Terminal viscous and elastic properties of linear ethene∕α-olefin copolymersFlorian J. Stadler and Helmut Münstedt Citation: J. Rheol. 52, 697 (2008); doi: 10.1122/1.2892039 View online: http://dx.doi.org/10.1122/1.2892039 View Table of Contents: http://www.journalofrheology.org/resource/1/JORHD2/v52/i3 Published by the The Society of Rheology Related ArticlesHigh frequency linear rheology of complex fluids measured from their surface thermal fluctuations J. Rheol. 57, 441 (2013) Is shear banding a metastable property of well-entangled polymer solutions? J. Rheol. 56, 1413 (2012) Microrheology, microstructure, and aging of physically cross-linked poly(vinyl alcohol)/poly(ethylene glycol)blends J. Rheol. 56, 797 (2012) A visco-hyperelastic formulation for the rheology of immiscible blends J. Rheol. 56, 767 (2012) Microstructure and deformation micromechanisms of concentrated fiber bundle suspensions: An analysiscombining x-ray microtomography and pull-out tests J. Rheol. 56, 593 (2012) Additional information on J. Rheol.Journal Homepage: http://www.journalofrheology.org/ Journal Information: http://www.journalofrheology.org/about Top downloads: http://www.journalofrheology.org/most_downloaded Information for Authors: http://www.journalofrheology.org/author_information

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Terminal viscous and elastic properties of linearetheneÕ�-olefin copolymers

Florian J. Stadlera) and Helmut Münstedtb)

Institute of Polymer Materials, Friedrich-Alexander-UniversityErlangen-Nürnberg, Martensstr. 7, 91058 Erlangen, Germany

(Received 27 February 2007; final revision received 11 February 2008�

Synopsis

everal linear ethene/�-olefin copolymers with butene, hexene, octene, dodecene, octadecene, andexacosene as comonomers were characterized in linear-viscoelastic shear flow. Creep and creepecovery measurements were used to obtain the zero shear-rate viscosity �0 and the steady-statelastic recovery compliance Je

0. The correlation between the zero shear-rate viscosity and theeight average molar mass �0�Mw� established for metallocene catalyzed high densityolyethylene �mHDPE� was found to be obeyed by all samples containing comonomer contents upo 29 wt%. For the linear steady-state elastic compliance Je

0 an increase with growing molar mass

w or comonomer content wc was observed. © 2008 The Society of Rheology.DOI: 10.1122/1.2892039�

. INTRODUCTION

During recent years much attention has been paid to the influence of long-chainranches on rheological properties. For the assessment of their properties, the influence ofolar mass Mw and molar mass distribution �MMD� on rheological properties has to be

eparated from that of branching. Therefore, it is important to know the effect of Mw andMD on the rheological behavior of linear polymers.Especially the dependence of the zero shear-rate viscosity �0 on the mass-average

olar mass Mw has gained growing interest during recent years, as a deviation from thatorrelation, is a good indication of long-chain branching �e.g., Vega et al. �1998�; Malm-erg et al. �1999�; Wood-Adams et al. �2000�; Gabriel and Münstedt �2002�; Piel et al.2006a�; Stadler et al. �2006c��. In contrast to other rheological properties, which arenfluenced by the existence of long-chain branches and a broadening of the molar massistribution, the relationship �0�Mw� has been shown to be independent of the molar massistribution for polystyrene �PS� �e.g., Münstedt �1980�� and linear polyethylene �e.g.,aun and Münstedt �1983�; Carella et al. �1984�; Münstedt and Auhl �2005�; Stadler et al.

2006b��, for example, but is significantly influenced by the presence of LCBs �e.g.,ünstedt �1986�; Wood-Adams �1998�; Janzen and Colby �1999�; Shroff and Mavridis

1999�; Gabriel �2001��.

�Present address: Unité de Physique et de Chimie des Hauts Polymères, Université catholique de Louvain,Croix du Sud, 1, B-1348 Louvain-la-Neuve, Belgium.

