Rheol Acta (2011) 50:613–629DOI 10.1007/s00397-011-0538-1

ORIGINAL CONTRIBUTION

Melt strengthening of poly (lactic acid) through reactiveextrusion with epoxy-functionalized chains

Yves-Marie Corre · Jannick Duchet · Joël Reignier ·Abderrahim Maazouz

Received: 12 October 2010 / Revised: 24 January 2011 / Accepted: 25 January 2011 / Published online: 1 March 2011© Springer-Verlag 2011

Abstract Poly (lactic acid) is an industrially mature,bio-sourced and biodegradable polymer. However, cur-rent applications of this eco-friendly material are lim-ited as a result of its brittleness and its poorly meltproperties. One of the keys to extend its processingwindow is to melt strengthen the native material. Thispaper considers the chain extension as a valuable solu-tion for reaching such an objective. An additive basedon epoxy-functionalized PLA was employed duringreactive extrusion. The reaction times as a functionof chain extender ratios were determined by moni-toring the melt pressure during recirculating micro-extrusions. Once residence times were optimized, reac-tive extrusion experiments were performed on a twinscrew extruder. Size exclusion chromatography pro-vided information about the molecular weight distri-butions (MWD) of the modified PLAs and revealedthe creation of a high molecular weight shoulder. Therheological experiments highlighted the enhancementof the melt properties brought about by the chainextension. Shear rheology revealed some enlarged andbimodal relaxation time spectra for the extended mate-rials which are in accordance with the MWD analysis.Such a modification directly amplified the shear sen-

Y.-M. Corre · J. Duchet · J. Reignier · A. MaazouzUniversité de Lyon, 69361, Lyon, France

Y.-M. Corre · J. Duchet · J. Reignier · A. Maazouz (B)CNRS, UMR 5223, Ingénierie des Matériaux Polymères,INSA Lyon, 69621, Villeurbanne, Francee-mail: abderrahim.maazouz@insa-lyon.fr

A. MaazouzHassan II Academy of Science and Technology,Rabat, Morocco

sitivity of modified PLAs. Regarding the rheologicaltemperature sensitivity, it was found to be decreasedwhen the chain extender content is raised as shownfrom the Arrhenius viscosity fit. The reduction of thepolar interactions from neat to highly chain-extendedPLAs is here proposed to explain this surprising re-sult. Chain extension was also found to impact on theelongational melt properties where strain hardeningoccurred for modified PLAs. Investigation of the chainextension architecture was made from the rheologicaldata and revealed a long-chain branched topology forthe modified PLAs.

Keywords Poly(lactic acid) · Shear rheology ·Reactive extrusion · Extensional rheology · Meltstrengthening

Introduction

Environmental concerns and oil resource depletionhave caused the plastics industry to show a considerableinterest in agro-sourced polymers. In order to become adecent substitute for oil-based materials, biodegradablepolymers from renewable resources need to demon-strate competitive properties regarding those of theiroil-based counterparts.

Poly(lactic acid) (PLA) possesses many physicalcharacteristics rendering it suitable for replacing com-modity polymers (Vert et al. 1995). Besides being bio-compatible and available from renewable resources,PLA also demonstrates high strength, thermoplasticprocessability, good grease and oil resistance and anexcellent aroma barrier (Wehrenberg 1981; Lipinskyand Sinclair 1986; Lunt 1998; Drumright et al. 2000).

614 Rheol Acta (2011) 50:613–629

Nevertheless, the brittle nature of this polyester re-duces its use to very limited applications.

In order to overcome this drawback, previous lab-oratory studies have mainly been focused on modi-fying the PLA through branching reactions, polymerblending and charge filling (Dorgan and Joshua 1999;Palade et al. 2001; Zhou et al. 2007). There are alsonumerous reports on blending PLA with plasticizersfor biomedical (Yolles et al. 1976; Yolles 1978; Henryet al. 1985) as well as for film applications (Labrecqueet al. 1997; Martin and Avérous 2001; Ljungberg andWesslén 2002, 2003, 2005).

Regarding processing, PLA is characterized by apoor melt strength which keeps it away from specificprocesses such as film blowing, film foaming or bi-oriented film extrusion. This drawback, in addition tomelt degradation problems (Lopez Arraiza et al. 2007)arising from PLA’s polyester nature, puts the studies ofthis material apart from those of commodity polymers.

To enlarge its processing window and thereby alsoits applications field, PLA needs to be melt strength-ened. Chain modification is the main reported way toobtain enhanced melt properties for PLA (Gruber et al.1996; Tuominen et al. 2002; Yingwei et al. 2005; Zhouet al. 2007; Pilla et al. 2009; Mihai et al. 2010). Theuse of so-called chain branchers or extenders basicallyleads to an increase in the molecular weight which iseventually coupled with chain branching depending onthe functionality of the additive. The tailoring of thisnumber allows the creation of specific chain structuresas reported by (Dorgan et al. 2000). The active enti-ties can be carboxylic, hydroxyl, peroxide, isocyanateor epoxide groups reacting with carboxyl or hydroxylchain ends of PLA. The present work is based onan epoxide chain extender reacted with PLA throughreactive extrusion. Physicochemical characterizationscoupled with rheological experiments were expected tobring essential information on the chain modificationand its influence on the melt properties.

Experimental

Materials

This study was based on commercially available mate-rials. An injection grade of semi-crystalline poly(lacticacid) (PLA 3051D®) was provided by Natureworks®.The main properties of this PLA are summarized inTable 1. The PLA’s crystalline properties are governedby its enantiomeric composition (L/D ratio), and it hasbeen reported by Baratian et al. (2001) that increasingthe content of D eniantiomer reduces the crystallization

Table 1 Main properties of PLA 3051D 1

PLA 3051D® properties

D-enantiomer ratio (%) 4.15Melt flow index (210◦C/2.16 kg) 16.5 g/10 minGlass transition temperature 60◦CCrystalline melt temperature 156◦C

ability of the polyester. A low D content thus results ina semi-crystalline polymer while a D ratio greater than10% leads to mostly amorphous polyester. As reportedin Table 1, the D-enantiomer ratio of our investigatedPLA is 4.15% which is in accordance with its semicrystalline property.

A chain extender called Cesa®-Extend OMAN698493was provided by Clariant® and consisted in a PLAreacted with 30 wt.% of a multifunctional epoxide(Joncryl® 4368-BASF®). The general formula for thislast styrenic-glycidyl acrylate copolymer is given inFig. 1. The patented formulation (Campbell et al.2000) describes a highly polydisperse oligomer present-ing chains with variable epoxide functionalities ( f >

4), and its specific feature is to broaden the gel-freeprocessing window (Villalobos et al. 2006).

