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•

•

DETERMINATION OF ZERO-SHEAR

VISCOSITY OF MOLTEN POLYMERS

By

Mélanie Boudreault

Department of Chemical Engineering

McGili University, l\'lontreal

November 1997

A Thesis submitted to the faculty ofGraduate Studies and Research in partial fuifillment

ofthe requirements ofthe degree ofMaster of Engineering

co Mélanie Boudreault 1997

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•

•

•

ABSTRACT

Measuring the zero-shear viscosity of a molten polymer is not at all

straightforward. Available rheometers are unable to operate at shear rates low

enough to measure this important property, especially for polymers that have a very

broad molecular weight distribution or a high degree of long chain branching. A new

falling baIl viscometer, the Magnetoviscometer (MVM), has recently been developed

in Austria for the measurement of melt viscosity at very low shear rates.. The

primary objective of the research was to evaluate this instrument as a tool for the

routine measurement of the zero-shear viscosity. Another objective was ta develop a

reliable and convenient method to prepare samples. Experiments performed near the

maximum allowable stresses for various resins are in good agreement with dynamic

data obtained using a rotational rheometer. The tvlVM allows for the measurement of

viscosity in a range of shear rates not accessible ta MOst rheometers.

•

•

•

Il

RÉSUMÉ

Mesurer la viscosité newtonienne d'un polym~re fondu s'avère difficile dans

la plupart des cas. Les rhéomètres disponibles commercialement sont souvent

incapables d'opérer à des taux de cisaillement assez bas pour mesurer cette

importante propriété, surtout pour les matériaux ayant une distribution de masses

moléculaires très large ou un haut degré de branchements. Le magnétoviscosimètre

(MVM), un nouveau rhéomètre utilisant le principe de Stokes, a récemment été

développé en Autriche. Le premier objectif de cette recherche était d'évaluer cet

instrument lors de mesures de routine de la viscosité newtonienne. Un deuxième

objectifétait de mettre au point une méthode fiable et pratique pour la préparation des

les échantillons. Les mesures effectuées pour différents polymères sont en accord

avec les données dynamiques obtenues à l'aide d'un rhéomètre rotationnel. Le MVM

mesure donc la viscosité des polymères fondus dans un intervalle de taux de

cisaillement qui n'est pas accessible à la plupart des autres rhéomètres.

•

•

•

III

ACKNOWLEDGEMENTS 1REMERCIMENTS

J'aimerai tout d'abord remercier le directeur de mes travaux, Dr Dealy. Son

excellente supervision et son dévouement pour ses étudiants ont contribué à faire de

cette maîtrise une merveilleuse expérience et un moyen d'apprentisage exceptionnel.

1would like to thank Bernhard Pammer, Michael Ringhotèr from Anton Paar,

and Sean Race from Paar Physica. Their great help and patience in answering my

numerous questions was much appreciated. They gave me aU the additional

information about the MVM and the press that 1needed.

Je voudrais aussi remercier les étudiants qui m'ont entouré et encouragé :

François, Marie-Claude, Paula, Ranjit. Merci pour toutes ces petites discussions qui

m'ont beaucoup servi à orienter le cours de mes recherches.

Pour terminer, j'aimerai remercier ma famille et mes amis: ma mère, mon

père, Thierry, Sophie, Marc-Antoine et tous ceux que je ne nomme pas mais qui ont

été là et qui ont su m'encourager et me conseiller.

•

•

•

TABLE OF CONTENTS

ABSTRACT

RÉsUMÉ

ACKNOWLEDGEMENTSlRElvŒRCIMENTS

TABLE OF CONTENTS

LIST Of FIGURES

LIST OF TABLES

1. lNTRODUCTION

2. ~ORTANCE OF THE ZERO-SHEAR VISCOSITY

2.1 Dependence of viscosity on shear rate

2.2 Dependence of viscosity on molecular weight

3. METHOOS Of MEASUREING VISCOSITY AT LOW SHEAR-RATES

3.1 Falling body viscometer

3.1.1 Falling ball viscometer

3.1.2 Falling needle viscometer

3.1.3 Centrifuge ball viscometer

3.2 The Magnetoviscometer

3.2.1 Principle ofoperation

IV

i.

Il.

iii.

vi.

vii.

1.

3.

5.

7.

10.

10.

Il.

