activation energies of lcb ldpe's

Determination of method-invariant activation energiesof long-chain branched low-density polyethylenes

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Redistribution Ute Kener, Joachim Kaschta, and Helmut Mnstedta)

Institute of Polymer Materials, Friedrich-Alexander-UniversityErlangen-Nrnberg, Martensstrasse 7, D-91058 Erlangen, Germany

(Received 29 January 2009; final revision received 6 April 2009

Synopsis

he idea to use the temperature dependence of rheological properties, especially the flowctivation energy, as a tool to investigate branching structures is well-known from literature.owever, there is no common method to obtain activation energies, which are independent of theeasuring quantity chosen, particularly, in the case of slightly thermorheologically complex

olymers like low-density polyethylene LDPE. Hence, differing activation energies result, whichannot unequivocally be correlated with the branching structure. This paper describes a method forhe determination of method-independent activation energies for thermorheologically complexolymers like LDPE. From a generalized approach to the time-temperature superposition principle,vertical shift factor is introduced, which is related to the temperature dependence of the linear

teady-state compliance. In the case of the complex LDPE, a decrease in the linear steady-stateompliance with temperature is found. Taking this experimentally determined shift factor intoccount leads to activation energies independent of the rheological quantity chosen. These valuesan be taken to analyze differences of the branching architecture.

2009 The Society of Rheology. DOI: 10.1122/1.3124682

. MOTIVATIONThe time-temperature superposition and following from that the construction of master

urves has been known from literature since 70 years. Initially this method developedmpirically, but in 1950 Ferry established the general theoretical background for theuperposition of linear viscoelastic properties of polymers Ferry 1950; 1980.

This principle is based on the fact that, in the case of thermorheologically simpleolymers, all relaxation times involved exhibit the same temperature dependence, i.e.,

T = T0aTT,T0 , 1

ith T being the actual and T0 being the reference temperature.The shift factor aT is a function of temperature. For polymer melts at temperatures not

oo far away from the glass transition temperature Tg, the so-called WLF-equation holds

Author to whom correspondence should be addressed; electronic mail: [email protected] by The Society of Rheology, Inc.1001. Rheol. 534, 1001-1016 July/August 2009 0148-6055/2009/534/1001/16/$27.00

subject to SOR license or copyright; see http://scitation.aip.org/content/sor/journal/jor2/info/about. Downloaded to IP:147.27.58.93 On: Tue, 21 Apr 2015 17:43:40

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1002 KENER, KASCHTA, AND MNSTEDT

Redistribution log aTT,T0 = d1T T0

d2 + T T0, 2

1 and d2 are constants specific for a material.For temperatures significantly higher than Tg, an Arrhenius-equation of the type

aT = expEaR 1T 1T0 3s valid. Ea is the activation energy and R is the universal gas constant.

Deduced from the Rouse theory Ferry 1950; Rouse 1953 an additional verticalodulus shift factor bT is introduced according to Eq. 4,

GT =1bT

GT0 . 4

his additional contribution is required in order to correctly superimpose relaxationoduli in accordance with the theory. bT considers the change of the density with the

emperature T and is defined as

bT =T00T

. 5

ccording to Eq. 4 the relaxation modulus G requires a vertical shift with bT. However,his vertical shift is very small, if the measuring temperatures differ less than 100 C seeec. IV. In many cases this shift lies within the limits of the uncertainty of the measure-ent and hence is often neglected.The time-temperature superposition principle is widely used in practice in order to

xtend the time or frequency range of rheological measurements. This method reduceshe experimental effort to cover the large time window often required for a completeescription of the rheological behavior of polymer melts.

The flow activation energy varies with the molecular structure and branching topo-raphy. For example, branched polymers exhibit higher activation energies than linearnes Bersted 1985. Therefore, analyzing the temperature dependence of rheologicalroperties may become interesting for getting an insight into the branching structure ofolymers.

