Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 170

Fig. 4.5 A change from
kinetic to diffusion regime
is accompanied by a change
in the effective activation
energy of polymerization

( ' !( 5

( HI → ( 5

( HI → ( '

( ' ( 5

α

energy of the initial stages should be close to the activation energy of the chemical
reaction, E R (Fig. 4.5 ). As polymerization advances, the molecular weight of the
polymer product increases and viscosity of the reaction medium rises. This slows
down the molecular mobility, and at some point the rate of diffusion would drop
below the rate of the chemical reaction. That is, k D would become smaller than k R .
Again, the overall process rate still would be limited by the slowest step, which at
this stage of the process is diffusion. The further the process progresses into dif-
fusion regime, the closer the effective activation energy approaches the activation
energy of diffusion (Fig. 4.5 ). Note that the respective dependencies of the effective
activation energy on conversion have been previously obtained [ 15 ] for a process
involving two consecutive reactions.
It should be emphasized that, as shown in Fig. 4.5 , a transition from a kinetic to
diffusion regime can be accompanied by either decrease or increase in the effective
activation energy. A particular type of dependence is defined by the relative values of
E R and E D . If E D is larger than E R , the dependence increases. However, it decreases
when E D is smaller than E R . Generally, the E D values for diffusion of molecules
inside a polymer can take on values from a rather wide range. To be more specific,
the experimentally measured E D values have been reported [ 16 , 17 ] to be as small as
10 and as large as 160 kJ mol − 1 . One of the key factors that define the magnitude of
E D is the size of the diffusing molecule. Generally, the larger the diffusing molecule
the bigger the activation energy of its diffusion is. Therefore, if the process rate in
the diffusion regime is determined by diffusion of large molecules such as polymer
chains or their long segments, the E D value is likely to be larger than E R . On the other
hand, when the rate is limited by diffusion of small molecules such as a monomer or a
short segment of a polymer chain, the E D value can be expected to be smaller than E R .

4.2.2 Isoconversional Treatment of Polymerization

Because polymerization produces a significant amount of heat, the kinetics
of the process is convenient to follow by means of DSC. The application of an