Chemistry Reference
In-Depth Information
6.3 Estimation of Kinetic Constants from DTA-TGA Data
Obtained by Dilution-Based Techniques
Let us consider the heat balance for the thermograph cells shown schematically in
Fig. 6.1.
For the working cell
(
CM
+
cm
)
d
(
T
ref
+
Δ
T
)
=
Qm
d
dt
−
α
−
T
0
]
.
S
[(
T
ref
+
Δ
T
)
(6.1)
dt
For the reference cell
CM
dT
ref
dt
=
−
α
S
(
T
ref
−
T
0
)
,
(6.2)
with the initial conditions
t
= 0,
T
ref
=
T
0
=
T
0in
,
= 0, where
T
0in
is the
initial temperature of the oven wall,
T
ref
is the reference substance temperature,
C
and
M
are the heat capacity and weight of the reference substance, while
c
and
m
are the heat capacity and weight of the reagent.
Subtracting Eq. (6.2) from Eq. (6.1) and using inequality
CM
Δ
T
= 0,
η
cm
, one obtains
the following original equations for the DTA signal:
CM
d
(
Δ
T
)
dt
=
Qm
d
dt
−
α
S
Δ
T
,
(6.3)
d
dt
= ˙
η
(
T
,
η
)
,
(6.4)
with the initial conditions
t
= 0,
= 0.
Equation (6.3) is strictly valid for a static (isothermal) mode. In this case, the tem-
perature dependence of the thermophysical parameters of the cell can be neglected
under the assumption that
C
= const and
Δ
T
= 0,
η
= const in the experiment. Under the
conditions of programmed heating (dynamic modes), instead of Eq. (6.3) one can
write
α
C
(
T
)
M
d
(
Δ
T
)
dt
=
Qm
d
dt
−
α
(
T
)
S
Δ
T
(6.5)
with the same initial conditions.
Integration of the left hand side of Eq. (6.5) with respect to
t
over the interval
0-
t
end
(the moment at which the process ends, when
1) using the tabular temper-
ature dependence of the inert substance (intermediate mathematical manipulations
are omitted)
η
≈
C
(
T
)=
a
+
bT
,
(6.6)
gives, for dynamic heating with rate
T
=
ω
,
t
end
t
C
(
T
)
d
(
T
)
dt
Δ
M
dt
=
M
ω
b
Δ
Tdt
.
(6.7)
0
0