Several studies in literature already deal with the relationship between moleculartructure and rheological properties of polyethylenes. Some of them try to interpret tem-erature dependencies and flow activation energies in relation to branching e.g., Raju etl. 1979; Carella et al. 1986; Wasserman and Graessley 1996; Vega and Santamara1998; Shroff and Mavridis 1999; Vega et al. 1999; Villar et al. 2001; Wood-Adamsnd Costeux 2001; Starck et al. 2002; Bonchev et al. 2003; Ye et al. 2005.owever, there is no convincing method for the determination of activation energies,hich are independent of the rheological quantities taken and, therefore, suitable for

nalytical purposes. Mostly, the zero-shear viscosities are used, but the data obtained areignificantly different in many cases from the results derived from the storage, loss, oromplex modulus. Sometimes even the relaxation spectra are used to determine thectivation energy. The results differ widely depending on the evaluation method makinghe activation energy a somewhat dubious tool for the characterization of the moleculartructure of polymers. This situation becomes evident from the literature discussed in the

ollowing.


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1003ACTIVATION ENERGIES OF LDPE

Redistribution Linear, high density polyethylene HDPE is known as thermorheologically simple. Inhe literature, an activation energy of about 27 kJ/mol independent of molar mass andolar mass distribution is reported e.g., Raju et al. 1979; Wasserman and Graessley

1996; Stadler et al. 2007. In contrast, in the case of commercial low-density poly-thylene LDPE both thermorheological simplicity and complexity are reported in theiterature. For example, Jacovic et al. 1979, Meiner 1987, and Laun 1987 investi-ated the activation energy of LDPE as a function of the shear stress far into the nonlin-ar viscoelastic regime with capillary rheometry. Thermorheological complexity resultingn a stress-dependent activation energy was observed. Moreover, activation energies de-ived from different rheological properties provide different activation energies in thease of the same LDPE. For example, Wood-Adams and Costeux 2001 published acti-ation energies of thermorheologically complex polyethylenes long-chain branched HD-Es resulting from the storage and loss modulus, the zero-shear viscosity, as well as theirpectra, which do not match each other.

Others determined the activation energy simply by means of zero-shear viscosities.he resulting shift factors are often checked by constructing master curves of G and in double-logarithmic plots. The data may superimpose in a coarse approximation,

oncealing a slight but physically relevant thermorheological complexity if regardedore precisely. Such a distinct value of the activation energy is often found for LDPE in

he literature. In general, the insertion of long-chain branches is believed to be respon-ible for the thermorheological complexity of polyethylenes. A sensitive but qualitativeay to check the thermorheological behavior offers the plot of the phase angle versus

he absolute value of the complex modulus. Data of thermorheologically simple materialseasured at different temperatures lead to a good superposition, while data of ther-orheologically complex materials split up with temperature van Gurp and Palmen

1998.Mavridis and Shroff 1992 published a new approach toward the evaluation of acti-

ation energies of thermorheologically complex polymers like LDPE, which show aplit-up in G. They found that there exists a vertical modulus shift larger than thealue predicted by Eqs. 4 and 5, which allows the construction of a master curve. Thishift is empirically determined and applied toward the data in such a way that a ther-orheologically simple behavior is obtained. By that way a constant, stress-independent

ctivation energy is determined. This study is often cited and the vertical shift is accord-ngly performed. However, there exists no explanation so far, why the vertical shifthould be larger than the prediction from the theory of rubber elasticity and what itshysical meaning is. Thus, the question remains how to gain reliable physically basedctivation energies.

Additional contradictions in literature result from partly incomplete molecular charac-erizations making it difficult to relate activation energies to a definite architecture of theolymer.

The aim of this paper is to establish a method for the undisputable determination ofctivation energies. Consequently, the careful analysis of the temperature dependence ofheological properties combined with a reliable molecular characterization will open up aew approach toward the use of activation energies for an analytical characterization ofranching. This paper lays the experimental foundations for such a method.

I. MATERIALSThe molecular structure was characterized by means of a high-temperature size exclu-ion chromatograph PL 220, Varian Inc. equipped with Shodex columns UT 807 1x


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Redistribution nd UT 806M 3x coupled with a multiangle laser light scattering MALLS apparatusWyatt Dawn EOS, Wyatt Corp. at 140 C. 1,2,4-trichlorobenzene TCB was used ashe solvent.