•

•

•

3.2.2 Peak/Peak measurements

3.2.3 Middle Range measurements

3.2.4 High-pressure ceU for the magnetoviscometer

4. EXPERIMENTAL lVIETHOOS

4.1 Experimental Materials

4.2 Sample Preparation Techpique

4.2.1 Design of the press

4.2.2 Procedure

4.3 Magnetoviscometer operation

5. RESULTS AND DISCUSSION

5.1 Temperature in MVM

5.2 Effect ofSample Preparation Technique on the zero-shear

viscosity measurements

5.3 MVM versus RDA II values

5.4 Reproducibility

6. SUMMARY AND RECOMMENDATIONS

REFERENCES

APPENDIX A: Experimental data

v

19.

21.

21.

23.

24.

27.

30.

33.

36.

40.

46.

49.

51.

53.

• LIST OF FIGURES

vi

Figure 2.1 Viscosity versus shear rate for several temperatures - l\;leissner's

data for low density polyethylene. 4.

Figure 2.2 Log 110 versus log M for several palymers. The data are shifted ta

avoid overlap. The lines shown have slopes of 1.0 (lefi portion)

and 3.4 (right portion). 6.

Figure 3.1 Faxen correction ofdifferent order. 9.

Figure 3.2 CentrifugaI acceleration. 12.

Figure 3.3 Measurement principle. 14.

Figure 3.4 Pieture of the magnetoviscometer 15.

• Figure 3.5 MVM arm with the magnets 15.

Figure 3.6 Shear rate distribution around the bail 18.

Figure 3.7 PeaklPeak measurement evaluation. 20.

Figure 3.8 Middle range measurement evaluation. 20.

Figure 4.1 a) Mother cell for pp measurements, b) Mother cell tor

MR measurements. 25.

Figure 4.2 Picture ofthe cells: the measuring cells are on the left and the

mother cell is on the right 26.

Figure 4.3 Design ofthe MVM press. 28.

Figure 4.4 Picture ofthe MVM press 29.

Figure 4.5 a) eut for a pp measurement, b) cuts for a MR measurements. 31.

• Figure 5.1 Temperature in MVM. 33.

vii

• Figure 5.2 Variation of the room temperature near the MVNI arm: eftèct

ofair conditioning. 35.

Figure 5.3 Parameter Analysis, before elimination ofdefective samples. 38.

Figure 5.4 Parameter Analysis, defective samples eliminated. 39.

Figure 5.5 Viscosity curves for 0803-1 at a temperature of 150aC. 42.

Figure 5.6 Viscosity curves for 335A at a temperature of 150aC 43.

Figure 5.7 Viscosity curves for 335B at a temperature of 150aC 44.

Figure 5.8 Viscosity curves for 335C at a temperature of ISOaC 45.

Figure 5.9 PDMS at 30°C. 48.

•

•

LIST OF TABLES

Table 1 List of the resins tested. 23.

Table 2 Temperature in the MVM peak/peak arm: with and without cover. 34.

Table 3 One-halt fraction ofthe 2k design. 36.

Table 4 Evaluation of the noise. 37.

Table 5 Viscosity results for 335A, 3358, and 335C. 46.

•

•

•

CHAPTERI

INTRODUCTION

A rheological property that is frequently used ta characterize thermoplastic resins

is viscosity, because it is relatively easy to measure. Using severaI instruments e.g.

capillary rheometer, cane-plate rheometer, etc., the viscosity can be measured over severa!

decades of shear rate, but to obtain the complete curve is impractical as a tool for routine

quality control, as tao much time and labor are required. For this type of application, a

single-point measurement is preferred. The zero shear viscosity is an attractive candidate,

because it is very sensitive to molecular weight.

However, measuring the zero-shear viscosity is not straightforward, as available

rheometers are unable to operate at shear rates low enough ta measure the zero shear

viscosity. It is particularly difficult to measure this quantity for polymers that have a very

broad molecular weight distribution or a high degree of long chain branching. The basic

problems are the detection ofvery slow motions and very small forces. [n sorne cases, the

motion of the fixture is sa slow that it cannat be detected, or a rneasurement takes sa

much times that the polymer degrades.

The magnetoviscometer (MVM) was recently developed in Austria for the express

purpose ofmeasuring the zero-shear viscosity, and a prototype has been loaned to McGiU

University for evaluation.

