How to determine the parameters of polymer

crystallization for modeling the injection-molding

process?

Severine A.E. Boyer, Luisa Silva, Mounia Gicquel, Samuel Devisme,

Jean-Loup Chenot, Jean-Marc Haudin

To cite this version:

Severine A.E. Boyer, Luisa Silva, Mounia Gicquel, Samuel Devisme, Jean-Loup Chenot, etal.. How to determine the parameters of polymer crystallization for modeling the injection-molding process?. edited by P. Boisse, F. Morestin, E. Vidal-Salle, LaMCoS, INSA de Lyon.11th ESAFORM Conference on Material Forming, Apr 2008, Lyon, France. 1 (Supplement 1),pp.Pages 599-602, 2008, <10.1007/s12289-008-0327-2>. <hal-00510263>

HAL Id: hal-00510263

https://hal-mines-paristech.archives-ouvertes.fr/hal-00510263

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1 INTRODUCTION

The correlation between phase�transitions of

polymersandextremeandcomplexconditionsisof

greattechnologicalandacademicinterest[1].Inthis

field,many polymer products aremanufactured by

injection�molding,aprocessthathasthepotentialto

mass�produce with complex shape. End�use

properties of the final injected parts are directly

related to the final micro�structural and hierarchic

organization of macromolecules, i.e. spherulite,

shish�kebab, transcrystallinity zone and teardrop�

shapedspherulite.

To understand the micro�structural development, it

is necessary to describe the liquid/solid transition

under complex and coupled thermo�mechanical

conditions.

Crystallization inmolten polymers results from the

nucleationevent,inamoreorlesssporadicmanner,

and the growth of nuclei into crystalline entities,

which spread over the entire volume at the end of

the transformation. To describe the overall kinetics

during the primary crystallization under quiescent,

isothermal, conditions Avrami’s model is themost

widely used, partly because of its firm theoretical

basis leading to analytical mathematical equations

[2�5].

Thispaper reportsanumberofaspects that include

the following: the description of the methods for

obtainingandtreatingthekeyparametersneededin

crystallizationmodels, the optimization of the data

by the inverse genetic algorithm method, the

introductionof themodels intoa3D finite element

code.Adiscussionispresentedthatprovidesinsight

into the benefit of using different techniques and

analysis methods in the investigation of polymer

crystallization.

ABSTRACT:Tounderstandtherelationshipbetween‘polymers�processingconditions�structures�properties’,

crystallization is one of the major concerned phenomena. A general crystallization model derived from

Avrami’sworkhasbeendevelopedatCEMEFandimplementedintoa3Dfiniteelementcodeforinjection�

moldingnamedRem3D®.Itgivesaprecisedescriptionofthecrystallizationevent,allowsthedetermination

of morphological features, but it requires a reliable determination of the crystallization parameters. The

experimental procedures adopted to capture relevant experimental parameters are presented. The

determination of overall kinetics, density of potential nuclei with activation frequency of nuclei into

crystalline entities, and growth rate is carried out with polarized optical microscopy (POM) and is

supplemented by small angle light scattering (SALS). The treatment of data is performed by a classical

methodorusinganinversegeneticalgorithmmethodtoextracttheparametersnecessarytoourmodel.The

2D simulation of the crystallization, illustrated with Rem3D®, reproduces the experimental reality quite

accurately,inthecaseofanisothermalandstaticcrystallization.Thisisappliedtotwopolymers,anisotactic

homopolymerpolypropyleneiPPandapolyether�blockamidePEBAX®.

Keywords:Liquid/SolidTransition,Polymers,Modeling,Simulation,Injection�Molding.

Howtodeterminetheparametersofpolymercrystallizationformodeling

theinjection�moldingprocess?

S.A.E.Boyer1,L.Silva

1,M.Gicquel

1,S.Devisme

2,J.�L.Chenot

1,J.�M.Haudin

1

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2 THEORETICALBACKGROUND

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Starting from Avrami’s hypotheses, we recently

proposed a newnumerical approach [4,5].Original

Avrami’s theory was extended to treat non�

isothermal crystallization. The key equations of

crystallization were cast into a general differential

system that is integrated numerically. They

underlinetheinfluenceoftheprocessingconditions,

namelytemperaturewithcooling�rateandshearrate,

on: the transformedvolume fraction, thedensity of

potential nuclei together with the activation

frequency of nuclei into crystalline entities, the

growth rate of entities, and the morphological

features.

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The set of differential equations involve the

identification of three kinetic parameters, namely

N0(T(t)), q(T(t)) and G(T(t)). The term N0(T(t)) is

the initial density of potential nuclei, q(T(t)) the

activationfrequencyof thesenucleiandG(T(t)) the

growth rate of the semi�crystalline entities, which

are supposed to be disks (discoids) in 2D and

spherulitesin3D.Thekineticparametersaredefined

as a function of temperature T as shown in the

system(1)ofequationsbelow.

