ORIGINAL CONTRIBUTION

The effect of molecular structure on rheological behaviorof tubular LDPEs

Masood Khabazian Esfahani &Nadereh Golshan Ebrahimi & Ehsan Khoshbakhti

Received: 2 June 2014 /Revised: 26 October 2014 /Accepted: 10 November 2014 /Published online: 26 November 2014# Springer-Verlag Berlin Heidelberg 2014

Abstract Molecular characterization of low-density polyeth-ylene has long been faced with many challenges. Due to thelack of control over the radical polymerization under veryhigh pressures, the low-density polyethylene (LDPE) molec-ular structure is very complex. This paper uses the attenuatedtotal reflectance (ATR)–Fourier transform infrared character-ization method to introduce a measuring tool to calculate theaverage number of branches in LDPE molecular chain.Among 28 gel permeation chromatography (GPC)-analyzedLDPEs, two GPC-identical tubular LDPE were chosen. Thebranching structures of the LDPEs are investigated by the van-Gurp Palmen plot. To clarify the difference between rheolog-ical behavior of LDPEs, GPC, temperature rising elutionfractionation, ATR, dynamic oscillatory shear, andelongational stress growth coefficient tests were performed.It was found that high molecular weight portion of LDPE 2has higher number of branches than LDPE 1, which is respon-sible for the different rheological behavior.

Keywords Rheology . Polyethylene . FTIR . Structure .

Gel permeation chromatography

Introduction

Nowadays, many polymerization methods are employed toproduce different kinds of polymers or even the same polymer

with different molecular structures, each of which is engineeredto meet special processing needs. Characterization of molecularstructure of polymers, on one hand, determines the molecularstructure of existing polymers and, on the other hand, helpsengineers to feedback control the polymer molecular structureby changing the polymerization control factors. Low-densitypolyethylene (LDPE) as a highly consumed commodity poly-mer is produced radically under high pressures. In such acondition, polyethylene with many side branches is produced.Radical polymerization of LDPE under high pressures leads tothe formation of two types of branches, short- and long-chainbranches. The former is created by intramolecular hydrogentransfer via transient ring formation, whereas the latter is dueto the intermolecular hydrogen transfer (Roedel 1953).Understanding the topology of branches is very crucial forprocessing reasons. In this respect, many characterizationmethods have found their way into polymer molecular structuredetermination. Gel permeation chromatography (GPC) withrefractive index as detector is a very powerful tool to determinethe molecular characterization of linear polymers (Moore 1964);however, for branched polymers, this technique faces someproblems. Podzimek (1994) used multiangle laser light scatter-ing (MALLS) coupled with intrinsic viscometer (IV) detector todetermine the side-chain branches. In another research, Yau andGillespie (2001) used temperature rising elution fractionation(TREF) in addition to MALLS and IV detectors to characterizepolyolefins. Tribe et al. (2006) used Fourier transform infrared(FTIR) as GPC detector to determine short-chain branches inpolyethylene. Suárez and Coto (2013) compared GPC-IV withGPC-MALLS results and showed that GPC-IVismore sensitivetowards lower values of molecular weight whereas GPC-MALLS is more sensitive to higher values of molecular weight.

End group analysis by FTIR is also used to charac-terize short-chain branches (Bryant and Voter 1953) andlong-chain branches in polyethylene (Rugg et al. 1953).The bending mode of −CH3 happens at 1378 cm−1.

M. Khabazian Esfahani :N. G. Ebrahimi (*) : E. KhoshbakhtiPolymer Engineering Department, Chemical Engineering Faculty,Tarbiat Modares University, P.O. Box 14115-114, Tehran, Irane-mail: ebrahimn@modares.ac.ir

M. Khabazian Esfahanie-mail: Masood.khabazian@modares.ac.ir

E. Khoshbakhtie-mail: Ehsan.khoshbakhti@modares.ac.ir

Rheol Acta (2015) 54:159–168DOI 10.1007/s00397-014-0822-y

This peak represents chain end groups together withside branches (Krimm et al. 1956). Attenuated totalreflectance (ATR), as a variant to FTIR, is also usedto investigate the chemical bonds. This technique scansthe surface of the material with the penetration depth of1 μm (Schuttlefield and Grassian 2008). For ATR-FTIR,as the surface of the scanned material and the penetra-tion of evanescent wave are constant, by applying thesame pressure between the sample and the ATR crystal,one can be sure that the same amount of sample isscanned by laser beam, which consequently means thatthe peaks from one sample can quantitatively be com-pared with the other samples.