�

Author to whom correspondence should be addressed; electronic mail: helmut.muenstedt@uni-erlangen.de

2008 by The Society of Rheology, Inc.697. Rheol. 52�3�, 697-712 May/June �2008� 0148-6055/2008/52�3�/697/16/$27.00

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The dependence of the zero shear-rate viscosity �0 on the mass average of the molarass Mw of many linear polymers can be described by the well-known relationship �e.g.,erry �1980��

�0 = K1 · Mw� for Mw � Mc, �1�

�0 = K2 · Mw for Mw � Mc, �2�

nd

Mc � �2 ¯ 3� · Me. �3�

� is reported to lie between 3.4 and 3.6. K1 and K2 are parameters dependent on theolymer type and the temperature, Mc is a critical molar mass which is approximatelywo to three times the entanglement molar mass Me, depending on the polymer �Fetters etl. �1999b��. According to the literature Mc is around 3000 g /mol for polyethyleneGraessley and Edwards �1981�; Stadler et al. �2006b��.

As ethene/�-olefin copolymers are gaining more and more technical importance, theirheological properties are of great interest, particularly in the light of metallocene cata-ysts, which allow a more regular incorporation of comonomers than the older Ziegler–atta-catalysts. Of high fundamental relevance in this aspect is the question how

omonomers of higher molar mass than those used in practice today influence rheologicalroperties.

Utracki and Schlund �1987� found that the viscous and elastic properties of ZN-LDPEs are unaffected by the type and content of the comonomer. However, they only

nvestigated grades with densities down to 0.918 g /cm3 with butene, hexene, and octenes comonomers, which correspond to a maximum of 5 mol % comonomer. Wood-Adams1998� did not find an influence of the comonomer content �butene� on the dynamiciscosities even at comonomer contents up to 21 wt% �12 mol % �.

The questions remain, whether �-olefins distinctly longer than octene1 have an influ-nce on the �0-Mw correlation and, which is the limit of the comonomer content, leavinghe rheological behavior unaffected.

The question whether in general short-chain branches of ethene/�-olefin copolymersnfluence the �0-Mw correlation is of great interest, as most of the commercially availableinear mPEs and LCB-mPEs �long-chain branched metallocene catalyzed polyethylene�ontain sizable amounts of comonomers. This interest is twofold. If the type and contentf the comonomer would not influence the �0-Mw relationship valid for PE homopoly-ers, it could be used for the determination of Mw from �0. Moreover, a deviation from

his relation would give a hint to the existence of long-chain branches in short-chainranched ethene copolymers.

In this publication samples with comonomer lengths up to 26 C �hexacosene� andeight comonomer contents wc up to 29 wt% are investigated, which are significantlyigher than those of commercial products.

The main aims of this article are to compare the molar mass dependence of the zerohear-rate viscosity of linear high density polyethylene �HDPE� with that of thethene/�-olefin copolymers and to investigate how the elastic recoverable compliance Je

0

s influenced by the presence of short-chain branches.The linear steady-state elastic compliance Je

0 is often not easy to measure because ofhe long measuring times necessary to reach the steady state. Moreover, this quantity is

Octene is the longest comonomer used commercially today.

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ot straightforward to interpret with respect to molecular quantities, as it dependstrongly on the molar mass distribution and the branching architecture of the molecules.ery few datasets have been published for the linear steady-state elastic compliance Je

0 ofinear mPE. So far, only Gabriel and Münstedt �1999� and Stadler et al. �2006c� showedata of this quantity for linear mPE �more data have been published on LCB-mPE�.urthermore, no systematic investigations are known on the molar mass dependence of

he linear steady-state elastic compliance at constant MMD �except for monodisperseamples�. This can mainly be attributed to the great experimental demands of performingorrect creep recovery tests and the lack of availability of sample series with the sameMD but well defined other parameters.