•

•

•

CHAPTER 1: lNTRODUCTION

The objectives ofthis work were as fol1ow:

1. Ta develop a methad to prepare samples for use in the MV1v1.

2. Ta evaluate the MVM and compare its results with low-trequency dynamic data.

3. To evaluate the suitability of the MVM as a tool for routine quality control.

4. To determine the limitations of the MVM.

2

•

•

3

CHAPTER2

IMPORTANCE OF THE ZERO-SHEAR VISCOSITY

2.1 Dependence of viscosity on shear rate

The viscosity ofmolten polymers depends on a number of factors, including shear rate,

temperature, pressure, and resin composition (chemical structure, molecular weight distribution

and presence of long chain branches, nature and concentration of additives, fillers, etc.). The

viscosity of a molten thennoplastic decreases sharply as the shear rate is increased1, but at

sufficiently low shear rates, it becomes independent of shear rate. The limiting low-shear rate

value is called the zero-shear viscosity, 110. Figure 2. 1 is a plot of viscosity versus shear rate at

severa! temperatures for a typical, commercial, low-density polyethylene. These data were

obtained by Dr. J. Meissner with a specially modified Weissemberg Rheogoniometer. These

ïrnpressive measurements were never repeated, because of the enonnous time and expense

involved.

At high shear rates, data often fall very close ta a straight line on a log-log plot,

and a power law can thus be used to describe the dependence of the viscosity on shear rate

in this region:

k '/1-1Tl = ·r (2-1)

•For a Newtonian tluid, n=1 and K= vïscosity. As written above, the power law has

severa! basic tlaws, and a better fOrOl is:

(2-2)

•4

•

•

1010 - 4 10 3 10 -2 10 -1 1 10 102 103

Y(5 ')

Figure 2.1. Viscosity versus shear rate for several temperature­Meissner's data for low density polyethylene l

. Temperatures, from topta battom are (OC) : 115, 130, 150, 170, 190, 210, 240.

.104

where À. is a materia! constant with units of time. However, the zero-shear viscosity must

be knowü ta use this farm.•CHAPTER 2: lMPORTANCE OF THE ZERO-SHEAR VISCOSITY 5

•

2.2 Dependence of viscosity on molecular weight

It is known that rheological properties depend on molecular weight distribution,

and it has been proposed2 that viscosity or complex viscosity data can be used to infer the

MWD of linear commercial polymers. Knowing the rvlWD of a resin is sometimes very

critical, because a small change can render a resin useless for its intended application.

The strong dependence of polymer viscosity on shear rate is attributed to the strong effect

of shearing on the entanglement densityJ. At low molecular weights, there are no

entanglements, and the viscosity is proportional to the molecular weight and varies little

with r over a wide range of shear rates. As the molecular weight increases, a point is

reached where '1(1 starts to increase much more rapidly over a tàirly narrow range of M.

Above this range, the slope of the curve of log 'lu versus log M reaches a value of about

3.4-3.5 for Many linear polymers. For monodisperse polymers, this implies:

'70 =kN/3~ {2-3}

For polydisperse materials, it is often round that

(2-4)

•where Mw is the weight average molecular weight. Figure 2.2 iIlustrates this behavior.

As the moiecular weight increases above the critical vaIue for entanglement, Mc,

where 110 starts to rise with Mwl.", the melt becomes strongly dependent on shear rate,

eventually approaching a power-Iaw (Eqn. 2-1).

•

•

o~C)

.2+1-

~tJ)zoo

o 1 2 3 4

CONSTANT + logM

5 6

6

•

Figure 2.2. Log 110 versus log M for several polymers. The data areshifted ta avoid overlap. The lines shown have slopes of 1.0 (leftportion) and 3.4 (right portion)l.© 1968 by Springer Verlag.

•7

CHAPTER3

METHOOS OF MEASURING VISCOSITY AT LOWSHEARRATE

3.1 Falling body viscometer

3.1.1 Falling ball viscometer

The absolute viscosity ofa Newtonian liquid can be determined tram a measurement of

the time required for a ball to faIl a certain distance in a cylinder containing the liquid3. It is

probably the simplest and certainly one of the oldest methods tbr measuring viscosity. The

viscosity is calculated trom:

• where: t=

" = t . (Sb - Sl' ). B

time for ball to fall tram one mark to another on a glass cylinder

(3-1)

•

Sb= specifie gravity ofthe ball

SF specifie gravity ofthe tluid at the measuring temperature

B= ball constant

The ball constant can be determined by calibration for a given shape offalling body and

size ofcontainer. Stokes' equation can be used to derive an exact equation for a sphere falling

under the influence ofgravity in an infinite sea ofNewtonian liquid:

(3-2)

where VrxJ is the terminal velocity, d is the ball diameter, Pb and Pr are the densities of the ball

and tluid, and g is the acceleration due to gravity.

