Polymer Physics

kinetic selection is also called the chain-folding principle of polymer crystalliza-
tion, as illustrated in Fig.10.12.
Since the lamellar thickness is limited by the fold length of polymer chains, the
melting point of lamellar crystal is much lower than the equilibrium melting point
of the infinitely large crystal of polymers. Let us estimate how much decrease in the
melting point of lamellar crystals. Assuming the lamellar crystal as in a rectangular
shape, witha,bandlas the length, width and thickness, respectively, and withs
andseas the lateral and fold-end surface free energies, respectively, as illustrated in
Fig.10.13, the free energy of a lamellar crystal is

DGm¼ablDf 2 abse 2 als 2 bls (10.20)

Since the lateral sizes are much larger than the thickness (a,b>>l), from
DGm¼ablDf 2 abse¼0, one obtains

Df¼

2 se

l

(10.21)

and
Df¼DhTmDsDhð 1 

Tm

Tm^0

Þ (10.22)

Fig. 10.12 Illustration of the
kinetic selection of the
metastable chain-folding state
of polymer crystallization as
the conventional route for the
phase transition

Fig. 10.13 Illustration of the
sizes of polymer lamellar
crystals

202 10 Polymer Crystallization