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Polymer Degradation and Stability 95 (2010) 1148e1159

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Polymer Degradation and Stability

journal homepage: www.elsevier .com/locate/polydegstab

Crystallization kinetics of virgin and processed poly(lactic acid)

R. Pantani*, F. De Santis, A. Sorrentino, F. De Maio, G. TitomanlioDept. of Chemical and Food Engineering, University of Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy

a r t i c l e i n f o

Article history:Received 23 September 2009Received in revised form19 April 2010Accepted 24 April 2010Available online 21 May 2010

Keywords:Poly(lactic acid)Crystallization kineticsInjection mouldingExtrusionCold crystallizationPVT

* Corresponding author. Tel.: þ39 89964141; fax: þE-mail address: rpantani@unisa.it (R. Pantani).

0141-3910/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.polymdegradstab.2010.04.018

a b s t r a c t

Poly(lactic acid) (PLA) is an emerging material mainly because it can be synthesized from renewableresources and is thus environmentally and ecologically safe. The mechanical properties, above all thethermal resistance of PLA are determined by the crystalline content: the heat deflection temperature ofcrystalline PLA can reach 100 �C, whereas amorphous PLA loses mechanical properties at temperaturesslightly higher than 60 �C. However, PLA has a low crystallization rate, so that after processing it remainsmostly amorphous. This characteristic heavily limits the use of PLA for commercial applications. Manystudies have been recently published on the crystallization kinetics of PLA. The effect of processing onthis feature is however often neglected. In this work, the significance of processing on the crystallizationkinetics of a commercial PLA was investigated. Two processing methods were explored: extrusion andinjection moulding. The obtained materials, and the starting pellets of virgin polymer, were analyzed bycalorimetry in order to obtain the crystallization kinetics. Two protocols were adopted to determine thecrystallization rates during cooling from the melt or heating from the solid. The parameters of a kineticequation were determined for all the materials and protocols adopted and it was thus possible todescribe the evolution of crystallinity during heating and during cooling.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Growing environmental awareness has motivated researchersfrom industry and academia to develop products from bio-basedmaterials. Among bio-based polymers, poly(lactic acid) (PLA) isa promising candidate to replace petroleum-based plastics becauseof its high stiffness and strength, which are comparable to poly-styrene, at least at room temperature. PLA is a versatile polymersynthesized from renewable resources and thus environmentallyand ecologically safe.

Today, the main formation methods for PLA are based on meltprocessing [1]. This approach involves heating the polymer aboveits melting point, shaping it to the desired forms, and cooling tofreeze form and dimensions. Among the technologies for meltpolymer processing, extrusion and injection moulding arecurrently the most important for volume of material processed.

The range of application of PLA is severely limited by its lowglass transition temperature: due to the value of Tg, which is below60 �C, the heat deflection temperature of PLA is too low for manyinteresting applications.

On the other hand, it is well known that PLA crystallinity caninduce significant improvements in stiffness, strength, heat

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deflection temperature and chemical resistance [2]. The heatdeflection temperature of crystalline PLA can reach 100 �C [3].Obtaining a highly crystalline article of PLA remains difficult,however, due to the low crystallization rate. The minimum crystal-lization half time, t1/2, of a pure sample of PLA is of the order of severalminutes, which is an extremely long time if compared to the coolingtimes experienced by the polymer during extrusion and injectionmoulding, which is of the order of 1 s. Many researchers havetherefore spent significant efforts to study the crystallization kineticsof PLA and the possibility of selecting suitable nucleating agents toimprove the crystallization rates [4]. Most of studies, however, referto virgin PLA, and the effect of processing is almost always neglected.

Indeed, PLA is extremely sensitive to processing conditions sothat a significant reduction in molecular weight takes place due tothermal and mechanical degradation [2,5]. It is therefore clear thatthe study of the crystallization kinetics of virgin PLA can lead toresults that can be of limited use for the application to processedmaterial. Furthermore, the comparison of crystallization rates ofvirgin and nucleated material can be misleading if the virginmaterial does not follow exactly the same mechanical treatment ofthe nucleated, or melt mixed one.

Moreover, the effect of previous thermal history is extremelysignificant: it has been shown in the literature that PLA presentscompletely different crystallization behaviour when cooled fromthe melt (melt crystallization) or heated from the solid (coldcrystallization) [6]. This aspect can be quite relevant for selecting

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e1159 1149

suitable post-processing steps to increase the crystallinity insidethe products.

2. Material and methods

The material adopted in this work is a commercial grade PLAproduced by Natureworks with the trade name 2002D. Accordingto the material data-sheet the melt flow index is equal to 6, thussuitable for both extrusion and injection moulding, and the D-LAenantiomer content is about 4%. The molecular weight distributionwas determined by a size exclusion chromatography. It was foundthat Mn ¼ 145,000 and Mw ¼ 235,000.

