Hoffman-Lauritzen Theory for Crystallization
Hoffman-Lauritzen Theory in crystallization kinetics of polymers is the theory describing the temperature dependence of crystal growth rate of polymers.
This dependence K(T) is used in Crystallization According to NakamuraCrystallization according to Nakamura is the crystal growth model for non-isothermal crystallization kinetics during cooling.Nakamuraequation for crystallization during cooling.
According to Hoffman-Lauritzen theory, the crystal growth depends on both melting temperature Tm of polymer and its glass transition temperature Tg.
From one side, the crystallization rate at temperature T is faster for higher supercooling ΔT=Tm-T. From other side, the crystallization rate is slower by closing to the temperature T∞=Tg-30, where the motion associated with viscose flow cases.
where:
- A is the pre-exponential factor
- U is the activation energy of segmental jumps in polymers; this parameter has a universal value of 6.3 kJ/mol
- T∞ =Tg – 30 K is the temperature at which the viscose flow is finished; this temperature is 30 K below the glass transition temperature Tg
- KG is the kinetic parameter for nucleation
- ∆T=Tm-T is the supercooling from the equilibrium melting point Tm and
- f=2T/(Tm+T) is the correction factor.
This equation has positive values only for the temperature range between T∞ and Tm. Above the melting temperature, the material is in the liquid state and no crystallization takes place. Below T∞, the material is in the glassy state, where any viscous motion has finished, and where no more crystallization occurs, too.
Kinetics Neo
This theory is used in Kinetics Neo software as model based CrystallizationKinetics for Nakamura and Sbirrazuolli Reaction typesReaction type is the elementary mechanism of one individual reaction step in multi-step chemical reaction. Reaction type f(Cr, Cp) describes dependence of the reaction rate for individual reaction step on the concentrations of reactant Cr and product Cp for this step.reaction types.
Reference
[1] Vyazovkin, S.; Burnham, A.K.; Favergeon, L.; Koga, N.; Moukhina, E.; Pérez-Maqueda, L.A.; Sbirrazzuoli, N. (2020). ICTAC Kinetics Committee recommendations for analysis of multi-step kinetics. Thermochimica Acta689, 178597. https://doi.org/10.1016/j.tca.2020.178597
[2] Patel, R.M., Crystallization kinetics modelling of high density and linear low density polyethylene resins. Journal of Applied Polymer Science 2011, 124(2): 1542-1552.
https://doi.org/10.1002/app.35177
[3] Vyazovkin S., Sbirrazzuoli N. 2004 Isoconversional Approach to Evaluation the Hoffman-Lauritzen Parameters (U* and Kg) from the Overall Rates of nonisothermal Crystallization, Macromolecular Rapid Communications, 2004, 25. 733-738.
https://doi.org/10.1002/marc.200300295