Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 222

where the subscripts l and s represent, respectively, the liquid- and solid-state pro-
cesses. Then the difference between E s and E l should be equal to the enthalpy of
melting, ∆ H m . Assuming that A l ≈ A s and taking into account that for many organic
solids ∆ H m is about 5 kcal mol − 1 , the ratio of k l / k s at 100 ﾰC should be expected to
be around 800.
However, one should take notice of two important facts [ 138 ]. First is that the
experimentally measured k l / k s ratios are commonly found to be no more than a
few decades. Second, the E s and E l values are frequently determined to be insigni-
ficantly different, as should be expected considering the typically small values of
∆ H m . Extensive recent work [ 139 ] on the thermal decomposition of solid explosives
also suggests that the E s and E l values are usually equal within the experimental
error limits. An example of isoconversional evaluation of the activation energies
for the solid- and liquid-state process is a study of the thermal decomposition of
hexanitrostilbene [ 140 ]. At slow heating rates (≤ 0.4 °C min − 1 ), the process can be
carried out below the melting point of the compound, i.e., in the solid state, whereas
at faster heating rates (≥ 2.5 ﾰC min − 1 ) it takes place in the liquid state. The applica-
tion of an isoconversional method to the solid-state decomposition yields activation
energy around 200 kJ mol − 1 . For the liquid-state process, the isoconversional acti-
vation energy appears to be only marginally smaller than this value.
It should be kept in mind that when the activation energy decreases significantly
in the liquid state, it can be a sign of change in the reaction mechanism. For instance,
unimolecular decomposition can become bimolecular. Also, the acceleration does
not have to be linked uniquely to a decrease in the energy barrier. The rate increase
can be associated with an increase in the frequency of intermolecular collisions and,
thus, with a larger value of the preexponential factor in the liquid state. Last but not
least, the reaction does not have to accelerate on transition from the solid to liquid
state. As a matter of fact, there are many reactions that proceed faster in the solid
than liquid state [ 141 , 142 ]. Ultimately, the size and sign of the effect of the phase
transition on the reaction rate depends on the reaction mechanism.
A good example of a reaction whose rate remains practically unaffected by a phase
transition is the thermal decomposition of ammonium nitrate [ 143 ]. The compound
melts at 169.5 ﾰC [ 102 ] and can be decomposed isothermally below and above this
temperature, i.e., in the solid and liquid state, respectively. Isoconversional analysis
of the isothermal data on solid- and liquid-state decomposition yields the E ʱ depen-
dencies displayed in Fig. 4.48 . It is seen that for the most part of the process the
activation energies for the solid- and liquid-state decomposition are nearly identical.
Of course, one cannot expect any significant difference in the E s and E l values be-
cause the enthalpy of ammonium nitrate melting is only 6.4 kJ mol − 1 [ 144 ]. Further
kinetic analysis suggests [ 143 ] that in both liquid and solid state the decomposi-
tion obeys the same reaction model, which is the model of a contracting cylinder
(N12 in Table 1.1). The rate constants estimated for the liquid- and solid-state pro-
cess fall on a single Arrhenius plot presented in Fig. 4.49 . The respective values of
the activation energy and preexponential factor are: E = 92 6 kJ mol − 1 and log( A /
min − 1 ) = 9.0 0.6. That is, both liquid- and solid-state decomposition of ammonium