new developments for the mechanical characterization of materials · 2011. 1. 4. · new...

Korea-Australia Rheology Journal December 2010 Vol. 22, No. 4 317

Korea-Australia Rheology JournalVol. 22, No. 4, December 2010 pp. 317-330

New developments for the mechanical characterization of materials

N. Dingenouts and M. Wilhelm*

Institute for Technical Chemistry and Polymer ChemistryKarlsruhe Institute of Technology (KIT), D-76131 Karlsruhe, Germany

(Received May 25, 2010; accepted June 11, 2010)

Abstract

Rheology as a science of flow of matter is highly influenced by the topology and morphology of the inves-tigated materials, e.g. polymer molecules. Within this publication three current developments will be pre-sented. In the first part, the direct influence of molecular structure on the non-linear mechanical propertiesand the processing will be presented. In a second part, rheological methods, e.g. elongation rheology or non-linear shear (especially FT-Rheology) are further developed. Finally the combination of rheological mea-surements with a second characterization method (NMR, X-ray, dielectric spectroscopy etc.) is described.These new combinations gain unique information about molecular dynamic and structure of time and sheardependant phenomena.

Keywords : FT-Rheology, capillar rheology combined methods, Rheo-SAXS, Rheo-Dieelectric Rheo-NMR

1. Introduction

Rheology is the science of deformation and flow ofmaterials (Macosko, 1994), where polymers are a typicalclass of materials in the field of rheological characteriza-tion (Larson, 1999; Macosko, 1994). Rheology has aspectsof a fundamental point of view by studying the flowbehavior of complex fluids, but also from the technicalpoint of view of polymer processing, e.g. extrusion. Inpolymeric materials, the final morphology in phase sep-arating systems and the topology of the polymer moleculesare molecular parameters with a high impact on the flowbehavior of the final material. Both the linear regime ofoscillating rheology and advanced rheological methods,e.g. non-linear oscillating rheology or elongation rheology,are needed for the full examination of these flow prop-erties. Therefore, methods studying the influence of topol-ogy and morphology on the resulting mechanicalproperties are of fundamental and technical interest.

Within this publication three current developmentswithin our group at the Karlsruhe Institute of Technology(KIT) will be presented.

(1) In the first part, a direct interrelation between molec-ular structure via NMR spectroscopy, non-linear rheologyand optimum processing conditions (e.g. extrusion) ofpolymer materials focused on melt flow instabilities will bepresented. The effect of polymer topology on non-linearrheology and processing instabilities like shark skin, melt

fracture or gross melt fracture can now be determined dur-ing the processing using special piezoelectric transducersand advanced data processing (Filipe et al., 2009; Palza et

al., 2010).(2) The extension of the linear oscillatory rheology into

the non-linear regime using large amplitude oscillatoryshear (LAOS) (Krieger an Niu, 1973; Giacomin and Dealy,1993; Wilhelm et al., 1998; 1999; Wilhelm, 2002). Thefocus will be on the quantification of the generatedmechanical higher harmonics (FT-Rheology) for differentmaterial classes. Additionally low viscose elongation rhe-ology utilizing the capillary break up rheometer (CaBER)was further developed to allow the simultaneous mea-surement of the forces, respective stress, was achieved(Klein et al., 2009).

(3) Since rheology is an inherent macroscopic method,the understanding of the involved length scales, time scalesand structural ordering on a molecular scale is of greatimportance. This can only be achieved if a second, molec-ular method is applied during the rheological measure-ments. For time or shear dependant phenomena a trulysimultaneous determination of mechanical and molecularproperties is essential. Within our group we have so farexperimentally realized a unique rheo-SAXS combination(Hyun et al., 2008) to correlate mechanical non-linearitieswith structural ordering, e.g. for liquid crystalline samples.Molecular dynamics on the length scale of the end-to-endvector (e.g. 10~50 nm) of a polymer sample can be quan-tified towards the relaxation times and distribution usingthe combination of rheology and dielectric spectroscopy(Hyun et al., 2009) (rheo-dielectric). To determine more

*Corresponding author: [email protected]© 2010 by The Korean Society of Rheology

N. Dingenouts and M. Wilhelm

318 Korea-Australia Rheology Journal

local molecular motions the combination of NMR relax-ometry (T1 and T2) with rheology is beneficial since theNMR relaxation parameter are mostly determined via shortrange dipole-dipole couplings (Kahle et al., 2008) coveringtypically 1~2 nm.

2. Polymer Topology and Melt Flow Instabilities

The detailed characterization of polymer topology isspectroscopically very demanding. Especially the precisedetermination of long chain branching in polyethylene is ofhigh technical importance. Substantial improvement wasdone recently using melt state NMR (Klinke et al., 2006;Pollard et al., 2004; Parkinson et al., 2007) where branch-ing down to 1 branch in 10,000 CH2-groups could be deter-mined in half of a day measuring time using an optimized500 MHz NMR spectrometer. Having characterized themolecular structure, FT rheology (see next chapter) allowsto correlate this with the non-linear response (Vittorias et

al., 2007) of the material.The polymer topology affects the non-linear mechanical

response but also the instabilities, e.g. in polymer extrusionprocesses with high throughput conditions. The extrusionvelocity is limited by melt flow instabilities which changethe appearance and properties of the extrudate. Althoughthese instabilities have been well known for severaldecades (Larson, 1992; Denn, 2001), their origins andmechanisms are still not clear, as each one has its owncharacteristics and dependence on shear rate and on thepolymer properties. There are three main instabilities,namely: sharkskin, spurt (or stick-slip), and gross meltfracture. At low shear rates the polymer surface is smoothwithout any kind of perturbations. Increasing the shear ratecan lead to the appearance of sharkskin. Sharkskin consistsof a periodic surface instability with both small amplitudesand high characteristic frequencies. The appearance ofsharkskin depends on the material chosen (El Kissi andPiau, 1994) and it has been related with short chain branch-ing in the polymer. In the flow curve (a plot of the volumeflux against the pressure) this instability is generally relatedwith a change of the slope (Denn, 2001; Wang, 1999; Hillet al., 1990). At higher shear rates some polymers show aspurt instability that is characterized by periodic smooth/rough regions in the extrudate, associated with large butslow pressure oscillations inside the barrel. A discontinuityin the flow curve is observed under these conditions and inpressure controlled rheometers a hysteresis appears (Wang,1999; Wang and Drda, 1996). Finally, at high shear ratesmore pronounced instabilities appear which are due to bulkphenomena, e.g. helicoidal defect, melt fracture, spiraldefect, etc. These instabilities are called gross melt frac-ture. The common characteristic of the last instabilitiesseems to be its origin in the entrance of the die section dueto turbulences or vortex formations in the barrel (Denn,

2001; Legrand and Piau, 1998; Tao and Huang, 2005).The origin of the melt flow instabilities is discussed

widely in literature. The sharkskin instability, for example,seems to be related to a singularity in the polymer flowaround the die-exit. This idea is supported by a consid-erable amount of experimental observations (Migler et al.,

2002; Mackley et al., 1998; Rutgers and Mackley, 2000;2001; Arda and Mackley, 2005; Venet and Vergnes, 2000).The well known dramatic change in the flow dynamic atdie-exit is caused by a high velocity gradient at the die-exitwhere the flow evolves from e.g. a laminar shear flow withno-slip boundary condition, to a plug flow with free sur-face boundary condition. This singularity associated withthe die-exit has been simulated and correlated with bire-fringence observations. Stress oscillations close to the exit,with a period similar to the formation of the instabilities,were found (Migler et al., 2002; Rutgers and Mackley2000; 2001; Arda and Mackley, 2005; Venet and Vergnes,2000). Based on the above observations several theorieshad been developed to explain the sharkskin instability, asfor example those related with the melt rupture or crackingwhen the polymer leaves the die-exit (El Kissi and Piau,1994; Cogswell, 1977), or theories based on the coil-stretch transition in a zone still inside the die, but veryclose to its exit (Barone et al., 1998; Wang and Drda,1997). Nevertheless, all these interpretations are in con-tradiction with theories based on the constitutive origin ofthe sharkskin inside the die (die-land region) (Shore et al.,

1996; Moleenar et al., 1998; Bertola et al., 2003; Palza et

al., 2009).The situation is similar for the other melt flow insta-

bilities. In case of the spurt instability, there is a generalagreement that the origin is due to changes in the fluid-dynamic boundary conditions associated with a reversibletransition from a non-slip (or stick) to a slip behavior at thedie-wall (Wang, 1999; Barone et al., 1998). In viscoelasticfluids the slip condition has been showed experimentally asa drastic increase in the velocity of the fluid at areas closeto the wall when the polymer reaches a critical stress value(Lim and Schowalter, 1989; Migler et al., 1993; Münstedtet al., 2000). One of the problems with theories based onslip processes is the assumption of a non-slip condition formodels that are able to predict the spurt instability fromconstitutive equations (Denn, 2001; Aarts and van de Ven,1999; den Doelder et al., 1998). This is in clear contrastwith the above-mentioned experimental findings.

