Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 69

Fig. 3.3 Schematic repre-
sentation of vaporization or
sublimation of different form
samples placed in cylindrical
pan. a Sample in the form of
continuous volume of a liquid
or solid substance. b Sample
in the form of individual
droplets ( left ) or crystals
( right )

This is because the logarithmic derivative of f ( ʱ ) is zero at a constant value of ʱ
(Eq. 1.12). Therefore, Eqs. 3.8 and 3.11 would remain true under the isoconver-
sional conditions. That is, for the process of vaporization or sublimation, one should
generally expect the isoconversional values of E ʱ to be practically independent ʱ
and close to the value of the process enthalpy. Some systematic dependencies as
well as deviations may occur naturally because the enthalpy depends on tempera-
ture in accord with the Kirchhoff's law:[ 18 ]

T

0 0

2

(3.13)

∆ HT HT CT

P

() () = ∆ + ∫ ∆ d ,

2 1

T

1

where Δ H 0 is the standard enthalpy change at the temperatures T 1 and T 2 , and Δ C P
is the heat capacity change due to a transition from the condensed to gaseous state.
However, the issue of using proper reaction models arises when isoconversional
analysis is applied to determine the preexponential factor and reaction model. An
instructive example of isoconversional analysis of vaporization of 2,2′-bipyridyl
is given by Vecchio et al. [ 23 ] (Figs. 3.4 and 3.5 ). As seen in Fig. 3.4 , the E ʱ
values do not practically depend on ʱ . The respective average activation energy
is 61 2 kJ mol −1 . The value agrees very well with the independently measured
enthalpy of vaporization, 59 2 kJ mol −1 [ 23 ]. The reaction model of vaporization

Fig. 3.4 E ʱ dependence
for vaporization of
2,2′-bipyridyl. (Reproduced
from Vecchio et al. [ 23 ] with
permission of Elsevier)