Improved experimental characterization of crystallization kinetics

EUROPEAN

European Polymer Journal 41 (2005) 2297–2302

www.elsevier.com/locate/europolj

POLYMERJOURNAL

Improved experimental characterizationof crystallization kinetics

Felice De Santis a, Gaetano Lamberti a,*, Gerrit W.M. Peters b, Valerio Brucato c

a University of Salerno, Department of Chemical and Food Engineering, Via Ponte don Melillo, 84084 Fisciano (SA), Italyb Eindhoven University of Technology, Department of Mechanical Engineering Den Dolech 2, 5600 Eindhoven, The Netherlands

c University of Palermo, D.I.C.P.M., Viale delle Scienze, 90128 Palermo, Italy

Received 23 February 2005; received in revised form 21 April 2005; accepted 23 April 2005

Available online 28 June 2005

Abstract

Polymer solidification occurring in many processes, like for instance injection molding, compression molding and

extrusion, is a complex phenomenon, strongly influenced by the thermo-mechanical history experienced by the material

during processing. From this point of view, characterization of polymer crystallization in the range of processing con-

ditions, i.e. including high cooling rate, is of great technological and academic interest. Quiescent, non-isothermal crys-

tallization kinetics of two polypropylene resins were investigated using a new method, based on fast cooling of thin

samples with air/water sprays and optical detection of the crystallization phenomenon. The range of cooling rates

attained in this experimental study is considerably larger than that achieved by traditional methods. Quiescent crystal-

lization kinetics of the resins is also investigated by the means of DSC, operated under isothermal conditions with a

limited degree of under-cooling and for constant cooling rates up to about 1 K s�1. The results demonstrate the impor-

tance of performing fast cooling experiments to gather reliable crystallization kinetics data.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Crystallization kinetics; Isotactic polypropylene; Real-time measurements

1. Introduction

It is well known that the final crystalline fraction in a

polymer relates to the final products properties. This

fraction is determined by the crystallization kinetics

and the thermal and mechanical history of the material.

In this paper, we will limit ourselves to the influence of

0014-3057/$ - see front matter � 2005 Elsevier Ltd. All rights reservdoi:10.1016/j.eurpolymj.2005.04.032

* Corresponding author. Tel.: +39 089964077; fax: +39

089964057.

E-mail address: [email protected] (G. Lamberti).

the thermal history, specifically the cooling rate. Tradi-

tional methods for investigating the crystallization kinet-

ics are usually limited to isothermal and/or slow heating/

cooling rate analysis, mainly carried out using DSC

technique. However, solidification during industrial pro-

cesses occurs under much higher cooling rates than the

ones involved in these experiments. The aim of this work

is to present a recently developed method for character-

izing crystallization kinetics at high cooling rates and to

compare the performance of a well stated crystallization

kinetics model, tuned by isothermal runs, to the experi-

mental results, and, from that, to stress the need for such

experiments.

ed.

2298 F. De Santis et al. / European Polymer Journal 41 (2005) 2297–2302

2. Materials and methods

2.1. Materials

The materials used were two different commercial iPP

resins. The first one (a nucleated grade K2Xmod, Bore-

alis,Mw = 365,000,Mn = 67,000), was studied before by

traditional methods also by Zuidema et al. [1], who

found a temperature only dependent density of nuclei

and growth rate

NðT Þ ¼ n1T þ n2 ð403� 413 KÞ;ð1Þ

GðT Þ ¼ Gmax exp �2 ðT � T refÞ2

b

" #ð363� 393 KÞ;

ð2Þ

where n1 = �2.6087 · 1013 m�3 K�1, n2 = 6.5783 ·1015 m�3, Gmax = 8.1 · 10�6 m s�1, Tref = 356.8 K, b =1126.9 K2.

The second one (non-nucleated grade T30G, Mon-

tell, Mw = 481,000, Mn = 75,000) was also studied

previously, by Lamberti [2]. The isothermal half-crystal-

lization time, i.e. the time at which 50% of final crystal-

linity content is obtained, was determined with

a standard DSC apparatus (Mettler DSC30) and

described by

1

t1=2ðT Þ¼ 1

t01=2exp � U

R � ðT � T 0g þ T1Þ

" #

� exp � j2 � ðT 0mÞ2 � ðT 0m þ T Þ

2T 2 � ðT 0m � T Þ

" #; ð3Þ

where t01=2 ¼ 5.75 10�15 s, U/R = 2068.8 K, j2 = 3.171,

T 0g ¼ 263.15 K, T 0m ¼ 463.15 K and T1 = 51.6 K.

