*email: [email protected] received: 5.7.04

28 Applied RheologyVolume 15 · Issue 1

Influence of the Molar Mass Distribution on the ElongationalBehaviour of Polymer Solutions in Capillary Breakup

J. P. Plog, W.-M. Kulicke*, C. Clasen

Institute for Technical and Macromoleculare Chemistry,University of Hamburg, Bundesstr. 45, 20146 Hamburg, Germany

*Email: [email protected]

Received: 5.7.04, Final version: 17.12.04

Abstract:Commercially available, blended methylhydroxyethyl celluloses with similar weight-average molar masses butvarying molar mass distributions were characterized by different techniques like steady shear flow and uniax-ial elongation in capillary breakup experiments. The determined relaxation times t were then correlated withthe absolute molar mass distribution acquired via SEC/MALLS/DRI (combined methods of size-exclusion-chro-matography, multi angle laser light scattering and differential refractometer). In order to describe the longestrelaxation time of the polymers in uniaxial elongation via integral mean values of the molar mass distribution,defined blends of polystyrene standards with varying molar mass distributions were characterized. The obtaineddata was scaled via different moments of the molecular weight distribution and could be correlated with theresults obtained for the methylhydroxyethyl celluloses.

Zusammenfassung:Kommerziell erhältliche Methylhydroxyethylzelluloseblends mit ähnlichem gewichtsgemittelten Molekularge-wicht aber unterschiedlicher Molekulargewichtsverteilung wurden mittels verschiedener Methoden wie sta-tionäres Scherfliessen und uniaxialer Dehnung in Kapillaraufbruchexperimenten charakterisiert. Die ermittel-te Relaxationszeit t wurde dann mit der absoluten Molekulargewichtsverteilung in Beziehung gesetzt, die durchSEC/MALLS/DRI (Kombination von Grössenausschluss-Chromatographie, Vielwinkellaserlichtstreuung und dif-ferentielle Refraktometrie) gemessen wurde. Um die längste Relaxationszeit der Polymere in uniaxialer Deh-nung durch integrale Mittelwerte der Molekulargewichtsverteilung zu bestimmen, wurden defnierte Polysty-rolblendstandards mit unterschiedlicher Molekulargewichtsverteilung charakterisiert. Die erhaltenen Datenwurden mit verschiedenen Momenten der Molekulargewichtsverteilung skaliert und konnten in Beziehunggesetzt werden mit den Ergebnissen für Methylhydroxyethylzellulose.

Résumé:Nous avons caractérisé des mélanges commerciaux de méthyle-hydroxyéthyle de cellulose possédant des poidsmoléculaires moyens identiques, mais dont les distributions en poids sont différentes, au moyen de différentestechniques comme l’écoulement en cisaillement constant et l’extension uniaxe obtenue à l’aide d’un capillaireà rupture de filament. Les temps de relaxation mesurés ont été corrélés avec les distributions en masses molairesobtenues par SEC/MALLS/DRI (méthodes combinées de chromatographie à exclusion de tailles, diffusion delumière à angles multiples et réfractomètre différentiel). Dans le but de décrire les temps de relaxation les pluslongs des polymères en élongation uniaxe à partir des valeurs moyennes intégrales de la distribution en poidsmolaires, des mélanges définis de polystyrènes standards possédant des distributions en poids molaires variéesont été caractérisés. Les données obtenues ont été quantifiées au moyen des différents moments de la distrib-ution en poids moléculaires, et ont pu être corrélés avec les résultats obtenus pour les méthyle-hydroxyéthylesde cellulose.

Key words: Elongational rheology, polystyrene blends, MHEC, MWD

© Appl. Rheol. 15 (2005) 28-37

Applied Rheology Vol.15-1.qxd 18.03.2005 11:21 Uhr Seite 28

29Applied RheologyVolume 15 · Issue 1

1 INTRODUCTION

The influence of the molar mass distribution(usually referred to as MWD (molecular weightdistribution) in literature) and the polydispersi-ty, Mw/Mn, on the rheological properties of poly-mers is of great importance for diverse technicalapplications and polymer processing. The exper-imental detection of the discrete influence of thepolydispersity on the rheological properties andalso of the polydispersity itself is not easily toachieve quantitatively.

