High strain extensional rheometry of polymer melts:Revisiting and improving the Meissner design

R. J. Andrade, P. Harris, and J. M. Maiaa)

Department of Macromolecular Science and Engineering,Case Western Reserve University, Cleveland, Ohio 44106-7202

(Received 14 July 2013; final revision received 23 April 2014;published 21 May 2014)

Synopsis

A new extensional rheometer limited in achievable strain only by sample rupture is presented. The

rheometer is based on the Meissner design of two pairs of counter-rotating rollers pulling a sample

of fixed length but is small enough to fit inside the oven of a standard rotational rheometer and thus

is dubbed the Meissner Extensional Rheometry Accessory (MERA). The true strain rate is

calculated by visually accessing the sample during deformation using a high-speed digital camera.

Extensional experiments were performed on three materials representing a wide range expected

rheological behavior, a styrene-butadiene rubber blend, a linear polystyrene, and a branched low-

density polyethylene. The MERA was able to accurately replicate the results of the well-known

Sentmanat extensional rheometer (SER) design in terms of onset of strain-hardening and absolute

transient extensional viscosity values. However, due to its design, it was possible to achieve

homogeneous extensional flow up to real Hencky strains in excess of 8, which corresponds to a

linear stretch in excess of 3000. By comparison, the SER is limited to one drum revolution, which

corresponds to a Hencky strain of 3.5–4.0 or a maximum linear stretch of approximately 50.

Previously the highest Hencky deformations reported in the literature are for the filament stretching

extensional rheometer and Rheometric Scientific RME apparatus and in both cases approach 7,

which corresponds to a linear stretch of approximately 1000. VC 2014 The Society of Rheology.[http://dx.doi.org/10.1122/1.4875349]

I. INTRODUCTION

Controlled elongation of polymer melts has been the subject of a relatively strong

computational, theoretical, and experimental efforts over the years [see, for example,

Meissner (1971, 1985a, 1985b); Petrie (1979); M€unstedt and Laun (1981); M€unstedt

et al. (2005); Hassager et al. (1998); McKinley and Hassager (1999); Maia et al. (1999);

Joshi and Denn (2003, 2004); Wang et al. (2007); Wang and Wang (2008)] for two main

reasons. The first is that it is the dominant mode of deformation in many industrially

important processes, such as fiber and melt spinning, film blowing, and blow molding. In

other industrial processes, such as film and sheet extrusion, the last phase before solidifi-

cation is often an elongational deformation resulting in molecular orientation and anisot-

ropy of the final product. The second reason is that the study of this type of flow allows

an insight into the molecular structure of the materials to be gained. In fact, extensional

a)Author to whom correspondence should be addressed; electronic mail: joao.maia@case.edu

VC 2014 by The Society of Rheology, Inc.J. Rheol. 58(4), 869-890 July/August (2014) 0148-6055/2014/58(4)/869/22/$30.00 869

behavior is very dependent on structure, e.g., molecular weight, molecular weight

distribution, degree of branching, nature and strength of the interface in polymer blends,

etc., as shown in some of our previous works [Barroso and Maia (2002); Ares et al.(2009); Silva et al. (2007); Silva et al. (2010)].

Various techniques have been developed for measuring elongational flow properties

of polymer melts, which are normally based on three main types of design: Fiber-

windup, filament stretching with length variation, and filament stretching at constant

length [see, for example, Meissner (1969); Meissner and Hostettler (1994); Macosko and

Lorntson (1973); Padmanabhan et al. (1996); M€unstedt (1975); Laun and M€unstedt

(1976, 1978); Bach et al. (2003a, 2003b); Ishizuka and Koyama (1980); Maia et al.(1999); Barroso and Maia (2005); Andrade and Maia (2011); Sentmanat (2004);

Sentmanat et al. (2005)]. All these designs have pros and cons, as we detail below.

The fiber windup design is characterized by the sample being clamped between two

rollers or one roller and a fixed point. In both cases, the roller(s) rotate and wind up the

filament. This design was first proposed by Macosko and Lorntson (1973) and more

recently updated by Padmanabhan et al. (1996). This method is of simple implementa-

tion, requiring only a small amount of sample, and is highly versatile, which allows

designs based on it, such as the Sentmanat extensional rheometer design [SER;

Sentmanat (2004); Sentmanat et al. (2005)], to be used as an accessory to rotational rhe-

ometers. Still, there are some drawbacks, the main of which is that there is an upper limit

on Hencky strain of approximately 4, since at higher deformations, the sample starts

wrapping on itself after one revolution, which changes the boundary conditions and

obviously affects negatively the flow homogeneity. The upper Hencky strain limit of

approximately 4 in these designs is important for two reasons, one technological and one

of a more scientific nature. First, some of the most important and common industrial

processes often involve higher elongations (e.g., the maximum Hencky strain in fiber-

spinning is in excess of 5 and can, indeed, approach 6), so having a direct knowledge of

the melt behavior at such high strains and strain rates is important. Second, accessing

polymer dynamics at very high strains is important to understand failure and rupture

mechanisms, especially branched polymers and elastomers, which only fail and rupture

at strains well above 4.