I. EXPERIMENT

. Materials

The samples investigated were synthesized using metallocene catalysts. The number inhe designation stands for the length of the comonomer used. While butene �4 C�, hexene6 C�, and octene �8 C� are used commercially today in ethene/�-olefin copolymersLLDPEs�, the longer comonomers dodecene �12 C�, octadecene �18 C�, and hexacosene26 C� can be found as laboratory samples, only.

The syntheses of the ethene/�-olefin copolymers designated with F �see Table I� wereublished by Kaminsky et al. �2005� �F8C, F18C, F26C� and Piel et al. �2006b� �F12F,18F, F26F�. For these samples the catalysts system �Ph2C�2,7-di-tertBuFlu��Cp��rCl2 /MAO was used �the molecular structure of this catalyst can be found, e.g., in Pielt al. �2006b��. Some rheological data on these samples are published by Stadler et al.2006a, 2006c, and 2007�. The other products are designated with L. They are commer-ially available metallocene catalyzed LLDPEs.

. Measurement of the comonomer content

The measurement of the molar comonomer content nc was carried out according tone of the three following methods, which are found to give very similar results

ABLE I. Molecular data of the linear ethene/�-olefin copolymers.

ameMw

�kg/mol�Mw /Mn

���Mw

bb

�kg/mol�l

�CnH2n�bnc

�mol %�cwc

�wt %�dsc

�wt %�e Method

8 86 2.1 84 8 about 1a about 3.9a 2.9a DSC4 114 2.0 106 4 6.8 12.7 6.4 Melt-state NMR6 115 2.2 102 6 5.9 15.8 10.6 FTIR8C 153 2.0 141 8 2.7 10.0 7.5 Melt-state NMR18C 161 1.9 136 18 2.2 16.8 15.0 Melt-state NMR26C 174 2.1 136 26 2.3 23.4 21.6 Melt-state NMR12F 210 2.0 179 12 3.4 17.4 14.5 Solution NMR18F 216 1.9 177 18 2.7 20.0 17.8 Solution NMR26F 234 2.1 170 26 3 28.7 26.5 Solution NMR

Approximation of comonomer content from melting point and crystallinity �Stadler et al. �2005��.Comonomer length in number of carbon atoms.Molar comonomer content.Weight comonomer content.Side chain content.

�10% �:

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Melt-state nuclear magnetic resonance �NMR� spectroscopy described in detail byKlimke et al. �2006�.Solution NMR described by Piel et al. �2006b�.Fourier transform infrared �FT-IR� spectroscopy according to the method described byKraft �1996�.

For the sample L4 measurements by FTIR �nc=7.5 mol % � and melt-state NMR �nc

6.9 mol % � were carried out. The results of the two methods are comparable. Theamples F8C, F18C, and F26C were characterized by both NMR methods �solution stateMR: Kaminsky et al. �2005�; melt-state NMR: Klimke et al. �2006�; Stadler et al.

2006c��. For these samples the highest differences between the two NMR methods were.4 mol %. The composition of the samples is listed in Table I.

. SEC-MALLS

Molar mass measurements were carried out by means of a high temperature sizexclusion chromatograph �SEC, Waters, 150C� equipped with refractive index and infra-ed �PolyChar, IR4� detectors. All measurements were performed at 140 °C using 1,2,4-richlorobenzene as the solvent. The separation was performed by a set of 4 SEC-columns3 Shodex UT806M, 1 Shodex UT807�. The high temperature SEC was coupled with aultiangle laser light scattering �MALLS� apparatus �Wyatt, DAWN EOS�. Details of the

xperimental SEC-MALLS setup and the measuring conditions were previously pub-ished by Stadler et al. �2006b�.

