Solidification criteria and rheology during solidification Giuseppe Titomanlio University of Salerno Italy PIAM Winter School, January 15-19, 2007 Aussois, France

What do we mean by solidification criteria? Non flow temperature, T nf : Solidification temperature, T s : The two temperatures in principle can be very different 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 They are often regarded as a single temperature and.... they can also be very close

About non flow and solidification criterion Amorphous polymers Tg: WLF Semicrystalline polymers T g changes with Pressure and cooling rate Both non flow and solidification conditions are determined by crystallinity, X nf and X s and thus by crystallization temperature and kinetics

Amorphous polymers, aPS reported by Zoetelief. Solidification temperature was chosen as indicated by Zoetelief as Ts(P)=100°C+0.051K/bar8.6 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 Dependence upon cooling rate q: 2log (q/1°C/s) Dependence upon pressure P: P *0.05 °C/bar Often non flow and solidification temperatures are regarded as a single temperature, for amorphous polymers T, [ºC] P, bar Tg (P, T’) DOW PS 678E

Outline 2.Observations and modelling of rheology evolution during crystallization 3.Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization kinetic models 4.Solidification Criterion and its relevance on internal stresses and warpage 1. Non flow and solidification temperatures

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

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

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

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

Crystallization determines a network? physical Gel Point [Winter et al.1986]

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 Eterogeneous nucleation Nuclei density depends upon temperature

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

Film of growing spherulites during scansioni Felice iPP T30G

Morfologie in funzione della velocità di raffreddamento - 2 Ny 6 Fig.9 50 micron

SEM 0.02 K/s 50 K/s90 K/s 2 K/s Morphology vs cooling rates, iPP T30G

AVERAGE DIAMETER OF SPHERULITES iPP T30G Diametro(T) calorimetry iPP T30G Quenching esperiments

 annealing at 160°C to erase any crystalline memory  rapid cooling to 98°C  constant stress is applied, polymer viscosity is monitored  crystallization determines a viscosity upturn PB200 RHEOLOGICAL EVIDENCE of crystallization  T

Effect of flow Flow enhances crystallization rate

Polipropilene T30G Viscosity upturn during crystallization Crystallinity increases during calorimetric measurements Crossing both informations at the same temperature and time, the evolution of viscosity with crystallization is obtained   o Only total crystallinity?

Viscosity Models and relationships EquationAuthorderivationparameters  /  0 =1+a 0  a Katayama 85Suspensionsa=99  /  0 = (1-  /a 0 ) -2 Metzner 85 also Tanner 2002Suspensionsa=0.68 for smooth spheres  /  0 =1+(  /a 1 ) a2 /(1-  /a 1 ) a2 Tanner 2002Empical, based on suspensions a 1 =0.44 for compact a 1 =0.68 for spherical crystallites  /  0 = exp(a 1  a2 ) Shimizu 85; also Zuidema 2001, and Hieber 2002 Empirical  /  0 =1/(  -  c ) a0 Ziabicki 88Empirical  c =0.1  /  0 =1+a 1 exp(-a 2 /  a3 ) Titomanlio 97; also Guo 2001, and Hieber 2002 Empirical  /  0 = exp(a 1  + a 2  2 ) Han, 97Empirical  /  0 = 1+a 1  +a 2  2 Tanner 2003Empirical a 1 =0.54, a 2 =4,  <0.4 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] [i] Katayama K, Yoon M G. Polymer crystallization in melt spinning: mathematical simulation. High- Speed Fiber Spinning 1985: Only total crystallinity is considered ! !

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

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

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

Non flow and solidification conditions For crystalline polymers: are determined by crystallinity, X nf X s For amorphous polymers: T g (P, cooling rate) for both conditions, most commercial codes adopt a single constant temperature : T s =T nf =const.

Outline 1.Non flow and solidification temperatures 2.Observations and modelling of rheology evolution during crystallization 2.Observations and modelling of rheology evolution during crystallization... 24: suspensions or.... physical crosslinks 3.Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization Kinetic models 4.Solidification Criterion and its relevance on internal stresses an warpage

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

Thermomechanical history changes with position dT/dt, pressure, flow Termomechanical history (dT/dt, pressure, flow) is a strong function of position, in injection moulding P3P2P4 z y The flow affects both crystallization kinetics and crystalliz. morphology z Cooling rate is a strong function of distance from the cool wall and depends opon flow directio(low flow rate), temperatures Solidification pressure Cooling rate and pressure at 100°C; Simulated Morphology changes mainly with the distance from mould wall and also along the flow path

“Standard” sample P2P3P4 Micrographs taken in a polarized optical microscope of “Standard” sample along flow direction. Morphology distribution in inj. moulded samples P3P2P4 x y iPP T30G Morphology changes with the distance from the skin and slowly along the flow direction Sferulite dimensions increase with the distance from the skin

DIAMETER OF SPHERULITES Slow High T High P Fast

Both non flow and solidification conditions For crystalline polymers: are determined by crystallinity For amorphous polymers: T g (P, cooling rate) In order to calculate X nf and X s, the crystallization kinetics has to be defined and implemented in the codes Calorimetric isotherms, BA238G :

Calorimetric and PVT cooling scans, BA238G

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

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

Characterised Quenching experiments

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

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

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

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

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

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

Outline 1.Non flow and solidification temperatures 2.Observations and modelling of rheology evolution during crystallization 2.Observations and modelling of rheology evolution during crystallization... 24: suspensions or.... physical crosslinks 3.Role of non flow criterion in the simulation of injection moulding and identification of the proper crystallization Kinetic models 4.Solidification Criterion and its relevance on internal stresses an warpage

The solidification cristallinity 1.consider a layer which goes under stress during the cooling of the object 2.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 This is a simplification, which replaces a dettailed knowledge of the evolution of rheology with crystallization 3.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) 4.at crystallinities higher than that which gives rise to condition 2 the material behaves as a solid, this identies X s 5.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

Solidification criterion: How big is Xs? A slight melting may reduce the moduli by orders of magnitude X s is probably close to X eq BA230G

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

Small points to remember 1. 1.Viscosity has been related only to total crystallinity 2. 2.Non-flow condition is different from solidification condition, which is determined by the value of the relaxation time compared to cooling time 3. 3.A low value of X nf (5%) was often found adequate to describe experimental viscosity increase, X s is larger than X nf 4. 4.Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describe injection moulding (crystallization, flow, pressure evolution, orientation, morphology) 5. 5.Experiments performed at high cooling rates ( k/s) need to be considered 6. 6.Solidification pressure, temperature and crystallinity are relevent to shrinkage, treir distribution are relevance to internal stresses and warpage

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