ATR is a light characterization method. Unlike itscounterpart, FTIR, ATR only scans the surface of thematerial. The evanescent wave with a penetration depth

of 1 μm travels through the sample. The intensity ofATR peak depends on the area of scanning surface andon the applied pressure between the sample and theATR crystal. One difficulty of FTIR is that quantitativecomparison of sample is relative; however, having aconstant scan volume in ATR makes this method anabsolute measure of characterization. In other words,with a constant scan volume and pressure between sam-ple and ATR crystal, the intensity of bending peak ofmethyl at 1378 cm−1 for the two samples is a compar-ative scale of CH3 (branches) presence in the samples;the higher the peak intensity, the higher the number ofbranches in the sample. In Fig. 1, circles represent theATR crystal; the number of CH3 groups in a constantvolume depends on the number of average molecularweight of the polymer and the average number ofbranches per molecule. For a linear sample, the numberof methyl end groups decreases by increasing the num-ber average molecular weight (Fig. 1a). For a branchedsample, the number of methyl groups increases withincreasing the average number of branches per molecule(Fig. 1b). To evaluate the sensitivity of ATR-FTIR to-wards the presence of methyl groups in polyethylenechemical structure, LDPE 1 is blended with a linear

Fig. 1 Relationship between the number of CH3 groups and a numberaverage molecular of weight of polymer and b average number ofbranches per molecule

Fig. 2 Focused absorbance ATR-FTIR peaks

Table 1 Peak intensitiesof LDPE/HDPE blendsand the pure materials,comparison of measuredpeak intensities andmixing rule

Material ATR peakintensities

Mixingrule

HDPE 0.32 –

HD/LD (75/25) 0.46 0.49

HD/LD (50/50) 0.61 0.66

HD/LD (25/75) 0.80 0.83

LDPE 1 1 –

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high-density polyethylene (HDPE) at weight ratios of25, 50, and 75 %. Figure 2 shows the focused absor-bance ATR-FTIR peaks, normalized with respect toLDPE 1. As concentration of LDPE decreases, the peakintensity of methyl group at 1378 cm−1 also decreases.Table 1 represents the normalized values of methyl peakintensities for the blends and the pure materials with thevalues from the mixing rule. There is a very goodcorrelation between the peak intensities and the mixingrule values, which means that the peak intensity at1378 cm−1 has a linear relation with the concentrationof methyl groups.

Equation (1) describes the relation between the averagenumbers of methyl group in a LDPE molecule and the ATRpeak intensity at 1378 cm−1.

LDPEnCH3¼ k

PI1378LDPEMn

ð1Þ

where k is a constant and PI1378 is the intensity of methylbending at 1378 cm−1. For a specific ATR crystal type andconstant pressure between the sample and the crystal and byhaving a linear polyethylene (there are only two methylgroups existing for each polymer chain), the equation constantcan be determined (k=8.14×106).

TREF is also used to investigate the branching struc-ture of LDPE (Kulin et al. 1988). This separation tech-nique is based on the ability of semicrystalline polymersto crystallize at different temperatures in accordance tothe chain topologies. It is assumed that long-chain

branches do not affect the elution temperatures (Johnand Ronald 2006).

Parallel to the aforementioned characterization tech-niques, rheology as an easy to access and powerfulmethod has made its way into polymer characterizationfield. Janzen and Colby (1999) determined low level oflong-chain branches in high-density polyethylene bymelt Newtonian viscosity, which could not be deter-mined by GPC or NMR. Later on, Shroff andMavridis used intrinsic and zero shear viscosities todefine long-chain branching index of scarcely branchedpolyethylenes (Shroff and Mavridis 1999). Stadler(2012) utilized rheology as a tool to detect very lowconcentration of long-chain branches in metallocene cat-alyzed polyethylene. It is very common for linear vis-coelastic data to plot one property against the other.Trinkle et al. (2002) used the correlation of loss angleversus the logarithm of the absolute value of complexmodulus (van-Gurp Palmen plot) to determine the topol-ogy of branches in polymer. The van-Gurp Palmen plotshowed sensitivity towards length and amount ofbranches for long-chain branched polyethylenes (Lohseet al. 2002). For nonlinear viscoelastic, on the otherhand, the transient uniaxial/biaxial elongational viscosityis a very important property. Most of the polymerprocessing operations such as fiber spinning, film blow-ing, and blown molding impose such deformation onpolymer chains (Münstedt et al. 2006). Some polymersshow the rise in uniaxial elongational viscosity abovetrouton ratio. It is demonstrated that the reason for thewell-known strain hardening of polyethylenes is thepresence of long-chain branches (Wood-Adams andDealy 2000). Many attempts have been made to model thisbehavior; most of these theories are based on Doi andEdwards (DE) tube model (Doi and Edwards 1978a, b, c).DE model assumes that, during the deformation, the tube

