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4.12 Polymer Crystals • 121(b)We now utilize Equation 4.8 to calculate the percent crystallinity of the
branched polyethylene withρc=0.998 g/cm^3 ,ρa=0.870 g/cm^3 , andρs=
0.925 g/cm^3. Thus,% crystallinity=ρc(ρs−ρa)
ρs(ρc−ρa)× 100
=
0 .998 g/cm^3 (0.925 g/cm^3 − 0 .870 g/cm^3 )
0 .925 g/cm^3 (0.998 g/cm^3 − 0 .870 g/cm^3 )× 100
=46.4%
4.12 POLYMER CRYSTALS
It has been proposed that a semicrystalline polymer consists of small crystalline re-
crystallite gions (crystallites), each having a precise alignment, which are interspersed with
amorphous regions composed of randomly oriented molecules. The structure of the
crystalline regions may be deduced by examination of polymer single crystals, which
may be grown from dilute solutions. These crystals are regularly shaped, thin platelets
(or lamellae), approximately 10 to 20 nm thick and on the order of 10μm long. Fre-
quently, these platelets will form a multilayered structure like that shown in the
electron micrograph of a single crystal of polyethylene, Figure 4.11. The molecular
chains within each platelet fold back and forth on themselves, with folds occurring at
chain-folded model the faces; this structure, aptly termed thechain-folded model,is illustrated schemat-
ically in Figure 4.12. Each platelet will consist of a number of molecules; however,
the average chain length is much greater than the thickness of the platelet.
Many bulk polymers that are crystallized from a melt are semicrystalline and
spherulite form aspherulitestructure. As implied by the name, each spherulite may grow to be
roughly spherical in shape; one of them, as found in natural rubber, is shown in the
transmission electron micrograph, the chapter-opening photograph for this chapter.
The spherulite consists of an aggregate of ribbon-like chain-folded crystallites (lamel-
lae) approximately 10 nm thick that radiate outward from a single nucleation site in
the center. In this electron micrograph, these lamellae appear as thin white lines. The
detailed structure of a spherulite is illustrated schematically in Figure 4.13. ShownFigure 4.11
Electron micrograph
of a polyethylene
single crystal.
20,000×. [From
A. Keller,
R. H. Doremus,
B. W. Roberts, and
D. Turnbull
(Editors),Growth
and Perfection of
Crystals.General
Electric Company
and John Wiley &
Sons, Inc., 1958,
p. 498.]