The above comparison between experimental evidenceand theoretical concepts clearly indicates the necessity ofmore advanced experimental setups and data analysis to gaina better understanding of the behavior of melt flow insta-bilities. Therefore we constructed a non-conventional set-upfor the evaluation of melt flow instabilities based on a cap-illary rheometer (GÖTTFERT Rheo-tester 2000) with a self-constructed, non conventional slit-die shown in Fig. 1.



This slit-die was specifically designed in order to allowthe evaluation of the pressure fluctuations at three differentlocations along its length at 3, 15 and 27 mm and namedT1, T2 and T3, respectively (Filipe et al., 2009). The totaldie length is 30 mm with a cross section of 3.0 mm×0.3 mm. The evaluation of the pressure was done via fastacquisition piezo-electric pressure transducers (model6812B, from KISTLER, Switzerland). The use of these fastresponse transducers, coupled with oversampling tech-niques (Wilhelm et al., 1999; van Dusschoten and Wilhelm,2001; Hilliou et al., 2004; Wilhelm, 2002), allowed a sub-stantial improvement by a factor of 103 and 102 in terms ofboth time and pressure resolutions when compared with aconventional set-up (Filipe et al., 2008; 2009). The limitingtime resolution ∆t is typically 1 ms after oversampling and5 mbar for the pressure resolution ∆P in our set-up. Suchdevelopment proved to be crucial to detect and characterizeinstabilities, which would not be detectable solely by theuse of conventional setups. More details about this set-upare found in the work of Filipe et al., (2008 and 2009).

The preliminary work done on this improved toolallowed the understanding of the effects of uniaxial exten-sional properties on the onset of melt flow instabilities(most specifically, stick-slip), for industrial broad molec-ular weight distributed polyethylenes (Filipe et al., 2008;

2009). Additionally, it was possible to elucidate the cor-relation of the onset of melt flow instabilities with materialstructural properties (molecular weight - Mw, molecular weightdistribution - MWD and topology) for industrial polyeth-ylenes possessing broad MWD.

In a recent publication (Palza et al., 2010) we combinedthis slit-die setup with a new mathematical framework toprocess the acquired time dependent pressure signals (seeScheme 1).

The collected pressure data were further treated usingstatistical analysis. After oversampling, Fourier analysis isperformed on the time dependent pressure data, and theobserved peaks at the frequency-domain are located at fre-quencies that are the inverse of the related time scale of theinstability. Our analysis will give a new perspective of themain parameters that characterize melt flow instabilitiescorrelating them with material structural properties such asMw, MWD and topology. Moreover, by measuring thecross-correlation function for the pressure signals comingfrom the transducers located along the die, we can evaluatethe dynamic of these phenomena.

To study the whole range of possible melt-flow insta-bilities, four commercial polyethylenes of different topol-

Fig. 1. Technical drawing of the home-made slit-die designed

with three high sensitive pressure transducers inside the

slit (0.3×3×30 mm3), labeled as T1, T2 and T3.

Scheme 1. Summary of the mathematical tools used to analyze

the data from our new set-up. The subscript i refers to

the different transducers. SD, spectral density; ACF,

auto-correlation function; FT, Fourier transform; CCF,

cross-correlation function; MA, moment analysis.

Table 1. Main characteristics of the polyethylenes studied

Sample Estimated topology Mw (kg/mol) Mn (kg/mol) Main instability

PE-L

PE-LCB

PE-7SCB

PE-13SCB

Linear

Long chain branching

Short chain branching

Short chain branching

193

186

100

85

20

20

45

37

Spurt

Gross Melt Fracture

Sharkskin

Sharkskin



ogies were chosen. PE-L is a linear high-density polyethylene and PE-LCB

is a long-chain branching low-density polyethylene, bothfrom Lyondel BASELL. Two ethylene/1-octene copoly-mers from Dow with a short chain branching (SCB) incor-poration of 7 (PE-7SCB) and 13 mol% (PE-13SCB) werealso studied. More Details about the samples can be foundin the work by Palza et al. (2010).

Using these samples and our self constructed slit-diecombined with the new mathematical evaluation schemewe could detect and characterize all 3 typical types of meltflow instabilities (Palza et al., 2010).

In order to analyze the effect of the long-chain branching,first the PE-L sample is studied as it is a linear polymerwith low amount of branching. By investigating the PE-LCB sample in comparison it is possible to analyze theeffect of the long-chain branching towards the pressurefluctuations inside the die. The cross-correlation functionbetween the transducers shows a drastic decrease in thebeginning reaching a non-zero but oscillatory values lateron. This means that the signals are basically not correlatedat short times. The different behavior between PE-L andPE-LCB under gross melt fracture conditions could beassociated with the higher elasticity in melt state of PE-Lthat explains its plug-flow fluctuations (Palza et al., 2010).

The spurt instability has been related with the presence oflong-chain branching in polyethylenes (Filipe et al., 2009).It seems nevertheless that there is a critical value for thedegree of long-chain branching. Above this threshold thepolymer does not develop this instability as PE-LCB inves-tigated in the work of Palza et al. (2010) has much higheramount of long-chain branching (3 LCB/ 1000 CH2) thanthe samples used in the work of Filipe et al. (2009) (lessthan 1 LCB/ 1000 CH2).

Short chain branching mainly influences the sharkskininstability. Fig. 2 shows the normalized pressure oscillationsfor the PE-7SCB sample at a shear rate of 315 s-1 togetherwith the respective Fourier analysis for the T2 signal.

Under these conditions PE-7SCB develops the sharkskininstability as a surface distortion appears in the extrudate.Noteworthy, the three transducers located inside the slit-dieare able to detect pressure oscillations. To the best of ourknowledge, the last finding is unique and it shows the highsensitivity of this new set-up.

The pressure fluctuations are around 0.05% with respectto the mean value. Comparing the pressure fluctuationsarising from sharkskin instability with those coming fromthe spurt instability (around 10%), a clear dependency ofthe relative pressure fluctuation with the kind of instabilityis observed. The PE-13SCB sample presents the samebehavior than PE-7SCB. The use of our new methodology,consisting of unique high sensitivity pressure detectiontogether with the application of an advanced mathematicalframework, allowed measuring directly inside the die, both

the amplitude and the frequency of pressure fluctuationsarising from sharkskin. Such analysis was not possibleuntil now and it was not reported by other researchers,mainly due to experimental limitations of the equipmentavailable. The nature of the pressure fluctuations associ-ated with sharkskin (low pressure deviations and very fastfrequencies) requires setups with very high pressure res-olution (∆P of around 5×10-3 bar) and extremely highacquisition rates (3×104 s-1). In addition, the behavior ofthe pressure along the die can be related with the origin ofthe sharkskin instability (Arda and Mackley 2005).

The sample with low amount of long-chain branchingdevelops spurt instability which is characterized by lowfrequencies (around 0.05 Hz) and high relative pressurefluctuations (around 10%). It was additionally observedthat this instability starts in a region inside the die and itpropagates along it. The cross-correlation function allows

Fig. 2. (a) Normalized pressure fluctuations for PE-7SCB sample

at a shear rate of 315 s-1 (curves are shifted for simplicity).

The mean values of the pressure are 341 bar for T1, 263

bar for T2, and 41 bar for T3. (b) The respective Fourier

transform for T2, in the inset an optical microscope pic-

ture of the resulting extrudate (taken from Palza et al.,

2010).



us to estimate the velocity of this propagation. Increasingthe amount of long-chain branching, the spurt instabilitydisappears and the gross melt fracture is observed in thewhole range of shear rates studied. In general, this insta-bility has higher frequencies (between 1 and 30 Hz) andlower I1/I0 values (between 0.1 and 0.05%) than spurtinstability. The sharkskin instability develops in sampleswith short-chain branching and it is characterized by highfrequencies (between 10 and 100 Hz) together with low I1/I0 values (around 0.01%). Our results open up the idea thatthis instability has its origin inside the die and not only atthe die-exit, and it gives new evidence towards a possibleconstitutive origin.

