Advanced avrami formula and its application to describing the isothermal crystallisation of polymers

• A simple, advanced avrami formula that gives a better fit was developed. • The rate of instantaneous and random nucleation can be determined with ease. • Model validated for many semi-crystalline polymers at various temperatures. The classic Avrami formula has widely been used to describe and characterize the crystallisation process of polymers. We showed that the Avrami formula is not correct for the random nucleation. To eliminate this and some problems of fitting the Avrami formula with integer exponent revealed in the literature, we modified the Avrami equation and derived a new extended formula that can describe instantaneous and random (time-dependent) nucleation simultaneously. This formula may give information on the crystalline structure of both types of nuclei; moreover, it makes it possible to determine the crystalline fraction developed from the instantaneous nuclei. The latter enables us to estimate, for example, the effect of nucleating agents numerically on the crystallisation process and the ultimate crystallinity. The applicability of the new formula was validated by performing isothermal crystallisation tests on poly(ethylene-terephthalate) (PET), polypropylene (PP), low- and high-density polyethylene (LDPE and HDPE) samples at various temperatures, which resulted in a better fit characterized by the much smaller relative maximum absolute error (0.4–2.9 %) related to that for the Avrami equation (1.9–15.9 %).