Before any test or processing, the material was dried for 24hunder vacuum at a temperature of 60 �C.

2.1. Rheometry

Frequency sweep tests were carried out with an Ares (Rheo-metric Inc.) rotational rheometer in a plateeplate configuration(D ¼ 25 mm, gap ¼ 1 mm) under nitrogen atmosphere. A constantstrain (5%) was applied while the frequency spanned from 0.1 rad/sto 100.0 rad/s. The tests were repeated twice on the same sample toverify the absence of viscosity changes during the measurement.

2.2. PVT analysis

A PVTcharacterization of PLA samples was carried out bymeansof a “Gnomix PVT Apparatus”. This instrument is able to detectchanges in specific volume as small as 0.0002 cm3/g. The polymerdensity was measured in isobaric mode both during cooling andduring heating at a rate of 1 �C/min at pressures between 100 and1000 bar.

The specific volume at room pressure and temperature wasobtained by a pycnometer. This allowed to obtain the referencevalue for the measured volume changes, so that the absolutespecific volume could be reported.

2.3. Calorimetry

Calorimetric tests were carried out by a “Mettler DSC 822” inflowing nitrogen atmosphere. To ensure reliability of the dataobtained, heat flow and temperature were calibrated with standardmaterials, indium and zinc.

DSC thermograms during cooling and heating scans wereobtained at rates of 1 �C/min and 10 �C/min from 25 �C to 200 �C.The sample weight was always about 8 mg. Before each coolingramp, the material was first kept for 5 min at 200 �C; before eachheating ramp, the material was first kept for 5 min at 200 �C andthen cooled at a rate of 100 �C/min to 25 �C. This allowed to obtainDSC thermograms of amorphous (molten or glassy) materials bothfor heating and cooling ramps.

The experimental protocol followed to investigate theisothermal crystallization kinetics for samples cooled from themeltis described in the following:

- the sample was kept at 200 �C for 5 min and then cooled ata rate of 10 �C/min to the chosen crystallization temperature,Tiso

- at Tiso the sample was kept for a given time, tiso- after this isothermal step, the sample was heated at a rate of10 �C/min to 200 �C.

The tests carried out according to this protocol were coded asTiso_tiso_m (Tiso in �C, tiso in min) where the last letter identifies theprotocol “from the melt”.

The experimental protocol followed to investigate theisothermal crystallization kinetics for samples heated from theglass is described in the following:

- the sample was kept at 200 �C for 5 min and then cooled ata rate of 10 �C/min to 25 �C

- it was than immediately heated at a rate of 10 �C/min to thechosen crystallization temperature, Tiso

- at Tiso the sample was kept for a given time, tiso- after this isothermal step, the sample was heated at a rate of10 �C/min to 200 �C.

The tests carried out according to this protocol were coded asTiso_tiso_s (Tiso in �C, tiso in min) where the last letter identifies theprotocol “from the solid”.

2.4. Polarized optical microscopy

Polarized optical microscopy (POM) observation was performedon a BX41 Olympus microscope equipped with a digital camera.The film samples, having a thickness between 100 mm and 200 mm,followed the same protocols “m” and “s” identified above, ina Linkam DSC600 hot stage in a flowing nitrogen atmosphere.

2.5. Processing

2.5.1. ExtrusionThe dried pellets were extruded in a Brabender DCE 330

machine (screw length 400 mm, L/D ¼ 20). The temperature of thecylinder was 200 �C. The screw velocity was 40 rpm, the torque19 N m. A round die having a diameter of 4 mm and a length of16 mmwas applied, so that the pressure at the screw tip was about15 bar. The residence time of the material inside the extruder wasabout 1 min. The material coming out from the extruded did notshow traces of degradation and preserved both colour and trans-parency of the virgin material.

2.5.2. Injection mouldingA reciprocating screw Negri-Bossi injection moulding press was

adopted to mould the material. Screw diameter was 25 mm andL/D¼ 22. The barrel temperature profile from the melting zone to theinjection chamber was: 170�Ce180�Ce200 �C, so that injectiontemperature was 200 �C. The holding pressure was 850 bar, and thefilling timewas 1.4 s. During injectionmoulding the screw rotates onlyduring batching: the rotation speed was 150 rpm for 1.5 s at eachmoulding cycle. The overall material residence time inside themachinewasabout15min.An instrumentedmouldwasadopted,witha rectangular cavity (nominal dimensions 120mm� 30mm� 2mm)and a line gate (thickness 1.5 mm). Pressure curves measured duringinjection moulding (not reported) confirmed that the material can becorrectly processed. Furthermore, no significant change in the pres-sure curve evolution was detected during the 20 consecutive cyclescorresponding to the material residence time inside the mould. Themoulded samples did not show traces of degradation and preservedboth colour and transparency of the virgin material.

The samples moulded by injection moulding press were codedas “injected”.