In summary, the use of our new set-up with high sensitivepressure transducers located inside a slit-die (now commer-cially available via Goettfert company) combined with anadvanced mathematical framework results in a substantialimprovement by a factor of 103 and 102 in terms of time(typically 1 ms) and pressure (typically 5 mbar) resolutionscompared with a conventional set-up. These improvementsallow to characterize for the first time the whole range ofmelt instabilities in-situ (Palza et al., 2010). The charac-teristic frequency and the relative pressure fluctuation of theinstabilities together with the time cross-correlation functionfor the data from the different transducers were analyzed.

Our novel approach might allow the development of an“intelligent” extruder able to detect automatically the onsetof melt instabilities. Under this new concept, the extruderitself will conduct the changes in the operational variablesthat would avoid these distortions increasing the through-put and lowering at the same time energy consumptions.

3. FT-Rheology, Elongation Rheology

Another focus of our work is the extension of the linearoscillating rheology into the non-linear regime using largeamplitude oscillatory shear (LAOS). This results in a highersensitivity of rheology to topology and morphology of thematerials under investigations. We developed a new eval-uation method of non-linear oscillatory rheology, the FT-Rheology (Wilhelm, 2002). FT-Rheology allows the quan-tification of the generated mechanical higher harmonics fordifferent material classes.

To explain the LAOS excitation and FT-Rheology analysisone might start with Newton’s law for the viscosity. Theshear rate dependant viscosity is Taylor expended as afunction of shear (Wilhelm et al., 1998; Wilhelm et al.,

1999; van Dusschoten and Wilhelm, 2001; Wilhelm, 2002).

(1)

(2)

In case the applied deformation is perfect sinusoidal defor-mation with a frequency ω1/2π and a shear amplitude ,

.

(3)

Putting equation (3) in (2) and finally into (1), the fol-lowing proportionalities are obtained

(4)

From eq. (4) it is clear that higher harmonics at odd mul-tiples of the fundamental frequency are present in the timedependant torque. These can be analyzed as a FT-Rheologyspectra after a Fourier transform (Wilhelm et al., 1999;Wilhelm, 2002)

The experimental set up is displayed in Fig. 3, com-mercial versions are recently also available (ARES G2,TA-Instruments).

A typical torque as a function of time is displayed in Fig. 4for a water-in-oil emulsion. In the literature several meth-ods for the analysis of the time dependant torque are pre-sented. Potential analysis of the large amplitude responseinclude the analysis of G’ and G’’ (Hyun et al., 2002), theseparation into characteristic functions (Klein et al., 2007),the extraction of the inherent non-linearity (Hyun and Wil-helm, 2009), FT-Rheology or even more complex analysismethods (Ewoldt et al., 2007). It is further possible to cor-relate the measured FT-Rheology spectra to the spectrapredicted by constitutive equations for two Newtonian flu-ids forming an emulsion with a known surface tension(Carotenuto et al., 2008).

The application of the FT-Rheology is not related to aspecific class of materials, it is a rather general method.Currently the focus is on the interplay of topology, spe-cifically long chain branching in polyolefines (Vittorias et

σ ηγ·=

η η0 η1γ· 2 η2γ

·4…+ +=

γ0

γ γ0eiω

1t

=

γ· iγ0ω1eiω

1t

=

σ η0 η1γ02ω1

2ei2ω

1t

η2γ04ω1

4ei4ω

1t

…+ + +( )γ0ω1eiω

1t

∝

σ aeiω

1t

bei3ω

1t

cei5ω

1t

…+ + +∝

Fig. 3. Experimental realization of the FT-Rheology as an exten-

sion of a commercial rheometer. The time dependant

deformation and the torque are externally digitized, Fou-

rier transformed and further evaluated with self developed

software.



al., 2007), the investigation of phase separating systems,e.g. block copolymers (Oelschlager et al., 2007; Langela et

al., 2002), but also thickeners (Kallus et al.,, 2001) andfood have been investigated (Hilliou et al., 2009). The timedependant development of the intensity of the higher har-monics allows the quantification of orientation and fatigue.

Polymer topology affects strongly extensional rheology,as well in melt as in solution. In polymer production, manydifferent means of processing soft materials, such as injec-tion molding, extrusion, fiber-spinning, and film formation,are used. Extensional deformation plays frequently animportant role in these processes. For the understanding ofthese technical processes the analysis of the dynamicalresponse of low viscous viscoelastic fluids under strongextensional flows is crucial and needs to be understoodalso from a fundamental point of view (Tripathi et al.,

2000a; Laun and Schuch, 1989; Sattler et al., 2008). Onedrawback of the instrumentation available is that only thediameter of a stretch filament is measured without an addi-tional information about the mechanical properties of thesample or the necessary forces. Therefore, an extension forlow viscose elongation rheology utilizing the capillarybreak up rheometer (CaBER) to allow the simultaneousmeasurement of the forces, respective stress (Klein et al.,

2009) was developed. The capillary breakup technique is a unique tool to deter-

mine the extensional properties of fluids by measuring thedecline of the diameter of a stretched fluid filament D(t).Different set ups have been developed to determine elon-gational viscosity for viscous solutions. They are mostlybased on two different designs: The filament stretchingdevices for high viscous fluids and the filament rheometers

for fluids with a viscosity ranging from 10 mPas to103 Pas. In case of the low viscous fluids a filament is cre-ated and then the diameter of the stretched filament at themiddle position is observed. The filament develops a bal-ance of the viscous, elastic, gravitational, and capillaryforces where the filament is pinched off by the fluids sur-face tension (Tripathi et al., 2000a,b; Sattler et al., 2008;Matta and Tytus, 1990; Bazilevskii et al., 1990; 1997;Anna et al., 2001).

The Capillary Breakup Extensional Rheometer (CaBER)is the only commercially available extensional rheometerthat can perform such measurements on low viscous fluids.This technique is limited to certain samples, because theyneed a specific sample viscosity and a specific surface ten-sion. Due to the limited information of delivering only thefilament diameter D(t) at one position this instrument isnormally used only as an indexer for relative comparison.We developed an extension of the CaBER that allows addi-tionally the measurement of the normal forces F(t) thatarise in the fluid filament during the stretching (Klein et

al., 2009). The measurement of the normal forces isachieved by using a highly sensitive and fast piezoelectricforce sensor (Anna et al., 2001; Anna and Mckinley, 2001;Gaudet et al., 1996; Kolte and Szabo, 1999; Steher et al.,

2000; Szabo 1997). In the original publication (Klein et al.,

2009), it was demonstrated in detail how the force mea-surement capability was build into a commercially avail-able CaBER. This was achieved via minor hardwaremodifications. These modifications include the incorpora-tion of the state-of-the-art piezo electric force sensor,where the charge was converted into an electrical potentialusing a charge amplifier. The acquisition and processing ofthe data was done with an ADC-card and self-written soft-ware including oversampling (van Dusschoten and Wil-helm, 2001). The results of the measurements on severalvery different samples proof the viability of the conceptand show that the normal force measurements give infor-mation on the sample that cannot be obtained with the orig-inal CaBER where only D(t) was available. Please beaware that in principle x(t) is additionally available via thestep motor allowing further quantities to be calculated, forexample, the separation energy (tack). Furthermore it couldbe shown that the theory described earlier gave a reason-able result for the elongational viscosity when related withliterature values of the shear viscosity.

4. Combined Methods

The macroscopic behavior of any complex fluid dependsstrongly on its microscopic structural parameters, e.g.microstructure or molecular topology. However, purelyrheological methods provide only macroscopic measure-ments (e.g. the measured torque or normal force response).This means that rheological techniques can only be used to

Fig. 4. Inset: Measurement of the time dependant torque in a rhe-

ometer. The sample was a water-in-oil emulsion and a

shear excitation of 0.1 Hz was applied. The FT-Rheology

spectrum of the torque allows the quantification of the

non-linearity via the odd higher harmonics of the fun-

damental up to about the 151-th of the fundamental.



determine macroscopic continuum-level averaged materialfunctions, in which case any information regarding micro-scopic or molecular structure is inherently indirect. Obtain-ing simultaneously information on the microstructure oreven molecular level structure is often needed for a betterunderstanding of the rheological behavior. Thus, severalmethods have been developed to cross this bridge withrespect to the length scales involved. One example is thesimultaneous measurement of rheological and optical prop-erties, e.g. via optical microscopy, light scattering or mea-surement of birefringence and dichroism. Other examplesare combination of SANS (small-angle neutron scattering)and SAXS (small-angle X-ray scattering) with rheology orRheo-NMR, a combination of true molecular informationvia NMR and rheology.