Fig. 3 Gel permeationchromatography graphs ofLDPEs

Table 2 Fraction temperatures

Fraction Fr-1 Fr-2 Fr-3 Fr-4 Fr-5 Fr-6 Fr-7

Temperature (°C) 40 50 60 70 80 90 100

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diameter is constant, and as a result, no chain stretching istaking place (Doi and Edwards 1987). Consequently, the mod-el predictions for elongational viscosity of long-chain-branchedpolymers fall well below the experiments. Molecular stressfunction (MSF) is a modification to the DE tube model. Thismodel can predict the uniaxial elongational viscosity of low-density polyethylene with only two fitting parameters (Wagneret al. 2003). Many attempts have been made to reduce thenonlinearity of these parameters (Abbasi et al. 2012;Rolón-Garrido and Wagner 2007). The MSF model as-sumes upon deformation; the backbone segmentstretches, and side-chain branches are compressed. Thisassumption introduces the parameter, f, into the DEextra stress tensor. This parameter is defined as therelative tension of a tube segment at time t (3kT/a(t))to that of the initial time (3kT/a0) (Wagner et al. 1998).

f t; t0

� �¼ a0

a t; t0ð Þ ð2Þ

In Eq. (2), a0 and a(t,t′) are the tube segment diameters attime zero and time t, respectively.

The extra stress tensor,σ(t), of the MSFmodel is describedby Eq. (3) (Wagner 2006).

σ tð Þ ¼Z

−∞

t

m t−t0

� �f 2 t; t

0� �

SIADE t; t

0� �

dt0 ð3Þ

In Eq. (3), m(t− t′) is the memory function, f is themolecular stress function, and SDE

IA (t, t′) is the measurestrain tensor with independent alignment assumption.

This paper uses Curie approximation to calculate themeasure strain tensor (Pattamaprom et al. 2000).

For long-chain-branched polymers, the molecular stressfunction f is the solution of Eq. (4).

d f 2

dt¼ ε� β f 2

1þ β � 1

f 4

S11−S22−f 2−1� �

f 2max−1� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS11 þ 1

2S22

r !

ð4Þ

whereε̇ is Hencky strain rate, β is the number of segments in atube section form, which one of them is the backbone segmentthat stretches and β−1 are side chain segments that compressunder the deformation. At very long time, the tube diameterreaches its minimum diameter; in such a case, the f reaches toits maximum value, which is expressed in Eq. (4) as fmax. Thisindicates the steady-state condition. For some polymers, fmax

is not a constant value; it may change as the value of strain ratedecreases (Abbasi et al. 2012).

Many articles used rheology as a complimentary charac-terization tool for conventional methods (Rolón-Garrido andWagner 2014; Rolon-Garrido et al. 2013).

Experimental

LDPE 1 and LDPE 2 were purchased from Ariya SasolPetrochemical Co. and Laleh Petrochemical Co., respectively.Both LDPEs are radically polymerized in tubular reactorsunder high pressure. HDPE is supplied by Bandar ImamPetrochemical Company.

Dynamic oscillatory shear was performed with Anton paarMCR 301 at 130, 160, and 190 °C under nitrogen atmosphereand superimposed at 160 °C by time–temperature superposi-tion. The amplitude of oscillation is chosen by dynamic am-plitude sweep test as to fall within the linear viscoelasticregime.

Table 3 Molecular characterization of LDPEs

Material Mn Mw PDI

LDPE 1 13,921 123,517 8.87248

LDPE 2 14,162 128,962 9.10562

Fig. 4 Superimposed storagemodulus of LDPEs

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All uniaxial elongational viscosity measurements wereperformed with a strain control rheometer ARES G2 withEVF fixture.