. Rheology

The samples were compression molded into circular disks of 25 mm in diameter andround 1 mm in height. Antioxidative stabilizers �0.5 wt% Irganox 1010 and 0.5 wt%rgafos 38 �Ciba SC�� were added to the laboratory samples. The commercial samplesere found to be sufficiently stable without additional stabilizer. More details are given

lsewhere �Stadler et al. �2006b��.The rheological data were acquired using a Bohlin Gemini and a TA Instruments

R-G2 with a 25 mm parallel plate geometry operated at 150°C. Depending on theolar mass Mw of the sample, the creep stress � was chosen between 2 and 20 Pa. For all

amples, it was proven that creep tests were performed in the linear range up to the steadytate by varying the creep stress � and the creep time t0.

A detailed description of the definitions and the conditions necessary to determineinear and steady creep recovery data is given by Gabriel et al. �1998�. Some of the creepata presented here were confirmed by measurements with the magnetic bearing rheome-er �MBR� �Link and Schwarzl �1985��. The MBR and the AR-G2 have several advan-ages over conventional air bearing rheometers, as the apparatus inherent friction is ratherow �see also Gabriel and Kaschta �1998��.

Since the acquisition of creep recovery curves requires quite a long time �the longestests took about two days�, for samples with high terminal relaxation times it was notossible to perform a comprehensive test series completely.

II. RESULTS

. Molecular characterization

The molar mass distributions of several samples are shown in Fig. 1. All the samplesn this article possess the same type of molar mass distribution �Mw /Mn=2� because a

chulz–Flory-molar mass distribution is usually observed for materials synthesized with

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701VISCOUS AND ELASTIC PROPERTIES OF LIN. LLDPEs

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etallocene catalysts. When normalizing the molar mass distributions with the peakolar mass �Fig. 1�b��, it becomes obvious that the samples have very similar molar mass

istributions and that these are rather symmetrical.The linear structure of several of the LLDPE-samples used for this study was already

hown by Gabriel and Münstedt �1999� �L4 and L6� and Stadler et al. �2006c� �F8C,18C, and F26C�. But also all the other samples follow the relation between the radius ofyration �s2�0.5 and the molar mass M valid for linear polyethylenes.

The results of the analytical characterization are given in Table I. An in-depth descrip-ion of the results of the melt-state NMR is given by Klimke et al. �2006� and theescription of the solution NMR spectra by Piel et al. �2006b�. The FTIR measurementas described by Stadler et al. �2005�.For the calculation of the weight comonomer content wc from the molar comonomer

ontent nc the relation

IG. 1. �a� Molar mass distribution dW /d log M as a function of the weight average molar mass MLS deter-ined by light scattering for several samples, �b� molar mass distribution dW /d log M normalized by the peakolar mass Mpeak for the samples of �a�.

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wc =nc · l

nc · �l − 2� + 2�4�

s used,2 where l is the length of the comonomer in numbers of carbon atoms and nc is theolar comonomer content. The variety in comonomer type and content is quite large with

hort-chain branch lengths between 2 and 24 C and weight average comonomer contents

c between 4 and 29 wt%.The molar mass of the backbone Mw

bb is determined from the comonomer content andhe molar mass by subtracting the parts of the short-chain branches sc not being includedn the backbone, according to

Mwbb = Mw · �1 − sc� �5�

ith

sc =nc · �l − 2�

nc · �l − 2� + 2. �6�

. Rheological characterization

. Zero shear-rate viscosity �0

A rheological quantity, giving some information on the molecular structure, is the zerohear-rate viscosity �0. Due to the good accuracy achievable, creep experiments in theinear range of deformation were used in this paper to determine �0. From the complianceas a function of the creep time t� the zero shear-rate viscosities were calculated accord-

ng to

limt�→�

J�t�� =t�

�0, �7�

r

log �0 = limt�→�

�log� t�

J . �8�

In Fig. 2�a� the creep compliances J for four samples of different molar masses arelotted as a function of creep time t�. The representation of these values according to Eq.8� is given in Fig. 2�b�. The terminal regime in creep was reached for the four samples.he shape of the creep functions is similar, which is a consequence of the linear structuref the molecules and their very similar molar mass distribution.