Currently, accessories based on the fiber wind-up design are offered commercially by

TA Instruments under the designation of extensional viscosity fixture [EVF, Hodder and

Franck (2005)], and by XPansion Instruments, as the SER [Sentmanat (2004); Sentmanat

et al. (2005)]. The latter is a multifunctional device that can be used not only to measure

extensional viscosity but also for peel and tear tests. The SER is probably the most wide-

spread instrument and consists of dual-windup drums that counter-rotate, with a sample

fixed using metal clamps and pulled at both ends, ensuring equal boundary conditions at

both ends. The SER is easy to use and provides accurate results in controlled rate mode,

up to a maximum Hencky strain of approximately 4. Also, because of its geometrical

configuration, it is subject to sample sagging (for high L/W ratios, or slender samples) or

the existence of a planar flow component (for low L/W ratios, or wide samples) [Nielsen

(2009)], if proper experimental care, i.e., sample dimensions and preparation procedures,

is not taken.

In the filament stretching with length variation design, the sample is fixed at the ends

by grips or clamps, and it is elongated by increasing the distance between the clamps.

This type of rheometer goes back to Cogswell (1968) and was improved upon by several

researchers, such as M€unstedt and coworkers (1975, 1976, 1979), who mounted the sam-

ple vertically in an oil bath for temperature control and to minimize sagging. The current

generation instrument [M€unstedt (1979)] imposes accurate real-time stress and rate

870 ANDRADE, HARRIS, AND MAIA

control via a feedback control loop with a maximum rate and stress deviation around 5%.

Although this solution can overcome the assumption of homogeneous deformation

because of the control, sample homogeneity is not guaranteed at high deformations due

to oil recirculation. Also, it is limited in both maximum stress (�105 Pa) and Hencky

strain (�4). More recently, Hassager and coworkers (2003a, 2003b) developed the fila-

ment stretching extensional rheometer (FiSER), which is based on the design of Sridhar

et al. (1991) rheometer for polymer solutions, itself a variation of the Cogswell design.

By replacing the oil bath with an oven and measuring the mid-filament diameter under

deformation to impose a constant strain-rate via a feedback control loop, some of the lim-

itations of the M€unstedt design, such as precision at high strains, were overcome. By

varying initial sample dimensions and making full use of the laser resolution, maximum

Hencky strains of almost 7 have been reported for the FiSER; nonetheless, it is still a

design in which the maximum achievable deformation is limited mechanically by the

maximal plate separation.

The filament stretching with constant length took its first steps with Meissner (1969),

who proposed a rheometer with the sample mounted in a horizontal position in an oil

bath and extended between rotary clamps. This design has the advantage over the previ-

ous ones of not being geometrically limited in Hencky strain. It was perfected over the

next 20 years and culminated in an instrument (RME) that was briefly offered commer-

cially in the 1990s by Rheometrics. In this final generation [Meissner and Hostettler

(1994)], the sample size is reduced and the sample is supported by inert gas flow in order

to avoid sagging and stretched by rotating metal belts in order to minimize slip. The main

drawbacks of this system were that it was very delicate and complex to operate, the qual-

ity of the results being extremely operator-dependent. For example, despite the use of

metal belts, slip at the pulling belts was still significant. Also, the samples were relatively

thick (typically around 2 mm), which meant that the tensile force is brought in via shear

at the surfaces of the sample, and therefore, the material in the core will lag behind the

surface material. These two factors combined meant that the effective strain rates could

be significantly lower (by 10–20%) than the nominal ones.

More recently, Ishizuka et al. (1980) and Maia and coworkers (1999, 2005, 2011)

developed what can be considered “half Meissner” designs. In both cases, the instruments

were a hybrid between a single wind-up drum design and the Meissner, since they used

only one pair of pulling counter-rotating rollers, with the other end of the sample fixed to

a force transducer. The instrument developed by Maia et al. (1999), in particular, was

designed as an accessory to a rotational rheometer. An inherent potential drawback asso-

ciated with the half-Meissner designs is that the kinematic conditions are different at the

two boundaries, which may cause problems for samples with low aspect ratio (<10), and

slip at the fixed clamp can induce real strain rates lower than the nominal ones. Both limi-

tations can be overcome by using samples with an aspect ratio higher than 10 and by

filming the evolution of the cross section in time and deriving the true strain rate from it.

