PIAM Winter School, January 15-19, 2007 Aussois, France

1. PIAM Winter School, January 15-19, 2007 Aussois, France Solidification criteria and rheology during solidificationGiuseppe TitomanlioUniversity of Salerno Italy gtitomanlio@unisa.it

2. What do we mean by solidification criteria? Solidification temperature, Ts : Viscosity is one or two orders of magnitude larger than every where else in the same cross secton Relaxation time is much larger than the cooling time Non flow temperature, Tnf : The two temperatures in principle can be very different and . . . . they can also be very close They are often regarded as a single temperature

3. About non flow and solidification criterion Semicrystalline polymers Both non flow and solidification conditions are determined by crystallinity, Xnf and Xs Amorphous polymers Tg: WLF Tg changes with Pressure and cooling rate and thus by crystallization temperature and kinetics

4. Tg (P, T’) P, bar • DOW PS 678E • Dependence upon cooling rate q: 2log (q/1°C/s) • Dependence upon pressure P: P *0.05 °C/bar Amorphous polymers, aPS T, [ºC] reported by Zoetelief. Solidification temperature was chosen as indicated by Zoetelief as Ts(P)=100°C+0.051K/bar 8.6 As mentioned above, a solidification temperature should depend also on cooling rate. If indeed this approach is followed, the following expression is obtained for Tsol: 8.7 where both the reference temperature and the constant describing the effect of Often non flow and solidification temperatures are regarded as a single temperature, for amorphous polymers

5. Non flow and solidification temperatures Outline Observations and modelling of rheology evolution during crystallization Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization kinetic models Solidification Criterion and its relevance on internal stresses and warpage

6. Semicrystalline Polymer Viscosity Amorphous Polymer Viscosity Viscosity Model Extrapolation Measurements Depend on the Solidification Conditions Mold Temperature Solidification Temperature Melt Temperature Solidification Processamorphous vs Crystalline behaviour Viscosity increase with crystallinity is always sharp

7. iPP T30G An example of quiescent crystallization Sferulites are seen when they are already big

8. Rheology vs crystallinity , suspension view 1. Small molecules: solid particles suspension Rheology changes with time because particles grow, with very small interactions. Interactions became relevant only at the end

9. A nucleus The small crystalline nuclei ACT AS physical crosslinks which produce an apparent molecular weigth increase with a parallel fast viscosity change. NUCLEI ACT AS PHYSICAL CROSSLINKS 3. A different, melt structure-based view

10. Master-Master curve 6 10 4 10 [Pa] 2 10 0 10 G', G'' -2 10 -3 -1 1 3 10 10 10 10 w a a [rad/s] T M Crystallization determines a network? physical Gel Point [Winter et al.1986]

11. Suspension vs Crosslinks based views? Suspension-like microstructure for low melt connectivity: • Low molecular weight • Low nuclei density Crosslinks for high melt connectivity: • High molecular weight • High nuclei density Nuclei density depends upon temperature Eterogeneous nucleation

12. Nuclei density changes with temperature and cooling rate Crystallization takes place at the temperature where crystallization time equals cooling time 121°C 123°C iPP T30G , s Eterogeneous nucleation: density = E(T) decreasing crystallization temperature or increasing cooling rate produces an increase of the number of nuclei and a decrease of particle dimensions thus, connettivity depends also upon cooling rate

13. Morphology vs cooling rates, iPP T30G 0.02 K/s 2 K/s 90 K/s 50 K/s SEM

14. Diametro(T) calorimetry iPP T30G Quenching esperiments AVERAGE DIAMETER OF SPHERULITESiPP T30G

15. h • annealing at 160°C to erase any crystalline memory T • rapidcooling to 98°C • constant stress is applied, polymer viscosity is monitored • crystallization determines a viscosity upturn RHEOLOGICAL EVIDENCE of crystallization PB200

16. Effect of flow Flow enhances crystallization rate

17. Polipropilene T30G Viscosity upturn during crystallization h/ho Crystallinity increases during calorimetric measurements Crossing both informations at the same temperature and time, the evolution of viscosity with crystallization is obtained h/ho Only total crystallinity?

18. ViscosityModels and relationships Only total crystallinity is considered ! ! Apart from eq. 17 adopted by Katayama and Yoon [[i]], all equations predict a sharp increase of viscosity on increasing crystallinity, sometimes reaching infinite (equations 18 and 21). All authors consider that the relevant variable is the volume occupied by crystalline entities (i.e. ), even if the dimensions of the crystals should reasonably have an effect. [i] Katayama K, Yoon M G. Polymer crystallization in melt spinning: mathematical simulation. High-Speed Fiber Spinning 1985: 207-223.

19. Shapes reproduced by equations of the Models All equations were adopted with a factor of about 20 at crystallinity sligtly above 5%

20. Effect of pressure and temperature on viscosity When the viscosity increases the curve shifts also on the left Viscosity and relaxation time increase with pressure iPP T30G

21. T30G: effect of cristallinity on viscosity The viscosity curve becomes higher and shifts on the left

22. Non flow and solidification conditions For crystalline polymers: are determined by crystallinity, XnfXs For amorphous polymers: Tg(P, cooling rate) for both conditions, mostcommercial codes adopt a single constant temperature : Ts=Tnf=const.