To contribute to the answer of the question how short-chain branches affect the rheo-ogical behavior, several different metallocene ethene/� olefin copolymers were analyzedith respect to the �0-Mw correlation. Their data are listed in Table II. The molar massistributions are almost identical with Mw /Mn lying between 1.9 and 2.2. In addition,alues for Je

0 are given in Table II, which are discussed in the next section.The zero shear-rate viscosities �0 as a function of the molar masses Mw are plotted

n Fig. 3. The full line represents the relation found for linear homopolyethylenes

nc was determined according to the methods described in detail in the respective publications �Stadler et al.

�2005�; Klimke et al. �2006�; Piel et al. �2006b��

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703VISCOUS AND ELASTIC PROPERTIES OF LIN. LLDPEs

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Stadler et al. �2006b��. It is evident that �0�Mw� does not depend on the type and contentf the comonomer used, as the deviations from the correlation for HDPE are statisticalnd lie within the error margin of the experiments.

IG. 2. �a� Creep compliance J as a function of creep time t� for samples with different molar masses Mw. �b�reep time divided by creep compliance as a function of creep time for the samples in �a�.

TABLE II. Rheological data of the linear ethene/�-olefin copolymers.

NameMw

�kg/mol�Mw /Mn

����0 at 150 °C

�Pa s�Je

0 at 150 °C�10−4 Pa−1�

L8 86 2.1 4,840 0.6L4 114 2.0 14,800a 0.7a

L6 115 2.2 14,200a 0.3a

F8C 153 2.0 51,230 2.2F18C 161 1.9 56,620 1.4F26C 174 2.1 86,520 1.6F12F 210 2.0 124,200 2F18F 216 1.9 145,800 3.4F26F 234 2.1 174,400 4

a

Gabriel and Münstedt �2002�.

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704 F. J. STADLER AND H. MÜNSTEDT

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The finding that the values of the copolymers with up to six carbon atoms in the sidehain come to lie on the line for linear ethene-homopolymer confirms literature dataWood-Adams �1998�; Gabriel and Münstedt �2002�� but from Fig. 3 it can moreover beoncluded that �0�Mw� of ethene/�-olefin copolymers is not influenced by the comono-ers, at least up to 26 C and 27 wt% of comonomer. This result is somewhat surprising,

s one should intuitively expect that the change in the molecular architecture, particularlyn the case of long comonomers such as hexacosene, would influence �0�Mw�.

At a first glance, the influence of the comonomer content could be regarded to beegligible for the rather small molar comonomer contents not exceeding 7 mol % at allnd lying around 3 mol % in the case of the longer comonomers. However, because ofhe length of hexacosene even such small comonomer contents as 2.3 and 3 mol %ccount for 23 and 29 wt% of comonomers, respectively �cf. Table I�. One feature of thehort-chain branches is that they are not entangled, as the lowest value found for thentanglement molar mass Me of PE in the literature is approximately 860 g /mol �corre-ponding to 60 CH2 units, �Fetters et al. �1999a��. This assumption is supported, further-ore, if one takes into account that for ethene/�-olefin copolymers higher entanglementolar masses Me, typically around 1800 g /mol, are reported �Vega et al. �1996�; Fetters

t al. �2002�; Garcia-Franco et al. �2005�; Stadler et al. �2005��.If one would assume, however, that according to these considerations only the back-

one contributes to the molecular interaction reflected by �0, the experimental findingsould not be explained. As the molar mass of the backbone Mw

bb is smaller than that of thehole molecule �cf. Table I�, �0 values below the relationship for linear polyethylenesould be expected. In order to interpret the results, an influence of the side chains on �0

as to be postulated, the physical mechanism of which has to be left open, however. Thehortening of the backbone has to be rheologically somehow compensated by the length-ning of the relaxation processes, due to not fully understood effects of the short-chainranches.

