Chemistry Reference
In-Depth Information
methods, an analytical approach is generally considered to be correct if the exper-
imental data can be linearized satisfactorily (additional information regarding the
fundamental limitations of this approach can be found in [5]). An evident drawback
of this technique is the “discrete” nature of the analytical approach, since only a
small part of the “continuous” information contained in the set of DTA and TGA
curves is used.
The use of experimental methods based on the continuous recording of the
measured characteristics (including all methods based on a programmed heating
schedule) allows one to obtain more kinetic information and to find an analytical ex-
pression that describes the studied process kinetics without any a priori assignments.
Historically DTA and TGA equipment were designed for qualitative chemical anal-
ysis. Therefore, commercially available devices were not always very convenient for
experimental studies of kinetics, particularly in relation to problems associated with
setting up controlled thermophysical conditions in the reaction cell, which are re-
quired to obtain a correct analytical description of the process. Quite frequently this
aspect was neglected under the assumption that one can obtain the required quan-
titative experimental data by decreasing the heating rate and the sample weight.
However, in many cases, these measures were found to be insufficient [8].
As a rule, the analytical approach used to determine the kinetic parameters of a
nonisothermal process from experimental data is based on the solution of the direct
kinetic problem related to the development of the process. In the case of thermogra-
phy (and similar techniques), this involves the programmed heating of the reacting
material. This problem can be solved by employing various assumptions that deter-
mine the correctness of the applied analytical approach. The analytical approaches
used can be divided into three groups.
a) In most works, the linear heating problem (the linear time dependence of the tem-
perature) is solved by using only one kinetic equation (see for example [9, 10]).
This approach is quite popular due to the simplicity of the computations involved.
In this case, the main drawback is the complete neglect of the system self-heating
(the change in the temperature of the material due to the chemical reaction: posi-
tive for an exothermic reaction and negative for an endothermic reaction), which
directly influences the reaction rate. Thus, the effects of heat release during the
reaction as well as heat exchange parameters (heat-transfer coefficient, heating
rate, thermal effect of the reaction, sample weight and others) cannot be taken
into consideration. To improve the situation, a sample weight and a heating rate
(and some other parameters) corresponding to the absence of self-heating are
sometimes assigned a priori using purely thermophysical approaches without tak-
ing into account the heat from the chemical reaction. A quasi-stationary tempera-
ture lag (
r
2
/
a
, where
is the linear heating rate,
r
is the sample radius,
and
a
is the sample temperature diffusivity) and the conditions corresponding to
asmall
Δ
T
qs
=
ω
ω
T
qs
are selected.
Such evaluations are possible only for a limited parameter range; in particular
for low thermal effects which do not result in noticeable self-heating. In the gen-
eral case, self-heating temperatures can exceed the quasi-stationary temperature
difference by many times and even by orders of magnitude [8].
Δ