Gel permeation chromatography was performed byPolymer Laboratory PL 210 with IV and RI as detectors.

LDPE is dissolved in 1,2,4-Trichlorobenzene (TCB) at 140 °Cwith 0.04 w/w. The volumetric flow rate was set to 0.6 ml/min.

The ATR-FTIR spectrum of the samples was collected withBruker-Vertex 80. The instrument resolution was set to1 cm−1.

Fig. 5 Superimposed lossmodulus for LDPEs

Table 4 The relaxation spectrumof LDPEs LDPE 1 LDPE 2

130 °C 160 °C 130 °C 160 °C

Gi λi Gi λi Gi λi Gi λi

5.74E+01 9.70E+01 7.08E−02 2.54E+02 7.94E+02 5.21E+01 7.12E−01 2.76E+02

3.79E+02 2.64E+01 8.61E+00 5.53E+01 4.41E+03 6.09E+00 4.83E+01 6.22E+01

1.36E+03 7.19E+00 3.35E+02 1.20E+01 1.40E+04 7.12E−01 7.12E+02 1.40E+01

3.37E+03 1.96E+00 1.30E+03 2.62E+00 3.29E+04 8.33E−02 2.09E+03 3.16E+00

7.14E+03 5.32E−01 4.55E+03 5.70E−01 6.69E+04 9.74E−03 5.97E+03 7.11E−011.29E+04 1.45E−01 1.04E+04 1.24E−01 6.61E+04 1.14E−03 1.20E+04 1.60E−012.16E+04 3.94E−02 1.98E+04 2.70E−02 2.73E+05 1.33E−04 2.19E+04 3.61E−023.44E+04 1.07E−02 4.04E+04 5.87E−03 7.22E+05 1.56E−05 3.84E+04 8.13E−034.70E+04 2.92E−03 4.98E+04 1.28E−03 2.70E+07 1.82E-06 5.72E+04 1.83E−031.34E+05 7.95E−04 1.54E+05 2.78E−04 2.36E+05 2.13E−07 1.35E+05 4.13E−04η0=39,100 (Pa s) η0=12,700 (Pa s) η0=81,800 (Pa s) η0=27,200 (Pa s)

Fig. 6 Dynamic viscosity ofLDPEs

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TREF was performed with a home-made apparatus.The 1 % solution of each sample was prepared instabilized xylene (0.1 % Irganox 1010) at 120 °C.After complete dissolution, the solution was pumpedthrough the column, and subsequently, the temperaturewas decreased to 50 °C with the rate of 1 °C/h. After30 min, the xylene was pumped through the columnwith a flow rate of 20 ml/min and precipitated inmethanol. The pumping was continued until no precip-itation is taking place. Afterwards, the temperature wasincreased to the second fraction, and this procedure wasrepeated until seven fractions are collected (Table 2).

To investigate the thermal stability of the LDPE 1 andHDPE, time sweep tests were performed with Anton paarMCR 301 for 10 min under the atmosphere of nitrogen at150 °C. Afterwards, the blending was done in a Brabenderinternal mixer at 150 °C for 5 min under nitrogen atmosphere.

Results and discussion

Figure 3 depicts the GPC graphs of LDPEs. Both LDPEs arenearly identical in GPC viewpoint. Table 3 represents themolecular characterization of LDPEs, which are derived fromGPC curves. As it is conspicuous, the molecular specificationsof both LDPEs are nearly the same except that LDPE 1 hashigher molecular weight fraction at higher values of molecularweight.

Dynamic frequency sweep test is performed for eachof the LDPEs at 130, 160, and 190 °C and superimposedat the reference temperature of 160 °C. Figures 4 and 5show the superimposed storage and loss moduli forLDPEs, respectively. Having fallen on the same trend,the time–temperature superposition holds for bothLDPEs. Although having the same molecular characteri-zation for GPC, the storage and loss moduli of LDPEs

Fig. 7 van-Gurp Palmen plots ofLDPEs together with a linearpolyethylene

Fig. 8 Uniaxial elongational viscosity of LDPE 1 at 160 °C

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differ considerably specially at low values of frequency.This shows that GPC data cannot differentiate betweenthese two rheologically different LDPEs.

Dynamic moduli are fitted with a 10-element Maxwellmodel. The relaxation spectrum is reported in Table 4. Lateron, these values are fed to the MSF model to plot theprediction.