The resulting masterbatch is a PLA multifunctional-ized with epoxide groups. As described in a processingpatent (Randall et al. 2006), these active groups aremainly associated with chain ends of polylactide but canalso remain as non-reacted multi-epoxide oligomers.Pilla et al. recently investigated this additive as a chainextender with the aim of enhancing the extrusion andinjection foamability of PLA (Pilla et al. 2009). Withthe same objective, Mihai et al. (2010) investigatedthis same chain extender on amorphous and crystallinePLAs.

Chain extension reaction mechanism

Polyester/epoxide reactions have been widely in-vestigated in the past (Bikiaris and Karayannidis 1996;

Fig. 1 General formula of Joncryl® 4368 (BASF®)

Rheol Acta (2011) 50:613–629 615

Fig. 2 Epoxide couplingreactions with PLA

+

+

a)

b)

PLA

O

R

O

R

PLA C OH

O

OH

PLA O

O

OH

R

PLAO

R

OH

Haralabakopoulos et al. 1999; Incarnato et al. 2000;Japon et al. 2000; Nguyen et al. 2001). The epoxidegroups can react with carboxyl or hydroxyl chain endgroups of polyester. The resultant couplings involveepoxide ring-opening reactions and the creation ofcovalent bonds via hydroxyl side group formation asillustrated in Fig. 2 in the case of PLA.

It has been shown that the epoxide reactivitywith polyester is greater with carboxyl groups thanwith hydroxyl groups (Tanaka and Bauer 1988;Haralabakopoulos et al. 1999, Japon et al. 2000, Nguyenet al. 2001, Lamnawar and Maazouz 2006, Lamnawaret al. 2010). Secondary reactions (transesterification,homopolymerization) can occur mainly depending onthe process temperature. Those unwanted chain cou-plings would lead to crosslinking and gelation. Suchphenomena must be avoided in order to maintain themelt homogeneity.

Reaction monitoring

The chain extension was monitored with the help ofa batchwise DSM micro-extruder (Midi 2000 Heerlen,The Netherlands), consisting in a conical co-rotatingtwin screws equipped with a recirculating channel. Theaxial force ( fN), also known as the melt pressure, wasused to control the evolution of the reactive extrusion.Experiments were conducted until a pressure plateauwas reached, at which point the reaction was consideredto be completed.

Various amounts of chain extender, i.e. from 1 to3 wt.%, were used. Notations and compositions of theformulations are given in Table 2. Raw PLA was pre-mixed with Cesa®-Extend and dried at 70◦C for 4 h.The processing temperature was set to 210◦C, and thescrew speed was fixed at 50 rpm.

Reactive extrusion

A Clextral twin screw extruder with an L/D ratio of36:1, and a diameter of 25 mm was employed in order

to process batches of 2 kg of each formulation. Thetemperatures of the extruder zones were all set to210◦C, with the exception of the feeding zone (75◦C).The residence time was calibrated by introducing acolored resin while feeding the extruder with neat PLAat a constant rate of 3.5 kg/H. The screw speed was theparameter in use to control the residence time. The ex-trudates were water-cooled, pelletized, and dried in thesame conditions as presented above. The samples werestored in PE bags containing silica gel. Those modifiedPLAs were then characterized through physicochemi-cal and rheological analysis.

Physicochemical characterizations

Acid value analysis

Titration of the acid value of neat and modified PLAshas been performed with the help of an automaticMettler-Toledo T70® titrator. The solution for titrationwas obtained by dissolving around 3 g of PLA in 60 mLof CHCl3. Direct titration of the carboxylic groups wasthen performed with the help of a solution of KOH inMeOH with a concentration of 2.03 × 10−2 mol L−1.A pH sensor (Mettler Toledo DG111-SC®) was usedto follow the evolution of the solution acidity and toreveal the equivalent volume Ve used to determine theacid value by the following equation:

AV = Ve × C (KOH) × M (KOH)

m (PLA)

Table 2 Sample codes and related concentrations

Sample name PLA (wt.%) Cesa® extend (wt.%)

PLA_0 100 –PLA_1 99 1PLA_1.5 98.5 1.5PLA_2 98 2PLA_2.5 97.5 2.5PLA_3 97 3

616 Rheol Acta (2011) 50:613–629

where Ve (millilitres) is the equivalent volume corre-sponding to the equilibrium pH plateau, C (KOH) isthe molar concentration (moles per litre) of KOH, M(KOH) is the molar mass (grams per mole) of KOHand m (PLA) is the weight (grams) of dissolved PLA.The acid value is given in milligrams (KOH) × pergram(Polymer) as a convention.

Molecular weight characterization

Molecular weight distribution (MWD) analyses wereperformed with a waters size exclusion chromatography(SEC) system equipped with a PLGel Mixed C column(Polymer Labs). The detection was carried out at 25◦Cwith the help of a refractometer (Waters 410 DR)coupled with a multi-angle light scattering (Wyatt MiniDAWN Treos) with an elution rate of 0.5 cm3 min−1.A calibration curve was obtained with polystyrenestandards with average molecular weight (Mw) rangingfrom 1.57 × 103 up to 6 × 105 g mol−1. The PLAsamples were dissolved in CHCl3giving solutions withconcentrations around 5 × 103 mg mL−1.

Rheological characterizations

Dynamic shear rheology

Melt rheology under dynamical shear was investigatedwith an ARES rheometer from Rheometrics. A parallelplate (Ø = 25 mm, gap = 1 mm) geometry was selectedfor the dynamic time and frequency sweeps under con-trolled strain. The heated chamber was continuouslypurged with nitrogen. Angular frequencies were sweptfrom 100 to 0.1 rad s−1, and testing was carried out at160◦C, 180◦C and 200◦C.

Capillary f low rheology

A pressure-controlled CEAST capillary rheometer(Smart Rheo 2000 twin) has been used to sort out flowmelt properties. Investigations were made at 180◦Cwith three 180◦ entry angle dies having a diameter of1 mm and respective length/diameter ratios of 30, 20and 5.

Elongational rheology

An elongational rheometer RME from RheometricScientific was used to determine the transient elonga-tional viscosity. Rectangular plates (60 × 10 × 2 mm)were clamped between two counter rotating pairs of

upper/lower belts. Heated chamber was raised to 160◦Cbefore starting experiments. As the sample cross sec-tion is reduced during the stretching, a video recorderwas used to monitor this variation during the test. Asreported by Schulze et al. (2001), the section shoulddecrease exponentially with the time if the strain rate isconstant. Since clamping is made between two movingbelts on each side of the sample, some slips can occurand result in a non homogeneous strain. The moni-toring of the section both allows to check if the strainrate is constant and to determine of the real strain rateapplied to the polymer.

Results and discussion

Chain extension process

Reaction characterization

Chain extender thermal stability The first step of thisstudy was to evaluate the thermal stability of the chainextender. Self-reaction would be responsible for gelformation and would reduce the efficiency of the ad-ditive. As this unwanted reaction is often due to highprocess temperatures, 1 h isothermals were performedat 230◦C, 250◦C and 270◦C on Cesa-Extend®. Clearly,no reaction took place below 250◦C, which means thathomopolymerization of the chain extender does notoccur at the processing temperature of 210◦C.

