Page 78 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Polymer Structure (Morphology) 41

TABLE 2.4
Avrami Values for Particular Crystallization Growth for Sporadic and Ordered
(or Predetermined) Nucleation
Crystallization Growth Overall
Pattern Sporadic Nucleation Ordered Nucleation Dimensionality
Fiber/rod 2 1 One
Disc 3 2 Two
Spherulite 4 Three
Sheaf 6

crystallites are ordered in the direction of the stress, the filament shrinks in diameter, and heat is

evolved and reabsorbed as a result of additional orientation and crystallization.
Crystallization often occurs over a wide area/volume almost simultaneously. It is similar to rain-
drops or grains of sand falling into water and setting up waves that progress outward until they over-
lap with one another. Avrami and others have studied the rate of crystallization and have derived
various relationships to describe and differentiate the various crystallizations. The rate of crystalli-
zation can be followed using dilatometry using the Avrami equation 2.14 that was developed to fol-
low the crystallization of metals. Here, the quotient of the difference between the specifi c volume,
V, at time t and the fi nal specifi c volume, V , divided by the difference between the original specifi c
f
t

volume, V , and the final volume is equal to an experimental expression where K is the kinetic con-
o
stant related to the rate of nucleation and growth and n is an integer related to the nucleation and
growth of crystals. In theory, the value of n is related to the dimensionality of the growing crystal-
linity (Table 2.4). The value of n has been calculated using several scenarios.
V − V
i f − n (2.14)
= e K t
V − V
o f
Table 2.4 contains values for two of these scenarios. These values are valid for only the initial
stages of crystallization.
Noninteger values for n are not uncommon. As noted before, depending on the particular condi-
tions several crystalline formations are possible and are found for the same polymer. Sperling has
collected a number of Avrami values for some common values given in literature. The range of
values for polyethylene is 2.6–4.0; that for poly(decamethylene terephthalate) is 2.7–4.0; that for PP
is 2.8–4.1; that for poly(ethylene oxide) is 2.0–4.0; and that for isotactic-polystyrene is 2.0–4.0.
The kind, amount, and distribution of polymer chain order/disorder (crystalline/amorphous) is
driven by a number of factors, including structure and processing. With respect to processing, it is
possible to influence polymer properties through a knowledge of and ability to control the molecular

morphology (structure). Crystalline structures can be disrupted by processing techniques such as
thermoforming and extrusion of plastics and drawings of films and fi bers.

Crystallization of polymers containing bulky groups occurs more slowly than polymers that do
not contain bulky substituents. In addition to crystallization of the backbone of polymers, crys-
tallization may also occur in regularly spaced bulky groups even when an amorphous structure is
maintained in the backbone. In general, the pendant group must contain at least 10 carbon atoms
for this side-chain crystallization to occur. Ordered polymers with small pendant groups crystallize

more readily than those with bulky groups. Rapid crystallization producing films with good trans-
parency may be produced by addition of a crystalline nucleating agent such as benzoic acid and by
rapid cooling.

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