reactants
become converted to the products by overcoming the same energy barrier, E . As dis-
cussed later, single-step pathways in condensed-phase and heterogeneous kinetics
are rather an exception than a rule. The application of the single-step equation to a
process whose rate may be determined by more than one step results in estimating
an activation energy that may be linked to more than one energy barrier. For this
reason, experimentally determined activation energy generally provides informa-
tion on an averaged or effective energy barrier that is the barrier that corresponds to
the actual temperature dependence of the experimentally measured process rate. It