Reaction monitoring Micro-extrusions were then per-formed in order to obtain information on the reactionprofile and residence time required for each selectedformulation. The melt pressure was used as a basicrheological response of the material to the chain ex-tension process. The influence of the chain extenderratio on the reaction profile displayed in Fig. 3 providesessential information to optimize the forthcoming re-active extrusion. For a better comparison, values werenormalized with respect to the initial force obtained forthe neat polymer (F0 (PLA_0)).

While the melt strength of neat PLA was drasticallyreduced within the first minutes of extrusion, the meltproperties of the modified samples were stabilized andeven strengthened. A low content of additive (PLA_1)seems to act as a stabilizer while higher contents enablea melt strengthening leading to a normalized force ratioup to 2.5 for PLA_3. The amplitude of the melt strengthenhancement is thus directly linked to the chain exten-der ratio for the investigated time range.

PLA_2 and PLA_3 show some oscillations of theaxial force when reaching the plateau. It seems to be

Rheol Acta (2011) 50:613–629 617

Fig. 3 The influence of thechain extender ratio on thereaction profile for reactiveextrusion performed at 210◦Cand 50 rpm on amicro-extruder

0,5

1

1,5

2

2,5

3

0 200 400 600 800

Time (s)

Fn/

Fo(

PL

A_0

)

PLA_0

PLA_1

PLA_1,5

PLA_2

PLA_2,5

PLA_3

the result of an improvement of the melt elasticityinducing stick and slip on the screw barrel wall. Withregard to the increased amplitude of the oscillations,the melt elasticity of PLA_3 is expected to be higherthan for the PLA_2 one. The forthcoming rheologicalcharacterizations should enable a quantification of theelastic melt properties of each sample.

As shown in Fig. 3, the reaction time is not linearlylinked to the amount of chain extender. A plateauseems rather to be reached at high additive levels.Two main hypotheses can be made for this limitation.On one hand, we can consider that the stoechiomet-ric balance is reached between active groups of PLAand the functional epoxides. On the other hand, asdescribed above, improved melt elasticity would reducethe diffusion of the molten polymer and gives rise to anuncompleted reaction.

Reactive extrusion processing Based on the micro-extrusion reaction monitoring, reactive extrusions runswere then performed on the Clextral twin screw ex-truder with the residence times reported in Table 3. Inorder to simulate a thermo-mechanical treatment, rawpellets of neat PLA (PLA3051D) were also extrudedwith a short residence time and then coded as PLA_0.For PLA_2 and PLA_3, two extrusions were necessaryto reach the reaction times suitable with the twin screwextruder in use (Table 4).

Validation of the extent of reaction The first chemicalinvestigation made on the resulting materials was todetermine their acid value (AV). As epoxy has beenreported to preferentially react with polyester carboxylgroup, the evaluation of the acid value is a good indi-cator of their consumption during the chain extension(Japon et al. 2000). Neat and chain extended PLAswere thus titrated, and the respective acid values arepresented in Fig. 4. In a logical way, AV is found tofirst increase from the raw pellet (PLA3051D) to theextruded one (PLA_0). This indicates that the thermo-mechanical treatment inherent to extrusion causedpolymer degradation leading to chain scissions withthe creation of new carboxyl groups. In an oppositeside, increasing the chain extender ratio led to a drasticdecrease in the AV thus revealing the efficiency of thisadditive on the chain coupling.

Acid value was also used to check if the residencetimes obtained from micro-extrusions comply with thereactive extrusion performed on the twin screw ex-truder. Four consecutive extrusions were thus per-formed on a 3 wt.% CE / PLA blend. Each extrusionwas performed at 210◦C with a residence time of 6 min.Resulting acid values summarized in Fig. 5 present aminimum obtained for the second extrusion. For thethird and fourth extrusion, acid value is rising up re-vealing a degradation of the polymer also reported byJapon at al. for chain extended PET (Japon et al. 2000).

Table 3 Screw speeds andthe resulting residence timeused for reactive extrusionsperformed on the Clextraltwin screw extruder at 210◦C

Sample 1st extrusion 2nd extrusion Total residence time (min)

RPM Residence time (min) RPM Residence time (min)

PLA_0 45 3 – – 3PLA_1 35 4 – – 4PLA_2 25 5.5 25 5.5 11PLA_3 25 5.5 20 6.5 12

618 Rheol Acta (2011) 50:613–629

Table 4 Average molecular parameters of PLAs modified by reactive extrusion at 210◦C with the Clextral twin screw extruder

PLA 3051D [Pellet] PLA_0 PLA_1 PLA_2 PLA_3

Mw (g mol−1) 1.48 × 105 1.37 × 105 2.11 × 105 2.60 × 105 2.90 × 105

Mn (g mol−1) 6.80 × 104 8.95 × 104 8.95 × 104 1.17 × 105 8.76 × 104

PI 2.2 2.4 2.4 2.2 3.3

The micro-extrusion monitoring is thus in accordancewith the reactive extrusion performed on the twin screwextruder. It can be advanced from this investigationthat a competition occurs between chain extension andchain scissions. Chain extended materials were thencharacterized by SEC in order to get information abouttheir MWD.

MWD analysis of the modif ied PLAs

The molecular modifications of PLA resulting fromthe twin screw reactive extrusions have been evaluatedby size exclusion chromatography. The MWD of thelinear and modified PLAs are plotted in Fig. 6. Theneat PLA displays a monomodal distribution with apolydispersity in accordance with conventional poly-esters. It is interesting to note that extruded neat PLA(PLA_0) have an altered Mw compared to pellets one.However, this thermo-mechanical-based degradationremains gentle (�Mw < 9%). The MWDs of modifiedPLAs slightly differ from neat PLA with the creation ofa high molecular weight shoulder resulting in a bimodalpopulation. Those dual distributions remain roughlycentred on the same peaks values. This would indicatethat the resulting chain structures are the same for allthe extended samples. In a counterpart, the evolutionof the original peak indicates that the high molecular

weight population grows at the expense of the lowmolecular weight one when chain extender is increased.As the chain diffusivity is lowered by the increase ofmolecular weight, it is easily understandable that lowmolecular species are preferably involved in chain ex-tending reaction.

Regarding the molecular modifications obtainedfrom reactive extrusion in terms of chain length anddistribution, it is reasonable to expect some evolutionsof the melt properties. Rheological experiments havethus been performed on neat and modified PLAs tocheck for mechanical improvements in the molten state.