3. Results

3.1. Rheometry

The results of rheological tests carried out on all the materialsadopted in this work are reported in Fig. 1.

102

103

104

0.1 1 10 100

Virgin 180°CExtruded 180°CInjected 180°CVirgin 200°CExtruded 200°CInjected 200°C

Virgin 220°CExtruded 220°CInjected 220°CVirgin 240°CExtruded 240°C

∗η]s aP[

Freq [rad/s]

180°C

200°C

220°C

240°C

Fig. 1. Complex viscosity of virgin and processed samples.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e11591150

Only slight differences can be evinced between virgin andextruded materials. At each temperature, the extruded samplespresent a slightly higher viscosity with respect to virgin ones. Thiscan be due to a partial polycondensation, which is known to takeplace in polyesters at low water content. Injected samples presenton the other hand significantly lower viscosities with respect to theother samples. It was not possible to obtain reliable data of viscosityfor injected samples at 240 �C. This is obviously due to a reductionof molecular weight due to mechanical and thermal degradation. Itis worth mentioning that the value of low shear rate viscosity ofa polymer is strongly dependent on the molecular weight.Assuming a power dependence with an exponent equal to 3.4,a factor 2 in viscosity becomes a factor 1.2 in molecular weight,which is a quite significant change.

Fig. 2. PVT characterization during heating and cooling scans at 1 �C/min for injectedtemperature are highlighted.

3.2. PVT analysis

Although the literature regarding PLA investigated severalaspects of this material, PVT diagrams are quite rare [1,7]. A PVTcharacterization of PLA injected samples carried out by means ofa “Gnomix PVT Apparatus” is reported in Fig. 2. The plots refer toheating and cooling scans at 1 �C/min. A peculiarity of PLA can beimmediately noticed: during cooling ramps PLA behaves like anamorphous material. At each pressure, during cooling from themelt, the specific volume decreases linearly with temperature untilthe glass transition temperature, Tg, is reached, and a change inslope takes place. Below Tg, the specific volume keeps ondecreasing linearly with temperature, but with a lower slope. Onthe contrary, during heating scans, the material behaves likea quenched crystalline polymer: starting from room temperaturethe specific volume follows the same path of the cooling rampsuntil a temperature is reached (indicated as Tcs in Fig. 2) wherecrystallization starts. At this temperature the specific volumedeparts from the line of the melt, assuming at each temperaturesmaller values. This is obviously due to the densification effect ofcrystallinity. On increasing temperature, the crystals start to meltand the specific volume gets closer and closer to the line of the meltwhich is reached at the completemelting temperature (indicated asTcm in Fig. 2). It can be easily evinced from Fig. 2 that the glasstransition temperature increases with pressure, as expected, butalso the temperatures Tcs and Tcm increase with pressure.Furthermore, the crystallization is somewhat inhibited by theincreasing pressure: the differences between the plots which referto the cooling and to the heating scans reduce on increasing pres-sure until no differences can be detected at 1000 bar.

3.3. Calorimetry

The DSC thermograms during cooling and heating scans at1 �C/min and at 10 �C/min are reported in Fig. 3. As mentionedabove, the starting material for each cooling and for each heatingramp was amorphous. The thermograms of the virgin materialshow no crystallization peak during cooling ramps, which obvi-ously means that the kinetics is not fast enough to allow crystalli-zation even at a very low cooling rate (1 �C/min). During heating, no

sample. The dependences on pressure of glass transition temperature and melting

Fig. 3. DSC curves during cooling and heating scans at 1 �C/min (left) and at 10 �C/min (right). The signals are arbitrarily shifted along the vertical axis. The arrows indicate the timecoordinate. The starting material was always amorphous.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e1159 1151

peak can be seen when the heating rate is 10 �C/min, whereasa very small melting peak can be detected at 149 �C when theheating rate is 1 �C/min. The thermogram obtained during heatingat 1 �C/min is analyzed in terms of crystallinity in the following(Fig. 14).

As far as the extruded material is concerned, similarly to thevirgin material, no crystallization peak is present during coolingramps. On the contrary, the thermogram obtained during heating at10 �C/min shows a small melting peak. In fact, the extrudedmaterial presents a clear crystallization peak at 113 �C duringheating at 1 �C/min and two separate melting peaks at 148 �C and154 �C. This suggests that the extruded material presents a muchfaster crystallization rate than the virgin one.

Regarding the injected material, during cooling ramps no clearcrystallization peak can be detected, even if at 1 �C/min somedeparture from the baseline can be evinced. During heating ramp at1 �C/min a clear crystallization peak is present at 98 �C and twomelting peaks are present at 145 �C and 154 �C. The crystallizationpeak starts at about 95 �C, and the melting peak ends at about160 �C: both temperatures are in fairly good agreement to theextrapolation at zero pressure of the temperatures indicated as Tcsand Tcm in the PVT behaviour. Also at the heating rate of 10 �C/minthematerial is able to crystallize (a peak is present at 124 �C). In thiscase, a single melting peak can be detected at 151 �C. These findingssuggest that the crystallization kinetics of the injected material ismuch faster with respect to the other two materials. Furthermore,DSC results confirm what already noticed on commenting PVTbehaviour: the crystallization rate during heating is much fasterwith respect to the rate during cooling.

