Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 68

Fig. 3.2 Arrhenius plots for
the temperature dependence
of the diffusion coefficient
of various gases in helium.
(Data taken from Seager et al.
[ 22 ])

Carbon dioxide
Argon
Benzene
Methanol
Ethanol

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

0.0016 0.00200.0024 0.0028 0.0032 0.0036

T -1 / K -1

3.2.2 Isoconversional Treatment

When it comes to applying an isoconversional method to treat the kinetics of vapor-
ization or sublimation, one should notice that neither Eq. 3.5 nor Eq. 3.9 includes the
value of the mass lost ( m ) in their respective right-hand sides. It means that if one
replaces the mass with the conversion, these equations would not include in their
right-hand sides any reaction model either. Although it may sound confusing, in fact
these equations do include one very specific reaction model, f ( ʱ ) = 1. This is called
the zero-order reaction model. This model represents a process whose rate remains
constant throughout the whole range of conversions from 0 to 1. However, the rate of
vaporization or sublimation is proportional to the free surface area (i.e., the surface
area that is in contact with surrounding gas or vacuum) of the condensed substance.
Then the rate of these processes would be independent of conversion only in a specific
case when the free surface area does not change with the process progress. This is a
reasonable assumption when, for example, vaporization rate is measured for a liquid
that fills one of cylindrical pans (Fig. 3.3a ) usually used in thermal analysis studies.
In this case, the free surface area of the liquid would be determined by the circular
cross-sectional area of the pan until the interface reaches the pan bottom and the liquid
breaks into several droplets. Nevertheless, when the condensed substance is present
in the form of individual droplets or crystals (Fig. 3.3b ), the free surface area as well
as the process rate would be decreasing with increasing the conversion. In this situa-
tion, the rate equation for vaporization or sublimation would have to include explicitly
some f ( ʱ ) of the decelerating type such as the model of contracting sphere or cylinder.
Note that the introduction of some explicit f ( ʱ ) in the right-hand side of Eqs. 3.5 or
3.9 would not affect the values of the isoconversional activation energy estimated as:

ER t
T

∂ ln( dd

1

α / )

=− .

(3.12)

α

−

∂

α