Melt rheology

Rheological experiments were used as a tool to evalu-ate the melt properties of the chain extended materials.Polymer structure, i.e. chain length, MWD, branching,etc..., directly influences the melt response during me-chanical solicitations. Dynamic rheology provides in-formation about the viscoelastic shear dependence andchain relaxation profile of polymer in the molten state.Since capillary extrusion involves high shear rates, thislast rheological experiment can reveal process limi-tation for high-throughput applications. In addition,elongational experiments reveal the melt behavior overmechanical stretching.

Fig. 4 The acid values of neatand chain-extended PLAs

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

PLA 3051D PLA_0 PLA_1 PLA_2 PLA_3

A.V

(m

g K

OH

/g p

oly

mer

e)`

Rheol Acta (2011) 50:613–629 619

Fig. 5 Influence of thenumber of extrusion cycle onthe acid value of PLA_3reacted at 210◦C with aresidence time of 6 min foreach cycle

0,6

0,7

0,8

0,9

1,0

1,1

1,2

1,3

1,4

0 1 2 3 4

Extrusion cycle

A.V

(m

g K

OH

/g p

oly

mer

e)`

Melt stability

The melt stability over time is the first parameter toevaluate when dealing with chain extension processes.Since the loss in melt strength is due to the polymerdegradation, it is important to evaluate the degradationtime scale for neat and extended PLA obtained fromthe Clextral twin screw reactive extrusions. Dynamicaltime sweep measurements were conducted at 200◦Cwith 5% strain amplitude at 100 rad s−1. The meltstability is depicted in Fig. 7 by the evolution of thenormalized storage modulus (G′(t)/G′(0)) with time. Itappears that chain extended PLA delays the degrada-tion process onset and reduces its kinetic. It can thus

be noticed that a loss of about 15% of the normalizedstorage modulus occurs for PLA_0 after 10 min whilePLA_3 one remains roughly unaffected.

Shear viscoelasticity in the molten state

The viscoelastic shear sensitivity of neat and modifiedPLAs has been investigated during dynamic andsteady-shear experiments. The master curves of com-plex viscosities obtained from time–temperature shiftsare presented in Fig. 8. Viscosities from steady shearexperiments are also plotted on the same graph. Thoselast data obtained from capillary extrusions performed

Fig. 6 MWD of neat andmodified PLA from reactiveextrusion performed at 210◦Con the Clextral twin screwextruder

620 Rheol Acta (2011) 50:613–629

Fig. 7 The thermal stabilityof neat (PLA_0) andextended PLA (PLA_3) at200◦C under a nitrogenatmosphere for a 5% strain at100 rad s−1

0,8

0,85

0,9

0,95

1

0 100 200 300 400 500 600 700 800

Time (s)

G'(t

)/G

'(0)

PLA_0

PLA_3

through dies with different L/D ratios have been sub-mitted to Bagley and Rabinovitch corrections.

PLA rheology is found to be highly influenced by thechain extension. At an angular frequency of 0.1 rad s−1,the complex shear viscosity is 30-fold higher for PLA_3than for PLA_0 at 180◦C. However, respective vis-cosities converge when angular frequency is increased.At this shearing level, chain orientation and thermalenergy dissipation would be responsible for these closeresults. Such feature is extremely important for theprocessability of the extended samples because typicalextrusion shear rate lies in the range of 100 up to500 s−1. In this range, the viscosities of PLA_0 andPLA_3 are separated by less than a factor 2. Increasing

the CE ratio thus enhances the shear thinning behaviorof PLA and consequently shifts the Newtonian plateauto lower angular frequencies.

It is interesting to note that the Cox–Merz rela-tion (Cox and Merz 1958) (ω ≈ γ̇ ) between dynamicand steady-shear experiments is verified for neat PLAwhereas a growing divergence occurs when chain ex-tender content is increased. As reported by Al-Hadithiet al. (1992), some melt heterogeneities such as gella-tion, cross-linking or presence of fillers could be re-sponsible for this deviation. Seyed et al. (2010) andLehermeier and Dorgan (2001) described the samephenomenon while increasing the long-chain branchedcontent in linear/branched polymer blends, respec-

Fig. 8 Viscosities fromdynamic (full symbolexperimental data/solid lineCarreau–Yasuda Fit) andsteady (open symbolexperimental data/dashed lineguide for the eyes) shearexperiments of neat andchain-extended PLAsperformed at 180◦C

Rheol Acta (2011) 50:613–629 621

Table 5 Carreau–Yasuda parameters for neat and extended PLA at 180◦C

Sample ηo (Pa s) ωo (rad s −1)a θ(s) m n

PLA_0 1.90 × 103 27.5 0.04 0.9 0.62PLA_1 1.07 × 104 5.5 × 10−2 0.12 0.39 0.43PLA_2 6.05 × 104 5.2 × 10−4 0.98 0.31 0.33PLA_3 5.14 × 105 1.4 × 10−6 9.19 0.23 0.28

aη(ωo) = 0.8 ηo

tively, for PP and PLA. This last result could be an indi-cator of the presence of long-chain branched structurein our modified PLAs.

The solid lines in Fig. 8 correspond to the fits ofthe dynamic data obtained from the Carreau–Yasudamodel described in Eq. 1. Such a model allows a quan-tification of the melt rheological behavior by providingparameters which describe the chain relaxation process(Table 5).

η (ω) = η0[1 + (θ.ω)m] n−1

m (1)

As noticed above for low angular frequencies, thezero shear viscosity (η0) drastically increases from neat(PLA_0) to highly chain extended (PLA_3) material.Chain relaxation is the main parameter governing thismelt property. The characteristic relaxation time (θ),evaluated from this fitting, increases with the chainextender level. PLA_0 relaxation time differs fromPLA_3 one by a factor 200. Similar tendencies forbranched polycarbonate have been reported by Liuet al. (2004).

As described above for the MWD analysis, a shoul-der relevant to high molar mass is generated duringchain extension and get larger by increasing the CEcontent. The relaxation time is in the same time hugely

increased from PLA_0 to PLA_3. This characterizes anunambiguous influence of this new population on thechains relaxation even for a low content of the chainextender.

The critical shear rate (ω0) is described by Graessley(1975) as the onset of the shear rate dependence withthe viscosity. This parameter is mainly influenced bythe polydispersity as shown by Muñoz-Escalona et al.(1999) on monomodal and bimodal polyethylene whichis in a good agreement with the present data. As de-termined from the MWD analysis, the polydispersityis increasing with the chain extension process and re-sults in a reduced ω0 value. The Newtonian/Power lawtransition factor (m) and the power law index (n) arelogically lowered with the increasing shear sensitivity.

Based on the work of Mead (1994) and Honerkampand Weese (1993), the Orchestrator software calculatesthe linear relaxation spectrum H(λ) according to Eq. 2.