The molecular characteristics are given in Table I. LDPE 2 and LDPE 3 are commer-ial tubular grades, which differ in molecular weight. The LLDPE L63 is a commercialinear low density polyethylene with 1.2 mol.-% hexene as comonomer from NMReasurements synthesized by a metallocene catalyst. Figure 1 shows the determined

adii of gyration rg20.5 as a function of the molar mass MLS. rg

20.5 smaller than 20 nmannot be detected. In the case of the LLDPE L63, the linear relationship known fromiterature is valid indicating the absence of long-chain branches Beer et al. 1999. Theong-chain branches in LDPE result in a contraction of the molecules and thus the radii ofyration deflect from the linear relationship between rg

20.5 and MLS. The deviation of thewo LDPE investigated from the linear reference is similar in the range of equal molarasses. LDPE 2 possesses higher molar masses than LDPE 3, which are significantly

ranched.The radii of gyration of the two LDPE have been truncated at molar masses below

00 000 g/mol as indications for non-ideal separation in the GPC became visible. In thisolar mass regime, highly branched molecules of very high molar mass Podzimek et

l.2001 and/or high molar mass stars Frater et al. 1997 may elute together with lowolar mass species making an interpretation with respect to structure impossible.

TABLE I. Molecular characteristics.

TmC

Mwkg/mol Mz/Mw Mw/Mn

LLDPE L63 123.5 113 1.7 3.2LDPE 2 110.0 230 17.2 13.7LDPE 3 106.7 150 18.3 12.0FIG. 1. Radii of gyration as a function of molar mass.


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Redistribution II. RHEOLOGYThe polymer pellets were stabilized with the antioxidants Irganox 1010 and Irgafos

68 from Ciba 0.5 wt % each. Disks with a diameter of 25 mm and a height of 2 mmere hot-pressed under vacuum.Dynamic-mechanical as well as creep and creep-recovery experiments were conducted

ith a Bohlin Gemini C-VOR rheometer using a plate-plate geometry. The measurementsere performed under a nitrogen atmosphere granting a sufficient thermal stability. Data

or each material were obtained for at least four different temperatures in the range from30 to 210 C. A new sample was used for each measurement. Reproducibility waserified.

Stress-controlled dynamic-mechanical experiments were performed in the linear re-ime for frequencies between 100 and 0.01 s1. Stationarity and linearity with regard toreep and creep-recovery experiments were ensured according to the method described inetail in the literature e.g., Gabriel et al. 1998.

V. RESULTS AND DISCUSSIONThe thermorheological behavior in the linear viscoelastic regime can qualitatively be

istinguished by plotting the phase angle as a function of the magnitude of the complexodulus at different temperatures. Figure 2 shows this plot for the three polyethylenes

nvestigated. In the case of the LLDPE L63, all curves superimpose pointing at ahermorheological simplicity. In contrast, the curves of the two branched polyethyleneso not superimpose. There is a slight split-up between the data at different temperatures.clear trend with temperature can be observed: the higher the temperature the larger the

hase angle at the same modulus. This behavior is a result of thermorheological com-lexity, which is therewith affirmed. G is more sensitive toward changes in theemperature dependency than double-logarithmic plots of rheological data like the storagend loss moduli as a function of the angular frequency.

The slight thermorheological complexity found for the two LDPE samples is in con-rast to the observation of Stadler et al. 2008b that the LDPE investigated there, is

IG. 2. G-plot of the three polyethylenes. LDPE 3 is shifted by the factor of 2 along the modulus axis forhe matter of a better distinction.hermorheologically simple. The reason for this discrepancy of the very similar products