Working in the non-linear regime of rheological char-acterization, the morphology of the sample is not inde-pendent of the applied shear. Shear flow can produceshear-aligned structure, e.g. blockcopolymers exhibit mac-roscopic orientation induced by LAOS flow. Other time orshear rate dependent phenomena are shear induced crys-tallization or vulcanization. Thus, truly simultaneous char-acterization of both length scales under investigation isnecessary.

In the last years, we developed three new and uniqueinstrumentations combining rheology with dielectric spec-troscopy (Hyun et al., 2009), NMR-relaxometry (Kahle et

al., 2008) and SAXS (Hyun et al., 2008) respectively.These combinations enable rheological measurements withtruly simultaneous characterization on different time andlength scales.

• Dielectric spectroscopy – rheology

As a complementary method to rheo-optical techniques,the rheo-dielectric combination is applicable to any mate-rial having permanent electrical dipoles or charge-inducedelectrical dipoles. Rheo-dielectric setups allow for simul-taneous measurements of dielectric and viscoelastic prop-erties and have been used to study liquid crystals(Capaccioli et al., 2007; Watanabe et al., 1998; 1999), thedynamics of polyisoprene chains (Watanabe, 2001; Watanabeet al., 2003; 2005), block-copolymers (Watanabe, 2001),carbon nanotube networks dispersed within polymer melts(Alig et al., 2008) and carbon black suspensions (Watanabeet al., 2001). This method has also been extended to thenonlinear regime under LAOS flow (Höfl et al., 2006;Capaccioli et al., 2007; Hyun et al., 2009).

The dielectric property reflects the orientational corre-lation of two segments at two separate times (e.g. t0=0 andt1=τ) and can be converted to the fluctuations of the dipoleof the molecules. A special case is the dielectric relaxationbehavior of flexible polymer chains of the so-called Stock-mayer type-A polymer (Kremer and Schönhals, 2003;Watanabe et al., 2002; Stockmeyer and Burke, 1969)

where the overall electric dipole is directly related to themolecular end-to-end vector. The dielectric spectroscopyreflects for these type of polymers the normal mode of theglobal chain motion (Watanabe, 1999). Thus the rheo-dielectric method enables us to investigate the globalmolecular chain dynamics under linear and non-linear flowconditions.

There are several reports of combining dielectric spec-troscopy with rheology in the literature, mainly by thegroup of Watanabe (1999, et al., 2002). They used dielec-tric cells based on capacity bridges in constant flow in amercury bath. Recently, we presented first measurementson the dielectric response of 1,4-cis-polyisoprene in oscil-latory flow (Höfl et al., 2006) using our new developedequipment (Hyun et al., 2009), consisting of a ARES-Rhe-ometer (TA Instruments) and a very sensitive dielectricALPHA-Analyzer (Novocontrol Technologies). TheARES-Rheometer is a strain controlled rheometer. Thestress (torque) and strain (displacement) data wereacquired by an ADC card (PCI-MIO-16XE; NationalInstruments) using self-developed software. An additionalPC controls the ALPHA-analyzer. The ALPHA-Analyzeris able to measure about 12 orders of magnitude frequencyrange (3×10-5Hz~1×107Hz), 16 orders of impedance range(10-2

Ω~1014Ω) and 15 orders of capacity range (10-15 F~

1 F). These ranges exceed the capacitance bridges used informer rheo-dielectric measurements by several decades ineach quantity.

Fig. 5 shows the experimental setup of the combination ofa rheometer and a dielectric analyzer in situ. To realize thisrheo-dielectric setup, a new measuring plate and fixture hadto be constructed and parts of the oven were modified.

The ceramic insulation between the parallel plate and fix-ture has a low coefficient of thermal expansion. ThusINVAR steel with an extremely low temperature coeffi-cient of 1.3×10-6 K-1 (conventional steel 13×10-6 K-1) isused for the new measuring plate and fixture. The closedoven system ensures temperature control and additionalelectric shielding. It is absolutely necessary to shield elec-tronic noise using the dielectric analyzer at low impedancerange. As a first step, dielectric measurements were con-ducted without shear and compared to dielectric spectrataken from the literature (Watanabe, 2001).

The normalized dielectric experimental results on thedielectric response of 1,4-cis-polyisoprene (PI) are shownfor monodisperse PI 50 kg/mol (at 25oC and 40oC) and PI70 kg/mol (at 25oC) in Fig. 6 (left). The dielectric relax-ation behavior of this type-A polymer (1,4-cis-polyiso-prene) has been investigated intensively by Watanabe(2001) under steady shear. Our normalized results showsimilar superposition as compared with results ofWatanabe. We compared experimental data with two verysimple chain models (pure reptation and reptation withCLF). At the low frequency region (ω<ωpeak), the dielec-



tric loss properties of PI 55 kg/mol, 70 kg/mol and 80 kg/mol are followed by pure reptation theory, (Watanabe, 2001). At the high frequency region (ω >ωpeak), the dielectric loss of of PI 55 kg/mol, 70 kg/mol and80 kg/mol are characterized by a power-law relationship,

such as the generalized model combining rep-tation with CLF in the fixed tube (the pure reptation modelshows , as seen in Fig. 6-left). Thus reptationwith CLF (contour length fluctuation or tube fluctuation,plotted as a line in Fig. 6a), for example, removes most ofthe discrepancy between experiment and theory. Theexperimental data and reptation with CLF show the pre-dicted power-law relationship, , although a littlebit broader at the low frequency region with the CLFmodel. This means that the CLF model also is not suf-ficient to fully explain the dielectric spectrum. Therefore,the tube model incorporating more complex mechanism,

for example, CR (constrain release) or DTD (dynamic tubedilation) has to be considered.

Fig. 6 (right) displays the dielectric spectra as a functionof ωdiel/2π under large amplitude oscillatory shear (LAOS)with different strain amplitudes for the PI 55 kg/mol usingour unique setup. The intensity decreases with increasingstrain amplitude without changing the peak position andshape. This means that LAOS affects neither the relaxationtime nor the spectrum of the normal mode process. Thedecrease in intensity can be explained by the alignment ofchains in the direction of the applied shear field.

A quantitative interpretation is done in the literature(Hyun et al., 2009). In summary, we have shown that fora single model system as 1,4-cis-polyisoprene the dielectricproperties of a type-A-polymer reflects the molecularweight of the polymer. In addition, the constraints of achain in a melt need to be considered by an appropriate

ε″ ω1

∝

ε″ ω1 4⁄–

∝

ε″ ω1 2⁄–

∝

ε″ ω1 4⁄–

∝

Fig. 5. Setup of the combination of a rheometer and a dielectric analyzer allowing determination of raw stress data and the dielectric

spectra in situ. (a) schematic construction, (b) detailed representation of the geometry, (c) picture of the final geometry.

Fig. 6. Left: Normalized dielectric constant (ε0-ε )/∆ε and dielectric loss / peak versus normalized frequency (ωdiel/ωpeak) of linear PI

55 kg/mol at 25oC and 40oC, PI 70 kg/mol at 25oC, and PI 80 kg/mol at 20oC. The dashed line indicates the prediction of the

reptation model (Eq. 6), the solid line the prediction of the CLF-model (Eq. 7).

Right: PI 55 kg/mol at 10oC for varying shear amplitudes. (taken from Hyun et al., 2009).

′ ε″ ε″



molecular chain model. This shows the sensitivity of thecombination of LAOS and dielectric spectroscopy for con-straints of polymer chains.

Therefore, dielectric spectroscopy combined with rhe-ology is an ideal method for the examination of moleculardynamics in complex polymer materials with phase-sep-aration or filler particles in equilibrium and under non-lin-ear oscillatory shear conditions.