The presence of a two melting peaks has been already reportedin the literature for PLLA [8] and has been ascribed to recrystalli-sation: small and imperfect crystals changed successively intomorestable crystals through the melting and recrystallisation process.

All the thermograms measured during heating show the char-acteristic endothermic peak related to the relaxation of macro-molecules which occurs in the same temperature range as the glasstransition [9]. It can be stated that the processing did not induceany significant change in the glass transition temperature, whichresulted to be about 55e57 �C (heating ramp at 1 �C/min).

3.4. Virgin PLA

Fig. 4 reports, for three of the temperatures analyzed, themelting behaviour of virgin PLA after a crystallization step lasting

for different times according to protocol “m” (left plots) and “s”(right plots). For both protocols, two endothermic peaks areclearly detected when crystallization takes places at the temper-atures of 95 �C (Fig. 4a and b), 100 �C (not reported) and 105 �C(Fig. 4c and d). This phenomenon was analyzed in detail in theliterature for PLLA [10] and attributed to recrystallisation ofimperfect crystals. On increasing isothermal times, the relativeheight of the lower temperature peak increases with respect tothe higher temperature peak. Probably, increasing the isothermaltime allows the formation of more stable crystals and thus limitsthe occurrence of recrystallisation. For isothermal crystallizationat temperatures higher than 105 �C a progressive shift of themelting peak toward higher temperatures can be noticed onincreasing isothermal time. This indicates the formation of largercrystals.

The total heat absorbed during melting (namely the time inte-grals of the peaks) is reported in the top diagrams of Fig. 6. It can benoticed that at each temperature and for each time, the heatreleased during melting is always larger when the protocol “s” isapplied. If it is assumed that no relevant change of crystallinitytakes place during the heating step, the heat of melting is directlyproportional to the extent of crystallization developed during theisothermal step. This would suggest that at each temperature thecrystallization kinetics is faster when the sample crystallizes duringheating than during cooling, confirming the PVT and DSC resultspresented above.

3.5. Extruded PLA

The diagrams of Fig. 5 report the melting behaviour of extrudedPLA after crystallization for several times starting from the melt(left column) and from the solid (right column). For both protocols,two endothermic peaks (even more than two for the test coded“90_120_s” reported in Fig. 5b) are clearly detected when crystal-lization takes places at the temperature of 90 �C. As already noticedfor the virgin material, on increasing isothermal times, the relativeheight of the lower temperature peak increases with respect to thehigher temperature peak.

The total heat absorbed during melting (namely the time inte-grals of the peaks) is reported in the bottom diagrams of Fig. 6.Consistently to what already noticed for virgin material, at eachtemperature and for each time, the heat released during melting isalways larger when the protocol “s” is applied.

Fig. 4. Melting peaks of virgin PLA during heating after isothermal steps for different times and at different temperatures according to protocol “m” (left column) and “s”(right column).

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e11591152

3.6. Injected PLA

Fig. 7 reports the melting behaviour of injected PLA after crys-tallization starting from themelt (protocol “m”, Fig. 7a) and from theglass (protocol “s”, Fig. 7b). Just one isothermal time at eachtemperature is reported, since formost of the temperatures analyzed,injected PLAwas able to fully crystallize at times shorter than 30min.For both protocols, two endothermic peaks are clearly detectedwhencrystallization takes places at temperatures below 110 �C. Onincreasing isothermal temperature, just one peak is present at highertemperatures the higher is the isothermal temperature.

Themaximumvalue of the heat released during melting after theisothermal crystallization steps (normally corresponding to the valuemeasured after the longest isothermal step) is reported in Fig. 8a for

all the materials analyzed. For the same crystallization temperature,the heat released is about the same, independently on the protocoladopted. This would suggest that the quantity of amorphous insidethe growing crystalline structures does not depend on the protocoladopted. All the samples showa general increase of the heat of fusionwith the isothermal temperature. The average value of the heatreleased was about 25 J/g. The minimum value is reached for thevirgin material at 90 �C. Probably, at that temperature the mobility isnot enough to allow an efficient crystal growth, so that a relevantamorphous portion remains incorporated inside the crystallinestructures (spherulites). The onset of the melting peak after theisothermal crystallization steps (namely the melting temperature) isreported in Fig. 8b for all the materials analyzed. As expected, all themelting temperatures increase with the crystallization temperature.

Fig. 5. Meltingpeaksof extruded PLAduring heatingafter isothermal steps fordifferent times and at different temperatures according to protocol “m” (left column) and “s” (right column).