To elucidate this influence of the side chains a little bit more from the experimentalbb

IG. 3. �0-Mw correlation for ethene/�-olefin copolymers. The error bars for Mw are equivalent to an uncer-ainty of �5% in Mw. The error bars for �0 correspond to the standard deviation of several measurements of theame material. The line represents the correlation between �0 and Mw established by Stadler et al. �2006b�.

oint of view, in Fig. 4 the ratio of the measured �0 and the values �0 calculated

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705VISCOUS AND ELASTIC PROPERTIES OF LIN. LLDPEs

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ccording to Eq. �1� for the various Mwbb, determined according to Eqs. �5� and �6� and

isted in Table I, are plotted as a function of the weight concentration wc indicating arowing effect of the comonomer on �0 calculated from the molar mass of the backbone.t is interesting to note that, according to Fig. 4, this influence seems to be independent ofhe length of the comonomer but increases with its weight content.

. Linear steady-state elastic compliance Je0

The reversible deformation r�t0 , t� obtained from the creep recovery test is defined as

r�t0,t� = �t0� − �t0,t� , �9�

here t is the time of recovery and t0 the previous creep time. For t0→�, the elasticompliance Jr�t� is defined as

Jr�t� =�0

r�t�. �10�

The elastic compliance Jr�t� is shown for several samples in Fig. 5. The two samplesf lower molar mass reach a distinct plateau value, which is the linear steady-state elasticompliance Je

0, as the preceding creep test was performed in the linear range of deforma-ion. It is evident that the time to reach the plateau increases with Mw. The reason for thiss the increase of the maximum retardation time with molar mass.

In Fig. 6 Je0 for all the copolymers investigated is plotted semilogarithmically. Je

0

ncreases with the molar mass Mw despite the fact that the molar mass distributions arebout the same within the measuring accuracy of the SEC-MALLS �cf. Table I�. Thencrease of Je

0 with Mw is significantly higher than the experimental uncertainty of thexperiment.3 The relation between Je

0 and Mw for the copolymers can be described by thempirical relation

From our experience it can be stated that the measurement of Je0 above 10−4 Pa−1 is possible with an error of

about �10% while the uncertainty of elastic compliances below that limit is around �20%. This uncertainty

IG. 4. �0 /�0bb as a function of the weight comonomer content wc. The error bar of �0 /�0

bb ��20% � isquivalent to a �5% error in Mw; the error bars of wc correspond to an uncertainty of �0.1 mol % in theomonomer content.

is marked in Fig. 6 by the error bars.

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log Je0 = c1 + Mw · c2 �11�

ith c1=−4.76223 and c2=5.6417510−6 mol /g, whose parameters do not have a physi-al meaning, however. Possible explanations for this dependence are given in the con-lusions. The finding of Je

0 significantly increasing with Mw is somewhat surprising, if theiterature is taken into consideration.

For nearly monodisperse PS it was proven by Nemoto �1970�, Plazek and O’Rourke1971�, Montfort et al. �1986�, and Plazek �1975� that the elastic compliance Je

0 is almostndependent of the molar mass Mw beyond a critical molar mass Mc� of approximately05 g /mol. Plazek and O’Rourke �1971� found a very weak increase of Je

0 by a factor ofbout 1.5 with molar mass for polystyrenes between 105 and 107 g /mol. Auhl et al.2006� affirmed this molar mass independence for monodisperse polyisoprenes byynamic-mechanical measurements.

FIG. 5. Linear elastic compliance Jr�t� of L8, L4, F18C, and F12F.

IG. 6. Linear steady-state elastic compliance Je0 as a function of the weight average molar mass Mw. The full

ine describes the fit according to Eq. �11�.

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Orbon and Plazek �1979� and Münstedt �1986� report that even a small amount of aigh molecular component increases Je

0 or De0 distinctly.4 Therefore, the increase in Je

0 byfactor of 1.5 found by the group of Plazek might also be a consequence of a very weakigh molecular component, which could not be detected by the analytical methods.