• NMR-relaxometry - rheology

Nuclear magnetic resonance using spectroscopy andrelaxation measurements have long been used to observemolecular motion and the complex dynamic of polymerchains. NMR relaxation measurements have been con-ducted in polymer solutions, where the chain motion is rel-atively fast, and with polymers in the melt or solid state,where the molecular motion is substantially slower andmay vary over many orders of magnitude. Theory andexamples of this well-established method can be found inseveral textbooks (e.g. Schmidt-Rohr and Spiess, 1994;Bovey and Mirau, 1996). The most important relaxationtimes are the spin-lattice relaxation (T1) and the spin-spin-relaxation time (T2). The spectral density J(ω) as the Fou-rier transform of the fluctuations of the local fields Bloc

affects the relaxation times of the magnetization. This is inanalogy to dielectric spectroscopy where the polarizationfluctuations P(t) are the basic effect (see below). The relax-ation rates (1/T1, 1/T2) are essentially proportional to thespectral density at the Larmor frequency (1/T1 (γ Bloc)²J(ωL) , respective 1/T2 (γ Bloc)² J(ω=0)). Due to the 1/r6

dependence of homo dipolar relaxation of the protons,local dynamics in the 10 MHz (ωL) and at low frequencies(ω 0 for T2) are tested by low-field NMR relaxationmeasurements. Beside the typically used relaxation timesT1 and T2, there are several other possibilities to quantifydynamics including double quantum NMR techniques athigh or low magnetic field (Dollase et al., 2001; Saal-wächter and Heuer, 2006).

The first idea of using NMR on a polymeric sampleunder shear was published by Martins et al., in 1986. Con-ventional rheology measures macroscopic mechanicalproperties linked to dynamic changes on the molecularlevel. Therefore, a method quantifying the local moleculardynamic such as NMR is complementary to rheologicalinvestigations. The combination of mechanical shear withNMR was applied to complex systems. A review of theevaluation of this technique is given by Callaghan (1999,2006). The typical rheo-NMR equipments are basedmainly on a high-field NMR-instrument and allow apply-ing shear, but lacking the determination of mechanicalproperties. In the first experiments, a normal cylindricalNMR cuvette was rotated once to simulate rheologicalflow (Martins et al., 1986; Veron et al., 1999). Morerecently performed experiments use motor driven cells in

Cuette-geometry (Callaghan and Gil, 2000; Lopez-Gonzálezet al., 2006), but all reported equipment use a modified cellin an NMR-instrument supplemented by external rheo-logical measurements. The performed experiments can bedivided into two main areas (Callaghan 1999, 2006): NMRfor flow visualization and NMR for localized spectroscopysuch as relaxation and diffusion studies. However, themechanical properties of the observed materials were neversimultaneously defined in these investigations, furthermoreonly constant shear was applied and stresses were notquantified.

We followed another approach for our new combinationof rheology and NMR (Kahle et al., 2008). The rheometeris the central instrument; the 1H-NMR relaxometer isplaced as an extension of a commercial rheometer toachieve a combination that offers the measurement of allrheological properties and simultaneous NMR relaxationmeasurements (T1, T2) without spatial resolution. OurNMR instrument uses the amplifier, receiver and NMR-Software of a commercial Bruker Minispec spectrometer.To ensure the possibility of truly simultaneous measure-ments, a unique low-field NMR-magnet array fitted into arheometer instrument is necessary.

This unique magnet array is based on an idea of K. Hal-bach (1985) who proposes a special arrangement of per-manent magnets for high field magnets. Recently, theHalbach-design was further improved for high homogeneityof field with a new arrangement named MANDHALA(Magnet Arrangements for Novel Discrete Halbach Lay-out) by Raich and Blümler (2004). Using this design, ourNMR magnet is build by two layers of an array with each32 permanent magnets. The NMR probe head, includingthe RF coil and the electrical circuit, is placed between thetwo layers. The design and the first prototype of the mag-net – probe head system is shown in Fig. 7.

The resulting magnetic field strength in the sample isabout 0.23 T, corresponding to a proton frequency ofapproximately 9.5 MHz. The observed magnetic fieldinhomogeneity ∆B/B within the sample is in the order of0.5%. This corresponds with a line width of about 50 kHz.Note that this resolution is fully adequate for the deter-mination of molecular dynamics via relaxation measure-ments, but unacceptable for spectroscopic measurements(chemical shift, etc.).

As a first test of our NMR design we perform relaxationmeasurements using the [π-τ-π/2]m inversion recovery (T1)and [π/2-(τ-π-τ)n]m Carr-Purcell-Meiboom-Gill pulse sequence(CPMG-sequence, for T2), with m the number of accu-mulated scans. The results can be described by an expo-nential decay for only one single relaxation time or by astretched exponential function (I(t)=I0*exp(t/τ)β) for amonomodal distribution of relaxation times.

The results of these tests are shown in Fig. 8. It showsrepresentative experimental spin-lattice (left) and spin-spin

≅

≅

≅



(right) magnetization decay carried out on water and rub-ber at room temperature.

With these tests we have shown the potential of our pro-totype for simultaneous measurements of rheological prop-erties and 1H-NMR relaxation rate measurements.

• SAXS - rheologyRheology provides only information on the macroscopic

behavior of the samples. Apart from the local dynamicsalso the regular microstructure and packing of the sampleeffects the mechanical properties. Due to the typical sizedimensions of structures in polymeric and colloidal sam-ples the method of choice for characterization of the micro-structure and ordering is small-angle scattering.

Therefore, the list of attempts of this combination is con-siderably. It starts in the early 90’s of the last century with

the combination of a simple couette cell supported byexternal rheological measurements combined with small-angle neutron scattering (SANS) (Ashdown et al., 1990) orsmall-angle X-ray scattering (SAXS) (Safina et al., 1990).Similar to the combination Rheo-NMR, shear is appliedbut mechanical measurements are not performed simul-taneously. There are several examples of different shearcells used, including cylindrical flow cells (Hamley et al.,

2006), couette cells (Ashdown et al., 1990; Safinya et al.,

1990; Panine et al., 2003; Rathgeber et al., 2007), toothgeometry (van Ekenstein et al., 2003) and cone-plategeometry (Caputo et al., 2002). More rarely attempts ofintegrating a plate-plate geometry in a scattering beam arereported: a ring-shaped parallel plate in a neutron beam(Noirez and Lapp 1997), parallel plate geometry workingonly on films (Okamoto et al., 1994; Garcia-Gutiérrez et

al., 2008) and a plate operating with the rotation axis hor-izontal with Teflon bearing seals (Hongladarom et al.,

1996). Most of the reported attempts were carried out atsynchrotrons or neutron reactors, but there are also twoattempts using laboratory SAXS equipment (van Ekensteinet al., 2003; Okamoto et al., 1994).

As far as we know, there are only two records of trulysimultaneous equipment reported in literature, one labo-ratory equipment build in Groningen at the Dutch Polymerinstitute (van Ekenstein et al., 2003) and one build at theEuropean Synchrotron Radiation Facility (ESRF) inGrenoble (Panine et al., 2003). The latter equipment is lim-ited to Couette-geometry rotating perpendicular to the pri-mary beam and to samples with very high scatteringcontrast due to the large background of the beam windows.Recently, they modified the setup with parallel plate geom-etry usable only for films (Garcia-Gutiérrez et al., 2008).

The value of the Rheo-SAXS combination, even nottruly simultaneous, is unquestionable proven by all theseattempts to realize a combination of these two. Two

Fig. 7. Left: Design of magnet and probe head containing the

electrical components for matching and tuning the circuit.

The cover of the magnet and the probe head are made of

POM, the part surrounding the RF-coil in Teflon.

Right: Photo of the NMR-Magnet and the probe head spe-

cifically built for the Rheo-NMR-instrument.

Fig. 8. T1 (left) and T2 (right) measurements on water () and a rubber sample (). Solid lines are fits using single exponential (T1)

or stretched exponential (T2) decay functions (see text for further explanation).



recently examples of the value of this combination werepublished by our group, examinating block copolymersand their micro phases (Ölschläger et al., 2007, Langela et

al., 2002). The construction of the combined Rheo-SAXS instru-

ment (Hyun et al., 2009) at variable temperature was con-ducted in cooperation with Dr. Bernd Struth, HasylabHamburg, Germany. The experiment is equipped with a2D-dectector in single photon counting mode (IPS) offer-ing the possibility of fast 2D-SAXS measurements withhigh sensitivity (1 to 106 photons per pixel).