Eder and Janeschitz-Kriegl [3] studied the growth

rate of iPP alpha phase, for several iPPs. Data analysis

was performed on the basis of the Lauritzen and Hoff-

mann equation (Eq. (38) on page 559 in [4]) in which

the coefficients Kg has been substituted by j3T 2m0 andthe correction factor f (f ¼ 2T=ðT 0m � T Þ, as given byEq. (10b) on page 540 in [4]) has been directly inserted

in the second exponential term

GðT Þ ¼ G0 exp � U

R � ðT � T 0g þ T1Þ

" #

� exp � j3 � ðT 0mÞ2 � ðT 0m þ T Þ

2T 2 � ðT 0m � T Þ

" #ð4Þ

ngðtÞ ¼1

2Sr0Sr0 þ ln

IO;iIO;f

� ��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln

IO;fIO;i

� �� �2þ Sr0 Sr0 � 2½

s8<:

with G0 = 4.36 · 108 m s�1 and j3 = 2.7979. Assuming adependence on temperature only of the nuclei density as

well as of the growth rate, it is straightforward to obtain

[2,5]

NðT Þ ¼ lnð2Þ4p3GðT Þ3t1=2ðT Þ3

ð5Þ

leading to the expression for the nuclei density that is

used in this work. Eqs. (3)–(5) are used to describe the

crystallization kinetics of the grade T30G. The model

proposed does not take in account for regime transition

at different under-cooling, i.e. the parameter j3, whichshould change with crystallization regime, has been

taken as a constant.

2.2. Methods

Slow cooling runs in addition to isothermal tests were

performed using differential scanning calorimetry (Met-

tler DSC30). The crystallinity evolution during DSC

tests was evaluated by applying a correction to the data

as was suggested by Eder and Janeschitz-Kriegl [3]. The

equivalent heat transfer coefficient c was evaluated fromtemperature relaxation after melting indium. A value of

14.5 mW K�1 was found.

Fast cooling runs were carried out by means of a new

method described in detail elsewhere [6]. A schematic of

the apparatus is depicted in Fig. 1. It includes a hot

(oven) section and a cold (quench) section. Sample heat-

ing is attained by two radiating electric heaters while the

cooling is done with a couple of nozzles that spray both

faces of sample holder with gas or gas–liquid (typically

air and water). This cooling system was designed to cover

a large range of cooling rates (from 0.01 to 500 K s�1).

As shown in Fig. 1, the polymer sample, a thin film with

an embedded thermocouple is confined between two thin

glass slides that acts as a sample holder. In turn, the glass

slides are fastened to a sliding rod, which can be quickly

shifted from the hot to the cold section. In a typical

experiment the transmitted light and temperature are

monitored during the spraying of the sample holder [6].

Experimental tests confirmed a satisfactory reproduc-

ibility of the tests in the same conditions, i.e. at the same

cooling rate.

The evolution of the crystallinity during quench

experiments was determined by applying a recently pro-

posed analysis of the transmitted overall light IO(t,S) [6],

in which S is the thickness and t is the time. According

to this analysis, the degree of space filling ng is given by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðln IO;i þ ln IO;fÞ þ 4 ln IOðt; SÞ�

9=;; ð6Þ

Ovenzone

Quenchzone

Water/airspray

Laserbeam

Slidingrod

Electricheaters

Water/airspray

Laserbeam

Two-fluidnozzle

Fast-responsethermocouple

Two-fluidnozzle

Sampleholder

Polymer sample

ThermocoupleSample holder

Polymersample

Fig. 1. Quenching device scheme.

F. De Santis et al. / European Polymer Journal 41 (2005) 2297–2302 2299

where IO,i is the initial and IO,f the final recorded light

intensity and r0 the scattering coefficient, which can beeasily evaluated [6] from

r0 ¼ lnIO;iIO;f

� �1

Sð2ng;peak � 1Þ. ð7Þ

The value ng,peak is the degree of space filling at which amaximum in the light intensity is found. It can be eval-

uated [6] by

ng;peak ¼ lnIO;fIO;i

� �� ��1"ln

IO;minIO;i

� �

þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln

IO;fIO;min

� �ln

IO;iIO;min

� �s #; ð8Þ

where IO,min is the minimum recorded light intensity.

The half-crystallization temperature was determined

as the temperature at which the crystallinity level was

equal to one half of the final level (long time) attained

at the end of cooling runs both for DSC and quench tests.