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e1159 1153

For the same crystallization temperature, the melting temperaturesmeasured are about the same, independently on the protocol adop-ted. On extrapolating the data to intercept the line Tm¼ Tc, accordingto the Hoffman-Week method, it is clear that the following rela-tionship holds for the thermodynamic melting temperature: Tm(injected) > Tm (extruded) > Tm (virgin).

3.7. Microscopy

The POMmicrographs reported in the left column of Fig. 9 allowa comparison between the morphologies developing at the same

temperature (120 �C) according to protocol “m”. The reportedmicrographs have been snapped after 1 h from the start of theisothermal step. When the samples follow the protocol “m”,a limited number of spherulites can be detected which do notchange in number during time, indicating heterogeneous nucle-ation. The measured radial growth rates for virgin and extrudedmaterial are about the same (G ¼ 0.0032 mm/s), even if the numberof spherulites in the extruded material is much larger (Fig. 9aec).The growth rate is of the order of 0.003 mm/s. It has been shownthat the growth rate is a strong decreasing function of thepercentage of D-isomer content. Considering a D-isomer content of

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c d

Fig. 6. Melting peaks of virgin (top diagrams) and extruded (bottom diagrams) PLA during heating after isothermal steps for different times and at different temperatures. a) virginmaterial, protocol “m”; b) virgin material, protocol “s”; c) extruded material, protocol “m”; d) extruded material, protocol “s”.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e11591154

4%, the results found are in line with literature data [11]. As far asthe injectedmaterial is concerned (Fig. 9e), a faster growth rate wasmeasured (G ¼ 0.0055 mm/s). Evidently, the mechanical degrada-tion experienced during the injection cycle leads to the formationof lower-molecular-weight molecules which may increase the Gvalue [12].

When crystallization takes place at 110 �C (micrographs are notreported) the comparison between extruded and virgin samplesremains about the same: same growth rate but more crystals in theextruded material. The morphology of injected sample completelychanges: many small crystals rapidly fill the space, so that growthrate cannot be measured.

This situation is quite similar to the one taking place for all thesamples when the protocol “s” is applied. The micrographs taken

Fig. 7. Melting peaks of injected PLA during heating after isothermal steps for di

after 5 min of isothermal crystallization at 120 �C when theprotocol “s” is applied are reported in the right column of Fig. 9. Forall the materials, a few seconds after the isothermal start, manycrystals appear. Only the virgin sample (Fig. 9b) it was possible todetect circular shaped crystals of which the radial growth ratecould be measured. The growth rate very close to that measuredwhen the protocol “m” was adopted. This suggests that the differ-ence between the crystallization processes taking place at a giventemperature when the sample is either heated from the glass orcooled from the melt mainly relies on the number of nuclei.According to the heterogeneous nucleation process, an increasingnumber of nuclei is formed during cooling. These nuclei formduring cooling but cannot grow because of the very slow growthrate, and their formation is not detectable by DSC. Also the POM

fferent times and at different temperatures. a) protocol “m”, b) protocol “s”.

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]C°[ ni

m/C°01 ta gnitaeh gnirud kaep gnitle

m eht fo tesnO

Temperature of isothermal crystallization [°C]

a b

Fig. 8. a) Maximum value found for the heat released during melting after the isothermal crystallization; b) melting temperature.

Fig. 9. Left column: POM micrographs taken after 60 min of isothermal crystallization at 120 �C according to protocol “m” for a) virgin material, c) extruded material, e) injectedmaterial; Right column: POM micrographs taken after 5 min of isothermal crystallization at 120 �C according to protocol “s” for b) virgin material, d) extruded material, f) injectedmaterial; The pictures are 723 mm wide.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e11591156

images collected during cooling and subsequent heating did notshow any crystal. When the isothermal step is reached after thesubsequent heating, the growth rate becomes fast enough torapidly fill the interspaces between nearby nuclei.

4. Discussion

4.1. Identification of kinetic parameters

The relationship between the energy released during crystalli-zation, dH/dt (namely the signal detected by DSC once the baselineis subtracted, in W/g) and the crystallinity degree, x, is

dHdt

¼ ldxdt

(1)

in which l is the latent heat of crystallization of a fully crystallinePLA, which can be found in the literature to be 93 J/g [13]. Thecrystallinity degree is reported on a right vertical axis in Figs. 8aand 10.

The application of eq. (1) to the calorimetric signal measuredduring the isothermal step of both the protocols adopted in thiswork directly provides the evolution of the crystallinity degree.

However, when the crystallization rate is very slow (half crys-tallization times of 2 h or longer) the signal is so weak that it isdifficult to univocally identify a baseline. For the virgin andextruded materials, therefore, the time evolution of crystallinityduring the isothermal steps was measured by a different method:the heat absorbed during the melting following the isothermal step(reported in Fig. 6), which can be considered to a good approxi-mation equal to the heat released during the isothermal crystalli-zation, was converted to crystalline degree by the integral of eq. (1).For each isothermal crystallization the diagrams of Fig. 6 wereassumed to represent the time evolution of the crystallinity degreeduring the isothermal steps.