23. Outline Non flow and solidification temperatures Observations and modelling of rheology evolution during crystallization . . . 24: suspensions or . . . . physical crosslinks Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization Kinetic models Solidification Criterion and its relevance on internal stresses an warpage

24. P, bar P, bar experimental Thick gate experimental t, s t, s Thin gate Pressure evolution during injection moulding, BA238G

25. z y P2 P3 P4 Cooling rate and pressure at 100°C; Simulated z Cooling rate is a strong function of distance from the cool wall and depends opon flow directio(low flow rate), temperatures Solidification pressure Thermomechanical history changes with position Termomechanical history (dT/dt, pressure, flow) is a strong function of position, in injection moulding Morphology changes mainly with the distance from mould wall and also along the flow path The flow affects both crystallization kinetics and crystalliz. morphology

26. “Standard” sample P2 P3 P4 Morphology distribution in inj. moulded samples x y Morphology changes with the distance from the skin and slowly along the flow direction P2 P3 P4 iPP T30G Sferulite dimensions increase with the distance from the skin Micrographs taken in a polarized optical microscope of “Standard” sample along flow direction.

27. Fast Slow High T High P DIAMETER OF SPHERULITES

28. Both non flow and solidification conditions For crystalline polymers: are determined by crystallinity For amorphous polymers: Tg(P, cooling rate) In order to calculate Xnf and Xs, the crystallization kinetics has to be defined and implemented in the codes Calorimetric isotherms, BA238G:

29. Calorimetric and PVT cooling scans, BA238G

30. P, bar P, bar experimental Thick gate simulated t, s t, s BA230g-Comparison between expermental and simulated pressure curves with Xnf = 5% Thermomechanical model with Kinetics calibrated by calorimetric and PVT experiments Poor comparison ! WHAY ?

31. BA238g; non-flow temperatures and final crystallinities obtained by simulation with Xnf 5% Non-flow temperature Thick gate Distance from the skin Crystallization kinetics was identifies by calorimetric tests (low cooling rate) Kinetics needs to account of behaviour at high cooling rates

32. Characterised Quenching experiments

33. Final crystallinity in quenched samples: comparison ….. model 1: Calorimetry ___ model 2: full data set models obtained by calorimetry usually give poor results at high cooling rates and should not be adopted for injection moulding

34. Calorimetric and PVT results: comparison Model 1: Calorimetric Model 2: full data set

35. T, [ºC] Solidification pressure Solidification time BA238G, solidification temperatures and pressures Solidification temperature Distance from the sample skin Distance from the sample skin y, mm Non-flow temperatures Xnf=5% Results of Simulation with full data crystalliztion kinetics accounting of the full data setin the crystallization Kinetics was required In order to acheive non-flow temperature on the whole cross section, in the simulation

36. P, bar P, bar P, bar experimental T, [ºC] Kinetics: full data set Thick gate Kinetics: DSC y, mm t, s t, s t, s BA230G - Comparison between expermental and simulated pressure curves with Xnf = 5%Kinetics from full data set (quenches included) Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describy injection moulding

37. Xc, [-] Xc, [-] Dettailed comparison y, mm y, mm Comparison for final crystallinity in position P3, BA238g Cystallinity distribution is essentially constant on the cross section consistently with experimental risults

38. P, bar P, bar P, bar DSC Kinetics Experimental Thin gate Kinetics: full data set (Quenches) t, s t, s t, s BA230G -Comparison between expermental and simulated pressure curves with Xnf = 5% Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describy injection moulding

39. Outline Non flow and solidification temperatures Observations and modelling of rheology evolution during crystallization . . . 24: suspensions or . . . . physical crosslinks Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization Kinetic models Solidification Criterion and its relevance on internal stresses an warpage

40. consider a layer which goes under stress during the cooling of the object • as long as relaxation time is small with rspect to cooling time, stresses relaxe and the solid will have the new geometry as reference configuration The solidification cristallinity • If, viceversa, relaxation time is long with respect to cooling time, relaxation will be negligible and the final solid will keep its initial reference configuration (under stress) • at crystallinities higher than that which gives rise to condition 2 the material behaves as a solid, this identies Xs • a simplified model for cooling stresses build up would consider the polymer as a melt at crystallinities lower than Xs and as a solid at higher crystallinities This is a simplification, which replaces a dettailed knowledge of the evolution of rheology with crystallization

41. A slight melting may reduce the moduli by orders of magnitude BA230G Solidification criterion: How big is Xs? Xs is probably close to Xeq

42. Schematic of cooling stesses build up and thus of warpage . Pressure free configuration Also contraction due to cooling and crystallization If they are constant over the whole section trey contribute only on shrinkage distributions of solidification temperature and Xs are relevant to cooling stresses distribution and to warpage

43. Small points to remember Viscosity has been related only to total crystallinity Non-flow condition is different from solidification condition, which is determined by the value of the relaxation time compared to cooling time A low value of Xnf (5%) was often found adequate to describe experimental viscosity increase, Xs is larger than Xnf Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describe injection moulding (crystallization, flow, pressure evolution, orientation, morphology) Experiments performed at high cooling rates (100-1000k/s) need to be considered Solidification pressure, temperature and crystallinity are relevent to shrinkage, treir distribution are relevance to internal stresses and warpage

44. I would be happy to discuss any comment Thank You