A critical review on applications of the Avrami equation beyond materials science

Abstract

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) formalization, often referred to as the Avrami equation, was originally developed to describe the progress of phase transformations in material systems. Many other transformations in the life, physical and social sciences follow a similar pattern of nucleation and growth. The Avrami equation has been applied widely to modelling such phenomena, including COVID-19, regardless of whether they have a formal thermodynamic basis. We present here an analytical overview of such applications of the Avrami equation outside its conventional use, emphasizing examples from the life sciences. We discuss the similarities that at least partially justify the extended application of the model to such cases. We point out the limitations of such adoption; some are inherent to the model itself, and some are associated with the extended contexts. We also propose a reasoned justification for why the model performs well in many of these non-thermodynamic applications, even when some of its fundamental assumptions are not satisfied. In particular, we explore connections between the relatively accessible verbal and mathematical language of everyday nucleation- and growth-based phase transformations, represented by the Avrami equation, and the more challenging language of the classic SIR (susceptible-infected-removed) model in epidemiology.

Mapping Crystallization Kinetics during 3D Printing of Poly(ether ether ketone)

“…38−40 The value of the Avrami exponent for sporadic nucleation is expected to be n = 1 + 3/2 = 2.5 for threedimensional growth, n = 1 + 2/2 = 2 for two-dimensional growth, and n = 1.5 for one-dimensional growth. 41 In this case, crystallization occurs under highly nonisothermal conditions. Thus, while the observed trend of n a in Figure 4c from 1.5 to 2.5 with an increase in temperature is suggestive of a transition from one-dimensional to three-dimensional growth, such a conclusion would require more detailed modeling or further observations.…”

“…The average Avrami exponent, as seen in Figure c, increases from about 1.5 to 2.5 with increasing bed temperature. Within the assumption of isothermal crystallization, n a reveals information about the mechanism and/or dimensionality of nucleation and growth. − The value of the Avrami exponent for sporadic nucleation is expected to be n = 1 + 3/2 = 2.5 for three-dimensional growth, n = 1 + 2/2 = 2 for two-dimensional growth, and n = 1.5 for one-dimensional growth . In this case, crystallization occurs under highly nonisothermal conditions.…”

Crystallization Behavior of Copolyesters Containing Sulfonates

“…The classical Avrami equation is often used to describe the primary stage of polymer isothermal crystallization kinetics, as shown in Equation (5) [ 42 ]. where is the relative crystallinity, %; is the Avrami index, which is a parameter related to crystallization mechanism and nucleation type [ 43 ]; and is the crystallization rate constant, which is related to nucleation density and nucleation growth rate, min −n .…”

Fragility and Tendency to Crystallization for Structurally Related Compounds

“…For (S)-NOO, the values of n vary between 3.40 and 3.84, whereas in the case of (S)-NSS, they are lower and range between 1.36 and 1.90, as can be seen in Table 4 and Figure 10 . Such results suggest that (S)-NOO can form co-existent three-dimensional crystallites, whereas (S)-NSS transforms to mainly one-dimensional crystallites, with instantaneous and sporadic nucleation most likely occurring in both materials [ 73 , 74 , 75 , 76 ].…”