This applies particularly for cellulosederivatives, because native polymers naturallyshow very broad molar mass distributions. Theprocessability of these cellulose derivativesdepend strongly on their MWD, which in turndepends on the origin of the specific cellulose [1].Therefore in technical applications cellulosesamples are usually blended to broaden theMWD and hence minimize the effect of the MWDof a single sample. However, already the initialmolar mass distribution of the sample that is tobe blended is not easy accessible and the “right”mixing ratio is often chosen on empirical trials ofthe material properties of the different mixingratios [1, 2]. Aim of this contribution is thereforeto correlate the relaxation times, determined viacapillary breakup extensional rheometry, ofblended polymers with the different moments ofthe MWD.

2 PROBLEM

For steady shear flows it has already been shownthat the broadness of the transition area fromNewtonian to the non-Newtonian flow regime isnot a quantitative measure for the molecularweight distribution of a polymer [3]. The longesttime of relaxation for shear flows t0, as the onsetof non-Newtonian flow, is an integral propertythat depends on the MWD [3 - 5]. Therefore the(empirical) correlation of the parameters of con-stituive equations as the transition parameter bin the modified Carreau model [6] to the molec-ular weight distribution strongly depends on thelimiting parameters of the fit and show onlysmall changes over a wide range of distributions.

A more accessible method for the detec-tion of the MWD is via SAOS (small amplitude

oscillatory shear). Here one can determine thespectrum of relaxation times for a polymer sam-ple, which can be directly correlated with themodes of relaxation of a discrete molar mass [7,8]. However this relaxation spectrum is super-posed by the molecular weight distributionwhich leads to a complex correlation of the spec-tra to the molecular weight distribution, that isstill discussed in literature [9 - 15].

A new method to determine the influ-ence of the MWD on the rheological characteris-tics is via elongational flows. While the elonga-tional investigation of polymer melts isestablished for quiet a while [16 - 18] the signifi-cantly lower viscous polymer solutions are stillhard to characterize in their elongational behav-iour. In the past years several methods for deter-mination of the elongational profile of polymersolutions have been introduced. This can be donevia pressure drop in porous media [19, 20],opposed jets [21], or via optical detection of thebirefringence of a polymer in a planar elonga-tional flow in a 4-roll apparatus [22, 23]. All thesemethods have serious drawbacks in terms oftime intensitivity and complex experimentalsetups in case of opposed jets and 4-roll appara-tus.

A new and fast method to determine thebehaviour of polymer solutions in uniaxial elon-gational flows is the commercially availableCaBER (Capillary Breakup Extensional Rheome-ter). Elongational strains of CaBER type experi-ments appeal to the longest relaxation time of apolymer coil due to the balanced stresses in a sur-face tension driven flow [24 - 26]. Therefore theproblem simplifies again to a correlation oflongest relaxation times to the molecular weightdistribution. Though it is not yet clarified viawhich integral mean value of the MWD integralvalues of the distribution of relaxation times canbe described.

Hence the aim of this contribution is todetermine this correlation between longestrelaxation times of CaBER type experiments withthe MWD of different polymers. This is to be donefirst via investigation of the behaviour of idealblended polymer standards with a defined MWDin uniaxial elongational flow in the CaBER exper-iment and second for a set of commercially avail-



able blended celluloseethers introduced in theintroduction.

3 EXPERIMENTAL SECTION

The polystyrene standards used for this workwere acquired from Polymer Labatories (PL) andPolymer Standard Sevices (PSS). The methylhy-droxyethyl celluloses (MHEC) used were madeavailable from a company involved in MHECchemistry.

Preparation of the samples wasachieved by solving the respective amount ofpolymer in the accordant solvent. Homogeniza-tion was achieved by permanent agitation overa period of time not shorter than 3 days (MHECin 2 wt% NaOH) at RT, at least 7 days (polystyrenein diethylphthalate) with alternating tempera-ture for at least 60 days for Boger fluids (poly-styrene in styrene oligomere). Intrinsic viscosi-ties, [h], where determined with an Ubbelohdecapillary IIc (polystyrene) or Ic (MHEC), in a water-tub temperated at 25.0 ± 0.05°C. Steady shearflow and SAOS measurements where carried outon a rate controlled ARES rheometer (TA Instru-ments) with cone and plate geometries. Elonga-tional characterization was done on a CaBERrheometer (ThermoHaake). Determination ofthe molar mass and its distribution of the MHECswas achieved using a combined method of sizeexclusion chromatography (SEC), multi-anglelaser light scattering (MALLS) and differentialrefractometer (DRI).