3. Modeling

Crystallization kinetics was modeled following the

same approach as used by Zuidema et al. [1] using

Schneider et al. rate equations [7], i.e. by solving the fol-

lowing set of nested differential equations:

_/3 ¼ 8pa;_/2 ¼ G/3;_/1 ¼ G/2;_/0 ¼ G/1;

8>>><>>>:

ð9Þ

where a is the time derivative of nuclei density, and /i

are auxiliary variables used to describe morphology of

undisturbed crystals. The Kolmogoroff–Avrami–Evans

approach was applied to account for spherulites

impingement

� lnð1� ngÞ ¼ /0; ð10Þ

where ng is the degree of space filling or relative crystal-linity. The absolute degree of crystallinity n is simply ob-tained by multiplying the degree of volume filling ng by alocal constant degree of crystallinity V1 of spherulites

(the so called ‘‘equilibrium crystallinity’’). For high cool-

ing rate tests, when the degree of space filling ng does notlevel to unity, even for long times, the remaining fraction

of material volume is assumed to be mesomorphic, lead-

ing to a material consisting of spherulites embedded in a

mesomorphic matrix [1]. A fourth order Runge–Kutta

method was used to solve numerically Eqs. (9) and (10).

4. Results and discussion

Fig. 2 shows the experimental determined degree of

space filling from DSC tests after data correction

according to Eder and Janeschitz-Kriegl [3]. Model pre-

dictions, using the parameter values given in Section

2.1, are also reported. The comparison shows that a

reasonable qualitative but a poor quantitative agree-

ment. The predictions overestimate the crystallization

rate at 0.033 K s�1, are fairly in agreement at

0.17 K s�1 and underestimate the kinetics at

0.50 K s�1, pointing out a too low dependency of the

model crystallization rate on temperature. Moreover,

110 120 130 140 150

0.0

0.2

0.4

0.6

0.8

1.0

110 120 130 140 150

0.0

0.2

0.4

0.6

0.8

1.0

Model 0.50 Ks-1

Deg

ree

of s

pace

fillin

g, d

imen

sion

less

Temperature,ºC

Experimental 0.50 Ks-1

Model 0.17 Ks-1

Experimental 0.17 Ks-1

Model 0.033 Ks-1

Experimental 0.033 Ks-1

Fig. 2. Degree of space filling evolution experimental (DSC) and model for iPP K2Xmod.

2300 F. De Santis et al. / European Polymer Journal 41 (2005) 2297–2302

the qualitative trend is not satisfactory at high crystal-

linity levels, i.e. at low temperatures, where the predic-

tions level to unit value, attained from crystallization at

low temperatures, i.e. for very long crystallization

times. This experimental result is most probably due

to secondary crystallization that is not taken into ac-

count in the crystallization kinetics model used here.

The temperature gap between prediction and data is

however restricted to few degrees, stating that the mod-

el fairly well predicts the crystallization behavior for

low cooling rates (DSC experiments).

Fig. 3 reports the measured and predicted degree of

space filling during quenching tests. It is worth noticing

80 90 100 110-0.4

0.0

0.2

0.4

0.6

0.8

1.0

80 90 100 110

, data and model, dT/

, data and model, dT/

, data and model, dT/

Deg

ree

of s

pace

fillin

g, d

imen

sion

less

Tempera

Fig. 3. Degree of space filling evolution

that characteristic cooling rates (defined at 343 K [8]) are

much higher than the cooling rates attainable in DSC

tests.

The comparison shows that the quantitative agree-

ment is even worse than in case of DSC experiments,

i.e. the low cooling rates. The predictions, strongly

underestimate the crystallization rate for all experi-

ments. Moreover, the gap between experimental data

and model predictions increases for an increasing cool-

ing rate, confirming the too weak dependence of model

crystallization rate on temperature.

A better, simplified way to outline the difference be-

tween model predictions and the experimental data is

120 130 140

120 130 140

-0.4

0.0

0.2

0.4

0.6

0.8

1.0

dt@343K = -1.1 K·s-1 KX2

dt@343K = -6.5 K·s-1 KX4

dt@343K = -17.2 K·s-1 KX5

ture,ºC

experimental (quench) and model.

0.01 0.1 10 100

0.01 0.1 10 100

0

25

50

75

100

125

150

0

25

50

75

100

125

150

, K2Xmod, exp, DSC and quenches, T30G, exp, DSC and quenches, K2Xmod, model, DSC and quenches, T30G, model, DSC and quenches

Hal

f-cry

stal

lizat

ion

tem

pera

ture

, °C

Cooling rate, K·s-1

1

1

Fig. 4. Crystallization temperatures (model and experiments), for T30G data from [6] as function of characteristic cooling rate.