( )( )001000 exp 66��� −−=

( )( )010 exp 66333 −−= (1)

( )( )010 exp 66777 −−=

The coefficients [N00, N01, q0, q1, G0, G1] are

determined directly from experiments or calculated

bythegeneticalgorithminversemethod.

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The crystallization laws were implemented into

Rem3D®, a 3D finite�element codewritten inC++.

It allows us to reproduce the crystallization

phenomena which occur during the injection

molding process, with the prediction of the

distribution of the transformed fraction and of the

number of potential and activated nuclei [6]. The

numerical resolution is based on a Runge�Kutta

StabilizedGalerkinintegrationscheme.

3 EXPERIMENTAL

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Thematerialsusedaregradesforinjectionmolding.

AnisotactichomopolymerpolypropyleneiPP(molar

mass:Mn=42500g/mol,Mw=213000g/mol)was

suppliedbyATOFINACompany(France)underthe

reference 3250 MR1. A poly(ether�block amide)

PEBAX®thermoplasticelastomerbasedonnylon12

and poly(tetramethylene oxide)was investigated. It

wasobtainedfromARKEMA(France).

Thin layersof polymerswerepushedon anoptical

cover glass in a transparent hot�stage. The molten

polymerwasmaintainedat210°Cduring5minand

cooled at �10 °C.min�1 down to the crystallization

temperatures, for isothermal studies, or at various

cooling�ratesdownto theendofcrystallization, for

non�isothermalstudies.

8(0 6�����3 ���

3.2.a PolarizingOpticalMicroscopy(POM)

The crystallization events and morphological

featureswereobservedundercrossedpolarizerswith

a polarizing LEICA�DMRX microscope (Leica�

microsystemes,France).

3.2.b Small�AngleLightScattering(SALS)

SALS patterns were collected by using a helium�

neonpolarizedlaser.Thewavelengthofthelaseris

λ = 0.6328 Im. The parallel, vertically polarized

light beam radiated by the laser is scattered by the

crystallizing polymer film and then analyzed by a

crossedpolarizer.

4 RESULTSANDDISCUSSIONS

In3D,itisdifficulttoaccuratelydeterminethethree

keyparametersofpolymercrystallizationnecessary

for modeling the injection�molding process. The

strategyistoidentifytheparametersin2D,andthen

totranslatetheinformationinto3D.

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The overall kinetics can be deduced from light

depolarization integration of the POM images,

which is proportional to the transformed volume

fraction. Knowing N0 and G(T) from the POM

images analysis (see after), the overall kinetics can

alsobecalculatedfromAvrami’sequation(2)in2D

growthandinstantaneousnucleation.

( ) ( )( )22

0exp1, �67��6 πα −−= (2)

The overall kinetics, deduced from light

depolarization integration and from Avrami’s

equation,wasplottedasafunctionoftime.Figure1

showsthewellagreementbetweenthetwomethods

ofdetermination.It impliesthatlightdepolarization

measurements can be used in the determination of

the overall kinetics when the kinetic parameters

N0(T(t)) andG(T(t)) cannot be determined directly

fromtheopticalobservations.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 300 600 900 1200 1500

Time (s)

Ove

rall

kin

etci

s in

2D

light depolarization

Avrami

Fig.1.Overallkineticsin2D(5Im�thicklayer)

ofiPPat126°C.

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Kinetic parameters are issued from the analysis of

each POM image of the time evolution ofNa(T) =

f(t), while crystallization occurs. Na(T(t)) is the

numberofactivatednuclei.

Nucleation parametersN0(T) and q(T) are deduced

from the number of spherulites centers Na(T(t))

observed.The finalnumberNa(T) isapproximated

to N0(T) (α(t) = 1). q(T) is calculated during the

first steps of nucleation. Nevertheless q(T) is

relativelydifficulttoestimate.KnowingN00,G0and

the overall kinetics α(t), q(T) can be deduced

directlyfromequation(3),whereα’(t)isdefinedby

Avramiastheextendedfraction.

( ) ( )( )

( )[ ] ( ) ( )[ ]�63�63�63

63

67�� 00

2

0

2

0

0

00 exp12

2' −−+−

= πα

(3)

ThegrowthrateG(T) isobtained fromthe increase

of spherulite radius as a function of time. It is

supposed that nucleation is instantaneous in

isothermal conditions. However, this procedure is

notpossiblewhenthemaximumspheruliteradiusis

unduly small and when spherulites are too

numerous.Itisthecaseofthepolyether�blockamide

PEBAX®.

Instead, use may be made of the light�scattering

method developed by Stein and Rhodes [7]. The

measurement of spherulite radius is based on the

laser�scattering theory for perfect spherulites, i.e. a

homogeneous anisotropic sphere in an isotropic

medium. The typical scattering pattern given by a

spheruliticfilmconsistsofafour�leafclovershape,

asillustratedinFigure2.Duringcrystallization,the

patternbecomesmoreintenseandsmaller.Withthis

method, it is possible tomeasure the radius r of a

sphereintherangeofhalfamicrontoafewmicrons

bymeansoftheequation(4).