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Redistribution s due to the use of different rheometers and various degrees of experimental diligence. Itemonstrates the care which has to be taken to get reliable information on the ther-orheological behavior of polymer melts.In the following, the thermorheological behavior of the polyethylenes is analyzed in

ore detail. For the linear polyethylene and LDPE 3, the flow activation energy can beetermined from rheological properties in the terminal zone like the storage, loss, oromplex modulus or the zero-shear viscosity. For this purpose, the shift factors aT wereetermined and plotted according to the Arrhenius relationship given by Eq. 3. The flowctivation energy is then derived from the slope of linear fits of the experimental valuesbtained. Figures 3a and 3b show the Arrhenius plots of the differently determinedhift factors for the LLDPE L63 and LDPE 3. The thermorheological simplicity of theLDPE L63 is again confirmed. All rheological quantities analyzed lead to the sameow activation energy within the experimental error. The mean value of about 29 kJ/mol

s in accordance with the literature e.g., Stadler et al. 2007. Such a behavior cannot beound for the LDPE 3. The flow activation energy derived from the phase angle is theighest. The value from the storage modulus G is about 4.6 kJ/mol lower, that one fromhe loss modulus G even differs by 8.3 kJ/mol. However, there is an agreement betweenhe results from G and the zero-shear viscosity 0 cf. Fig. 3b. These results areonfirmed by several studies in the literature. For example, Wood-Adams and Costeux2001 simulated the spectra of a thermorheologically complex material, which led alsoo differing activation energies in dependence on the rheological quantity chosen.

A detailed analysis of the activation energies in dependence on various rheologicaluantities outside the terminal zone is shown for LDPE 2 and LDPE 3 in Figs. 4 and 5.he evaluation of the phase angle results in approximately constant values, while thenalysis of the moduli leads to lower moduli-dependent activation energies, which againeflect the thermorheological complexity of LDPE. They are found to decrease withrowing moduli. These results demonstrate the difficulties to determine a material-pecific activation energy. For the determination of the activation energies, a vertical shiftsee Eq. 4 has been neglected.

Some more light on these findings is thrown by a more generalized approach to theime-temperature superposition principle, which includes a modulus shift and a time orrequency shift. Such a procedure was proposed by Verser and Maxwell 1970 in the

IG. 3. a Arrhenius plot of the shift factors from different rheological properties in the terminal zone for63. b Arrhenius plot of the shift factors from different rheological properties in the terminal zone for LDPE.ollowing way:


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Redistribution G,T0 = bTGaT,T , 6

G,T0 = bTGaT,T , 7

rom these definitions follows:

G,T0 = bTGaT,T , 8

tan ,T0 = tan aT,T . 9

ccording to these relationships, G should have the same shift factors as G and G,ut tan and, consequently, the phase angle is independent of the vertical shift factorT.

IG. 4. Activation energies of LDPE 2 derived from different rheological properties outside the terminal zone.IG. 5. Activation energies of LDPE 3 derived from different rheological properties outside the terminal zone.


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Redistribution As can be concluded from Figs. 4 and 5, the activation energies of LDPE 2 and LDPEdetermined from the temperature shift of the phase angle are independent of within

he accuracy of the measurements indicating a thermorheologically simple behavior ofhese two materials. However, the activation energies calculated from the shift factors of, G, and G, respectively, are distinct functions of the moduli. This finding can be

nterpreted as the result of a thermorheologically complex behavior.The fact that a constant activation energy is found from the phase angle in compari-

on to the contradictory results from G, G, and G supports the supposition that thehoice of the vertical shift factor bT plays a decisive role for the determination of thectivation energy, particularly, as according to Eq. 9 tan is not affected by a verticalhift of the moduli. Therefore, it can be assumed that this value may be the right quantityharacterizing a material and that by choosing adequate vertical shift factors an adaptionf the activation energies from the other methods can be obtained. The question remain-ng is how a physically reasonable shift factor bT could be determined. One way tochieve this goal is sketched in the following.

As for small , i.e. in the terminal range,

G,T = 0T2Je0T2 and

10G,T = 0T

re valid, it follows from Eq. 6 that

0T02Je0T02 = bT0T2

1aT

2Je0T2 or

0T02

0T2Je

0T0Je

0T=

bTaT

2 11

nd from Eq. 7 that

0T0 = bT0T1aT or

0T00T

=

bTaT

. 12

eplacing the ratio of the zero shear-rate viscosities in Eq. 11 by Eq. 12 results in

bT2

aT2

Je0T0

Je0T

=

bTaT

2 or bT =Je

0TJe

0T0. 13

his generalized approach by Verser and Maxwell 1970 leads to a vertical shift factor,hich is given by the temperature dependence of the linear steady-state compliance Je

0.

f the linear steady-state compliance is not temperature dependent, then bT=1, i.e., aertical shift does not have to be applied, if it is dependent on the temperature, however,vertical shift bT given by Eq. 13 has to be considered.Following from this general derivation of the vertical shift factor, the question arises

hich effect the application of the vertical shift factor would have on the thermorheo-ogical complexity presented in Figs. 4 and 5. For this purpose, the temperature depen-

ence of Je

0 has to be known.