This Rheo-SAXS experiment (Hyun et al., 2009) hasseveral characteristics realizing important improvementsover earlier attempts published in the literature. First, itcombines a fully functional rheometer with a 2D-SAXSequipment allowing not only defined shear conditions, butalso full mechanical characterization simultaneous with a2D-SAXS experiment. Second, it uses a unique beamdesign: Due to a novel innovation, a 90o- mirror for the X-ray beam, it was possible to use a rheometer in normal ver-tical position, the beam passing through the geometry fromthe bottom up (see Fig. 9). Although the mirror has areflectivity of only 3~5%, the intensity of the synchrotronallows still fast 2D-SAXS measurements with good sta-tistical accuracy.

Due to this unique beam design, it is possible to use aplate-plate or plate-cone-geometry and to observe a scat-tering pattern along the shear gradient direction and at dif-ferent distances to the center of the geometry. Thesepossibilities are not offered by any other existing realiza-tion of a Rheo-SAXS experiment.

In our new combined equipments, Rheo-SAXS, Rheo-NMR, Rheo-dielectric, a simultaneous determination oflocal polymer motion and the macroscopic mechanicalproperties is possible to ensure an exact detailed correla-tion between macroscopic characteristics and molecular

dynamics on different length scales. The dielectric spec-troscopy determines the mobility of whole polymer chains(~Rg), the NMR-relaxation measurements results in infor-mation about mobility in the spatial extension of singlemonomers (1~3 nm).

Our new equipment offers the possibility to explore theeffects of the local dynamics on the linear and non-linearmechanical properties, but also vice versa. An importantpoint is the observation of the local dynamics of the poly-mer chains when the material is under defined non-linearexternal strain (e.g. LAOS), respective stress. The materialproperties under strain are of high technical importance inall processing steps and relevant for long-time stability ofthe material, e.g. fatigue properties. The influence of strainon the local can be studied perfectly with our combinedequipments. With these unique combinations at disposal, itis possible to simulate stress and aging with the Rheometerand controlling in situ the changes on the molecular scaleby NMR-Relaxation and dielectric spectroscopy.

5. Summary

Rheology as the science of deformation and flow of mat-ter is developing into more complex flows, more advanceddata processing and more complex materials under inves-tigations. Some current trends, elongation rheology of lowvicious fluids and combined methods were presented indetail.

Acknowledgement

We would like to thank all current and former membersof the group, the generous help of Prof. Spiess and Prof.Wegner at the MPI-Polymer at Mainz. Additionally TA-Instruments, Goettfert company and Thermo Fisher formaking some of our ideas commercially available.

References

Aarts, A.C.T and A.A.F. van deVen, 1999, The occurrence of

periodic distortions in the extrusion of polymeric melts, Con-

tinuum Mech. Thermodyn. 11, 113-139.

Alig, I., T. Skipa, D. Lellinger and P. Potschke, 2008, Destruction

and formation of a carbon nanotube network in polymer melts:

Rheology and conductivity spectroscopy, Polymer 49, 3524-

3532.

Anna, S.L., G.H. McKinley, D.A. Nguyen and T. Sridhar, 2001,

An interlaboratory comparison of measurements from fila-

ment-stretching rheometers using common test fluids, J.

Rheol., 45, 83-114.

Anna, S.L. and G.H. McKinley, 2001, Elasto-capillary thinning

and breakup of model elastic liquids, J. Rheol. 45, 115-138.

Arda, D.R. and M.R. Mackley, 2005, The effect of die exit cur-

vature, die surface roughness and a fluoropolymer additive on

Fig. 9. Schematic design of the Rheo-SAXS experiment (left)

and picture of the current realisation at Hasylab in Ham-

burg, Germany.



sharkskin extrusion instabilities in polyethylene processing, J.

Non-Newtonian Fluid Mech. 126, 47-61.

Ashdown, S., I. Markoviæ, R.H. Ottewill, P. Lindner, R.C.

Obertür, and A.R. Rennie, 1990, Small-angle neutron-scat-

tering studies on ordered polymer colloid dispersions, Lang-

muir 6, 303-307.

Barone, J.R., N. Plucktaveesak and S.Q. Wang, 1998, Interfacial

molecular instability mechanism for sharkskin phenomenon in

capillary extrusion of linear polyethylenes, J. Rheol. 42, 813-

832.

Bazilevskii, A.V., V.M. Entov, M.M. Lerner and A.N. Rozhkov,,

1997, Failure of polymer solution filaments, Polym. Sci. Ser. A

39, 316-324.

Bazilevskii, A.V., V.M. Entov and A.N. Rozhkov, 1990, Breakup

of an oldroyd liquid bridge as a method for testing the rheo-

logical properties of polymer solutions, Proceedings of the 3rd

European Rheology Conference.

Bertola, V., B. Meulenbroek, C. Wagner, C. Storrn, A. Morozov,

W. van Saarloos and D. Bonn, 2003, Experimental evidence

for an intrinsic route to polymer melt fracture phenomena: a

nonlinear instability of viscoelastic poiseuille flow, Phys. Rev.

Lett. 90, 114502.

Bovey, F.A. and P.A. Mirau, 1996, NMR of Polymers, Academic

Press, Inc.

Callaghan, P.T., 1999, Rheo-NMR: nuclear magnetic resonance

and the rheology of complex fluids, Rep. Prog. Phys. 62, 599-

670.

Callaghan, P.T., 2006, Rheo-NMR and velocity imaging, Curr.

Opin. Coll. & Int. Sci. 11, 13-18.

Callaghan, P.T. and A.M. Gil, 2000, Rheo-NMR of semidilute

polyacrylamide in water, Macromolecules 33, 4116-4124.

Capaccioli, S., D. Prevosto, A. Best, A. Hanewald and T. Pakula,

2007, Applications of rheo-dielectric technique, J. Non-Crys-

talline Solids 353, 4267-4272.

Caputo, F.E., W.R. Burghardt, K. Krishnan, F.S. Bates, and, T.P.

Lodge, 2002, Time-resolved small-angle x-ray scattering mea-

surements of a polymer bicontinuous microemulsion structure

factor under shear, Phys. Rev. E 66, 041401.

Carotenuto, C., M. Grosso and P.L. Maffettone, 2008, “Fourier

transform rheology of dilute immiscible polymer blends: a

novel procedure to probe blend morphology, Macromolecules

41, 4492-4500.

Cogswell, F.N., 1977, Stretching flow instabilities at the exits of

extrusion dies, J. Non-Newtonian Fluid Mech. 2, 37-44.

Denn, M.M., 2001, Extrusion instabilities and wall slip, Ann. Rev.

Fluid Mech. 33, 265-287.

Doelder den, C.F.J., R.J. Koopmans, J. Molenaar and A.A.F. van

de Ven, 1998, Comparing the wall slip and the constitutive

approach for modeling spurt instabilities in polymer melt

flows, J. Non-Newtonian Fluid Mech. 75, 25-41.

Dollase, T., R. Graf, A. Heuer and H.W. Spiess, 2001, Local

order and chain dynamics in molten polymer blocks revealed

by proton double-quantum NMR, Macromolecules 34, 298-

309.

Dussschoten van, D. and M. Wilhelm, 2001, Increased torque

transducer sensitivity via oversampling, Rheol. Acta 40, 395-

399.

Ekenstein van, G.A., E. Polushkin, H. Nijland, O. Ikkala and ten

Brinke, 2003, Shear alignment at two length scales: comb-

shaped supramolecules self-organized as cylinders-within-

lamellar hierarchy, Macromolecules 36, 3684-3688.

El Kissi, N. and J.M. Piau, 1994, Adhesion of linear low-density

polyethylene for flow regimes with sharkskin, J. Rheol. 38,

1447-1463.

Ewoldt, R.H., C. Clasen, A.E. Hosoi and G.H. McKinley, 2007,

Rheological fingerprinting of gastropod pedal mucus and syn-

thetic complex fluids for biomimicking adhesive locomotion,

Soft Matter 3, 634-643.

Filipe, S., I. Vittorias and M. Wilhelm, 2008, Experimental cor-

relation between mechanical non-linearities in LAOS flow and

capillary flow instabilities for linear and branched commercial

polyethylenes, Macromol. Mat. Eng. 293 57-65.

Filipe, S., A. Becker, V.C. Barroso and M. Wilhelm, 2009, Eval-

uation of melt flow instabilities of high-density polyethylenes

via an optimised method for detection and analysis of the pres-

sure fluctuations in capillary rheometry, Applied Rheology 19,

23345.