Lohse et al. �2002� did not find a dependence of Je0 �determined from dynamic-

echanical data� on Mw for nearly monodisperse hydrated polybutadienes.So far not enough data of the elastic compliance Je

0 have been published for a con-incing answer to the question, whether Je

0 increases with the molar mass Mw for poly-isperse samples.

Gabriel and Münstedt �1999� found that the elastic compliance Je0 of metallocene

atalyzed polyethylenes �Mw /Mn�2� lies in the range of 510−5 Pa−1 and that it isuch higher �above 10−3 Pa−1� for samples with a broader MMD, especially for samplesith a distinct bimodality or high molecular shoulder. Besides the polydispersity long-

hain branches also increase Je0 distinctly �e.g., Gabriel and Münstedt �2002� and Stadler

t al. �2006c��.

V. EXPLANATIONS FOR THE MOLAR MASS DEPENDENCE OF THEINEAR STEADY-STATE ELASTIC COMPLIANCE Je

0

Several possible explanations for the molar mass dependence of Je0 are discussed in the

ollowing.

. High molecular weight component

In principle, a high molecular weight component could be the origin of the increasedlasticity observed. However, it is rather unlikely that the SEC-MALLS would not dis-lay such a high molecular component even at a low concentration, because the scatteringignal from MALLS depends on concentration c multiplied by the molar mass M, i.e.,M. Therefore, the sensitivity of the SEC-MALLS towards high molecular compo-ents is very pronounced in comparison to the conventional SEC. Besides that, a higholecular weight component is very unlikely from the point of polymerization kinetics.The metallocene catalysts normally lead to a narrow MMD of Mw /Mn=2 unless side

eactions occur or there is a significant change in the polymerization conditions. Suchffects are improbable, however, for the samples investigated.

The existence of a high molecular weight component can, therefore, be ruled outccording to the reaction kinetics and the MALLS measurements. However, small differ-nces in the molar mass distribution cannot be fully excluded.

. Very low degree of long-chain branching

The sensitivity of the SEC-MALLS with respect to very low degrees of long-chainranching is limited. Therefore, the existence of small amounts of long-chain branchesannot principally be excluded from the results of SEC-MALLS. The catalyst, which wassed for synthesizing all the laboratory scale copolymers, is able to generate long-chainranches, as was shown elsewhere �Piel et al. �2006a�; Stadler et al. �2006a, 2006c��. Butt could convincingly be demonstrated that the use of comonomers reduces the introduc-ion of long-chain branches significantly �Stadler et al. �2006a, 2006c��. If small amountsf LCB would be the origin of an increase of Je

0 then the effect should become smallerith growing comonomer content �see Stadler et al. �2006c��, As Fig. 7 convincingly

0

De is the linear steady-state elastic compliance in elongation.

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emonstrates, just the opposite is the case. Another experimental finding, which speaksgainst the existence of long-chain branches, is the fulfillment of �0�Mw� established forinear ethene homopolymers for all the copolymers �Fig. 3� As was shown in the litera-ure, the deviation from �0�Mw� for LCB-mHDPE �and other polymers, too� is a veryensitive indicator of long-chain branches �e.g., Vega et al. �1998�; Wood-Adams �1998�;ood-Adams et al. �2000�; Aguilar et al. �2001�; Kokko et al. �2001a, 2001b�; Gabriel et

l. �2002�; Gabriel and Münstedt �2002�; Malmberg et al. �2002�; Auhl et al. �2004�; Pielt al. �2006a�; Stadler et al. �2006a, 2006c��.

. Influence of Mw on Je0 in polydisperse samples

The third explanation is that Je0 of polydisperse melts increases with Mw indeed. From

nvestigations on linear poly�methylmethacrylate� �PMMA� and polypropylene �PP� in-estigated by one of the authors, but not published yet, such a conclusion is not veryrobable.

