Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 28

methods for evaluating nonisothermal kinetics. A comprehensive overview of the
early methods is found in several topics [ 11 , 12 ]. The first isoconversional methods
proposed for treatment of nonisothermal kinetics appeared nearly simultaneously
in the 1960s. These were the differential method of Friedman [ 13 ] and the integral
methods of Ozawa [ 14 ] as well as of Flynn and Wall [ 15 , 16 ].
A simple rearrangement of Eq. 2.2 allows one to arrive at the equation of the
Friedman method:

f A E
RT

d
d

α

α
α

ln = ln[() α ] − ,

(2.5)

α

t

α , i , i

where the index i identifies an individual heating rate and T ʱ,i is the temperature
at which the extent of conversion ʱ is reached under i th heating rate. Then for any
given ʱ, the value of E ʱ is estimated from the slope of a plot of ln(d ʱ /d t ) ʱ,i against
1/ T ʱ,i . A great advantage of Eq. 2.5 is that it is applicable to not only linear heating
program but also any temperature program at all. In particular, one can apply this
equation to the actual sample temperature that may deviate from the preset non-
isothermal or isothermal programs because the thermal effect of a process induces
sample self-heating or self-cooling (see Sect. 1.3). The method is best applied to
the data of differential type such as heat flow in differential scanning calorimetry
(DSC). The application of the method to experimental data of the integral type such
as mass loss data in TGA reveals an important disadvantage caused by the need of
using numerical differentiation for estimating d ʱ /d t . The procedure dramatically
amplifies the noise present in experimental data. For this reason, numerical dif-
ferentiation has to be combined with smoothing. The latter must be performed with
great care because it is known to introduce a systematic error (shift) in the smoothed
data that would ultimately appear as a systematic error in the values of kinetic pa-
rameters.
The integral data are best treated by integral isoconversional methods that are
derived from the integral form of Eq. 2.2:

t

− E

∫

g ( α ) = A exp d . t

(2.6)

RT

0

If the temperature is raised at a constant rate:

TT t =+

0

β , (2.7)

where ʲ is the heating rate; integration over time can be replaced with integration
over temperature:

T

A − E

RT

A IET

∫ 0

(2.8)

g () α = exp dT ≡ ( , ,

β β

T