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Redistribution There are several studies concerning molecular influences like molar mass and molarass distribution on the elastic properties of polyolefins e.g., Carella et al. 1986;arella and Graessley 1984; Takigawa et al. 2006, but almost none regarding their

emperature dependencies. In the literature, linear steady-state compliances are mostlyetermined from the storage and loss modulus in the terminal regime of dynamic-echanical experiments. In many cases, this method leads to inaccurate results, particu-

arly if the moduli are low or the terminal regime is not reached at frequencies typicallyhosen not smaller than 0.01 s1. Due to the experimental limitations, the terminal re-ime for long-chain branched polyethylenes normally is not accessible. Expanding therequency range to lower frequencies results in such long measuring times that the ther-al stability of the material may cause problems.A convenient experimental way to determine linear steady-state compliances more

eliably are creep and creep-recovery experiments. These measurements are time con-uming and demanding with respect to equipment and know-how. For example, linearitynd stationarity are crucial and the thermal stability of the material investigated has to beaken into account. Details about creep and creep-recovery experiments and their perfor-ance can be found in the literature, e.g., Gabriel et al. 1998, Gabriel and Mnstedt

1999, and Stadler and Mnstedt 2008a.Linear steady-state compliances at different temperatures were measured in creep-

ecovery experiments, in order to determine the vertical shift factor bT defined by Eq.13. In Fig. 6 the results of creep and creep-recovery experiments for LDPE 2 at 170 Cre presented as an example for typical investigations performed. Three experimentsiffering in the preceding creep time tc or the applied creep stress are shown. Each set ofarameters leads to the same steady-state compliance of 6.7104 Pa1, i.e., the linearteady-state value of Je

0 is obtained.Figure 7 compares creep-recovery experiments at different temperatures in the range

etween 130 and 210 C for LDPE 2. The preceding creep times tc to reach the steady-tate had to be chosen the longer, the lower the temperature. The corresponding linearteady-state compliances distinctly depend on temperature. They are listed in Table II.igher temperatures lead to distinctively lower values of the linear steady-state compli-

nce.

IG. 6. Exemplary results of creep and creep-recovery experiments on LDPE 2. tc is the creep time; tr is theime for recovery.Table II gives the linear steady-state compliances Je0 for all the three polyethylenes.


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Redistribution he values result from at least three different measurements at each temperature. TheLDPE L63 exhibits a temperature-invariant linear steady-state compliance of about.8105 Pa1, which is in the order of typical linear polyethylenes but significantlyower than the values for LDPE 2 e.g., Pedersen and Ram 1987; Gabriel and Mnstedt1999; Pen et al. 2003; Stadler and Mnstedt 2008a. The temperature independecef Je

0 results in bT=1 cf. Eq. 13 and is in good agreement with the thermorheologicalimplicity of LLDPE L6-3 demonstrated in Figs. 2 and 3a.

A temperature dependence of Je0 is found for LDPE 3, too. The values are significantly

ower, however, than those of LDPE 2.The question arises now whether master curves can be obtained by applying the

ertical shift factor bT experimentally determined from the temperature dependence ofhe linear steady-state compliances.

Figure 8 shows the G-plot of the two long-chain branched polyethylenes, apply-ng the vertical modulus shift. The curves measured at different temperatures superim-ose well indicating that accounting for bT by using the temperature-dependent steady-tate compliances yields thermorheological simplicity. Using the temperature-dependentensity function of Fig. 9 for a vertical shift does not result in a master curve of aomparable perfection.

