Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 66

on the strength of the inter- and intramolecular bonds, vaporization and/or sublima-
tion may or may not be accompanied by decomposition. For example, a typical
covalent compound such as a hydrocarbon is held in the condensed phase by weak
van der Waals forces. It would undergo vaporization or sublimation at temperatures
that are too low to break the strong covalent bonds and cause decomposition of the
compound. However, decomposition may readily occur in ionic compounds that are
held in the condensed phase by strong ionic forces. Decomposition can complicate
significantly the kinetics of vaporization or sublimation that by itself is relatively
simple.
In 1913, Langmuir [ 15 , 16 ] proposed an equation that describes the rate of va-
porization in vacuum:

d
d

m
t

M
RT

(3.5)

−= γ P ,

2

where d m /d t is the rate of mass loss per unit of the surface area, M is molecular mass
of the gaseous compound, P is the vapor pressure of the compound, R is the gas con-
stant, T is the temperature, and ʳ is the accommodation coefficient. The latter was
taken to be close to unity for reasonable molecular masses, e.g., it is 0.98 for carbon
dioxide [ 16 ]. The equation was derived from the Knudsen equation [ 17 ] for the ef-
fusion rate through an orifice that lies in the foundation of the Knudsen method for
determining molar mass or/and the vapor pressure from the mass loss rate data [ 18 ].
We can isolate the temperature-dependent parameters in Eq. 3.5 and write it in a
more convenient form using the extent of conversion:

d
d

α
t

(3.6)

−0.

= Const PT ,

where Const collects all temperature-independent parameters. The vapor pressure
in Eq. 3.6 depends on temperature in accord with the Clausius-Clapeyron equa-
tion:[ 18 ]

PC H
RT

=− ∆

(3.7)

ln ,

where C is a constant and Δ H is the enthalpy of vaporization or sublimation. Then
with regard to Eq. 3.7, Eq. 3.6 can be used to derive the activation energy of the
process as follows:

dlnd d
d

( α

1

/ t ) 1

2

=−

=−

(3.8)

ER ∆ H T .

−

T

The second term in Eq. 3.8 does not exceed a few kilojoules in any reasonable
temperature range and thus can be neglected. Therefore, Eq. 3.8 suggests that if one