The presence of the cylinder walls reduces the terminal velocity, and the commonly•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE

used Faxen equation[ol,SI gives the correeted velocity to the 5th arder:

VIJ =V·!.:

where: le =[1-2.l04{~)+2.09{~)' -O.95{~)'r

D = measuring cell diameter

v = actual ball velocity as measured

VIl = correeted ball velocity, reJated to viscosity by (3-2)

8

(3-3)

(3-4)

•

•

The correction is actually an infinite series. One can show that the 5th order approximation

given by (3-4) is a good approximation for the ball diameters used in this work (2 and 3 mm).

The Faxen equation up ta order lOis shown in Fig. 3. 1.

le =[1-2.104{~)+2.09{~)' -O.95{~)' -1.37{~r +3.87{~)' -4.19{~r +··r(3-5)

Mol~nSince the MVM is intended for use with meù polymers, which are viscoelastic, it is

essential ta know how viscoelasticity affec1 the flow around a sphere in the limit of very1\

et dl/.slow flow. Becke~ MeKiniey, RaSiliUSSeIi, and 1(a99ager (1994t' and Arido and McKinley

(1997)7 have shown that at very small Deborah numbers (ratio of relaxation time of fluid

ta charaeteristic time for the deformation) the flow of a viscoelastic tluid does, indeed,

approach that predicted by Stoke's equations, i.e., that of a Newtonian fluid at small

Reynolds numher.

•9

0.5

op

..:... 0 ---- ---------- ----------------.a-- --..- ........ --- ..-- -.

~

~

• - - - - - -f1-0.5 _. .,_____• __ ·.0

--- f3------_. --'"-- --

f5----te

f8_. - - f10

-10 0.5 1 1.5 2 2.5 3 3.5 4 4.5

d(mm)

Figure 3.1. Faxen correction for various arder ofapproximation.

•

•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE

3.1.2 FaIling Needle Viscometer

10

ln this methocL a slender cylinder with hemispherical ends (the needle) is used instead

of a sphere, still under the influence of gravityH. 9. For Newtonian tluids, the creeping tlow

expression for the viscosity, incIuding the wall etfect, is:

(3-6)

•

•

with K < 0.03, where K = d/D, d is the diameter of the needle and D the diameter of the

container. This equation assumes an infinitely long needle.

For a power law tluid, r = K(y) n , the following equation gives the terminal velocityl:

3-7)

where A(n,K) is a function arising from the solution of the flow field bet\veen the needle and

the cylinder wall.

A laser is sometime used for the detection of the needle111, but this is not useful when

the melt is opaque or degrades with time.

3.1.3 Centrifuge Bali Viscometer

This is a variation of the falling baIl vÏscometer. Here, the tluid is contained in a

horizontal cylindrical glass tube and the ball is subjeeted to centrifugai acceleratian11. ln arder

ta maintain constant acceleration for a ball moving in the chamber (see figure 3.2), the

following relation must hold:

(3-8)

where RPM1 and RPM2 are respectively, the revolutions per minutes of the rotor at position PI

(measured trom the center of rotation) and rime t = tl, and at position P:! and t = t2. The

centrifugai acceleration ac ofa ball at position P(cm) and motor speed RPl\4 is:

•CHAPTER 3: METROnS OF MEASURING VISCOSITY AT LOW SHEAR RATE 11

(3-9)

The viscosity is calculated tram:

(3-10)

•

•

where 0) is the speed ofthe motor in RPM'I and b and c are empirical constants.

This instrument has sorne good features~ the temperature can be maintained trom

ambient to over 400°C, and only 0.5 ml ofsample is required. A wide range ofviscosities can

be accommodated, trom 10-1 to lOS Pa-s. In theory, IOIU Pa·s is achievable, but ooly one-data

point per day can be obtained.

3.2 Magnetoviscometer

[n the falling ball method, gravity is the driving tàrce for the motion of the sphere. To

obtain the zero-shear viscosity ofa typical polymer melt, this is often insufficient, because the

ternûnal velocity is too small. By adding a magnetic field to the gravityl2. 13. 1", the time of

experiments becomes shorter, sa that degradation ofthe polymer can be avoided.

