Crystallization of Polymers. Volume 1, Equilibrium Concepts

42 Fusion of homopolymers
Fig. 2.12 Melting temperature of n-alkanes as a function of chain length. Solid curve
calculated from Flory–Vrij analysis.(1) Experimental results: Ungar et al. (13); Flory
and Vrij (11), Lee and Wegner (14); □ Takamizawa et al. (28).
temperatures that are obtained by differential scanning calorimetry.(18,29) Although
melting temperatures can be obtained by this technique that are comparable
to those from conventional adiabatic calorimetry and dilatometry, special care and
procedures need to be adopted. There is also the question of the purity of the compounds
with respect to chain length, chain structure and chemical impurities. These
points need to be clarified before any real shortcomings in the theory are addressed.
In the discussion of the fusion of the n-alkanes up to now, only the extreme
states of perfect crystalline order and of a completely molten liquid have been
considered. It is conceivable that, for chain molecules, the molecular crystals may
undergo partial melting with disruption of the planar arrangement of the terminal
CH 3 groups. This possibility is illustrated in Fig. 2.8B where m methylene units
from the terminal sequences of each molecule are conformationally disordered, or
melted. This change can be termed pre-melting and is a prelude to complete melting.
Of interest here is this very specific type of pre-melting. Other types of pre-melting
due to impurities, or inclusion of a second component, or the advent of the so-called
“rotator phase” (31) have also been discussed in reference to the n-alkanes. In the
present discussion of pre-melting in the n-alkanes, only conformational disorder,
which is confined to sequences of methylene groups at the chain ends, will be of
concern. Gauche conformers are introduced, causing disorder that involves trans
bond orientation as well as gauche ones.
In their classical work Flory and Vrij also analyzed this pre-melting phenomenon.
They let m CH 2 units from the terminal sequences of each molecule be melted. Thus
n − m consecutive units from the center of the molecule occupy a crystalline zone
comprising similar sequences from neighboring chains. The fairly drastic alteration