The logarithms of the linear steady-state compliances of the LDPE investigated arelotted in Fig. 9 as functions of the inverse absolute temperature. In the temperatureange given, they follow an Arrhenius relationship. There is a slight difference between

ABLE II. Linear steady-state compliances at different temperatures for the materials investigated.

C

Je0

105 Pa1

130 140 150 170 190 210

LDPE L63 n.d. 3.80.4 3.70.3 3.80.2 3.90.3 3.90.8DPE 2 81.30.4 n.d. 73.50.6 66.60.9 59.90.8 55.00.5

FIG. 7. Creep-recovery experiments at different temperatures for LDPE 2.DPE 3 44.80.8 n.d. 41.20.8 38.10.7 34.80.3 32.40.5


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Redistribution he temperature dependencies of the two branched polyethylenes, but they are signifi-antly stronger than that of the density of LDPE 2 plotted in Fig. 9, for comparison.

For a quantitative discussion, the measured functions GaT ,T and GaT ,T wereorrected by bT and then the activation energies determined. The results are given in Fig.0. Within the accuracy of the measurements the activation energies obtained from theorrected shifts are the same as that from the phase angle . An average activation energyf 67 kJ/mol is found for the LDPE 2.

The same method was applied to LDPE 3. The results are plotted in Fig. 11. Again,dentical activation energies can be found independently of the rheological quantityvaluated, if the vertical shift factor bT is considered. The activation energy follows as 56J/mol. The activation energies obtained for the two LDPE are significantly differentndicating the possibility of using them for the characterization of the molecular structure.

Determining the activation energies directly from the temperature dependence of theero-shear viscosities as done frequently in the literature naturally gives values smaller

IG. 8. G-plot of the two long-chain branched polyethylenes considering the vertical shift factor bT.DPE 3 is shifted along the modulus axis by the factor of 2 for the matter of better distinction.IG. 9. Temperature dependence of the linear steady-state compliance branched polyethylenes in comparisono the density correction.


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Redistribution han those from the other methods after applying a vertical shift factor. Considering theertical shift factor according to Eq. 13, however, leads to distinctively higher values,hich are consistent with the analysis from other rheological properties. The correctionf the zero-shear viscosities according to Eq. 12 leads also to a flow activation energyround 67 kJ/mol.

. CONCLUSIONSThe long-chain branched polyethylenes investigated are thermorheologically complex.

heir activation energies are dependent on the determination method chosen and, except

FIG. 10. Activation energies for LDPE 2 obtained from different vertically corrected rheological properties.FIG. 11. Activation energies for LDPE 3 obtained from different vertically corrected rheological properties.


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Redistribution or the phase angle evaluation, not constant. For example, G and G cannot behifted to give a master curve and, therefore, the activation energy is not a constantuantity.

It was shown that the introduction of a vertical shift factor bT as defined in Eq. 13eads to satisfactory master curves and following from that to constant activation ener-ies. This shift factor does not take the temperature dependence of the density intoccount as it is usually done but is based on the temperature dependence of the linearteady-state compliance.

However, it is not obvious, why the linear steady-state compliance should change withemperature. Generally, the linear recoverable compliances Jrt can be related to theiretardation spectra in the following way:

Jrt = i

Ji1 et/i . 14

i are the retardation times and Ji the retardation strengths. For a thermorheologicallyimple polymer the temperature dependence of the compliance is given by

Jrt,T = i

Ji1 eaTTt/i , 15

ndicating that all retardation times i are shifted by the same shift factor aTT if theemperature is changed. From these simple relationships, it becomes obvious that a tem-erature change leaves the shape of Jrt ,T unaffected and that the linear steady-stateompliance

Je0T = lim

tJrT =

iJi 16

s temperature independent.Such a behavior is found for the LLDPE L63 cf. Table II, which is known to be

hermorheologically simple.In the case of the thermorheologically complex LDPE, the temperature dependence of

e0 and that of the retardation times i have to be considered. Applying these shifts aaster curve can be obtained as Figs. 12a and 12b demonstrate. This experimental

esult can be described by introducing temperature-dependent retardation strengths JkT,.e.,

Jrt,T = i

JiT1 eaTTt/i 17

ith

JiT = bTT,T0JiT0 . 18

he thermorheological complexity of the two LDPE investigated, therefore, can formallye interpreted by a temperature dependence of the retardation strengths in addition to thesual temperature shift of the retardation times found for thermorheologically simpleaterials.Recent investigations point out, however, that the separability of the temperature de-

endence as found for the LDPE of this paper is not generally valid for long-chainranched polyethylenes.