G∗(ω) =+∞∫

−∞

H (λ) iωλ

λ (1 + iωλ)dλ (2)

The weighted relaxation spectra λ.H(λ) presentedin Fig. 9 reflect the time distribution of chainsrelaxation for neat and chain extended PLAs. Thislast extrapolation corroborates the observations made

Fig. 9 Weighted relaxationspectra of neat and chainextended PLAs at 180◦Cunder 5% strain

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0,001 0,01 0,1 1 10 100 1000 10000λ (s)

H(λ

) . λ

(P

a.s)

PLA_1PLA_0

PLA_2

PLA_3

622 Rheol Acta (2011) 50:613–629

Fig. 10 Storage modulus as afunction of shear rate for neatand extended PLAs under5% strain at 180◦C

1,E+00

1,E+01

1,E+02

1,E+03

1,E+04

1,E+05

1,E+06

0,01 0,1 1 10 100 1000ω (rad.s-1)

Sto

rag

e m

od

ulu

s G

' (P

a)

PLA_0PLA_1PLA_2PLA_3

earlier by the Carreau–Yasuda fit. By gathering SECchromatograms and rheological relaxation spectra, it isobvious that even a small amount of high-molecular-weight population considerably enlarges the responsetime of the melt. Dorgan and Joshua demonstratedan equivalent phenomenon when comparing linearPLA with 6-armed PLA stars (Dorgan and Joshua1999). The bimodal profile observed on MWD plotsis here well reflected in terms of relaxation timedistribution. Two main relaxation peaks can be clearlyidentified for PLA_2 and PLA_3. The same doubletime relaxation distribution has already been observedby Wood-Adams and Costeux for long-chain branchedPE (Wood-Adams and Costeux 2001). Those bimodalspectra are broadly distributed which could either be at-tributed to the polydispersity of the extended materialsand to the chain entanglement of species with different

relaxation time scales. The modification of the chaintopology induced by chain extension would shift therelaxation mechanism from the reptation mode to thefluctuation and stress release mode (Seyed et al. 2010).

As the storage modulus is sensitive to the melt elas-ticity of a polymer network, Fig. 10 reports G′ valuesfor neat and extended PLAs as a function of the shearrate at 180◦C under 5% strain. As described in variousstudies (Nam et al. 2005; Park et al. 2006), increas-ing the extending/branching level results in higher G′(ω) values compared to linear counterpart especiallyfor low angular frequencies. Storage modulus becomesless shear sensitive when CE content is increased thusrevealing a cohesive network formation. However, asalready observed for the viscosity, the storage modulustends towards the same value for higher frequencies.At this shear level, the molecular weight distribution

Fig. 11 Evolution of thedynamic shear viscosity atω = 0.1 rad s−1as function oftemperature for neat andmodified PLAs. Solid line isthe Arrhenius fit used for theflow activation energycalculation

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

0.00209 0.00214 0.00219 0.00224 0.00229 0.00234

1/T (K-1)

η [ ω

=0.

1 ra

d.s-1 ]

(P

a.s)

Rheol Acta (2011) 50:613–629 623

Table 6 Flow activation energy parameters from Arrhenius plots of data obtained at ω = 0.1 rad s−1for neat and modified PLAs

Sample A0(Pa s) Ea/R(K) Ea(kJ mol−1) Fit accuracy [R2]

PLA_0 5 × 10−8 11060 91.95 0.9985PLA_1 4 × 10−5 8715 72.45 0.9991PLA_2 1.9 × 10−3 7442 61.88 0.9897PLA_3 2.93 × 10−1 5560 46.23 0.9913

constitutes the governing parameter (Han and Jhon1986) and the influence of the chain structure is min-imized. As reported in the SEC analysis, the chainextended materials are characterized by some bimodalprofiles centered on similar peaks values which couldexplain the convergence to close storage modulus val-ues.

Melt f low behavior

The modification of the polymer chain structure in-volves some rheological improvements in terms ofshear sensitivity. As conventional melt processing is acontinuous process, it is important to investigate themelt flow properties of our PLAs. One of the main in-teresting parameter is the flow activation energy whichcan be calculated from oscillatory shear rheology. Thefirst part of this paragraph is dedicated to this studywhile the second one is focused on the rod stabilityduring capillary extrusion under different conditions.

Melt f low activation energy Melt processing is gov-erned by the flow properties of the polymer in themolten state. Dynamic shear experiments performed attemperatures of 160◦C, 180◦C and 200◦C allow the de-termination of the flow activation energy (Ea) of neat

and modified PLAs. Based on an Arrhenius equation,this main flow property is conventionally determinedby the following Eq. 3 at zero shear rate i.e. when theNewtonian plateau is reached.

η0 (T) = A0 × exp(

Ea

RT

)(3)

where η0 (Pascal second) is the zero shear viscosity,A0 (Pascal second) is the pre-exponential factor, Ea isthe flow activation energy (Joules per mole), R is thegas constant (R = 8.314 J mole−1 K−1) and T is thetemperature (Kelvin).As we only have an estimationof the zero shear viscosity from the Carreau–Yasudafit and as this last model has been discussed for thedetermination of such a parameter for branched mate-rial (Christopher et al. 2004), this study was made for alow angular frequency of 0.1 rad s−1where experimentaldata exist. The evolution of η (0.1 rad s−1) for the neatand modified PLAs as a function of 1/T is reportedin Fig. 11. The Arrhenius fit allows the determinationof Ea for each sample, and results are summarizedin Table 6. Unexpected results reveal a reduction ofthe flow activation energy with the increase of the CEcontent. A linear relation exists between Ea and theCE content since a drop of −14.8 kJ mol−1/wt.% CEis determined. For instance, PLA_0 presents an Ea of

Fig. 12 Apparent flow curvesfor neat and modified PLAsextruded at 180◦C through adie with an L/D = 30. Rodedefect onsets are indicated byarrows

10000

100000

1000000

10 100 1000 10000

Apparent shear rate (s-1)

Ap

par

ent

shea

r st

ress

(P

a)

Stability transition

PLA_0

PLA_1

PLA_2

PLA_3

624 Rheol Acta (2011) 50:613–629

91.95 kJ mol−1while PLA_3 oneis only 46.23 kJ mol−1.As Ea is reported to be independent of Mw, this clearlyindicates that the linear structure of neat PLA hasnot only been extended but also branched. The usualconsequences of a chain branching process is the in-crease of the flow activation energy as reported bydifferent authors mainly on polyolefins (Savvas 2000;Wood-Adams and Costeux 2001). Although this lastphenomenon is widely reported in literature, some dis-crepancies exist (Munari et al. 1989; Lehermeier andDorgan 2001; Mc Kee et al. 2005). Lehermeier and al.and Munari et al. showed that Ea was quite unaffectedby the branching process for PLA and PET, respec-tively. The chain structure topology like branch densityand length in comparison with the backbone structureis usually presented to be a key factor explaining thisEa deviation. In our case, the chain stacking and thebranched length could be involved in this uncommonevolution of flow activation energy with chain exten-

sion. One other explanation could come from the polarinteractions between chain entities (i.e. hydrogen bond-ing). As seen previously, the chain extension reducesthe carboxyl content of the modified PLA. Such areduction would decrease those weak bonding fromneat to modified PLAs. As reported by Wool (2005) foracetylated triglyceride, increasing the polar interactionsby means of acetylation leads to a higher Ea. This iseasily understandable since an increase in temperaturewould disrupt those intermolecular interactions. Hsiehet al. (2001) used the same assumption to describe theEa evolution of hyperbranhed polyesters with variousmolecular weights. In our case, the modified PLAswould be less sensitive to the thermal variation thantheir neat counterpart due to reduced polarity. To thedifference of Wool’s observations (Wool 2005), thePLA viscosity does not decrease with the reduction ofpolar interactions (i.e. COOH content) since the chainextension simultaneously reinforces the melt strength.

