Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 112

This is a well-familiar form of a first-order rate equation. Equation 3.71 can now be
used to derive an equation for the isoconversional activation energy. As usual, it is
done by taking the logarithmic derivative of the rate (Eq. 3.71) at a constant extent
of conversion. This leads to Eq. 3.72: [ 129 ]

∂ (

)

ER t
T

ln dd α /

1 2 T

T

(3.72)

=−

=

A + .

α

− 1 2

∆ T

∂ ( ∆ )

α

Note that because the derivative is taken at a constant extent of conversion, the
obtained result is independent of the type of the reaction model used in Eq. 3.71.
In Eq. 3.72, E ʱ is the temperature-dependent activation energy estimated by an
isoconversional method. The right-hand side of this equation represents a theoretical
E versus T dependence determined by a single parameter A . By its meaning, A is al-
ways positive and so is the expression in the brackets. At very early stages of meting,
when temperature is just above the nonequilibrium melting temperature ( T m ), Δ T is
close to zero so that E ʱ can take on extremely large values. However, the E ʱ values
would decrease as Δ T continues to increase throughout the melting process. Overall,
the nucleation model predicts that the effective activation energy of melting should
exhibit a decreasing dependence on temperature. Also, fitting the theoretical E versus
T dependence to the experimental one should afford estimating the parameter A and
possibly the lateral surface free energy, if other parameters composing A are known.

3.7.2 Isoconversional Treatment

DSC is an efficient way of measuring the polymer melting kinetics. However, a
straightforward application of an isoconversional method to polymer melting data
presents a certain challenge. The problem is that the DSC melting peaks shift
very little when changing the heating rate. For example, a tenfold increase in the
heating rate shifts the DSC melting peak for PET by less than 3 ﾰC (Fig. 3.42 ).

Fig. 3.42 DSC curves of
PET melting at the heat-
ing rates 2 and 20 ﾰC min −1 .
Heat flow is normalized to
the sample mass and heating
rate. PET poly (ethylene
terephthalate). (Adapted from
Vyazovkin et al. [ 129 ] with
permission of Wiley)

0

-2

-4

-6

-8

2 o C min -1
20 o C min -1

-10

-12

210 220230 240250 260270 280290 300

T / o C