Biomedical Engineering Reference
In-Depth Information
Analysis by x-ray scattering shows that there are no complete ordered
structures for crystalline polymers; fusion usually occurs inside an interval
of temperature (Ward and Sweeney, 2004).
the mechanism of polymer crystallisation comprises two simultaneous
processes:
• macromolecules stiffening in axial conformation, and
• macromolecular aggregation through parallel axes ('bundles' linked by
intermolecular forces).
the primary morphological element is therefore the lamella, which can
propagate in two directions. in conditions of high viscosity, one direction
is preferred to the other and a
fi bril
is formed. The fi brils grow like the
spokes of a bicycle wheel from a central nucleus, forming a spherulite (Figs
2.19 and 2.20). the development of spherulites is arrested by the contact
with other growing spherulites (Kausch and SpringerLink (Online Service),
2005). the number of nuclei that are formed is in direct proportion to the
difference between crystallisation temperature (
T
c
) and melting point. this is
very important because changing the
T
c
makes it possible to obtain different
mechanical properties.
Crystallisation kinetics are described by the Avrami equation:
VV
VV
e
VV
-
VV
-Kt
n
[2.4]
•
V
•
VV
-
VV
=
0
VV
0
VV
VV
•
V
•
VV
where
V
is the specifi c volume at the starting point (
V
0
), at a specifi c
moment (
V
) and at the end of crystallisation (
V
•
). the constants (
K
and
n
)
are dependent on the kind of nucleation, and
t
represents the time (Sperling,
2006). the traditional model adopted to describe crystalline polymers is the
'
fringed micelle model
' of Hermann
et al.
(1930). This is shown in Fig. 2.21.
The model gives this defi nition of degree of crystallinity:
=
j
cc
[2.5]
j
cc
r
cc
w
c
where
w
c
represents the mass fraction, ϕ
c
is the volume fraction, while
r
and
r
c
are the densities of entire sample and crystalline fraction, respectively.
2.19
Spherulite formation.
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