4 RESULTS AND DISCUSSION

4.1 INFLUENCE OF THE MWD ON THE FLOWBEHAVIOUR OF MHEC

In the following chapter the influence of the MWDon the rheological behaviour of the MHECs is to bediscussed. The investigated MHECs were specifi-cally blended from three different celluloses withdifferent intrinsic viscosities ([h]cellulose3 < [h]cel-lulose2 < [h]cellulose1) by the producing company toobtain different MWDs but almost the same Mw.This is usually done to tune the flow properties ofa specific sample to a specific application. The

blended samples were hydroxyethylated after-wards. In Table 1 the different blending ratios andthe DS (degree of substitution for the methylgroup at one glucose monomer unit) and MS(molar degree of substitution for the hydroxyethylgroup because of multiple substitution) of theinvestigated MHECs are summarized. In additionto this the intrinsic viscosities of the pure cellulosesamples are listed.

A general problem of native cellulosederivatives is that molecularaly disperse solu-tions are hard to obtain since the cellulose back-bone tends to form aggregated clusters in solu-tion via H-bonds of unsubstituted OH-groups. Tosupress this formation of aggregated structuresall rheological measurements of the MHECs wereaccomplished in a solvent consisting of 2 wt%NaOH in water.

Figure 1 shows that the investigatedMHECs do not show significant differences interms of their shear viscosity, only the sampleMHEC 2 gives a slightly higher zero shear viscos-ity than the other two samples. Via fitting of theexperimental data to the modified Carreaumodel one can determine the longest relaxationtime t0 of steady shear flow.

(1)

with b being a transition parameter and n beingthe slope of the flow curve. These calculatedrelaxation times, listed in Table 2, show no quan-titative differences.

Still these samples show a differentbehaviour in the practical application as indroplet breakup, filament formation and nozzleextrusion. A method to quantitatively access

h h t g= +( )⎡⎣

⎤⎦0 1 o

b n b

10-2 10-1 100 101 102 10310-2

10-1

100

101

102

MHEC 1 MHEC 2 MHEC 3 Carreau Fit for MHEC 1 Carreau Fit for MHEC 2 Carreau Fit for MHEC 3

h / P

as

g / s-1

Table 1 (above): Blendingcomposition, DS (degree of

substitution for themethyl-group) and

MS (molar degree ofsubstitution for the

hydroxyethyl-group) of theinvestigated MHECs 1-3.

Figure 1 (below): Shearviscosity h versus shear rate

g· for MHECs 1-3, 2 wt%,dissolved in aqueous NaOH

(2 wt%) at 25°C.



these properties is via extensional flow. Figure 2shows the results for uniaxial elongation deter-mined with the CaBER experiment for the sameMHEC solutions shown in Fig. 1.

From Fig. 2 one can see very clearly thatthe elongational flow field has a different effecton the MHECs. The MHEC solutions show pro-nounced differences in filament breakup. Thesample MHEC 3 shows a considerably higherbreakup time then the blending composition ofthis sample would suggest, since its MWD is themost narrow over all. Via the time dependentdecrease of the filament diameter one can direct-ly evaluate the longest relaxation time, t0.According to Anna and McKinley in the spectrumof relaxation times of the elasticity modulus

(2)

in CaBER like experiments only the longest relax-ation time is excited [26]. For this reason only themoldulus of the longest relaxation time, G0, hasto be taken into account for further considera-tions. For the time dependent filament diameterat intermediate times one comes to the follow-ing, in regards to Entov and Hinch, slightly cor-rected expression [27]

(3)

with s being the surface tension of the investi-gated fluid. The decrease of the filament diame-

DG D

D et

=⎛⎝⎜

⎞⎠⎟

−⋅0 0

1 3

03

40

st

G t G ei

t

i

Ni

es

( ) = ⋅−

=∑ t

0

mod

ter for a viscoelastic fluid therefore depends onlyon the elastic modulus, G0, the initial filamentdiameter, D0, and the longest relaxation time, t0.The arising question is which mean averagemode of the relaxation time resp. the MWD isappealed to by uniaxial elongation. To approachthis problem, defined polystyrene blends werefirstly investigated to quantify the influence ofthe molar mass respectively the MWD on theelongational flow behaviour.