F. De Santis et al. / European Polymer Journal 41 (2005) 2297–2302 2301

provided by Fig. 4 where experimental and predicted

half-crystallization temperatures are reported versus

characteristic cooling rates for both materials.

Based on past experience and the rather good agree-

ment found here, the characteristic cooling rate as

defined above was adopted as the parameter that consis-

tently represents the thermal history of the sample for

quench tests.

For both materials the model predicts fairly well the

low cooling rate crystallization behavior, whereas it loses

its reliability at higher cooling rates, where it strongly

underestimates the crystallization temperature, the dif-

ference becoming larger with increasing cooling rate for

both materials. Since the isothermally tuned model is

not able to describe the high cooling rate tests, these

experiments confirm the need for an extended description

of the crystallization kinetics under high cooling rates.

5. Conclusions

For two materials, a nucleated and a non-nucleated

iPP, the crystallization kinetics model parameters, deter-

mined from experiments under isothermal conditions:

(i) Provide a fairly satisfactorily description of slow

cooling rate tests, performed with traditional

DSC, suggesting that simple, standard experi-

ments, can provide the parameter values that reli-

ably describe crystallization kinetics.

(ii) Are not able to provide a satisfactory description

of crystallization kinetics during high cooling

rates. In particular, they strongly underestimated

the half-crystallization temperature, leading to a

severe limitation of their applicability in model-

ing/simulation of polymer transformation pro-

cesses that typically involve high cooling rates.

The models used here, are insufficient to describe the

real behavior of a crystallizing iPP (for example, Fig. 6

in [9]). It is required to account for another phase devel-

oping in the same temperature range [10] or to modify

the kinetic model, for example with a cooling rate

dependent term [9]. However, to work out this issue is

beyond the scope of the present paper.

Summarizing: the model, proposed and tuned to de-

scribe the isothermal crystallization, was found to de-

scribe the isothermal as well as the slow cooling rates

tests (confirming the validity of parameters value found

by tuning), whereas the model was found largely inaccu-

rate in description of high cooling rates tests. Thus, there

is the need for improvement in modeling to describe the

high cooling rates behavior, accounting for different

phenomena.

The results reported in this work emphasize the need

of using crystallization data gathered under ‘‘processing

condition’’ for model tuning. Only in this way, a reliable

description of the crystallization behavior can be

obtained.

Acknowledgment

The authors kindly acknowledge Ing. Angelo Giann-

attasio for the help in performing most of the experi-

mental work.

2302 F. De Santis et al. / European Polymer Journal 41 (2005) 2297–2302

References

[1] Zuidema H, Peters GWM, Meijer HEH. Influence of

cooling rate on pVT-data of semicrystalline polymers.

J Appl Polym Sci 2001;82(5):1170–86.

[2] Lamberti G. A direct way to determine iPP density

nucleation from DSC isothermal measurement. Polym

Bull 2004;52:443–9.

[3] Eder G, Janeschitz-Kriegl H. Crystallization. In: Mejier

HEH, editor. Materials science and technology. Process-

ing of polymers, vol. 18. Wiley-VCH Verlag GmbH; 1997.

p. 269–342.

[4] Hoffmann JD, Davis GT, Lauritzen JI. In: Hannay NB,

editor. Treatise on solid state chemistry, vol. 3. New

York: Plenum Press; 1976. p. 497–614 [chapter 7].

[5] Patel RM, Spruiell JE. Crystallization kinetics during

polymer processing—analysis of available approaches for

process modeling. Polym Eng Sci 1991;31(10):730–8.

[6] Lamberti G, De Santis F, Brucato V, Titomanlio G.

Modeling the interactions between light and crystallizing

polymer during fast cooling. Appl Phys A: Mater Sci

Process 2004;A78(6):895–901.

[7] Schneider W, Koeppl A, Berger J. Non-isothermal crys-

tallization of polymers: system of rate equations. Int Polym

Process 1988;2(3–4):151–4.

[8] Piccarolo S, Alessi S, Brucato V, Titomanlio G. Crystal-

lization behavior at high cooling rates of two polypro-

pylenes. NATO ASI Series, Series C: Mathematical

and Physical Sciences 1993;405(Crystallization of Poly-

mers). p. 475–80.

[9] Lamberti G, Titomanlio G. Crystallization kinetics of

iPP. Model and experiments. Polym Bull 2001;46(2–3):

231–8.

[10] Coccorullo I, Pantani R, Titomanlio G. Crystallization

kinetics and solidified structure in iPP under high cooling

rates. Polymer 2002 2003;44(1):307–18.