Dynamic viscosity of LDPEs is plotted in Fig. 6. The zeroshear viscosity of LDPE 2 gets a higher value than that of

LDPE 1. The transition to power law region for LDPE 2happens sooner than that for LDPE 1. This shows thatLDPE 2 has more branches than LDPE 1.

As it has already been mentioned, the van-Gurp Palmenplot is very sensitive towards molecular architecture. Figure 7illustrates the van-Gurp Palmen plots of LDPEs together witha linear polyethylene. As it can be seen, both plots show thesame trend, which means that both LDPEs have nearly thesamemolecular structure. This is an expected result since both

Fig. 9 Uniaxial elongational viscosity of LDPE 2 at 160 °C

Fig. 10 Uniaxial elongational viscosity of LDPE 1 at 130 °C

Rheol Acta (2015) 54:159–168 165

LDPEs are produced in tubular reactors. Another feature ofthe van-Gurp Palmen plot is the verification of time–temper-ature superposition (Gurp and Palmen 1998). When the van-Gurp Palmen plot of the same polymer at various temperatures

holds to the same line, the time–temperature superpositionprinciple holds. Figure 7 shows that the time–temperaturesuperposition holds for both LDPEs.

One manifestation of the presence of long-chain branches inpolymer molecular structure is the rise in stress growth coeffi-cient above trouton ratio in startup of extensional flow, the so-called strain hardening. Figure 8 shows the uniaxial elongationalviscosity of LDPE 1 at different strain rates at 160 °C. The MSFmodel predictions are also depicted in the graph. As it is con-spicuous, at high strain rates, the MSF model predictions wellpredict the extensional viscosity; however, as the rate of straindeclines, the predictions of the MSF model get higher valuesthan the experiments. Contrary to LDPE 1, the MSF modelpredictions for LDPE 2 holds well even at low values of strainrates (Fig. 9). Since the zero shear viscosity of LDPE 1 is lowerthan that of LDPE 2, discrepancies between the MSF model

Fig. 11 Uniaxial elongational viscosity of LDPE 2 at 130 °C

Fig. 12 Temperature rising elution fractions of LDPEs

Fig. 13 Attenuated totalreflectance spectra of LDPEs

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predictions and the experimental values for LDPE 1 at low strainrates may be due to differences between molecular structures orenhanced sagging of LDPE 1 at longmeasuring times. To clarifythe cause of these discrepancies, uniaxial elongational viscositiesof both LDPEs are also measured at a lower temperature of130 °C. Figures 10 and 11 show the uniaxial elongationalviscosities of LDPE 1 and LDPE 2 at 130 °C with the MSFpredictions, respectively. As seen, the MSF model again over-predicts the viscosity of LDPE 1 and under-predicts the viscosityof LDPE 2 at low strain rates. Therefore, the discrepanciesbetween the MSF predictions and experimental data are due tothe differences between the molecular structures of LDPEs.

To investigate the branching structure of LDPEs, TREF testis performed. Figure 12 shows the TREF fractions of LDPEs.The weight percentage of LDPE 2, at low temperature frac-tions, is higher than that of LDPE 1; on the other hand, theweight percentage of LDPE 1 is noticeably higher than that ofthe LDPE 2 at high temperature fractions. This shows that themolecular structure of LDPE 1 is more linear than that ofLDPE 2. This is in accordance with the uniaxial elongationalviscosity results. Since the linear portion of LDPE 1 is higherthan that of LDPE 2, in contrast to LDPE 2, LDPE 1 has notshown the stain hardening behavior at low strain rates. At lowvalues of strain rate, time is enough for the relaxation of linearchains via reptation mechanism. The presence of a high por-tion of linear molecules in LDPE 1 facilitates the reptation

process. Because of this, the uniaxial elongational viscosity ofLDPE 1 falls well below the MSF model predictions.