More recently, a next generation instrument was developed, the controlled-stress exten-

sional rheometer [Maia et al. (2008); Andrade and Maia (2011)], while maintaining the

deformation kinetics of the original instrument [Maia et al. (1999)], is adapted to a

controlled-stress rheometer and, as such, allows experiments in accurate dual controlled

stress/rate to be performed via a feedback control loop.

The techniques above are by no means the only extensional rheometers for polymer

melts, although they are the most common ones for uniaxial extensional rheometry.

Worth mentioning from among the rest is the cross-slot extensional rheometer (CSER)

used recently by Auhl et al. (2011). In this design, the existence of a closed cell stagna-

tion point (SP) flow in a multipass rheometer was used together with flow induced

871HIGH STRAIN EXTENSIONAL RHEOMETRY

birefringence (FBI) patterns to measure the planar steady-state extensional response. This

geometry principle was pioneered by Taylor (1934) and subsequently used by other

authors to investigate the polymer behavior in extensional flow, e.g., Coventry and

Mackley (2008); Crowley et al. (1976); Frank and Mackley (1976); Janeschitz-Kriegl

(1983); Macosko et al. (1980); Schoonen et al. (1998); Scrivener et al. (1979); Soulages

et al. (2008); Verbeeten et al. (2001); Winter et al. (1979). Compared to filament stretch-

ing flows, the SP geometries have the advantage that elongational properties can be

investigated without a disturbance from free surface flow [Minoshima and White (1986)]

and localized necking. The CSER design can be used complimentarily to existing exten-

sional rheometers as it can measure high strain steady-state limits and does not require

the material to be strain-hardening.

As shown above, all the current uniaxial extensional rheometer designs suffer from

one or more drawbacks that prevent the easy and controlled testing of polymeric samples

up to ultrahigh strains. In this work, we present our third-generation extensional rheome-

ter design, which was purposely developed to overcome these issues. In particular, the

main design requirements were as follows:

1. It must have the ability to achieve very high Hencky strains, i.e., in excess of 6, which

should be limited only by sample rupture.

2. The deformation should be homogeneous up to sample rupture or the onset of necking,

namely, by imposing the same boundary conditions at both edges.

3. It must be adjustable to rotational rheometers as an add-on accessory.

4. It should be simple to use and robust.

5. It must allow visual access to the sample during deformation in order to allow for

monitoring/control of the deformation kinetics, i.e., strain rate, or dynamics, i.e., the

tensile stress.

The only design that inherently obeys requirements 1 and 2 above is that of a full

Meissner, i.e., with two pairs of counter-rotating rollers. Thus, the new rheometer, which

was miniaturized to fit inside the oven of a rotational rheometer and coupled to a digital

camera and an image acquisition software, is essentially a miniaturized and user-friendly

version of the Meissner design. This design is named the MERA [Maia et al. (2012)], for

Meissner Extensional Rheometer Accessory, and its general lay-out and appearance are

depicted in Figs. 1 and 2.

This design imparts similar strain histories to both ends of the sample and makes vis-

ual observation possible because sample visualization is performed at the mid-point and

necking or other experimental problems with any given experiment are easily spotted.

Also, it does away with need for separate temperature control by having the instrument in

a single frame that fits within the high-temperature chamber of the rotational rheometer,

similarly to the SER device (in fact, the vertically projected dimensions and areas are the

same, although the MERA is thicker than the SER). Sample loading is easily performed

by pulling the front rollers with the aid of a built-in spring, which is also used to keep the

clamping force on the rollers constant as the sample decreases in cross section during the

experiment. The rollers are readily changeable so that the best surface finish to avoid slip-

page for each material can be chosen. Also, there are very sharp wedges external to the

rollers that guarantee that the sample is ejected from the system after testing and does not

wrap around them. A more detailed explanation of the MERA is presented in Sec. II.

In the present study, we validate the MERA design, using three representative materi-

als at different ends of the viscoelastic spectrum, namely, a linear, relatively inelastic

polystyrene (PS), a branched, highly elastic polyethylene, and a highly elastic, highly

viscous bimodal styrene-butadiene rubber (SBR) melt.

872 ANDRADE, HARRIS, AND MAIA

II. THE MERA

The MERA design can be adapted to any rotational rheometer, although in this work,

we used an Anton Paar Physica MCR 501 as the host machine.

A. Operation

The principle of operation of the MERA apparatus is the counter-rotation of two sets

of two roller drums, which extensionally deform a sample until rupture. The deformation

is conceptually similar to mechanical tensile testing except that it is performed on the

melt. Figure 3 displays the general principle of operation of the MERA (top) and the gen-

eral view of the assembled instrument (bottom).

