Kinetic model of polymer crystallization with the lamellar thickness distribution

• Model predicts development of lamellar thickness distributions and average thickness.
• The approach combines Avrami and Hoffman models and a model of lamellar thickening.
• Thickening model accounts for doubling transformation and logarithmic thickening.
• Time-dependent distributions of doubled and un-doubled crystals are obtained.
• Fractions of doubled and un-doubled crystals vs. crystallization time are predicted.

Kinetic model of development of lamellar thickness distribution and average lamellar thickness during melt crystallization is proposed. The model bases on the Avrami–Evans and Hoffman–Lauritzen approaches to the crystallization and crystal growth kinetics and involves a thermal thickening model proposed in this paper which accounts for two processes – lamellar doubling transformation and logarithmic thickening of the doubled crystals. In the thickening model, continuity equation for the lamellar thickness distribution is proposed which includes a term responsible for fast creation of doubled crystals during a doubling time introduced as phenomenological parameter and a term which accounts for slow, logarithmic with time thickening subsequent to the doubling transformation. The model concerns melt crystallization in systems where the undercooling in the crystallization and melting processes refers to the same thermodynamic point – the thermodynamic equilibrium melting temperature.Analytical formulae for time-dependent lamellar thickness distribution vs. crystallization time are obtained by solving the continuity equation for the case of isothermal crystallization, as well as for the development of the average lamellar thickness of the doubled and un-doubled crystals during the crystallization time.The model predictions are illustrated by example computations for isothermal crystallization of PE grades characterized by high differences in the crystallization half-time resulting in high differences in the development of lamellar thickness distribution. Relative contributions of doubled and un-doubled crystals are predicted during the conversion and influence of the doubling time and logarithmic thickening parameters is discussed.

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