To have a quantitative measure of the number of branchesper molecule, this paper uses ATR-FTIR spectroscopy.Figure 13 shows the ATR spectra of LDPEs. The peak (at1378 cm−1) is related to the concentration of methyl groups ina constant volume of LDPEs. Equation (1) gives the averagenumber of methyl groups per molecule. Having two methylgroups at the end of each polymer chain, the average numberof branches per molecule is equal to the average number ofmethyl groups per molecule minus 2. Table 5 gives the valuesof peak intensities, number average molecular weight, andaverage number of branches per molecule of LDPEs.Needless to mention, these branches include both short- andlong-chain branches. To understand the branching distribu-tion, Fig. 14 draws the calculated radius of gyration versusmolecular weight of LDPEs together with linear reference. Asseen, both LDPEs have fallen on the linear reference line atintermediate molecular weights. However, at higher molecularweights, the radius of gyration of LDPE 2 falls below theradius of gyration of LDPE 1. This shows that, at high mo-lecular weight portions, the hydrodynamic volume of LDPE 2is less than that of the LDPE 1, which means that at highmolecular weight interval the LDPE 2 molecule has highernumber of branches per molecule than LDPE 1.

Conclusions

Although both LDPEs have almost the same GPC plots, theirrheological behavior differs considerably in Newtonian andnon-Newtonian regions. It is concluded that the branchingstructure of polymer is responsible for the different rheologi-cal behaviors. However, van-Gurp Palmen shows that thetopology of branches is the same for both LDPEs. It has beenseen that the predictions of MSF model over-predict the

Table 5 Parameters used to calculate the average number of branchesper LDPE molecule

Material ATR peak intensityat 1378 cm−1

Mn

(kg/mol)Average numberof branches permolecule

LDPE 1 0.020371 13,921 10

LDPE 2 0.024926 14,162 12

Fig. 14 Calculated radius ofgyration versus molecular weightof LDPEs

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uniaxial elongational viscosity of LDPE 1, which means thatthe parameter fmax decreases as the strain rate decreases. Thisbehavior is temperature independent, which means that thelower viscosity of LDPE 1 at low strain rates is not due tosagging at long measuring times and springs from its molec-ular structure. Together with the TREF results, it is concludedthat the large linear chain portion of LDPE 1 is responsible forthe decrease in uniaxial elongational viscosity predictions.ATR-FTIR is used to calculate the average number ofbranches per LDPE molecule. It is shown that the averagenumber of branches per molecule is higher for LDPE 2 thanfor LDPE 1. In comparison to the radius of gyration ofLDPEs, it has been concluded that LDPE 2 has higher numberof branches per molecule at high molecular weight portions.Therefore, having higher number of branches especially athigh molecular weight portions is responsible for highervalues of zero shear viscosity and uniaxial elongational vis-cosity at low strain rates for LDPE 2 than for LDPE 1.

References

Abbasi M, Ebrahimi N, Nadali M, Khabazian Esfahani M (2012)Elongational viscosity of LDPE with various structures: employinga new evolution equation in MSF theory. Rheol Acta 51:163–177.doi:10.1007/s00397-011-0572-z

Bryant WMD, Voter RC (1953) The molecular structure of polyethylene.II. Determination of short chain branching1. J Am Chem Soc 75:6113–6118. doi:10.1021/ja01120a006

Doi M, Edwards SF (1978a) Dynamics of concentrated polymer systems.Part 1—Brownian motion in the equilibrium state. J Chem SocFaraday Trans 2: Mol Chem Phys 74:1789–1801

DoiM, Edwards SF (1978b) Dynamics of concentrated polymer systems.Part 2—molecular motion under flow. J Chem Soc Faraday Tran 2:Mol Chem Phys 74:1802–1817

Doi M, Edwards SF (1978c) Dynamics of concentrated polymer systems.Part 3—the constitutive equation. J Chem Soc Faraday Trans 2:MolChem Phys 74:1818–1832

Doi M, Edwards SF (1987) The theory of polymer dynamics. ClarendonPress/Oxford University Press, Oxford/New York

Gurp M, Palmen J (1998) Time–temperature superposition for polymericblends. Rheol Bull 67:5–8

Janzen J, Colby RH (1999) Diagnosing long-chain branching in polyeth-ylenes. J Mol Struct 485–486:569–584

John D, Ronald L (2006) Structure and rheology of molten polymersfrom structure to flow behavior and back again. Hanser Publishers/Hanser Gardner Publications, Munich/Cincinnati

Krimm S, Liang CY, Sutherland GBBM (1956) Infrared spectra of highpolymers. II: Polyethylene. J Chem Phys 25:549

Kulin LI, Meijerink NJ, Starck P (1988) Long and short chain branchingfrequency in low density polyethylene (LDPE). Pure Appl Chem 60:1403–1415. doi:10.1351/pac198860091403