A polymeric sample, in either rod or slab format, is placed between the rollers, and the

MCR shaft rotates in a counterclockwise direction, which in turn rotates gearing (Fig. 4)

in order to rotate the paired counter-rotating rollers. Visualization is performed using a

digital camera attached to the exterior of the oven (in our case, a Lumenera Lm075 VGA

Mini USB 2.0, 60 fps at full 640� 480 resolution).

The internal dimensions of the oven (60 mm diameter) of the host rotational rheometer

primarily dictate the size of the MERA. Due to the spacing of gearing of off-center drive

axle, the overall dimensions of the MERA are approximately 42� 40 mm (L�W). The

device, as shown in Figs. 2 and 3 above, rests on a stationary rod/thermocouple with an

upper shaft extending from the air piston head, both of which vertically extend into the

Physica’s CTD 450 oven. The former provides a stationary base for the rheometer, while

the latter supplies a rotational velocity to the drive axle of the MERA. Similarly, the sta-

tionary base contains a thermocouple that allows for temperature measurements within

the oven. The drive axle rotates a gear and in turn transmits power to one of the primary

axles. In total, there are seven low-friction titanium nitride coated steel and brass gears

(see Fig. 4).

FIG. 1. The MERA.

873HIGH STRAIN EXTENSIONAL RHEOMETRY

B. General components

Figure 4 displays the internal components of the MERA, including the roller drums,

axles, gearing, and bearings. All meshing gears are made to horology-level precision

specifications and were designed to have equal number of teeth providing a gear ratio

and angular velocity ratio equal to 1, thereby producing a torque ratio, or mechanical

advantage, also equal to 1. The five axles are made of stainless steel construction and are

coated with a low friction coating. All axles are axially contained within two low friction

bearings and contain points at either ends to promote a low normal force. Both the bear-

ings and precision axles are developed for signal integrity and friction (noise) reduction.

C. Interchangeable roller drums

The roller drums that make contact with the sample have been coated with a nickel-

Teflon coating to promote removal from roller drums and easy cleaning. The roller drums

have a major diameter of 6.35 mm and are spaced 6.35 mm when viewed from the side,

allowing the rollers to make slight contact. Similarly when viewed from the front, the

rollers have a spacing of 12.70 mm. Several types of surface finishing can be applied to

the rollers, including highly polished, sand-blasted to different degrees, vertical grooving,

FIG. 2. Different views of the MERA: (a) Isometric; (b) side; (c) front; (d) back.

874 ANDRADE, HARRIS, AND MAIA

cross-hatching of a diamond pattern, etc. The type of roller to be used during experimen-

tation is dependent upon sample surface and bulk properties and must be chosen to elimi-

nate slip at the rollers. Rollers were designed with ease of removal and installation in

mind. This is accomplished by removing its base, and sliding the rollers out of the coated

axles, as shown in Fig. 5. Four socket-head cap screws are first removed from the base of

the MERA, which allows for the base to slide off of the bottom alignment pins. Once the

base has been removed, the four roller drums easily slide off of the four roller axles. The

reverse process holds for reassembly of new roller drums. The whole process takes only a

few minutes.

Slip is further minimized by the existence of four adjustable springs, as depicted in

Fig. 6. This coupled with the fact that the front rollers of each pair can move in an inward

direction (see Sec. II E) provides a virtually constant clamping force as the sample

becomes thinner upon testing. The actual clamping force is imposed at the beginning of

the experiment by the level of tightening of the springs. This is chosen in a way that it is

not so low that there is slippage at high strains or so high that friction will be too high.

Both these effects are easily detected in the torque curve and can be compensated for.

D. In-process material strippers

Steel brackets containing extremely sharp metal strippers, (sharper than razor blades)

provide very close spacing to the roller drums (approximately 25 lm), as shown in Fig. 7.

FIG. 3. Operation principle (top) and assembled view (bottom) of the MERA.

875HIGH STRAIN EXTENSIONAL RHEOMETRY

This allows for complete sample material removal (scrapping) during the elongational

test, which is important because any residue left on the rollers during testing will nega-

tively impact the integrity of the torque output signal and deformation homogeneity.

With these strippers, a very clean separation of the sample from the rollers without any

noticeable effect on the torque signal is usually observed. When that is not the case, the

experiment in question is disregarded.

E. Sample loading

Sample loading and unloading is performed in the simple fashion depicted in Fig. 7.

Prior to sample loading, a small handheld pulling device pulls the front of the instrument

and subsequently the rollers apart, allowing for the loading of the sample. The sample is

loaded from the side of the instrument with a pair of tweezers. The sample typically

extends past the rollers and material strippers prior to operation. As mentioned before,

the spring loaded shoulder bolts control the compression force applied to the sample.

