Polymer Physics

Here assumes that

Tm^0 

Dh

Ds

(10.23)

whereDhis the heat of fusion in each unit of volume, andDsis the melting entropy
in each unit of volume, so one obtains theGibbs-Thomson equationfor the melting-
point depression due to limited lamellar thickness, as given by

Tm¼Tm^0 ð 1 

2 se

lDh

Þ (10.24)

The thickness of lamellar crystals normally exhibits a broad distribution, so their
melting points also cover a broad temperature range, which is often calledthe
melting range. Note that the melting range usually occurs far below the equilibrium
melting point.

10.3.4 Morphology of Polymer Crystals

The morphologies of polymer crystals and their evolution provide important infor-
mation on the crystallization mechanisms as well as the relationships between the
crystalline states and their performances. The situations of polymer crystallization
can roughly be divided into three types: crystallization from quiescent amorphous
states of polymers, crystallization in company with polymerization, and crystalli-
zation induced by pre-orientation. In the quiescent solutions or melt phases of
polymers, the morphology of polymer crystals changes from simple to complex
with the increase of polymer concentrations or the decrease of temperatures. The
most basic morphology is the single lamellar crystals. They can branch into
axialites, or even into spherulites when the density of branching becomes high
enough. Crystallization in company with polymerization often results in the nascent
fiber crystals, for instance, the celluloses, or another example, PTFE whose fiber
crystals are obtained from the gas sedimentation polymerization. Under the shear or
elongational flow fields, shish-kebab crystals and fiber crystals are often observed.
In the following, we make an extensive introduction on various crystal
morphologies that are unique to polymers.

1. Single lamellar crystals

When slowly cooled from the melt or solutions, polymers tend to crystallize into
a single layer of lamellar crystals mainly constituted by the folded chains. Keller
et al.’s discovery of lamellar crystals in 1957 established the foundation for our
understanding to the morphology of polymer crystals. The lamellar single crystals
often display the regular geometric shapes reflecting its internal crystal symmetry in
the unit cell. According to the Bravais-Friedel law (Bravais 1849 ), the most
significant crystal facets of the single crystal often contain the largest spacing of

10.3 Crystalline Structures of Polymers 203