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virgin

extruded+injected

b

d

Fig. 10. Best fitting by eq. (2) of some of the data already reported in Fig. 6. a) virgin matprotocol “m”; d) extruded material, protocol “s”.

According to the well known Avrami model, the time evolutionof crystallinity in isothermal conditions can be expressed as

x ¼ xmax�1� exp

�� ln 2$ðKðTÞtÞn�� (2)

where K is the kinetic constant, n is the so-called Avrami index andxmax is the maximum attainable value for x, which can depend ontemperature. Adopting eq. (2), the kinetic constant is equal to thereciprocal of the half crystallization time.

At each temperature, the values of K, xmax and nwere identifiedby best fitting the data of crystallinity reported in Fig. 6 with eq. (2).For each material, it was found that it was possible to obtain a gooddescription of data by adopting a single value of the Avrami indexfor all tests, which resulted to be equal to 2.8 for the virgin materialand to 2.7 for the extruded one. These values are sufficiently closeto 3 to confirm a spherical growth of heterogeneously nucleatedcrystals. The values of xmax for each condition resulted to be, withinthe experimental error, equal to the results reported in Fig. 8a (rightaxis). The results of the fitting procedure are compared with theexperimental data in (Fig. 10).

In order to check the validity of the method adopted to obtainthe parameters of eq. (2), for some of the tests in which the calo-rimetric signal was clear enough, a comparison was carried outbetween experimental data and the results of eq. (1) in isothermalconditions adopting the time dependence on x provided by eq. (2)and the values of K, xmax and n obtained above. The results arereported in Fig. 11a and b for virgin and extruded material,respectively. Although the description of data is not perfect, it caneasily be seen that the half crystallization times (namely the time atwhich a peak is reached) are correctly described.

The values of the kinetic constant (namely the reciprocal of thecrystallization half time) found by the best fitting procedure arereported in Fig.12 for virgin (circles) and extruded (squares)materialas a function of temperature. As also evinced on commenting theexperimental data, at each temperature the crystallizationwhen the

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0.2

0.24

0.28

0.32

]g/J[ gnitlem gnirud debrosba tae

H

isothermal time [min]

]-[ eerged ytinillatsyrC

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

90s105s120s90s_mod105s_mod120s_mod

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

]g/J[ gnitlem gnirud debrosba tae

H

isothermal time [min]

]-[ eerged ytinillatsyrC

virgin

extruded

erial, protocol “m”; b) virgin material, protocol “s”; c) extruded and injected material,

Fig. 11. Best fitting by eqs. (1) and (2) of the calorimetric signal in isothermal conditions for some of the tests carried out with virgin and extruded materials. The parameters aregiven in Table 1.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e1159 1157

material is cooled from the melt (protocol “m”) is slower than whenthe material is heated from the glass (protocol “s”). The extrudedmaterial presents a much faster kinetics with respect to the virginone, with kinetic constants about one order ofmagnitude larger thenfor the virgin material if protocol “s” is applied”. This result can beinterpreted in terms of the mechanical degradation which thematerial undergoes during processing. Considering, however, thatthe low shear rate viscosity did not reveal a significant reduction inmolecular weight, the enhancement of crystallization rate goesbeyond what could be expected. Probably a limited number ofsmaller chains can induce a significant increase in thenucleation rate.

As far as the injected material is concerned, in all cases exceptfor the test at 120 �C carried out according to protocol “m”, thecalorimetric signal was strong enough to allow a clear determina-tion of the baseline. The kinetic parameters were therefore

0.0001

0.001

0.01

0.1

1

80 90 100 110 120 130

virgin_mvirgin_sextruded_mextruded_s

injected_minjected_sVirgin_mVirgin_s

Extruded_mExtruded_sInjected_mInjected_s

10-5

0.0001

0.001

0.01

Kine

tic c

onst

ant [

1/m

in]

Temperature [°C]

Kine

tic c

onst

ant [

1/s]

Fig. 12. Kinetic constants (namely reciprocal of half crystallization time) as a functionof temperature for all the materials and protocols adopted in this work. Lines refer tothe results of eq. (3) with the parameters given in Table 1.

identified at each temperature by a best fitting procedure based onthe comparison of eq. (1) with the experimental calorimetric signalin isothermal conditions. eq. (2) was adopted to obtain the timeevolution of crystallinity. Also for the injected material, it waspossible to adopt a single value for the Avrami index n, whichresulted to be equal to 2.9. The results of the best fitting procedureare reported in Fig. 13.