Springs can be replaced as needed to change the amount of normal force applied outside

of the compression zone of the supplied springs. When fully tightened, the springs still

allow for movement of the front assembly for the capability of sample loading and

unloading. An approximately 3.0 mm stroke is imposed to allow for sample placement

between the roller drums. Figure 7 (left) displays the MERA when fully closed and

(right) when opened to a distance of 3.0 mm (small inserted figures display the zoomed

near side view). Once a sample has been loaded, the springs supply sample pressure dur-

ing testing and allows the rollers in each pair to come closer as needed during sample

thinning.

FIG. 4. Isometric view displaying the detailed assembly of axles, gearing, bearings, and roller drums.

876 ANDRADE, HARRIS, AND MAIA

When the rollers touch, the yellow gears in Fig. 4 have their correct center-to-center

distance of 6.35 mm and roll on their pitch diameters. From this position, the outer rollers

can only move by 0.8 mm before the gears fully disengage. This limits the thickness of

the sample and might introduce additional noise when operating close to this gap. In the

loading position with an inter-roller distance of 3 mm, the gears are fully disengaged.

However, the samples themselves are only 0.8 mm thick when solid. As the sample soft-

ens/melts upon heating, the rollers come together by virtue of the springs, and the final

roller separation at the beginning of the experiment is half or even less (depending on the

FIG. 5. Isometric exploded view displaying the disassembly for the interchangeable drum rollers. Four screws

release bottom assembly, and then, the rollers slide off.

877HIGH STRAIN EXTENSIONAL RHEOMETRY

spring clamping force) than the original separation while cold. The actual clamping force

is set by an initial calibration; it must be the minimal value that provides a no-slip pull on

the sample. In addition, the gears are helical, which maximizes the contact surface for

any separation and thus minimizes the problem. At no point was slip at the rollers

observed, which would happen if the rollers were not engaged enough to provide full

traction throughout the entire experiment.

F. Validation

As mentioned before, the MERA was designed as an accessory to common rotational

rheometers, such as the Anton Paar MCR 501 used in this work. One inherent potential

drawback of this arrangement is related to the working principle of the host rheometer. In

fact, it is impossible to decouple the empty torque due to instrument friction from that

arising from the deformation. In instruments limited in Hencky strain, such as the SER or

the EVF, this is normally not a significant problem because the experiments are

FIG. 6. Isometric view displaying the rear components used for adjusting the compression springs.

FIG. 7. Isometric view displaying the opening for the sample loading procedure as well as the very sharp

blades. The front assembly is attached using spring-loaded shoulder bolts. Left: Closed position; Right: Open

position (�3.0 mm maximum opening).

878 ANDRADE, HARRIS, AND MAIA

effectively limited to one roller rotation (which equates to a Hencky strain of approxi-

mately 4) and, thus, are usually stopped before the sample has a chance to become very

thin. If the MERA accomplishes its purpose of achieving high strains (well in excess of

6.0), then eventually its inherent empty friction torque will become of the order of magni-

tude of that due to sample deformation. Consequently, even if the deformation is still ho-

mogeneous at high strains, it will not be possible to calculate the tensile stress, and hence

the extensional viscosity, up to the end of the experiment.

Given this inherent potential limitation, it is necessary to minimize it by minimizing

the empty torque due to parts friction when empty. Tests performed on empty in the

MERA show that it has an average empty friction torque of 2� 10�4 Nm. By comparison

with the SER, for example, which has an empty friction torque of approximately

5� 10�5 Nm, the MERA has a higher empty friction due to the higher number of gears

(7 as opposed to 2), which was to be expected. As shall be seen below, this level of empty

friction torque in the MERA still allows experiments to be performed up to very high

strains. In fact, the flow generally ceases to be homogeneous or the sample ruptures well

before the empty torque becomes significant. In any case, if this does not happen, data

are only analyzed for torque levels as at least 10 times above the empty friction torque.

A second limitation inherent to using a host rotational rheometer is that of instrument

inertia, so extreme care should be taken to make sure it is not affecting the data. For

example, experiments at nominal strain rates in excess of 5 s�1 are typically over in less

than 1 s (with any instrument). One way to overcome this potential issue is to film the

sample under deformation and measure the true deformation rate. Significant deviations

from the nominal value or nonconstant strain rates are an indication that instrument iner-

tia is no longer negligible.

Finally, a potential issue specific to the MERA is that due to its relatively high mass,

the actual temperature may be lower than the set temperature. With that in mind, temper-

ature measurements were performed at different time intervals for a range of set tempera-

tures, as shown in Table I. The results clearly show that after 5 min of thermal

equilibration in the oven, the actual rheometer temperatures differ from the set value

between 0.82 and 1.85 �C, although they do increase with increasing temperature, as

expected. These variations are acceptable in most cases but must be taken into considera-

tion when setting the temperature in actual experiments.

