Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 7

Fig. 1.5 Three major types
of integral kinetic curves
obtained under isothermal
conditions: 1 decelerating; 2
accelerating; 3 autocatalytic
(sigmoid)

1.0

1

3

0.5

2

0.0

t

Then from the f ( ʱ ) dependencies presented in Fig. 1.4 , we can identify three major
types of heterogeneous kinetics: decelerating, accelerating, and autocatalytic. For
the decelerating kinetics, the rate is continuously decreasing as the process pro-
gresses from ʱ = 0 to 1. This type of behavior is represented by the diffusion models
and the models of contracting geometry. This is also the typical behavior for the
homogeneous kinetics that obey the reaction-order model (Eq. 1.8). For the accel-
erating kinetics, the rate is constantly increasing throughout the process progress.
The power law models provide an example of such behavior. The autocatalytic
models describe processes whose rate passes through a maximum. The Avrami-
Erofeev models of nucleation and growth are typical representatives of such kinetic
behavior.
The three types of heterogeneous kinetics are also easy to recognize from the
integral kinetic curves, ʱ versus t, obtained under isothermal conditions (Fig. 1.5 ).
The decelerating kinetic curves are almost linear in the initial portion but start to
bend at larger extents of conversion and ultimately reach a plateau as ʱ approaches
1. The accelerating and autocatalytic kinetic curves demonstrate little change at
the lowest extents of conversion, sometimes featuring a distinct plateau. The latter
is also called an induction period. Past this period, the curves starts to bend at a
continuously increasing angle. In the accelerating curves, this trend persists until
completion, i.e., ʱ = 1. In the autocatalytic curves, acceleration switches to decelera-
tion at some intermediate extent of conversion. This gives rise to the characteristic
sigmoid shape of the curves. The respective reaction models and kinetics are some-
times referred to as sigmoid.
Speaking of indentifying particular reaction models (Fig. 1.4 ) rather than the
types of kinetics (Fig. 1.5 ), a quick review of Fig. 1.4 immediately reveals that
many of the models do not show a significant difference especially in certain ranges
of ʱ . Considering that all models largely oversimplify the reality, experimental data
tend not to follow the models accurately. It is frequently found that experimental
data fall between two model dependencies, or coincide with one model at smaller