4.2 Influence of the MWD on the flowbehaviour of polystyrene

The polystyrene solutions investigated wereblended from different narrowly distributedpolystyrene standards with varying molar mass-es to achieve an approx. constant molar mass Mwof 4.7 · 106 g/mol with different MWDs varyingin Mw/Mn from approximately 1 to 1.84 (manu-facturers specifications were used for primaryevaluation of molar mass distribution). The truemolar masses of the polystyrene standards wereacquired via viscosimetry and the Mark-Houwink-Sakurada equation [28]

(4)

with Kh = 8.62 · 10-3 cm3/g and a = 0.736, and arelisted together with the intrinsic viscosities of thepolystyrenes in Tab. 3. In Table 4 the absolutecomposition of the investigated polystyreneblends are listed together with the width of theMWD. The flow curves shown in Fig 3 for these

h h⎡⎣ ⎤⎦ = K Ma

10-2

10-1

100

6420

MHEC 1 Fit to Eq. 2 MHEC 2 Fit to Eq. 2 MHEC 3 Fit to Eq. 2

D / D

0

t / s

Table 2 (above): Longestrelaxation times of steadyshear flow and CaBERexperiments for theinvestigated MHECs 1-3.

Figure 2 (below): Filamentdiameter versus time for theMHECs 1-3, 2 wt% in NaOHat 25°C.

Table 3: Molecular para-meters of the investigatedpolystyrene standards.



blends (1 wt% in diethylphthalate) show approx-imately the same flow characteristics. In contrastto this the results of uniaxial elongation in aCaBER experiment are shown in Fig. 4 for thesame polystyrene blends.

Fig. 4 shows, that in contrast to steadyshear flow experiments one can determine pro-nounced differences in the capillary thinningbehaviour for the investigated polystyreneblends. In the linear regime of this semi-loga-rithmic plot one can evaluate longest relaxationtimes according to Eq. 3. The longest relaxationtime in uniaxial elongation increases with a fac-tor 2 from blend 1 to blend 3. For a correlation oflinear viscoelastic terms like h0 and J0 with theMWD of a polymer, different approaches have

been made in literature [29 - 31] with the gener-al form

(5)

with P being a correction term that depends ondifferent modes of the MWD and a and aM beinga viscoelastic characteristic value of the distrib-uted and the mondisperse sample. To correlatethe relaxation behaviour of the polystyreneblends with the MWD, a model equation wassearched for, that directly relates the ratio ofrelaxation times of monodisperse (blend 1) andpolydisperse samples with the MWD. The factorP in the majority of approaches is of the form

(6)

with Mx being the x-mean molar mass

(6a)

and y and c being empirical or theoreticalpredicted parameters. Least square fits of theexperimentally obtained values of t0 and t0, M asour characteristic viscoelastic properties as a func-tion of P (Eq. 6) for several different x-mean dis-tributions and c and y as fitting parameters wereaccomplished to determine the best suited Mx. Asshown in Fig. 5, the best correlation could beobtained for Mx as the z + 2 average molar mass.

The least square fit of the data in Fig. 5gave the following equation to describe the

Mn M

n MXi i

x

i ix= ∑

∑ −1

PMM

X

Wy

c

=⎛

⎝⎜⎞

⎠⎟

ˆ ˆa a PM=

0.0 0.5 1.0 1.510-3

10-2

10-1

100

linear regime for evaluation of 0according to Eq. 3

Blend 1.0 Blend 1.1 Blend 1.2 Blend 1.5 Blend 2.0 Blend 3.0

D / D

0

t / s

1

1

polystyrene blends in diethylphthalate..... least square fit of y (Eq. 6)

2

2

t 0 / t 0,

M

Mz+2 / Mw

10-1 100 101 102 10310-3

10-2

10-1

100

polystyrene blends in DEP

Blend 1.0 Blend 1.5 Blend 1.1 Blend 2.0 Blend 1.2 Blend 3.0

h /

Pas

g / s-1

Table 4 (left above): Blendcomposition and values ofpolydispersity Mw / Mn for

investigated polystyreneblends.

Table 5 (right above):Longest relaxation times of

uniaxial elongation forinvestigated polystyrene

blends.

Figure 3 (left middle): Shearviscosity h versus shear

rate g for polystyreneblends, 1.0 wt% in

diethylphthalate at 25°C.

