Polymer Physics

with Avrami equation (Liu and Mo 1991 ;Mo 2008 ), to derive the relationship
under same crystallinity at the same time, as given by

logKþnlogt¼logK 0 qloga (10.46)

Therefore,

loga¼logð

K 0

K

Þ^1 =q

n

q

logt (10.47)

Accordingly, on a series of crystallinity versus time curves (see Fig.10.31b), one
can take the data points along the horizontal equal-crystallinity line, and then obtain
the ratios of the Avrami indexes and the rate constants separately from the slope and
the intercept of log(a) versus log(t). The experiments have verified that a better
linear relationship can be obtained in comparing this approach to the conventional
Ozawa method.
As a matter of fact, the above approach based on the changes in Avrami index or
Ozawa index to obtain the information about the changes of crystal nucleation
modes and of crystal growth dimension, is a scaling analysis to the time evolution
of crystal morphology from the phenomenological point of view. The similar
scaling analysis has also been widely applied in the other areas of polymer physics.

Question Sets

1. Why do we say that if polymer chains are more rigid, the melting points are
   higher; if the inter-chain interactions are stronger, the melting points are higher
   too?


2. Why do flexible polymer chains prefer to make chain folding upon polymer
   crystallization?


3. Why does the melting of polymer crystals exhibit a wide temperature range?


4. What is the role of a nucleation agent?


5. Why do we say that the Avrami analysis is also a kind of scaling analysis?

References

Avrami M (1939) Kinetics of phase change. I General theory. J Chem Phys 7:1103–1112
Avrami M (1940) Kinetics of phase change. II Transformation-time relations for random distribu-
tion of nuclei. J Chem Phys 8:212–224
Avrami M (1941) Kinetics of phase change. III Granulation, phase change, and microstructure
kinetics of phase change. J Chem Phys 9:177–184
Bassett DC, Frank FC, Keller A (1959) Evidence for distinct sectors in polymer single crystals.
Nature (London) 184:810–811
Becker R, Do ̈ring W (1935) Kinetische Behandlung der Keimbildung in u ̈bersa ̈ttigten Da ̈mpfen.
Ann Physik 24:719–752

References 219