Fig. 13 Rod shape of neat and chain extended PLAs extruded at 180◦C through a L/D = 30 die at different apparent shear rates

Rheol Acta (2011) 50:613–629 625

In the same way, hyperbranched polyesters used byHsieh et al. (2001) have also their molar mass increasedwhile Ea decreased. Müller et al. also reported similarbehaviour for polybutadiene functionalized with polarstickers (phenyl urazole contact) (Müller et al. 1995).Tailoring the degree of functionalization is there usedto control the flow activation energy of such a thermoreversible network.

Melt f low stability The flow behaviour of neat andchain extended PLAs have been studied at variousshear rates during the capillary extrusions. Apparentshear stress versus apparent shear rate is presentedin Fig. 12. Rod defects are observed for the chainextended samples as illustrated in Fig. 13 and the ap-parent shear rates at which defects appear are reportedin Fig. 12 by some arrows. This critical shear rate isreduced when chain extender is increased. This phe-nomenon could explain the melt pressure oscillationsobserved for PLA_2 and PLA_3 during the reactionmonitoring where stick and slips at the barrel wallwere evocated. The swelling at the die is getting more

and more important with increasing the chain extendercontent and is an evidence of the improvement in themelt elasticity as previously reported.

On the other hand, the critical apparent shear stressseems to be weakly influenced by the CE content.This last parameter is used by Kim and Dealy as agross melt fracture criterion for polyethylene (Kim andDealy 2002a, b). They demonstrated for various PEthat the critical shear stress increases with increasinglong-chain branching (Kim and Dealy 2002a, b). Theopposite tendency is observed in our case since thecritical shear stress slightly decreases with the increas-ing chain extending ratio. A different branch structurecould explain the divergence of results.

This rheological characterization for high shear ratebrings some additional information about the structureand the processability of the modified PLAs. As re-ported in the previous part about dynamic rheology,the improved shear thinning is identified as a processingaid for such extended materials at moderate shear rate.However, capillary extrusions highlight some flow limi-tation at higher shear rate due to chain extension. Such

1.E+04

1.E+05

1.E+06

1.E+07

1.E+04

1.E+05

1.E+06

1.E+07

1.E+04

1.E+05

1.E+06

1.E+07

1.E+04

1.E+05

1.E+06

1.E+07

0.1 1 10 100 0.1 1 10 100

0.1 1 10 100 0.1 1 10 100

Time (s)

?e+

(P

a.s

)

Time (s)

?e+

(Pa.

s)

Time (s)

?e

+ (

Pa.

s)

Time (s)

?e

+ (P

a.s)

PLA_0 PLA_1

PLA_2 PLA_3

Fig. 14 Evolution of the uniaxial elongational viscosities of neat and chain extended PLAs as a function of time for variousstrain ratesat 160◦C

626 Rheol Acta (2011) 50:613–629

melt process also involves an elongational componentwhich is assumed to impact on the flow properties.Next part thus deals with the melt stretch ability of themodified materials.

Elongational viscoelasticity in the molten state

The melt strength is often reported as the elastic behav-ior of a polymer under shear. The previous section high-lights this kind of melt reinforcement provided by chainextension. In terms of processing ability, the melt resis-tance during stretching is more commonly employed.A link between these two specific properties has beenproposed by Cogswell (1972) by giving a relationshipbetween the elongational viscosity and the pressure atthe die during capillary extrusion experiments whichis governed by the melt elasticity. In this study, a uni-axial elongational rheometer was used to evaluate themechanical behavior of the samples under stretching inthe molten state. The elongational viscosities obtainedat 160◦C with strain rates (ε̇) ranging from around 0.1up to 1 s−1 are displayed in Fig. 14. The main observa-tion is that the chain extended PLAs display a strainhardening behavior under the investigated stretchingconditions. In the opposite, the neat PLA maintains alinear response over time for all the investigated strainrates. This is in a good agreement with the typicalresponse of a linear polymer during stretching.

The critical strain (εSH onset) for the onset of strainhardening is shifted to a lower value when the amountof CE is increased. Strain hardening thus appears ata Hencky strain of 1.06 for PLA_3 while a Henckystrain of 2 is required for the strain hardening onsetof PLA_1 at a strain rate of around 0.07 s−1. Theaforementioned increase in the relaxation time spectrawith chain extension could explain this earlier strainhardening. Widening the melt time response would thusreduce the chain orientation dynamic during stretchingleading to a reinforcement of the mechanical response.Stadler et al. (2009) worked on bimodal LDPE andassigned the observed strain hardening to both wideMWD and long-chain branching content. In the presentcase, we could obviously attribute this phenomenonto the MWD enlargement due to chain extension butwithout specific data about the chain extension topol-ogy (long-chain branching, short-chain branching, starbranching...). The next part will thus use these rheolog-ical data to investigate the chain structure topology ofthe modified PLAs.

Investigation of the chain extended structure

Trinkle et al. (2002) proposed a way to characterizethe polymer chain structure based on the reduced Van-Gurp-Palmen Plot. This is a plot of the loss angle (δ)as a function of the reduced magnitude of the complexmodulus |G*| = G*/G0

N. The resulting curve profile is

Fig. 15 ReducedVan-Gurp-Palmen plots ofneat and chain extendedPLAs obtained from mastercurves for a referencetemperature of 180◦C

Rheol Acta (2011) 50:613–629 627

independent of the type of polymer in use and can beused to describe the chain topology (i.e. long-chain,H-shaped or star-shaped branched structure) from theprofiles of model polymer proposed by Trinkle etal. (2002). This method has been conducted on ourrheological data in order to more deeply investigatethe modified PLAs chain structure. As illustrated inFig. 15, a transition exists between the neat PLA andthe modified samples. The rheological data of PLA_0result in a curve typical from linear polymers with agentle bend and a loss angle reaching 90◦C (Savvas2000; Trinkle et al. 2002; Fleury et al. 2004; Barrosoand Maia 2005). For the modified PLAs, the VanGurp Palmen plots are gradually shifted towards lowerphase angle values and none plateau at 90◦ can bereached like for PLA_0. This kind of flat profile hasbeen well identified by different authors to characterizethe presence of long-chain branching in the case ofbranched PE (Savvas 2000; Fleury et al. 2004; Barrosoand Maia 2005). The molar mass has been found to notinfluence the Van Gurp Palmen plot shape while thepolydispersity could also reduce the phase angle range(Savvas 2000). However in our case, the phase angleis drastically reduced whereas the polydispersity for atleast PLA_0, PLA_1 and PLA_2 remains quite similar.This would tend to indicate that the level of long-chainbranching grows with the increase of CE content.