The question remains, however, why the linear steady-state compliance should changeith temperature. The decrease in the steady-state compliances with increasing tempera-ure points to a temperature-dependent variation in the entanglement structure. A similar


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Redistribution ut mechanically induced change of the entanglement structure is postulated to explainhe findings of the influence of various deformation histories on rheological properties ofDPE Mnstedt 1981; Rokudai and Fujiki 1981. A quantitative explanation of theeculiar behavior typical of LDPE is still missing, however.

Nevertheless, the significant difference of the activation energies of LDPE 2 andDPE 3 offers the possibility to use the thermorheological behavior as an analytical tool.here is a considerable difference of about 10 kJ/mol between the activation energies ofDPE 2 and LDPE 3 if the vertical shift factor is considered.

The molecular characterization cf. Fig. 1 revealed a significant difference of theong-chain branching structure of the two LDPE: LDPE 2 is long-chain branched atigher molar masses than LDPE 3. But measurements of such kind are not easy and needsophisticated equipment. The determination of the activation energy is very sensitive toiscriminate between these structural differences and not difficult to perform from thexperimental point of view. The long-chain branches of the high molar masses of LDPE

could be related to the higher activation energy. The contribution of long-chainranches at low molar masses to the activation energy, as found in LDPE 3, seems to beeaker. This finding raises the question, which influence the chain microstructure has on

he thermorheological behavior and how relationships could be used for analytical pur-oses.

I. SUMMARYPolyethylenes can be thermorheologically simple or complex. LLDPE is consistently

lassified as thermorheologically simple in the literature. However, in the case of LDPEhermorheological simplicity and complexity are reported. A sensitive qualitative proof ofhe thermorheological behavior is the van Gurp and Palmen plot, which uncovered alight thermorheological complexity of the two branched polyethylenes of this study. Theetermination of flow activation energies from different rheological properties led toiverging values. Moreover, a temperature dependence of the linear steady-state compli-nces investigated with creep and creep-recovery experiments was observed for the twoDPE, but not for the LLDPE L63. Their temperature dependence is distinctly stronger

han that of the density often used in the literature as a vertical shift factor.For a more generalized approach of the time-temperature superposition principle, a

ertical shift factor b was introduced for the shift of G and G . A simple consideration

IG. 12. a Vertically shifted creep-recovery experiments of LDPE 2. b Vertically and horizontally shiftedreep-recovery experiments of LDPE 2.T ithin the terminal zone leads to an interpretation of the vertical shift factor by the ratio


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Redistribution f the temperature-dependent linear steady-state compliances. Thermorheological com-lexity could be avoided by applying the factor bT to the moduli before the time-emperature superposition. In the case of the phase angle, the factor bT is not involved.herefore, the phase angle yields the true activation energy without applying the newlyroposed correction factor. The evaluation of the activation energy from the zero-sheariscosities also needs the vertical shift factor bT. A constant activation energy indepen-ent of the rheological quantity chosen could be obtained by applying bT. Consequently,his correction offers the possibility to determine definite activation energies for variousolyethylenes as it was demonstrated for the two LDPE. These findings open up a prom-sing way to use activation energies for the characterization of long-chain branchedolyethylenes. The question how these activation energies are related to various molecu-ar structures is being addressed in more detail in further investigations.

CKNOWLEDGMENTSThe authors express their gratitude to Dr. F. Stadler for discussions and to Ir. X.

rooghag Universit catholique de Louvain for the NMR analysis of the LLDPE L63.

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activation energies of lcb ldpe's

Documents

reference temperature

function of temperature

activation energy

vertical shift factor

shift factor intoccount

common method

method developedmpirically

d1t t0d2 t t0