M5 Crystallization: Kinetics and Spherulitic Morphology

Topic

The nucleation of this polymer's thin crystalline lamellae—the same thin crystalline lamellae described by another model in this set as organized into spherulites embedded within an amorphous matrix—and their subsequent growth after nucleation, together follow Avrami kinetics over time. This is the same family of phase-transformation kinetics that describes, for two other distinct materials, the transformed fraction of a metal during recrystallization and the crystallized fraction of a glass during unwanted devitrification. Here, too, Avrami kinetics traces a characteristic sigmoidal growth curve: slow at first as the initial nuclei of these thin crystalline lamellae appear; faster subsequently as the nucleated lamellae grow and multiply; and slow again at the end as the expanding spherulites begin to impinge upon one another and deplete the available amorphous matrix. The fact that the nucleation of these thin crystalline lamellae is more rapid at the onset of crystallization means that the final crystallized fraction is reached sooner under this Avrami kinetic regime.

However, the growth of the polymer's spherulites is not governed solely by Avrami kinetics; according to Hoffman-Lauritzen theory, it is also limited by the diffusion of the polymer's molecular chain segments toward the growth front of each spherulite. At temperatures too close to the polymer's glass transition temperature, these molecular chain segments diffuse so slowly that the spherulitic growth rate drops, even though the thermodynamic driving force for crystallization is very high at that temperature. The fact that the polymer's crystallization temperature approaches its glass transition temperature means that—according to the Hoffman-Lauritzen theory—the diffusion of molecular chain segments is consequently slower, and the rate of spherulitic growth is likewise reduced.

For this reason, the model—based on Avrami kinetics and the chain-segment diffusion that limits spherulitic growth—produces the same spherulitic morphology described in greater detail by another model in this set, featuring thin crystalline lamellae embedded in an amorphous matrix; the equilibrium lamellar thickness and the crystallinity fraction determined by that other model (based on measured density or enthalpy of fusion) are ultimately the result of the very same Avrami kinetics and chain-segment diffusion (governed by Hoffman-Lauritzen theory) that underpin the model in question. If the polymer's crystallization halts before completion—due to excessively rapid cooling through the spherulitic growth temperature range—the resulting final crystallinity fraction is lower than what the Avrami kinetics would have yielded had the process been allowed to continue for a longer period.

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