Conclusions

PLA was chain extended through a reactive extrusionwith the help of an epoxide additive. This modificationwas performed in order to melt strengthen the neatpolymer with the objective to enlarge its processabilitywindow and rendering it suitable for new applicationfields. The reactive extrusion process has been moni-tored in order to optimize the chain extension processand to avoid the inherent degradation process. Asrevealed by SEC analysis, the chain extension drasti-cally modifies the molecular structure by adding a highmolecular weight shoulder to the monomodal MWDobserved for neat PLA. Such a new molecular dis-tribution results in an enlarged chain relaxation timespectrum. As a result, the melt rheology of the modifiedmaterials is found to be improved in term of thermalstability and melt strength over shearing and stretching.The shear sensitivity is thus amplified while the strainhardening appears when chain extension is performed.However, it has been shown that a too high exten-sion ratio can lead to some process limitations mainlydue to high melt elasticity. By selecting an optimized

chain extender ratio, it is thus possible to enhancethe processability of PLA for a specific process. Theknowledge of the branched structure topology stillneeds further investigation. The use of the reducedVan-Gurp-Palmen plots brought information about thetopology of modified PLAs and reveal curves specificfor long-chain branched polymers. Additional infor-mation about branch/backbone length ratio would beneeded to further investigate this chain extension.

Acknowledgements The authors would thank Pr. Jean-CharlesMAJESTE from our laboratory (Universté Jean Monnet–St Eti-enne (France)) for the extensional experiments.

References

Al-Hadithi TSR, Barnes HA, Walters K (1992) The relationshipbetween the linear (oscillatory) and nonlinear (steady-state)flow properties of a series of polymer and colloidal systems.Colloid Polym Sci 270(1):40–46

Baratian S, Hall ES, Lin JS, Xu R, Runt J (2001) Crystallizationand solid-state structure of random polylactide copolymers:poly(l-lactide-co-d-lactide)s. Macromolecules 34(14):4857–4864

Barroso VC, Maia JM (2005) Influence of long-chain branchingon the rheological behavior of polyethylene in shear andextensional flow. Polym Eng Sci 45(7):984–997

Bikiaris DN, Karayannidis GP (1996) Chain extension of poly-esters PET and PBT with two new diimidodiepoxides. II. JPolym Sci, A, Polym Chem 34(7):1337–1342

Campbell JD, Debling JA, Deyoung DJ, Giannakitsas I, DeanRSDD, Teymour F, Villalobos MA (2000) Process for pro-ducing polymers by free radical polymerization and conden-sation reaction, and apparatus and products related thereto.S. C. Johnson, Sturtevant

Christopher GR, César AG-F, Srivatsan S (2004) Extent ofbranching from linear viscoelasticity of long-chain-branchedpolymers. J Polym Sci, B, Polym Phys 42(9):1671–1684

Cogswell FN (1972) Converging flow of polymer melts in extru-sion dies. Polym Eng Sci 12(1):64–73

Cox WP, Merz EH (1958) Correlation of dynamic and steadyflow viscosities. J Polym Sci 28(118):619–622

Dorgan JR, Joshua SW (1999) Melt rheology of poly(lacticacid): entanglement and chain architecture effects. J Rheol43(5):1141–1155

Dorgan JR, Lehermeier H, Mang M (2000) Thermal and rheo-logical properties of commercial-grade poly(lactic acid)s. JPolym Environ 8(1):1–9

Drumright RE, Gruber PR, Henton DE (2000) Polylactic acidtechnology. Adv Mater 12(23):1841–1846

Fleury G, Schlatter G, Muller R (2004) Non linear rheology forlong-chain branching characterization, comparison of twomethodologies: fourier transform rheology and relaxation.Rheol Acta 44(2):174–187

Graessley W (1975) The entanglement concept in polymer rheol-ogy. Adv Polym Sci 18:1–179

Gruber PR, Hartmann MH, Kolstad JJ, Witzke DR, Brosch AL(1996) Method of crosslinking PLA. PCT 94/08 508

628 Rheol Acta (2011) 50:613–629

Han CD, Jhon MS (1986) Correlations of the first normal stressdifference with shear stress and of the storage moduluswith loss modulus for homopolymers. J Appl Polym Sci32(3):3809–3840

Haralabakopoulos AA, Tsiourvas D, Paleos CM (1999) Chainextension of poly(ethylene terephthalate) by reactive blend-ing using diepoxides. J Appl Polym Sci 71(13):2121–2127

Henry EW, Chiu TH, Nyilas E, Brushart TM, Dikkes P, SidmanRL (1985) Nerve regeneration through biodegradable poly-ester tubes. Exp Neurol 90(3):652–676

Honerkamp J, Weese J (1993) A nonlinear regularizationmethod for the calculation of relaxation spectra. Rheol Acta32(1):65–73

Hsieh TT, Tiu C, Simon GP (2001) Melt rheology of aliphatichyperbranched polyesters with various molecular weights.Polymer 42(5):1931–1939

Incarnato L, Scarfato P, Di Maio L, Acierno D (2000) Structureand rheology of recycled PET modified by reactive extru-sion. Polymer 41(18):6825–6831

Japon S, Boogh L, Leterrier Y, Månson JAE (2000) Reactiveprocessing of poly(ethylene terephthalate) modifiedwith multifunctional epoxy-based additives. Polymer41(15):5809–5818

Kim S, Dealy JM (2002a) Gross melt fracture of polyethylene. I:a criterion based on tensile stress. Polym Eng Sci 42(3):482–494

Kim S, Dealy JM (2002b) Gross melt fracture of polyethylene.II: effects of molecular structure. Polym Eng Sci 42(3):495–503

Labrecque LV, Kumar RA, Davé V, Gross RA, McCarthy SP(1997) Citrate esters as plasticizers for poly(lactic acid). JAppl Polym Sci 66(8):1507–1513

Lamnawar K, Maazouz A (2006) Rheological study of mul-tilayer functionalized polymers: characterization of inter-diffusion and reaction at polymer/polymer interface. RheolActa 45(4):411–424

