Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 2

position of a solid substance and thermal polymerization of a liquid monomer are
examples of a chemical process.
A change in temperature not only stimulates a variety of physical and chemical
processes but also affects their kinetics. There are many experimental techniques
that can be used for measuring the kinetics of thermally stimulated processes as
a function of temperature. Although the applications of the kinetic methodology
discussed in this topic are not limited to any particular experimental techniques, all
kinetic results collected here have been obtained by either differential scanning cal-
orimetry (DSC) or thermogravimetric analysis (TGA). Other applications include
mass spectrometry [ 1 , 2 ], infrared spectroscopy [ 3 , 4 ], dilatometry [ 5 ], rheometry
[ 6 ], thermomechanical, dynamic mechanical analysis [ 3 , 7 ], and acoustic measure-
ments [ 8 ].
DSC and TGA are the most common techniques falling under the umbrella of
thermal analysis. Detailed information on the techniques and their applications is
available elsewhere [ 9 - 11 ]. Briefly, TGA measures changes in the sample mass
that makes it suitable for monitoring the kinetics of mass loss in such processes
as vaporization, sublimation, decomposition, or of mass gain in oxidation. DSC
measures the heat flow either from or to the sample. Since practically any pro-
cess generates detectable heat flow, DSC has an extremely broad application range.
However, it is most commonly employed to measure the kinetics of processes that
occur without any mass change such as crystallization, melting, gelation, and po-
lymerization. Either technique, TGA or DSC, is capable of conducting measure-
ments under precisely controlled temperature conditions that can be isothermal or
nonisothermal. The latter typically means heating or cooling at a constant rate of
temperature change.
The rate of many thermally stimulated processes can be parameterized in terms
of T and ʱ as follows:

d
d

α

(1.1)

= ()( , kT f α

t

where t is the time, T is the temperature, ʱ is the extent of conversion, f ( ʱ ) is the
reaction model, and k ( T ) is the rate constant. The latter is almost universally repre-
sented by the Arrhenius equation:

− E

RT

kT A () exp = , (1.2)

where A is the preexponential factor, E is the activation energy, and R is the gas con-
stant. Equation 1.1 is quite different from the basic rate equation found in textbooks
dealing with homogeneous reactions in gases and solutions [ 12 ]:

d
d

C
t

kTC n

(1.3)

−= () ,