Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 115

of the Δ T value. An estimate of this value is obtained from individual DSC peaks as
an extrapolated onset temperature, T m, ʲ . The T m, ʲ value depends on the heating rate,
ʲ . A heating rate-independent value is found by extrapolation of the T m, ʲ values to
ʲ = 0, using an equation proposed by Illers: [ 133 ]

=+ 0.

T T a β .

(3.73)

m, β m

The intercept of the linear plot of T m, ʲ against ʲ 0.5 yields the value of T m that can be
used in fitting of Eq. 3.72 to the experimental E versus T dependence.
The fits of Eq. 3.72 to the experimental E versus T dependencies derived from
the Kissinger plots for melting of PET and PCL are seen in Fig. 3.44 . The fits are
quite satisfactory, considering that Eq. 3.72 has only one adjustable parameter. The
estimated values of the parameter A are 92 4 (PET) and 11.9 0.2 (PCL) kJ K
mol −1 . The value can be used to estimate the interfacial free energy, ˃ . It should be
noted that Δ G * in Eq. 3.68 is in joules, whereas A is estimated (Eq. 3.72) from the
values of E which are in joules per mole. With regard to this, A takes the following
form:

πσ 20
∆

A Nl

T

(3.74)

A m

= ,

H

f

where N A is the Avogadro number, 6 10 23 mol −1 . Solving Eq. 3.74 for ˃ yields:

AH
NlT

∆

f

(3.75)

σ =

0 .

π

Am

For polymers, the values of T 0 m and Δ H f are available from various literature sources,
e.g., from Wunderlich [ 113 ]. For PET, T 0 m = 553 K and Δ H f = 2.1 10 8 J m −3 . For
PCL, according to the literature data collected by Sasaki [ 126 ], T 0 m = 342.2 K and
Δ H f = 1.9 10 8 J m −3 . The lamellar thickness, l, can be estimated at T m by the Gibbs-
Thomson equation (3.64) from the literature values [ 107 , 126 ] of the fold surface
free energy ˃ e . For both polymers, l is about 15 nm [ 129 , 131 ]. By inserting the above
values in Eq. 3.75, one estimates the ˃ values to be 1.1 10 −3 J m −2 (PET) and 5.1
10 −4 J m −2 (PCL). Unexpectedly, both of these values are about an order of magni-
tude smaller than the values estimated from crystallization data: 1.2 10 −2 J m −2 for
PET [ 107 ] and 8.2 10 −3 J m −2 for PCL [ 126 ]. A similar observation has been made
in the original paper [ 121 ] by Toda et al., who found from their melting data that the
Thomas-Staveley ratio [ 134 ] is about an order of magnitude smaller than is typically
found from crystallization data on a variety of polymers. When applying the nucle-
ation model to melting of PCL, Sasaki [ 126 ] has also found the ˃ value to be an order
of magnitude smaller than that determined from crystallization data. It appears that
the analysis of the polymer melting kinetics in terms of the nucleation model yields
consistently the values of the lateral surface free energy which is about an order of
magnitude smaller than that derived from crystallization kinetics.