Lamnawar K, Baudoin A, Maazouz A (2010) Interfacial reac-tion at the polymer/polymer interface in multilayer systemsprobed by linear viscoelasticity coupled to FTIR and NMRmeasurements. Eur Polym J 46(7):1604–1622

Lehermeier HJ, Dorgan JR (2001) Melt rheology of poly(lacticacid): consequences of blending chain architectures. PolymEng Sci 41(12):2172–2184

Lipinsky ES, Sinclair RG (1986) Is lactic acid a commodity chem-ical? Chem Eng Prog 82:26–32

Liu C, Li C, Chen P, He J, Fan Q (2004) Influence of long-chain branching on linear viscoelastic flow properties anddielectric relaxation of polycarbonates. Polymer 45(8):2803–2812

Ljungberg N, Wesslén B (2002) The effects of plasticizers on thedynamic mechanical and thermal properties of poly(lacticacid). J Appl Polym Sci 86(5):1227–1234

Ljungberg N, Wesslén B (2003) Tributyl citrate oligomers asplasticizers for poly (lactic acid): thermo-mechanical filmproperties and aging. Polymer 44(25):7679–7688

Ljungberg N, Wesslen B (2005) Preparation and propertiesof plasticized poly(lactic acid) films. Biomacromolecules6(3):1789–1796

Lopez Arraiza A, Sarasua JR, Verdu J, Colin X (2007) Rhe-ological behavior and modeling of thermal degradation ofpoly(e-caprolactone) and poly(L-Lactide). Polym ProcessXXII 5:389–394

Lunt J (1998) Large-scale production, properties and commercialapplications of polylactic acid polymers. Polym Degrad Stab59(1–3):145–152

Martin O, Avérous L (2001) Poly(lactic acid): plasticization andproperties of biodegradable multiphase systems. Polymer42(14):6209–6219

Mc Kee MG, Unal S, Wilkes GL, Long TE (2005) Branchedpolyesters: recent advances in synthesis and performance.Prog Polym Sci 30(5):507–539

Mead D (1994) Numerical interconversion of linear viscoelasticmaterial functions. J Rheol 38(6):1797

Mihai M, Huneault MA, Favis BD (2010) Rheology and extru-sion foaming of chain-branched poly(lactic acid). Polym EngSci 50(3):629–642

Müller M, Seidel U, Stadler R (1995) Influence of hydrogenbonding on the viscoelastic properties of thermoreversiblenetworks: analysis of the local complex dynamics. Polymer36(16):3143–3150

Munari A, Pezzin G, Pilati F, Manaresi P (1989) Rheologi-cal characterization of highly branched poly(ethylenetereph-thalate). Rheol Acta 28(1):25–29

Muñoz-Escalona A, Lafuente P, Vega JF, Santamaría A (1999)Rheology of metallocene-catalyzed monomodal and bi-modal polyethylenes. Polym Eng Sci 39(11):2292–2303

Nam GJ, Yoo JH, Lee JW (2005) Effect of long-chain branchesof polypropylene on rheological properties and foam-extrusion performances. J Appl Polym Sci 96(5):1793–1800

Nguyen QT, Japon S, Luciani A, Leterrier Y, Månson JAE(2001) Molecular characterization and rheological proper-ties of modified poly(ethylene terephthalate) obtained byreactive extrusion. Polym Eng Sci 41(8):1299–1309

Palade LL, Lehermeier HJ, Dorgan JR (2001) Melt rheology ofhigh L-content poly(lactic acid). Macromolecules 34:1384–1390

Park HE, Dealy J, Münstedt H (2006) Influence of long-chainbranching on time-pressure and time-temperature shift fac-tors for polystyrene and polyethylene. Rheol Acta 46:153–159

Pilla S, Kim SG, Auer GK, Gong S, Park CB (2009) Microcellularextrusion-foaming of polylactide with chain-extender. PolymEng Sci 49(8):1653–1660

Randall JR, Cink K, Smith J (2006) Branched polylactic acidpolymers and methodof preparing the same

Savvas GH (2000) Long chain branching and polydispersityeffects on the rheological properties of polyethylenes. PolymEng Sci 40(11):2279–2287

Schulze JS, Lodge TP, Macosko CW, Hepperle J, Münstedt H,Bastian H, Ferri D, Groves DJ, Kim YH, Lyon M, SchweizerT, Virkler T, Wassner E, Zoetelief W (2001) A comparisonof extensional viscosity measurements from various RMErheometers. Rheol Acta 40(5):457–466

Seyed HT, Pierre JC, Abdellah A (2010) Rheological propertiesof blends of linear and long-chain branched polypropylenes.Polym Eng Sci 50(1):191–199

Stadler F, Kaschta J, Münstedt H, Becker F, Buback M (2009)Influence of molar mass distribution and long-chain branch-ing on strain hardening of low density polyethylene. RheolActa 48(5):479–490

Tanaka Y, Bauer RS (1988) Epoxy resins—chemistry and tech-nology. CRC, New York

Trinkle S, Walter P, Friedrich C (2002) Van Gurp-Palmen PlotII—classification of long-chain branched polymers by theirtopology. Rheol Acta 41(1):103–113

Tuominen J, Kylmä J, Seppälä J (2002) Chain extending of lacticacid oligomers. 2. Increase of molecular weight with 1,6-hexamethylene diisocyanate and 2,2′-bis(2-oxazoline). Poly-mer 43(1):3–10

Rheol Acta (2011) 50:613–629 629

Vert M, Schwarch G, Coudane J (1995) Present and Future ofPLA Polymers. J Macromol Sci, Part A 32(4):787–796

Villalobos MA, Awojulu A, Greeley T, Turco G, Deeter G (2006)Oligomeric chain extenders for economic reprocessing andrecycling of condensation plastics. Energy 31:3227–3234

Wehrenberg RH (1981) Lactic acid polymers: strong, degradablethermoplastics. Mater Eng 94(3):63–66

Wood-Adams P, Costeux Sp (2001) Thermorheological behav-ior of polyethylene: effects of microstructure and long-chainbranching. Macromolecules 34(18):6281–6290

Wool RP (2005) Properties of triglyceride-based thermosets. Bio-based polymers and composites. Academic, Burlington, pp202–255

Yingwei D, Salvatore I, Ernesto Di M, Luigi N (2005) Reactivelymodified poly(lactic acid): properties and foam processing.Macromol Mater Eng 290(11):1083–1090

Yolles S (1978) Time-release depo for anticancer drugs: releaseof drug covalently bonded to polymers. J Parenter DrugAssoc 32(4):188

Yolles S, Leaffe T, Ward L, Boettner F (1976) Controlled re-lease of biologically active drugs. B Parenteral Drug Assoc30(6):306–312

Zhou ZF, Huang GQ, Xu WB, Ren FM (2007) Chain exten-sion and branching of poly(L-lactic acid) produced by reac-tion with a DGEBA-based epoxy resin. Express Polym Lett1(11):734–739