Civil Engineering Reference
In-Depth Information
( )
()
−
R
d
ln
Hr
E
a
=
Eq. (9)
b
d
1
/
T
where
b
= constant for
n
=1
Hr
= heating rate (°C/min)
Using a point of equivalent weight loss beyond any initial weight
loss due to evolution of volatiles, a plot of ln(
Hr
) versus 1/
T
can be
constructed to obtain
E
a
and the pre-exponential factor (
A
). The results from
this approach plotted as estimated lifetime versus temperature can provide
useful information.
[46]
In the constant reaction rate approach, developed by Rouquero
[47]
and improved by Paulik, et al.,
[48]
the heating rate is adjusted as required by
the instrument to maintain a constant rate of weight loss. This is a high
resolution approach, which has proved to be very useful for samples
which decomposed reversibly,
[44]
such as inorganic materials, which lose
ligand molecules (e.g., water, CO
2
). Assuming a first order reaction, the last
two terms in Eq. (8) are constant, hence, the
E
a
can be obtained by plotting
ln [1/(1 -
x
)
n
] vs 1/
T
. The advantages of this approach are the ability to
evaluate multiple component materials and the need for only a single
experiment.
[44]
The dynamic heating rate approach consists in varying continu-
ously both the heating rate and the rate of weight loss, but the heating rate
is decreased as the rate of weight loss increases. This results in enhanced
resolution and faster experiments.
According to Sauerbrunn, et al.,
[44]
kinetic parameters can be
obtained from dynamic heating rate experiments using the equation devel-
oped by Saferis, et al.,
[42]
′
H
r
E
AR
( )
n
−
1
ln
=
−
a
−
ln
n
1
−
x
Eq. (10)
2
T
RT
E
a
where
H
´
r
=
heating rate at the peak (°C/min)
T
=
temperature at the peak (K)
A
=
pre-exponential factor
R
=
gas constant
n
=
reaction order
E
a
=
activation energy
x
=
degree of conversion
