E4 Partial Crystallinity: Spherulites and Lamellae

Topic

Unlike a ceramic material—whose ordered structure extends like a perfect crystal throughout its entire volume—or a glass—whose structure remains entirely amorphous—this polymer organizes its ordered regions into thin crystalline lamellae (sheets of molecular chains folded back on themselves within a narrow thickness). It then groups these thin crystalline lamellae—which grow radially from a single nucleation center—into spherulites; these spherulites are, in turn, embedded within an amorphous matrix that occupies the remainder of the polymer's volume. If the polymer develops a greater number of these thin crystalline lamellae within each spherulite, the volume fraction occupied by the spherulites relative to the amorphous matrix consequently increases.

The measured density of this polymer—which rises as the volume fraction occupied by the spherulites and thin crystalline lamellae relative to the amorphous matrix increases—determines the polymer's crystallinity fraction when compared to the reference densities of a fully amorphous polymer and a fully crystalline polymer. This is the same crystallinity fraction that is also determined—via a different experimental method based on the enthalpy of fusion derived from the corresponding calorimetric peak—by another model within this set. As the measured density of the polymer approaches the reference density of a fully crystalline polymer, the crystallinity fraction (derived from the density measurement) consequently increases, aligning with the results revealed by the enthalpy of fusion measured via the calorimetric method. Consequently, in this model—introduced via the concepts of spherulites and crystallinity fraction—the equilibrium lamellar thickness of these thin crystalline lamellae (determined by the Gibbs-Thomson effect and the Hoffman-Weeks relationship) dictates the polymer's observed melting point. A smaller equilibrium lamellar thickness exposes a larger interfacial area—per unit volume of the lamellae—between the crystalline phase and the surrounding amorphous matrix; according to the Gibbs-Thomson effect, this increased surface area depresses the observed melting point below that of a hypothetical crystal of the same polymer with infinite thickness. Conversely, if the equilibrium lamellar thickness—kinetically determined during crystallization (a process described in greater detail elsewhere in this set of models)—is greater, the depression of the observed melting point is correspondingly reduced (per the Hoffman-Weeks relationship), bringing the observed melting point closer to that of the infinite-thickness crystal—a reference point to which neither of the two comparison materials initially cited (the perfect ceramic crystal and the fully amorphous glass) bears any resemblance.

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