2

tan

sin4

09.4

max

=

�

!�

�

π

λ (4)

Rmaxisthedistancefromthecenterofthepatternto

thepointofmaximumintensityononelobe,anddis

anexperimentalconstant.

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Fig.2.Crystallizationsmallanglelaser�scattering

patternofPEBAX®in3D(150Im�thicklayer)at

151°Canddifferenttimest.

Theconfrontationof the resultsofG(T(t))between

POM and SALS is satisfactory. Respectively, it

gives agrowth rateof0.1023and0.0939Im.s�1 at

151 °Candof0.0694and0.0664Im.s�1 at153 °C

andof0.0422and0.0587Im.s�1at156°C.

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In crystallization, large discrepancies are found

between experimental data because of the

fluctuations of the nucleation parameters which

dependonthepolymerandonthenucleatingagents.

Thegeneticalgorithmmethodisappliedtoimprove

theresolutionofproblemslinkedtolowprecision.It

is a stochastic optimization method based on the

naturalselectionofDarwin.Theoptimizationofthe

kineticparametersisperformedontheexperimental

evolutionofthetransformedvolumefractionandof

thenumberofspherulites.

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Thematerial usedwas the iPP. The validity of the

model and the accuracy of our experimental

characterization were verified. Experimental

evolutionsofthetransformedvolumefractionandof

thenumberofspherulitesasafunctionofthetimeof

crystallizationarecorrectlydescribedbythemodel.

Simulation of a complete injection molding cycle

wasperformed.Anasexample,theinjectedpartwas

a2Dplate�shapedpart (thickness8mmand length

200mm).Thematerialwas injected at 230 °Cand

themoldtemperaturewas50°C.Kineticparameters

giveninTable1refertotheequation(1)withT0=

116°C.

Table1.IdentificationofthekineticparametersforiPP.

N00(inIm�3) q0(ins�1) G0(inIm.s�1)

5.87510�4 0.2669 1.3941

N01(in°C�1) q1(in°C�1) G1(in°C�1)

0.20635 0.2808 0.1940

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The distribution of the transformed fraction as a

functionofthetimeofcrystallizationisillustratedin

Figure 3. A thin solid layer appears at the borders

when thecalculation inRem3D® starts. It isdue to

thehighcoolingratewhenthepolymerisincontact

with the mold. Then, the crystallization occurs

slowly.

5 CONCLUSIONS

Our general differential model based on Avrami’s

hypotheses gives a good description of the

crystallizationevent.Itrequirestheidentificationof

key kinetic parameters: initial density of potential

nuclei,theiractivationfrequencyandgrowthrateof

crystallizedentities.

Opticalmicroscopy gives access to the parameters,

andcanbesupplementedbythelaserlight�scattering

whengrowingspherulitesaretoosmall.

Optimization of the parameters is performed by

meansofinversealgorithmmethod.

Itremainstogatheradditionalexperimentaldatathat

take into account the size distribution of the

crystallineentities,aswellastheeffectsofflowand

highcoolingrates.

ACKNOWLEDGEMENTS

Theauthorsexpress theirgratitudetoARKEMAfor technical

andfinancialsupport.

REFERENCES

1. S.A.E.Boyer, J.�P.E.Grolier,H.Yoshida, J.�M.Haudin,

and J.�L. Chenot, ’Phase transitions of polymers under

complex conditions’, Joint Conference of JMLG/EMLG

Meeting2007and30thSymposiumonSolutionChemistry

of Japan – Molecular approaches to complex liquids

systems,Fukuoka,Japan,(21�25November,2007).

2. M.Avrami,‘KineticsofphasechangeI’,J.Chem.Phys.,

7,(1939)1103�1112.

3. M. Avrami, ‘Kinetics of phase change II’, J. Chem.

Phys.,8,(1940)212�224.

4. J.�M.Haudin,andJ.�L.Chenot,‘Numericalandphysical

modeling of polymers crystallization’, Intern. Polym.

Process.,19(3),(2004)267�274.

5. J.Smirnova,L.Silva,B.Monasse,J.�M.Haudin,andJ.�L.

Chenot, ‘Identification of crystallization kinetics

parameters by genetic algorithm in non�isothermal

conditions’,Eng.Comput.,5(24),(2007)486�513.

6. L. Silva, C. Gruau, J.�F. Agassant, T. Coupez, and J.

Mauffrey, ‘Advanced finite element 3D injection

molding’,Intern.Polym.Process.20(3),(2005)265�273.

7. F. Van Antwerpen, and D.W. Van Krevelen, ‘Light�

scattering method for investigation of the kinetics of

crystallization of spherulites’, J. Polym. Sci.: Polym.

Phys.,Ed.10,(1972)2409�2421.