Lohse DJ, Milner ST, Fetters LJ, Xenidou M, Hadjichristidis N,Mendelson RA, García-Franco CA, Lyon MK (2002) Well-defined,model long chain branched polyethylene. 2. Melt rheological be-havior. Macromolecules 35:3066–3075. doi:10.1021/ma0117559

Moore JC (1964) Gel permeation chromatography. I. A new method formolecular weight distribution of high polymers. J Polym Sci Part A:Gen Pap 2:835–843. doi:10.1002/pol.1964.100020220

Münstedt H, Kurzbeck S, Stange J (2006) Importance of elongationalproperties of polymer melts for film blowing and thermoforming.Polym Eng Sci 46:1190–1195. doi:10.1002/pen.20588

Pattamaprom C, Driscroll JJ, Larson RG (2000) Nonlinear viscoelasticpredictions of uniaxialextensional viscosities of entangled polymers.Macromol Symp 158:1–14

Podzimek S (1994) The use of GPC coupled with a multiangle laser lightscattering photometer for the characterization of polymers. On thedetermination of molecular weight, size and branching. J ApplPolym Sci 54:91–103

Roedel MJ (1953) The molecular structure of polyethylene. I. Chainbranching in polyethylene during polymerization1. J Am ChemSoc 75:6110–6112. doi:10.1021/ja01120a005

Rolón-Garrido V, Wagner M (2007) The MSF model: relation of nonlin-ear parameters to molecular structure of long-chain branched poly-mer melts. Rheol Acta 46:583–593

Rolón-Garrido VH, Wagner MH (2014) Linear and non-linear rheologi-cal characterization of photo-oxidative degraded LDPE. PolymDegrad Stab 99:136–145. doi:10.1016/j.polymdegradstab.2013.11.014

Rolon-Garrido VH, Zatloukal M, Wagner MH (2013) Increase of long-chain branching by thermo-oxidative treatment of LDPE: chromato-graphic, spectroscopic, and rheological evidence. J Rheol 57:105–129

Rugg FM, Smith JJ, Wartman LH (1953) Infrared spectrophotometricstudies on polyethylene. I. Structure. J Polym Sci 11:1–20. doi:10.1002/pol.1953.120110101

Schuttlefield JD, Grassian VH (2008) ATR–FTIR spectroscopy in theundergraduate chemistry laboratory. Part I: fundamentals and exam-ples. J Chem Educ 85:279. doi:10.1021/ed085p279

Shroff RN, Mavridis H (1999) Long-chain-branching index for essential-ly linear polyethylenes. Macromolecules 32:8454–8464

Stadler F (2012) Detecting very low levels of long-chain branching inmetallocene-catalyzed polyethylenes. Rheol Acta 51:821–840. doi:10.1007/s00397-012-0642-x

Suárez I, Coto B (2013) Determination of long chain branching in PEsamples by GPC-MALS and GPC-VIS: comparison and uncer-tainties. Eur Polym J 49:492–498. doi:10.1016/j.eurpolymj.2012.11.015

Tribe K, Saunders G, Meißner R (2006) Characterization of branchedpolyolefins by high temperature GPC utilizing function specificdetectors. Macromol Symp 236:228–234

Trinkle S, Walter P, Friedrich C (2002) Van Gurp–Palmen plot II—classification of long chain branched polymers by their topology.Rheol Acta 41:103–113

Wagner MH (2006) The rheology of linear and long-chain branchedpolymer melts. Macromol Symp 236:219–227

Wagner MH, Bastian H, Ehrecke P, Kraft M, Hachmann P, Meissner J(1998) Nonlinear viscoelastic characterization of a linear polyethyl-ene (HDPE) melt in rotational and irrotational flows. J Non-Newtonian Fluid Mech 79:283–296

Wagner MH, Yamaguchi M, Takahashi M (2003) Quantitativeassessment of strain hardening of low-density polyethylenemelts by the molecular stress function model. J Rheol 47:779–793

Wood-Adams PM, Dealy JM (2000) Using rheological data to determinethe branching level in metallocene polyethylenes. Macromolecules33:7481–7488

Yau WW, Gillespie D (2001) New approaches using MW-sensitivedetectors in GPC TREF for polyolefin characterization. Polymer42:8947–8958

168 Rheol Acta (2015) 54:159–168