III. MATERIALS AND SAMPLE PREPARATION

PS Styron 615 (The Dow Chemical Company), polyethylene (low-density polyethyl-

ene, LDPE) Petrothene NA940000 (LyondellBasell Company), and a bimodal blend of

TABLE I. Time evolution of real temperature between the MERA rollers for different set oven temperatures.

Time (min)

Nominal temperature (�C) 0 1 2 3 4 5

130.32 129.1 129.2 129.3 129.3 129.4 129.5

160.31 157.7 158.2 158.6 158.9 159.2 159.4

190.34 177.7 187.2 187.9 188.4 188.7 189.2

220.33 215.8 216.4 217.2 217.7 218.2 218.6

250.35 245.7 246.5 247.1 247.6 248.1 248.5

879HIGH STRAIN EXTENSIONAL RHEOMETRY

SBR melt, the latter supplied by Professor Shi Qing Wang (University of Akron) were

used as a test materials. For linear-viscoelastic characterization, frequency sweep test

was performed in oscillatory shear flow with 25-mm plate–plate geometry with the

Physica MCR 501 rheometer and CTD450 convection oven (Anton Paar). From the stor-

age and loss modulus, discrete relaxation spectra were calculated using the IRIS software.1

Partial relaxation moduli gi and relaxation times ki as well as the (calculated) zero-shear

viscosities g0 are presented in Table II together with the molecular characterization of the

melts.

Extensional rheology specimens were prepared using a hydraulic press heated to

180 �C (PS and LDPE) and 80 �C (SBR). Rectangular polymer samples of dimensions

0.85� 6.5� 16 mm (H�W�L) were thus produced. The sample preparation and load-

ing procedure followed the recommendations laid out in our previous works [Barroso

et al. (2002)]. Prior to sample loading, the MERA fixture was heated to the desired value,

160 �C for PS, 130 �C for polyethylene, and 25 �C for the SBR blend, using the environ-

mental chamber of the host system. Once the oven temperature reached its set point, the

fixture sat at temperature for a minimum of 30 min prior to initial sample loading. The

loading procedure involved opening the oven chamber door and, using a pair of fine

tweezers, loading and securing the specimen onto the preheated MERA fixture, then clos-

ing the oven chamber door all within a time span of about 20–30 s. A second wait period

was then imposed prior to starting a test in order to allow the oven and sample specimen

to reach the test temperature and the latter to relax any residual stresses from the forming

stage. When sample sagging during this stage occurred, it was necessary to bring it back

up to the horizontal position manually prior to testing and monitor stress relaxation. Only

when the torque signal read zero and the sample was horizontal was testing initiated.

Upon test completion, the drums were carefully wiped clean with a soft disposable labo-

ratory wipe to remove any sample residue off the drum surfaces. The specimens for the

SER experiments were prepared following the same protocol, with strips at least

12.7 mm long. Sample loading followed the protocol described in Sentmanat (2005).

TABLE II. Molecular characterization and relaxation spectrum of materials obtained by dynamic shear

measurements.

PS 615 LDPE NA94000 SBR 70 K/1 M (80:20)

Mw¼ 256 kg/mol Mw¼ 585.5 kg/mol Mw¼ 453.9 kg/mol

Mn¼ 28.4 kg/mol Mn¼ 64.9 kg/mol Mn¼ 283.7 kg/mol

Mw/Mn¼ 9 Mw/Mn¼ 9 Mw/Mn¼ 1.6

g0¼ 8.166� 104 Pa s g0¼ 1.989� 105 Pa s g0¼ 4.19� l05 Pa s

Tg( �C)¼ 105 Tm( �C)¼ 110

160 �C 130 �C 25 �C

gi (Pa) ki (s) gi (Pa) ki (s) gi (Pa) ki (s)

8.390� 105 4.659� 10�4 6.683� 105 4.074� 10�4 1.043� 105 1.059� 10�2

5.722� 104 2.160� 10�2 3.396� 104 2.323� 10�2 8.571� 104 6.716� 10�2

4.151� 104 1.142� 10�1 1.659� 104 9.633� 10�2 7.715� 104 2.713� 10�1

2.587� 104 5.604� 10�1 9.896� 103 2.465� 10�1 1.605� 105 8.823� 10�1

9.892� 103 2.520� 100 9.416� 103 7.142� 10�1 3.774� 104 6.614� 100

2.296� 103 1.056� 101 7.771� 103 2.400� 100

2.642� 102 4.403� 101 9.927� 103 1.697� 101

1Winter, H. H., and M. Mours, IRIS Developments, http://rheology.tripod.com/ (2003).