Figure 4 (right middle):Filament diameter versus

time for polystyrene blends,1.0 wt% in diethylphthalate

at 25°C.

Figure 5 (below): Leastsquare fit of parameters

c and y to Mz+2/Mw forpolystyrene blends in

diethylphthalate.



dependency of the relaxation times from thewidth of the MWD

(7)

with

The integraly determined longest relaxation timeof uniaxial elongation in CaBER like experimentsof a distributed sample is hence mainly influencedby the Mz+2 mean molar mass of the MWD. How-ever, one has to keep in mind, that the correlationin Eq. 7 to the Mz+2 mean molar mass and the val-ues of c and y are so far purely empirical.

To point out the influence of a high-mol-ecular fraction on the flow behaviour in capillarybreakup, two polystyrene standards (2.8 · 106g/mol and 8.17 · 106 g/mol) were blended at a con-stant concentration of 250 ppm in styreneoligomer as the solvent. The resulting zero shearviscosity of these Boger fluids [32] is very highcompared to a solution in DEP, so that relaxationactions of the polymer coils are slowed down toa high degree which therefore leads to animproved detectability even at concentrationsbelow c* (critical overlap concentration). Theresults of steady shear flow measurements forthese Boger fluids are shown in Fig. 6.

Fig. 6 shows that almost no differencesin zero shear viscosity can be detected for the setof investigated binary Boger blends as expectedfor a mainly solvent dominated shear flow in adilute solution. In contrast to this, the results ofuniaxial elongation for this set of Boger blendsare shown in Fig. 7.

As shown in Fig. 7 a fraction of 0.31 wt%of the high-molecular species already results inmeasureable longer breakup times. Since theCaBER experiment reacts very sensitive to thelongest relaxation time of the high-moleclaredge of the MWD according to Eq. 3 tiny amountsof high-molecular species already lead to a pro-nounced influence on the elongational behav-

Mn Mn Mz

i i

i i+ = ∑

∑2

5

4

t

t0

0

2

1 22

,

.

M

z

w

MM

=⎛

⎝⎜⎞

⎠⎟+

iour. However, one has to keep in mind that incontrast to the blends in Fig. 4 these binaryblends do not have a constant weight averagemolar mass but rather an increasing Mw with anincreasing part of the high molecular weightspecies. Therefore, one would naturally expectthe relaxation time to rise with increasing part ofhigh molecular weight species. A better way toobserve the influence of the distribution is againto plot a reduced t0/t0, M. The required t0, M canbe obtained from the pure low and high molarmass solutions, since the relaxation time depen-dence scales with Mw3n for narrow distributions[9, 26], with n being the excluded volume coeffi-cient

(8)

We obtain

in good agreement with Anna and McKinley andcan therefore plot

The results are shown in Fig 8. From Fig. 8 one cansee that the relaxation times of the binary blendsdo not scale with the same exponent c as thepolystyrene blends in DEP (Eq. 7). Still, linear fit-ting of the data works out quiet well, as shown

t

t0

0

2

,M

z

w

fMM

=⎛

⎝⎜⎞

⎠⎟+

t010 1 621 6 10,

..M wM= ⋅ −

t010 1 62 0 0523 1 7 10,

( . . )( . . )M w M= ± ⋅ − ±

Figure 6 (above):Shear viscosity h versusshear rate g· for investigatedpolystyrene Boger fluids,0.025 wt% at 25°C.

Figure 7 (below):Filament diameter versustime for the investigatedpolystyrene Boger fluids,0.025 wt% at 25°C.

0 25 50 75 10010-3

10-2

10-1

100

c = 250 ppmpart of 8.17x106g/mol in wt%

90.0 1.00 50.0 0.31 10.0 0.10 3.20 0.00

D / D

0

t / s

10-1 100 101100

101

102

c = const. = 250 ppmpart of 8.17·10 6 g/mol in wt%

90.0 1.0 50.0 0.31 10.0 0.1 3.2

h / P

as

g / s-1.


in Fig. 8. However, we should keep in mind, thatwe are dealing not with a flory distribution, buta bimodal distribution of the molar mass. In addi-tion to this the styrene oligomers are a worse sol-vent than diethylphtalate and close to theta con-ditions. We therefore refrain from comparing cfor diethylphthalate and Boger fluid.

