Polymer Physics

PTFE shows a high melting point because of the strong interactions between polar
CF 2 groups.
The discussion above focuses only on the intrinsic level of chemical structures.
Some chemical factors at the extrinsic level affecting polymer melting points are
listed below.

1. Diluents

In 1949, Flory derived the equation for melting-point depression due to presence
or addition of diluents (with the volume fractionf 1 ) (Flory 1949 ), as given by

1

Tm



1

T^0 m

¼

R

DHu



vu

v 1

ðf 1 wf 12 Þ (10.16)

wherevuandv 1 are the molar volumes of repeating structural units and solvent,
respectively. Such a relationship has been well verified by the experiments
(Mandelkern 2002 ) and simulations (Hu et al.2003a).

2. Molecular weights

In 1963, Flory and Vrij proposed the Flory-Vrij equation (Flory and Vrij 1963 ).
They assumed the melting of short chains to be two steps. In the first step, all the
short chains were regarded as belonging to a long chain, which melted with the free
energy changeDGfor each chain unit. In the second step, the long chain was cut
into short chains with even chain lengths, which brought the free energy contribu-
tion of chain endsDGe, in addition to the conformational entropy lossRTlnr.
Therefore, the melting free energy became

rDGu¼rDGþDGeRTlnr (10.17)

The low molecular weight fractions of polymers contain many chain ends, which
serve as lattice defects in the large crystal to lower their melting points. The Flory-
Vrij equation has also been well verified by the experiments (Mandelkern 2002 ) and
simulations (Hu and Frenkel 2005 ).

3. Comonomers (either chemical, geometrical or stereo-irregular sequences)

In 1955, Flory applied the ideal-solution approximation (Flory 1954 ), and
assumed that the comonomer B could not enter the crystalline phase of A. He
derived that

1

Tm



1

T^0 m

¼R

lnXA

DHu

(10.18)

whereXAis the mole fraction of the monomer A,Ris the gas constant,DHuis the
melting enthalpy in each unit volume. This expression applies to those copolymers
with large comonomer units, so comonomers cannot enter the crystalline regions.

196 10 Polymer Crystallization