880 ANDRADE, HARRIS, AND MAIA

IV. RESULTS AND DISCUSSION

The first test of an instrument’s adequacy must be its measurement reproducibility. In

the case of the MERA, this is exemplified in Fig. 8 for three runs of the PS sample at a

nominal strain rate of 1.0 s�1. Clearly, the instrument is very precise with the results from

all experiments falling within 65% from each other.

All measurements shown in this study were video recorded to obtain a direct measure

of the real strain rates and Hencky strain imposed on the sample in both devices, MERA

and SER, for different elongational rates. For all materials and both devices, the tensile

stress growth coefficient is calculated using the real measured strain rates.

A. Polystyrene

Figure 9 shows the deformation homogeneity of PS for MERA experiments at various

nominal strain rates. As can be seen, image analysis shows homogeneous deformation

from the very onset of deformation until ultimate rupture of the samples for all experi-

ments. In order to analyze the development of the MERA at constant strain rate, Fig. 10

shows the calculated real strain rate at different Hencky strains. These results show that

for all strain rates, the MERA follows the linear viscoelastic (LVE) envelope, with an

homogeneous uniaxial elongational flow following W tð Þ ¼ W0 exp �_e=2ð Þ from the ear-

liest instants up to the yielding of polymer network (this is also observed on the SER

fixture).

Worth noting is that regardless of which instrument is used, sample deformations devi-

ate from constant strain rate, i.e., they yield, at similar times for both the SER and the

MERA before they rupture, as is shown in Fig. 12, even though the effect is not visually

apparent, i.e., the sample maintains constant cross section throughout for both accesso-

ries. This is further confirmation of previous reports by Joshi and Denn (2004), Lee et al.(2002), and Barroso et al. (2010) that indicated that failure and nonuniform deformation

may not be as closely related as is normally assumed. Also worth noting is that some-

times the real strain rates are higher than the nominal ones, which is unexpected. In fact,

FIG. 8. Illustration of MERA reproducibility for three experiments on PS at 160 �C at constant nominal strain

rate of 1.0 s�1. The true strain rate for each experiment is shown in the figure.

881HIGH STRAIN EXTENSIONAL RHEOMETRY

if anything, one would expect a real rate consistently lower than the nominal rate, either

due to slip or edge effects at the clamps, in both instruments. The explanation for this lies

in the fact that geometry-dependent parameters need to be included in the rheometer soft-

ware prior to the experiments and these are normally calculated as to yield a desired

FIG. 9. Images of MERA experiments on PS at various nominal strain rates and 160 �C.

FIG. 10. Evaluation of true stain rates using the MERA for PS at 160 �C. In all similar pictures, the dashed line

represents the cross section evolution for a homogeneous purely uniaxial extensional deformation.

882 ANDRADE, HARRIS, AND MAIA

strain rate. However, if they are slightly off, the real strain rates will differ from the nom-

inal ones, and this deviation can be either upward or downward. In any case, what these

results highlight is the importance of monitoring the real strain rate for each experiment,

under penalty of producing erroneous results.

Figure 11 shows the calculated extensional viscosities for both geometries at various

true strain rates. Clearly, the MERA allows as accurate measurements of the extensional

viscosity as the SER, and its results show the correct onset of strain-hardening for all

strain rates as well.

B. Low-density polyethylene

Figures 12 and 13 show the visual evidence of deformation homogeneity and strain

rate calculation for LDPE at 130 �C in the MERA, respectively. Again, the experiments

all show uniform deformation up to rupture and follow the mandatory exponential decay

for all strain rates and for all times. The small discrepancies observed between the real

rates and their nominal values are probably due to the issues discussed before for PS.

Due to the branched nature of LDPE, no signs of network yielding were observed up to

sample rupture.

The calculated extensional viscosities for both geometries at various true constant

strain rates are presented in Fig. 14. Again, the MERA is able to measure the extensional

viscosity accurately for all strain rates when compared with the SER.

C. Styrene-butadiene rubber

Figures 15 and 16 show the visual evidence of deformation homogeneity and strain

rate calculation for the SBR melt at 25 �C in the MERA and, again, the experiments all

show uniform deformation up to the onset of yielding and follow the mandatory exponen-

tial decay W tð Þ ¼ W0 expð�_e=2Þ for all strain rates and for all times. As in the case of

PS, a rate-dependent yielding of the network is observed at high Hencky strains. Figure

17 shows the particular example of a nominal strain rate of 1.0 s�1, where it can be seen

FIG. 11. Transient elongational viscosity for both experimental geometries (MERA and SER) as a function of

time for different strain rates for PS at 160 �C.