4.3 Influence of the MWD on the elongationalbehaviour of MHECs

Since the influence of the width of the MWD onthe elongational behaviour of polymer fluids wasinvestigated on polystyrene standards, theabsolute molar masses and their distributionswere determined for the investigated commer-cial MHECs 1-3 to correlate the results with theelongational behaviour shown in Fig. 2 in form ofthe thread thinning behaviour. Determination ofthe absolute molar masses and the molar massdistributions was achieved via coupled methodsof size exclusion chromatography (SEC), multiangle laser light scattering (MALLS), and differ-ential refractometer (DRI) [33]. The results of thelight scattering experiments for the three differ-ent MHECs are shown in Fig. 9 in terms of the dif-ferential molar mass distribution.

As shown in Fig. 9 the sample MHEC 1exhibits the broadest distribution of the molarmass that also is close to being bimodular. Theother two samples MHEC 2 and MHEC 3 follow upwith MHEC 2 having a broader distribution thanMHEC 3. All three samples have very similar weightaverage molar masses. The determined mean val-ues for the distribution and the polydispersities forthe MHECs are listed in Table 6 together with therecovery rates of the SEC. The recovery rate is thefraction of polymer that reaches the differentialrefractometer based on the amount of polymerthat was originally injected.

However the determined MWDs do notcorrelate with the results for uniaxial elongation forthe MHECs shown in Fig. 2 because sample MHEC 1with the broadest distribution and hence the high-est ratio of high molecular weight polymer does notshow the longest breakup time. Instead, as shownin Fig. 2 the sample MHEC 3 with the narrowest dis-tribution shows the longest breakup time. Asshown in table 6, the ratios of recovery for the lightscattering experiments indicate a rather largeamount of not molecularly dispersed sample thatis seperated from the solution by filtration and thefollowing pre-columns. To adjust the sample prepa-ration for the CaBER experiments to the samplepreparation for the light scattering measurementsthe MHEC solutions were centrifuged and againexamined via CaBER measurements. The results areshown in Fig. 10.

In contrast to Fig. 2 the centrifuged sam-ples show the order in breakup times expected


104 105 1060.0

0.2

0.4

0.6

0.8

1.0 MHEC 1 MHEC 2 MHEC 3

diff.

frac

tion

of m

olar

mas

s

molar mass [g/mol]

10 -2

10 -1

10 0

2 640

MHEC 1 ___ Fit to Eq. 2

MHEC 2 ----- Fit to Eq. 2

MHEC 3 ....... Fit to Eq. 2

D / D

0

t / s

Figure 8 (left above):Least square fit of para-

meters c and y to Mz+2/Mwfor polystyrene blends in

diethylphthalate and binarypolystyrene blends in

styrene oligomer.

Figure 9 (right above):Differential molecular

weight distributions (MWD)of the investigated

MHECs 1-3.

Figure 10 (right middle):Filament diameter versus

time for the centrifugedMHECs 1-3 at 25°C.

Table 6 (left middle): Molecular parameters of

investigated MHECs 1-3,determined via combined

methods of SEC/MALLS/DRI.

Table 7 (left below):Longest relaxation times ofuniaxial elongation for the

investigated centrifugedand non-centrifuged

MHECs 1-3.

1

1

polystyrene blends in diethylphthalate ...... least square fit of y (Eq. 6)

binary polystyrene blends in styrene oligomer - - - least square fit of y (Eq. 6)2

2

t 0 / t 0,

M

Mz+2 / Mw



from the distributions determined with lightscattering. Sample MHEC 1 with the broadestMWD shows the longest breakup time sampleMHEC 3 with the narrowest MWD the shortestbreakup time. The results of the CaBER experi-ments and the results of light scattering can thusbe correlated with the same sample preparation,because in both cases only the molecularly dis-persed fraction of the sample is characterized.The relaxation times evaluated from Fig. 10 viaEq. 3 are listed together with the relaxation timesof the non-centrifuged samples in Table 7.