Concerning the test at 120 �C according to protocol “m”, thecalorimetric signal during the isothermal step resulted to be toolow to be analyzed in a reliable way. Therefore, the same methodadopted for the virgin and the extruded material was applied. Theresults of the fitting procedure are reported in Fig. 10c.

The results of the dependence on temperature of the kineticconstant for the injected material are reported in Fig. 12 as trian-gles. When the protocol “s” is applied, the kinetic constant of theinjected material is about one order of magnitude faster ifcompared to the extrudedmaterial, and increasesmonotonically onincreasing the temperature. When the protocol “m” is applied thecrystallization kinetics of the injected material keeps faster withrespect to the other two materials, with the only exception of thepoint at 120 �C, at which the crystallization rates of the threematerials are of the same order of magnitude.

It is known from the literature [14] that PLLA samples presenta crystal modification named a when crystallization takes place attemperatures higher than 120 �C whereas the modification nameda0 (disorder a) develops at lower temperatures. Probably, themechanical degradation induced by processing, which inducesa significant increase of the crystallization kinetics at temperatureslower than 120 �C, does not influence dramatically the crystalli-zation kinetics of the a modification. On the contrary, when theprotocol “s” is applied, the increase of crystallization kinetics issignificant at all temperatures. This is a further clue that theisothermal crystallization taking place after a heating step concernsthe growth of nuclei generated at lower temperatures.

The results reported in Fig. 12 can be of extreme industrialimportance. In injection moulding, for instance, in order to obtaina fully crystalline sample it is necessary to keep the mould at about100 �C and adopt a permanence time inside the mould of about40 min (the half crystallization time for protocol “m” at 100 �C isabout 20 min). This is obviously impracticable. The same resultcould be obtained by injection moulding the sample in a conven-tional way (cycle time of the order of 1 min) in a cold mould, andadopting a post-processing step by heating the obtained samples inan oven at 100 �C for 10 min (the half crystallization time forprotocol “s” at 100 �C is about 5 min).

0

0.005

0.01

0.015

0.02

0.025

0 1000 2000 3000 4000 5000 6000

90_120_m90_120_m_mod100_60_m100_60_m_mod110_120_m110_120_m_mod

Sign

al [W

/g] (

pos=

exo)

Isothermal time

0

0.02

0.04

0.06

0.08

0.1

0.12

0 500 1000 1500 2000 2500

90_120_s90_120_s_mod100_60_s100_60_s_mod110_120_s110_120_s_mod

Sign

al [W

/g] (

pos=

exo)

Isothermal time

a b

injectedinjected

Fig. 13. Best fitting by eqs. (1) and (2) of the calorimetric signal in isothermal conditions for some of the tests carried out with injected material. The parameters are given in Table 1.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e11591158

4.2. Description of kinetic constants

The results of kinetic constant reported in Fig. 12 were obtainedby analyzing each temperature independently. In order to describethe effect of temperature on the kinetic constant an Hoff-maneLauritzen expression [15] can be adopted

KðTÞ ¼ A1exp�� A2

T � TN

�exp

� A3ðTm þ TÞ2T2ðTm � TÞ

!(3)

in which Tm is the melting temperature and TN is a temperaturenormally about 30 �C below Tg.

For each material and each protocol adopted, all the parametersof eq. (3), namely A1, A2, A3, TN and Tm were obtained by a bestfitting procedure based on the comparison of the results of eq. (3)and the data of kinetic constant reported in Fig. 12. Just twoconstraints were imposed: 1) for each material, independently onthe protocol adopted, the values of Tm were assumed to be thesame, following the indication provided by Fig. 8b; 2) the value ofTN (which is linked to Tg) was assumed to be the same for allmaterials and all protocols; indeed, no relevant change in Tg withmaterial or protocol was evidenced by experimental data.

The resulting parameters are reported in Table 1 and refer to theset which provides theminimumvariance between data andmodelresults. A sensitivity analysis was performed by imposing the valueof melting temperature, Tm, and letting the regression routine findthe values of the other parameters. The variance became very largewhen the set melting temperature was about 3 K larger or smallerthan the value reported in Table 1. The variance was also quitesensitive to the values of the parameters A2 and A3: about 10% of

Table 1Parameters of eq. (3) for the description of the dependence of kinetic constants upon te

Parameter Unit Virgin E

Protocol “s” Protocol “m” P

TN K 305 305 3Tm K 427 427 4A1 s-1 1.11 10�1 2.04 10�1

A2 K 3.45 102 3.98 102

A3 K2 4.08 104 3.32 104

n (eq. (2)) e 2.8

variation with respect to the values reported in Table 1 resulted ina change in the variance of a factor of about 4.

The results of eq. (3) are compared in Fig. 12 with the data ofkinetic constants. The description of data is very good, except forsome minor deviations. For instance, concerning the virgin mate-rial, experimental data show that at 95 �C the kinetic constantaccording to the protocol “m” is faster than that obtained byprotocol “s”; this crossover is predicted to take place at 90 �C.