883HIGH STRAIN EXTENSIONAL RHEOMETRY

that in that case a maximum Hencky strain of 8.1 was achieved under homogeneous de-

formation conditions. This equates to a linear stretch in excess of 3700, and to the best of

the authors’ knowledge, these are the first reported results ever of true Hencky strains in

excess of 8 being achieved for polymer melts under homogeneous deformation

conditions.

FIG. 13. Evaluation of true stain rates using the MERA for LDPE at 130 �C.

FIG. 12. Images of MERA experiments on LDPE at various nominal strain rates and 130 �C.

884 ANDRADE, HARRIS, AND MAIA

FIG. 14. Transient elongational viscosity for both experimental geometries as a function of time for different

strain rates for LDPE at 130 �C.

FIG. 15. Images of MERA experiments on SBR at various nominal strain rates and 25 �C.

885HIGH STRAIN EXTENSIONAL RHEOMETRY

Finally, Fig. 18 shows the calculated extensional viscosities for both geometries at

various true constant strain rates. The results clearly show that the onset and evolution of

strain-hardening are detected at very similar strains by both instruments, as expected.

However, although the SER results are limited in Hencky strain, those of the MERA are

not and it can clearly be seen that accurate viscosity measurements can be obtained with

the latter up to much higher strains. These measurements cannot, however, be continued

up to rupture because of the aforementioned issue with the superposition of the empty

torque signal on the actual torque from sample deformation. In the present case, we only

calculated the extensional viscosity up to a Hencky strain of approximately 5.5; above

FIG. 16. Evaluation of true stain rates using the MERA for SBR at 25 �C.

FIG. 17. Evaluation of the true stain rate at a nominal strain rate of 1 s�1 for SBR at 25 �C.

886 ANDRADE, HARRIS, AND MAIA

this, the influence of instrument friction was noticeable on the torque curve (more than

10% of the measured signal).

One final point worth of consideration is that at no point were we able to discern the

onset of a steady-state regardless of material, strain rate, or experimental geometry.

MERA experiments in particular should be sensitive to the presence of a steady state due

to the high strains involved, but we were not able to observe it. This obviously contrib-

utes to the on-going debate of whether or not steady flow can be achieved in constant-

rate experiments [Meissner (1979); Bach (2003)], and merits further future studies. By

contrast, steady-state can be achieved relatively easily in constant-stress experiments

[see, for example, Andrade and Maia (2011); Alvarez et al. (2013)].

V. CONCLUSIONS

A new extensional rheometer for high viscosity systems based on the Meissner princi-

ple, easy-to-use, versatile, and adaptable to commercial rotational rheometers was devel-

oped and demonstrated to be capable of achieving very high deformations, limited only

by sample rupture, even if accurate viscosity measurements were not possible at very

high strains due to the internal friction torque of the instrument. The rheometer, named

MERA, was designed with two pairs of counter-rotating rollers, thereby imposing similar

strain histories to both ends of the sample and ensures a uniform extensional deformation

during the elongational experiments. True strain rate is monitored by visually accessing

the sample during deformation using a high-speed digital camera.

Extensional experiments were conducted on three materials representing opposite

ends of expected rheological behavior, a highly elastic SBR blend, a branched LDPE and

a linear PS, and the results compared with those obtained using the well-known SER

design. The main results were as follows:

• The MERA was able to accurately replicate the results of the SER in terms of onset of

strain-hardening and absolute transient extensional viscosity values.

FIG. 18. Transient elongational viscosity for both experimental geometries as a function of time for different

strain rates for SBR at 25 �C.

887HIGH STRAIN EXTENSIONAL RHEOMETRY

• The MERA allowed experiments to be performed in homogeneous flow conditions up

to real Hencky strains in excess of 8 for one of the samples. By comparison, the SER

is physically limited to one drum revolution or a Hencky strain of 3.5–4.0.• No sign of a steady-state was observed at high Hencky strains for both fixtures and the

various strain rates and materials.• There are intrinsic limitations to coupling instruments such as the SER and MERA to

rotational rheometers. Not only is instrument inertia a factor at high strain rates, but at

very high strains, the sample becomes so thin the total torque will end up having a

non-negligible component due to instrument friction.

In conclusion, the new MERA design maintains all the advantages of the original

Meissner concept, namely the possibility of achieving very high strains, while improving

in critical areas, such as versatility, ease-of-use, accuracy at ultrahigh strains and cost.

ACKNOWLEDGMENTS

The authors acknowledge the financial support of FCT—Foundation for Science and

Technology, Portugal, through Grant SFRH/BD/62152/2009 and of the NSF STC Center

CLiPS—Center for Layered Polymer Systems (DMR Grant # 0423914). They are also

grateful to Professor Shi-Qing Wang for kindly providing the SBR polymer used.

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