García-Gutiérrez, M.C., J.J. Hernández, A. Nogales, P. Panine,

D.R. Rueda and T.A. Ezquerra, 2008, Influence of shear on the

templated crystallization of poly(butyleneterephthalate)/single

wall carbon nanotube nanocomposites, Macromolecules 41,

844-851.

Gaudet, S., G.H. McKinley and H.A. Stone, 1996, Extensional

deformation of newtonian liquid bridges, Phys. Fluids 8, 2568-

2579.

Giacomin, A.J. and J.M. Dealy, 1993, Large-amplitude oscil-

latory shear, in Collyer A.A. (Ed.), Techniques in Rheological

Measurements, Chapman and Hall, London.

Halbach, K., 1985, Permanent magnets for production and use of

highenergy particle beams, in: Proceedings of the Eighth Inter-

national Workshop on Rare Earth Cobalt Permanent Magnets

and their Applications, Dayton, Ohio, p. 103.

Hamley, I.W., V. Castelletto and P. Paras, 2006, Small-angle x-

ray scattering study of flow alignment of a thermotropic liquid

crystal in the nematic and smectic phases, Phys. Rev. E 74,

020701.

Hill, D.A., T. Hasegawa and M.M. Denn, 1990, On the apparent

relation between adhesive failure and melt fracture, J. Rheol.

34, 891-918.

Hilliou. L., D. van Dusschoten, M. Wilhelm, H. Burhin, E.R.

Rodger, 2004, increasing the torque transducer sensitivity of an

RPA 2000 by a factor 5 ~ 10 using advanced data acquisition”,

Rubber Chemistry and Technology 77, 192-200.

Hilliou. L., M. Wilhelm, M. Yamanoi, M.P. Goncalves, 2009,

Structural and mechanical characterization of k/i-hydrid car-

rageen gels in potassium salt using Fourier Transform rhe-

ology, Food Hydrocolloids 23, 2322-2330.

Höfl, S., F. Kremer, H.W. Spiess, M. Wilhelm, S. Kahle, 2006,

Effect of large amplitude oscillatory shear (LAOS) on the

dielectric response of 1,4-cis-polyisoprene, Polymer 47, 7282-

7288.

Hongladarom, K., V.M. Ugaz, D.K. Cinader, W.R. Burghardt, J.P.

Quintana, B.S. Hsiao, M.D. Dadmun, W.A. Hamilton, P.D.

Butler, 1996, Birefringence, X-ray scattering, and neutron scat-



tering measurements of molecular orientation in sheared liquid

crystal polymer solutions, Macromolecules 29, 5346-5355.

Hyun, K., S.H. Kim, K.H. Ahn and S.J. Lee, 2002, Large ampli-

tude oscillatory shear as a way to classify the complex fluids,

J. Non-Newtonian Fluid Mech. 107, 51-65.

Hyun, K., B. Struth, T. Meins and M. Wilhelm, 2008, In-situ

Rheo-SAXS study of shear induced alignment of liquid crystal

(8CB) in the smectic phase under LAOS, Proceedings of the

XV-th International Congress on Rheology, 1423-1425.

Hyun, K., S., Höfl, S. Kahle and M. Wilhelm, 2009, The rheo-

dielectric setup to measure dielectric spectra of 1,4-cis-polyiso-

prene under large amplitude oscillatory shear (LAOS), J. Non-

Newtonian Fluid Mech. 160, 93-103.

Hyun, K. and M. Wilhelm, 2009, Establishing a new nonlinear

coefficient Q from FT-Rheology, first investigations on entan-

gled linear and branched Polymer melts, Macromolecules 42,

411-422.

Kallus, S., N. Willenbacher, S. Kirsch, D. Distler, T. Neidhöfer,

M. Wilhelm and H.W. Spiess, 2001, Characterization of poly-

mer dispersions by fourier-transform rheology, Rheol. Acta 40,

552-559.

Kahle, S., M. Hehn, H.P. Raich, W. Nussbaum, P. Blümler and

M. Wilhelm, 2008, Combination of NMR relaxometry and

mechanical testing during vulcanisation, Kautsch. Gummi Kun-

stst. 61, 92-94.

Klein, C., H.W. Spiess, A. Calin, C. Balan and M. Wilhelm,

2007, Separation of the non-linear oscillatory shear response,

into a superposition of linear, strain hardening, strain softening

and wall slip response, Macromolecules 40, 4250-4259.

Klein, C.O., I.F.C. Naue, J. Nijmann, H. Buggisch and M. Wil-

helm, 2009, Addition of the force measurment capability to a

commercial available extensional rheometer (CaBER), Soft

Materials 7, 242-257.

Klimke, K., M. Parkinson, C. Piel, W. Kaminsky, H.W. Spiess

and M. Wilhelm, 2006, Optimisation and application of poly-

olefin branch quantification by melt-state 13C NMR spec-

troscopy, Macromol. Chem. Phys. 207, 382-395.

Kolte, M.I. and P. Szabo, 1999, Capillary thinning of polymeric

filaments, J. Rheol. 43, 609-625.

Kremer, F. and A. Schönhals, 2003, Broadband Dielectric Spec-

troscopy, Springer, Berlin.

Krieger, I.M. and T.F. Niu, 1973, A rheometer for oscillatory

studies of nonlinear fluids, Rheol. Acta 12, 567-571.

Langela, M., U. Wiesner, H.W. Spiess and M. Wilhelm, 2002,

Microphase reorientation in block copolymer melts as detected

via FT rheology and 2D SAXS, Macromolecules 35, 3198-

3204.

Larson, R.G., 1992, Instabilities in viscoelastic flows, Rheol. Acta

31, 213-263.

Larson, R.G., 1999, The Structure and Rheology of Complex Flu-

ids, Oxford University Press, New York.

Laun, H.M. and H. Schuch, 1989, Transient elongational vis-

cosities and drawability of polymer melts, J. Rheol. 33, 119-

175.

Legrand, F. and J.M. Piau., 1998, Spatially resolved stress bire-

fringence and flow visualization in the flow instabilities of a

polydimethylsiloxane extruded through a slit die, J. Non-New-

tonian Fluid Mech. 77, 123-150.

Lim, F.J. and W.R. Schowalter, 1989, Wall slip of narrow molec-

ular weight distribution polybutadienes, J. Rheol. 33, 1359-

1382.

López-González, M.R., W.M. Holmes, P.T. Callaghan, 2006,

Rheo-NMR phenomena of wormlike micelles, Soft Matter 2,

855-869.

Mackley, M.R., R.P.G. Rutgers and D.G. Gilbert, 1998, Surface

instabilities during the extrusion of linear low density poly-

ethylene, J. Non-Newtonian Fluid Mech. 76, 281-297.

Macosko, C.W., 1994, Rheology: Principles, Measurements, and

Applications, Wiley-VCH, New York.

Martins, A.F., P. Esnault and F. Volino, 1986, Measurement of the

viscoelastic coefficients of main-chain nematic polymers by an

NMR technique, Phys. Rev. Lett. 57, 1745-1748.

Matta, J.E. and R.P. Tytus, 1990, Liquid stretching using a falling

cylinder, J. Non-Newtonian Fluid Mech. 35, 215-229.

Migler, K.B., H. Hervet and L. Leger, 1993, Slip transition of a

polymer melt under shear stress, Phys. Rev. Lett. 70, 287-290.

Migler, K.B., F. Qiao and K. Flynn, 2002, Extensional defor-

mation, cohesive failure, and boundary conditions during

sharkskin melt fracture, J. Rheol. 42, 383-400.

Moleenar J., R.J. Koopmans and C.F.J. den Doelder, 1998, Onset

of the sharkskin phenomenon in polymer extrusion, Phys. Rev.

E 58, 4683-4691.

Münstedt, H., M. Schmidt and E. Wassner, 2000, Stick and slip

phenomena during extrusion of polyethylene melts as inves-

tigated by laser-Doppler velocimetry, J. Rheol. 44, 413-427.

Noirez, L. and A. Lapp, 1997, Shear flow induced transition from

liquid-crystalline to polymer behavior in side-chain liquid crys-

tal polymers, Phys. Rev. Lett. 78, 70-73.

Oelschlager, C., J.S. Gutmann, M. Wolkenhauer, H.W. Spiess, K.