. Influence of the comonomer on Je0

Another possible explanation is interactions between longer side chains in polydis-erse materials causing another very weak process not being described previously initerature. Such a very weak process could be a phase boundary relaxation caused by thehase separation of the long side chains �which are not entangled because they are toohort� from the backbone. In the melt this behavior was not reported, but Piel et al.2006b� published DSC �differential scanning calorimetry� and DMTA �dynamic-echanical thermoanalysis� data showing a crystallization of the tetracosene branches of26F, thus also a partial phase separation in the melt is thinkable.

From Fig. 7, it is evident that the increase in Je0 can be related to the comonomer

ontent wc and to the comonomer type. Je0 significantly increases with the weight content.

ot evident at first glance, however is the finding that the growth of Je0 is more pro-

FIG. 7. Elastic compliance Je0 as a function of the weight comonomer content wc.

ounced for the shorter comonomer �C18� than for the longer one �C26�.

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709VISCOUS AND ELASTIC PROPERTIES OF LIN. LLDPEs

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. CONCLUSIONS

The �0-Mw-correlation valid for linear polyethylene homopolymers was found to beulfilled for all the copolymers investigated. This result is of interest from two points ofiew. First, �0�Mw� can be used for the determination of Mw of ethene/�-olefin copoly-ers, second, a deviation from this relationship gives a hint to the presence of LCB. The

esult clearly indicates that the molar mass of the backbone Mwbb is not the crucial quantity

etermining the zero shear-rate viscosity �0. Even high lengths and contents of comono-er, e.g., up to 29 wt% hexacosene do not lead to a deviation from the �0-Mw-relation

stablished for mHDPE, although the lengths of the backbone are reduced significantly. Itas to be concluded from these findings that the introduction of comonomers leads to ahange in the molecular dynamics compared to linear polyethylenes, which compensateshe reduction of the backbone molar mass Mw

bb.The linear steady-state elastic compliance Je

0 for the copolymers with a narrow MMDf Mw /Mn=2 apparently increases with growing molar mass Mw. It has to be taken intoccount, however, that the compositions of the samples are different, i.e., the comonomerontents and the lengths of the comonomers differ.

This finding is surprising, as for nearly monodisperse anionic PS and PI samples andolymer melts with broader molar mass distribution �PMMA and PP, yet to be published�s well Je

0 was found to be molar-mass independent �above a critical molar mass Mc��.As the molar mass distributions can be considered to be at least very similar within the

ccuracy of the SEC, the apparent pronounced dependence of Je0 on the molecular struc-

ure cannot be attributed to a broadening of the MMD. Therefore, the introduction of theomonomer side chains has to be assumed as a probable source of the significant changen elasticity. A more model-related explanation of this conclusion is not easy. However,ome hints my be derived from the following observation.

Piel et al. �2006b� found on the same samples �F12F, F18F, and F26F� a weak peak inMTA measurements for F26F, an even weaker one for F18F and none for F12F, whichas interpreted as side chain crystallization, i.e., intrachain phase separation with subse-uent independent crystallization of the two phases. Therefore, it is not too speculative tossume that these phase boundaries to some extent still exist in the melt, and could haveome effect on the rheological properties. Open, of course, remains the question in whichay such a phase separation would influence rheological properties.

CKNOWLEDGMENTS

The authors would like to thank the German Research Foundation �DFG� for thenancial support of this work. Additionally, the contributions of I. Herzer and Dr. J.aschta �Erlangen� regarding the SEC-MALLS measurements, of Professor Dr. W. Ka-insky and Dr. C. Piel �University Hamburg� with respect to the synthesis of many of the

amples in this article, and of Dr. K. Klimke and Dr. M. Parkinson from the Max-Plancknstitute of Polymer Research in Mainz concerning the solid state NMR measurementsre gratefully recognized. Dr. J. Stange, Dipl.-Ing. J. A. Resch, Dr. D. Möller, and Dipl.-hem. M. Sturm �University Erlangen� made valuable contributions to this paper.

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