It should be considered that eq. (3) does not keep into accountany change in kinetics due to different regimes or crystal modifi-cations: being based on enthalpic phenomena the results of eq. (3)should be considered as the description of an overall crystallinitydegree. Concerning the values of the parameters listed in Table 1, itis worth mentioning that the relationship among the meltingtemperatures highlighted above is respected.

The identification of the values of the kinetic parameters allowsto predict the evolution of crystallinity degree also in non-isothermal conditions. In particular, adopting the non-isothermalformulation of the Avrami model due to Nakamura it is possible towrite:

x ¼ xmax

2641� exp

0B@� ln 2

0@Zt

0

KðTÞdt1A

n1CA375 (4)

The parameters of eq. (4) have been all determined. It istherefore possible to verify the prediction of eq. (4) by directcomparison with experimental results. As shown in the experi-mental section (Fig. 3), during calorimetric cooling ramps no clearcrystallization peak was detected for any of the three materials

mperature.

xtruded Injected

rotocol “s” Protocol “m” Protocol “s” Protocol “m”

05 305 305 30529 429 438 4388.37 101 8.18 101 6.85 101 1.69 108

6.08 102 5.46 102 5.40 102 8.24 102

6.01 104 9.77 104 4.95 104 3.11 105

2.7 2.9

0

0.05

0.1

0.15

0.2

0.25

0.3

0

5

10

15

20

25

80 100 120 140 160 180

Injected, 1°C/min, modInjected, 10°C/min, modExtruded, 1°C/min, modVirgin, 1°C/min, mod

Injected, 1°C/minInjected, 10°C/minExtruded, 1°C/minVirgin, 1°C/min

Cry

stal

line

degr

ee [-

]

Temperature [°C]In

tegr

ated

cal

orim

etric

sig

nal [

J/g]

Fig. 14. Comparison between model predictions and crystallinity evolution calculatedby DSC heating scans. Dots are experimental results as specified in the label.

R. Pantani et al. / Polymer Degradation and Stability 95 (2010) 1148e1159 1159

analyzed in this work. On the contrary, during the heating scans(protocol “s”) at 1 �C/min all the materials presented a clearcrystallization peak. This peak was integrated after subtractingthe baseline, and converted to crystallinity degree by dividing theresult by l ¼ 93 J/g. Eq. (4) was then applied by considering thetemperature evolution of K provided by eq. (3) with the param-eters reported in Table 1 (protocol “s”) and the Avrami indexdetermined above (n ¼ 2.8 for virgin, 2.7 for extruded and 2.9 forinjected material). For simplicity, a single value for xmax wasadopted, equal to 0.27, which is the average value evinced fromFig. 8a (right axis) for injected and extruded material and forvirgin material at temperatures higher than 100 �C. The compar-ison between data and predictions is reported in Fig. 14. For all thematerials at 1 �C/min and for the injected material also at 10 �Cthe calculations correctly describe the temperature at whichcrystallization starts and run very close to the data during thewhole crystallinity evolution. The plateau value is reasonably welldescribed. At temperatures of about 135 �C, the data show thestart of melting, until the melting is complete at a temperature ofabout 155 �C. Obviously, the predictions do not take into accountany melting and keep the plateau value.

5. Conclusions

In this work, the effect of processing on the crystallizationkinetics of a commercial PLA was investigated.

It was found that extrusion did not induce significant changes inlow shear rate viscosity whereas injection moulding causeda noticeable lowering in viscosity, which is a clear index of a lowermolecular weight due to mechanical and thermal degradation.

Two protocols were adopted which allowed us to determine thecrystallization rate during cooling from the melt (protocol “m”) andduring heating from the solid (protocol “s”).

The kinetic constants (namely the reciprocal of half crystalliza-tion times) in isothermal conditions were determined as a functionof temperature for all the materials and both the protocols.

It was shown that all the materials (both virgin and processed)presented a much higher crystallization rate during heating thanduring cooling. According to POM observation, this result wasascribed to the generation of nuclei at low temperature which growon increasing temperature.

Concerning the effect of processing, it was found that when theprotocol “s” is applied, the kinetic constant of the injected materialis about one order of magnitude faster if compared to the extrudedmaterial, which on turn is a factor about 2 faster with respect to thevirgin one. When the protocol “m” is applied the crystallizationkinetics of the injected material remain faster with respect to theother two materials, with the exception only of the point at 120 �C,at which the crystallization rates of the three materials are veryclose. This was justified considering the formation, at temperatureshigher than 120 �C, of a modification which probably is notsignificantly influenced by the mechanical degradation. The injec-ted material presented a faster spherulite growth rate with respectto the extruded and the virgin, which presented the same growthrate.

The parameters of a kinetic model were determined on the basisof isothermal crystallization data. The model was found to be ableto correctly predict the crystallization evolution during heatingscans.

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