Comparing the breakup behaviour of themolecularly dispersed samples of MHEC to thepolystyrene blends one can observe differences inthe shape of the curves. Whereas the polystyreneblends show a steady thinning in the semi-log plotof Fig. 4 in accordance with Eq. 4, for late times theMHECs show a sudden increase in the thinningrate and a fast breakup. Stelter et al. [34] showedthat the elongational behaviour of polymer solu-tions differs for ionic resp. non-ionic polymers. Themain reason for this is that ionic polymers formmore rigid and therefore more expanded polymercoils than non-ionic polymers of the same molarmass. This results in shorter breakup-timesbecause the coils are closer to their finite extensi-bility. This effect results qualitativly in differentshapes of the curves shown in Fig. 2 and Fig. 10 forthe rigid MHECs and in Fig. 4 and Fig. 7 for the moreflexible polystyrenes. Stelter et al. also showedthat this effect quantitativly results in two distincthE, t/t0 dependencies for flexible resp. rigid likebehaviour where hE, t refers to the terminal elon-gational viscosity that is obtained once the poly-mer chains have reached their finite extensibilitylimit [34]. In Fig. 11 the steady terminal elonga-tional viscosity is ploted versus the relaxationtimes for the investigated polymers. The terminalelongational viscosity hE, t has been determinedfrom the general transient elongational viscosity

that has been extrapolated at late times to itstime independent limit.

Fig. 11 shows that the polystyrene blendsin diethylphthalate correspond well to the behav-iour of flexible polymers in extensional flowsobserved by Stelter et al. (line 1). In comparison tothis the MHECs in NaOH show the expected lowervalues for hE, t/t0 since they are much more rigid.However, these values do not fit the trend for rigidlike behaviour found by Stelter et al. which is dia-grammed by line 2 in Fig. 11, but even lower values.Nevertheless a linear trend can be observed for therelaxation times of the MHEC solutions (line 3 inFig. 11). The shift of the linear trend to higher relax-ation times is probably due to higher concentra-tions used in this work and an even greater expan-sion due to the ionization by the NaOH. As theconcentrations used for the MHEC solutions arerelativly high (2 wt%) a structure buildup viahydrogen bonding may be an issue. These aggre-gates may have great influence on the elonga-tional behaviour of the MHEC solutions even in thecentrifuged state and superpose the resultsobtained for the single polymer coil.

However, the absolute measured MWDsof the MHECs can be consulted to evaluate theratio t0/t0, M qualitatively according to Eq. 7.With the CaBER relaxation times (see table 7) uni-form values for t0, M should be the result if Eq. 7is also valid for the MHECs. The evaluated valuesfor t0, M are listed in Table 8 for the MHECs 1-3.As Table 8 shows, the theoretical predictedlongest relaxation times for a hypotheticalmonodisperse MHEC sample are in goodagreement with each other. In addition to thisthe calculated longest relaxation time t0, M isin fairly good agreement with the longestrelaxation times for shear flow predicted by themodified Carreau model as shown in Fig. 1 andTab. 2.

4 CONCLUSIONS

The longest relaxation times, t0, obtained byCaBER like experiments for defined blends ofpolystyrene standards with a normal molecularweight distribution can be scaled into an expres-

hs

EmiddD dt

=−

/10-3 10-2 10-1 100100

101

102

103

3

21

polystyrene in diethylphthalate MHEC in NaOH

hE,

t / Pa

s

t / s

Fig. 11 (above): Comparisonof two distinct hE,t/t0dependencies for flexible (1)resp. rigid like behaviour (2)according to Stelter et al. toexperimental data.

Table 8 (below): Longestrelaxation times evaluatedaccording to Eq.7 for theinvestigated MHECs 1-3.


sion that correlates directly with specificmoments of the molecular weight distribution.This determined scaling law (see Eq. 7) can bedirectly assigned to blends of commercially avail-able, blended celluloseethers to obtain informa-tion on the MWD of these polymers. In compari-son to small amplitude oscillatory shear thismethod is faster and more sensitive.

The results could then be correlated withthe absolute molar mass distributions obtainedvia means of SEC/ MALLS/ DRI (see Fig. 8). It couldbe shown in this paper that uniaxial elongationin CaBER like experiments is a more sensitivemethod for the detection of the molecularweight distribution then steady shear flow forsamples with similar weight-average molarmass and therefore similar flow properties insteady shear flow experiments (see Figs. 1 and 3).Uniaxial elongation in CaBER like experimentsalso allows for a sensitive detection of non mol-ecularly dispersed fractions of the investigatednative cellulose derivative (see Figs. 2 and 9) andcan thus predict the processability of these poly-mers in elongational flows.

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*email: [email protected] received: 5.7.04

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