Knoll and M. Wilhelm, 2007, Kinetics of shear microphase ori-

entation and reorientation in lamellar diblock and triblock

copolymer melts as detected via FT-Rheology and 2D-SAXS,

Macromol. Chem. Phys. 208, 1719-1729.

Okamoto, S., K. Saijo and T. Hashimoto, 1994, Real-time SAXS

observations of lamella-forming block copolymers under large

oscillatory shear deformation, Macromolecules 27, 5547-5555.

Palza, H., I.F.C. Naue and M. Wilhelm, 2009, In-situ pressure

fluctuations of polymer melt instabilities in a viscoelastic pois-

seule flow: experimental evidence about their origin and

dynamics, Macromol. Rap. Comm. 30, 1799-1804.

Palza, H., S. Filipe, I.F.C. Naue and M. Wilhelm. 2010, Cor-

relation between polyethylene topology and melt flow insta-

bilities by determining in-situ pressure fluctuations and

applying advanced data analysis, Polymer 51, 522-534.

Panine, P., M. Gradzielski and T. Narayanan, 2003, Combined

rheometry and small-angle X-ray scattering, Rev. Sci. Instrum.

74, 2451-2455.

Parkinson, M., K. Klimke, H.W. Spiess and M. Wilhelm, 2007,

Effect of branch length on NMR relaxation properties in mol-

ten polyethylene-co-a-olefin model systems, Macomol. Chem.

Phys. 208, 2128-2133.

Pollard, M., K. Klimke, R. Graf, H.W. Spiess, M. Wilhelm, O.

Sperber, C. Piel and W. Kaminsky, 2004, Observation of chain

branching in polyethylene in the solid-state and melt via 13C-



NMR spectroscopy and melt NMR relaxation time measure-

ments, Macromolecules 37, 813-825.

Raich, H., Blümler, P., 2004, “Design and construction of a dipo-

lar Halbach array with a homogeneous eld from identical bar

magnets: NMR MANDHALAs”, Concepts Magn. Reson. 23B,

16-25.

Rathgeber, S., H. Lee, K. Matyjaszewski and E. di Cola, 2007,

Rheooscillations of a bottlebrush polymer solution due to

shear-induced phase transitions between a shear molten state

and a line hexatic phase, Macromolecules 40, 7680-7688.

Rutgers, R.P.G. and M.R. Mackley, 2000, The correlation of

experimental surface extrusion instabilities with numerically

predicted exit surface stress concentrations and melt strength

for linear low density polyethylene, J. Rheol. 44, 1319-1334.

Rutgers, R.P.G. and M.R. Mackley, 2001, The effect of channel

geometry and wall boundary conditions on the formation of

extrusion surface instabilities for LLDPE, J. Non-Newtonian

Fluid Mech. 98, 185-199.

Saalwaechter, K. and A. Heuer, 2006, Chain dynamics in elas-

tomers as investigated by proton multiple-quantum NMR,

Macromolecules 39, 3291-3303.

Safinya, C.R., E.B. Sirota and R.J. Plano, 1990, nematic to smec-

tic-A phase transition under shear flow: A nonequilibrium syn-

chrotron X-ray-study, Phys. Rev. Lett. 66, 1986-1989.

Sattler, R., C. Wagner and J. Eggers, 2008, Blistering pattern and

formation of nanofibers incapillary thinning of polymer solu-

tions, Phys. Rev. Lett. 100, 164502.

Schmidt-Rohr, K. and H.W. Spiess, 1994, Multidimensional

solid-state NMR and polymers, Academic Press, London.

Shore, J.D., D. Ronis, L, Piche and M. Grant, 1996, Model for

melt fracture instabilities in the capillary flow of polymer

melts, Phys. Rev. Lett. 77, 655-658.

Steher, M., G. Brenna, A.L. Yarin, R.P. Singh and F. Durst, Val-

idation and application of a novel elongational device for poly-

mer solutions, J. Rheol. 44, 595-616.

Stockmayer, W.H. and J.J. Burke, 1969, Dielectric dispersion in

branched polypropylene oxide, Macromolecules 2, 647-650.

Szabo, P., 1997, Transient filament stretching rheometer I: Force

balance analysis, Rheol. Acta 36, 277-284.

Tao, Z. and J.C. Huang, 2005, Study on the melt fracture of met-

allocene poly(ethylene-octene) in capillary flow, J. Appl.

Polym. Sci. 98, 903-911.

Tripathi, P., S.H. Spiegelberg and G.H. McKinley, 2000a, How to

extract the Newtonian viscosity from capillary breakup mea-

surements in a filament rheometer, J. Rheol. 44, 653-670.

Tripathi, P., P. Whittingstall and G.H. McKinley, 2000b, Using

filament stretching rheometry to predict strand formation and

“processability” in adhesives and other non-newtonian fluids,

Rheol. Acta 39, 321-337.

Venet, C. and B. Vergnes, 2000, Stress distribution around cap-

illary die exit: an interpretation of the onset of sharkskin defect,

J. Non-Newtonian Fluid Mech. 93, 117-132.

Veron, A., A.E. Gomes, C.R. Leal, J. Van Der Klink and A.F.

Martins, 1999, NMR study of flow and viscoelastic properties

of PBLG/m-cresol lyotropic liquid crystal, Mol. Cryst. Liq.

Cryst. 331, 2359-2367.

Vittorias, I., M. Parkinson, K. Klimke and B. Debbaut and M.

Wilhelm, 2007, Detection and quantification of industrial poly-

ethylene branching topologies via fourier-transform rheology

and simulation using the pom-pom model, Rheol. Acta 46,

321-340.

Wang, S.Q., 1999, Molecular transitions and dynamics at poly-

mer/wall interfaces: origins of flow instabilities and wall slip,

Adv. Polym. Sci. 138, 227-275.

Wang, S.Q. and P. Drda, 1996, “Superfluid-like transition in cap-

illary flow of highly entangled linear polyethylene melts”,

Macromolecules 29, 2627-2632.

Wang, S.Q. and P. Drda, 1997, Molecular instabilities in capillary

flow of polymer melts. Interfacial stick-slip transition, wall

slip, and extrudate distortion, Macromol. Chem. Phys. 198,

673-701.

Watanabe, H., T. Sato, M. Hirose, K. Osaki and M.L. Yao, 1998,

Rheo-dielectric behavior of low molecular weight liquid crys-

tals. 1. Behavior of nematic 5CB and 7CB, Rheol. Acta 37,

519-527.

Watanabe, H., T. Sato, M. Hirose, K. Osaki, M.L. Yao, 1999,

Rheo-dielectric behavior of low molecular weight liquid crys-

tals. 2. Behavior of 8CB in nematic and smectic states, Rheol.

Acta 38, 100-107.

Watanabe, H., 1999, Viscoelasticity and dynamics of entangled

polymers, Prog. Polym. Sci. 24, 1253-1403.

Watanabe, H., Y. Matsumiya, M. Kakiuchi and Y. Aoki, 2001,

Rheo-dielectric behavior of carbon black suspensions, Nihon

Reoroji Gakkaishi 29, 77-80.

Watanabe, H., 2001, Dielectric relaxation of Type-A polymers in

melts and solutions, Macromol. Rap. Comm. 22, 127-175.

Watanabe, H., S. Ishida and Y. Matsumiya, 2002, Rheodielectric

behavior of entangled cis-polyisoprene under fast shear, Mac-

romolecules 35, 8802-8818.

Watanabe, H., Y. Matsumiya and T. Inoue, 2003, “Rheo-dielec-

trics in oligomeric and polymeric fluids: a review of recent

findings, J. Phys.: Condens Matter 15, S909-S921.

Watanabe, H., Y. Matsumiya and T. Inoue, 2005, Dielectric and

viscoelastic study of entanglement dynamics: A review of

recent findings, Macromol. Symp. 228, 51-70.

Wilhelm, M., D. Maring and H.W. Spiess, 1998, Fourier-trans-

form rheology, Rheol. Acta 37, 399-405.

Wilhelm, M., P. Reinheimer and M. Ortseifer, 1999, High sen-

sitivity fourier-transform rheology, Rheol. Acta 38, 349-356.

Wilhelm, M., 2002, Fourier-transform rheology, Macromol.

Mater. Eng. 287, 83-105.

new developments for the mechanical characterization of materials · 2011. 1. 4. · new...

Documents