3.2.1 Principle ofoperation

The Magnetoviscometer is a falling ball instrument that makes use of a magnetic field

(15.161. It was developed by Paar and others at the University oflinz to overcome the problems

•12

1 1

1

1

0.8 ~1

1

0.6 j1

i1

0.4 .,

CIo * constantRPM =constant /1

:i!!.u..

08

06

04

a.l =constantRPlVI ~ constantPI(RPlVld2 = P2(RPM2)2

O'vO-----------.........-------l

0.806

Position la. u.)

0402080.6

Po""on (L u.J• a) b)

Figure 3.2. a) centrifugai acceieration is proportional to the baIl positionfrom rotation center at constant RPM; b) by decreasing the rotor RPMaccording to Eqn. 3.9, a constant centrifugai acceleration cao be obtained.

•

of previous falling body viscometers, Le., to get to a very low shear rate with only gravity as•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE

the driving force, the ball velocity is very small.

13

In arder ta increase the driving force for flow, and thus reduce the rime for an

experiment, an iron sphere is acted on by an inhomogeneous magnetic field in addition to the

gravitational force, within a measuring cell filled with the melt (see figure 3.3, 3.4 and 3.5).

Two permanent magnet fixtures generate the magnetic field. For example, the force for a 3 mm

sphere can be about 40 times stronger than the gravitational field. The magnetic tàrce F~I is:

cT!F.'v/ = m%.\/ H êc

where: m= ball mass

(3-11 )

;t\[ = magnetic susceptibility ofball material

H = magnetic field strength• aHax

x=

gradient ofmagnetic field strength in vertical direction

vertical distance abave the plane

It is assumed that the gradient of magnetic field is vertically uniform over the distance where

the time offall is measured.

The gravitational force, Fa, is given by:

(3-12)

• The viscous resistance (drag), Fv, of the melt opposes the force driving the ball. For a

Newtonian tluid this is:

•14

Fv =3· dK·x-l1· V-o

~ .. --~--"---"--- FM = mk·x...·H·aHlôxorFG =mt<· 9H..-----•

POLESHOE

Figure 3.3. Measurement principle.

•

•

•

•

15

Figure 3.4. Picture of the magnetoviscometer.

Figure 3.5. MVM ann with the magnets.

•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE 16

(3-13)

•

The tenninal ball velocity, VŒJ, is detennined by the balance of viscous resistance and

magnetic force, Fv = FM + Fa, or from the balance ofviscous resistance and gravitational force,

Fv= Fa in the absence ofthe field. It usually takes 0.01 to lOs for the baU to reach 99.9% ofits

tenninal velocity. The ball position is monitored by an induction coil. The inductance of the

coil increases when the ferromagnetic ball is introduced. At constant velocity, this produces a

sinusoidal function of time. There are two types of measurement: peak/peak measurement,

used for low viscosity fluids, and middle range measurement.. tor higher viscosity tluids.

Measurement procedure l\Jleasurable viscosity range "Peak/Peak measurement 10 to 5x10-J Pa.sMiddle Range measurement IOxIOJto 5xl05 Pa.s

A nominal shear rate is detined as follows:

. V"y=c--d

(3-14)

Values ofthe factor c between 0.4 and 2.0 have been proposed in the literature and a value of

c=1.3 is used for the MVM.

The shear rate distribution around a sphere moving at constant velocity in a Newtonian

tluid can be derived as follows:

•

Y· =-r~(~J +.!. cJvr

rO... aoor r r

The solution ofStokes equations gives the velocity distribution:

(3-15)

(3-16)

•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE

(3a a

J)

VII =-V·cosf) 1--+-.4r 4r'

(3a ,,3)

Vr =V 'cos8 1--+-.2r 2r'>

Thus, the shear rate is:

1. 1 ,[ • ( 1. 3a a3 1. .. ( 1 Ja li;)l

Irrt/l=~ casB --"'--., ----;-)T:sm8 ---. ""--l)Jr 2r - r r 2,. - 2,.

17

(3-17)

(3-18)

(3-19)

Figure 3.6 shows the shear rate distribution around the baIl. At the location r = a and

8 = 0, the shear rate has its maximum value:

•. f' f'yTf1 InuL\( ==:;- =-,_a ,

The maximum shear stress is thus:

r==,,·Y

(3-20)

(3-21 )

•

The MVM software calculates a ··shear rate". and it is of interest to see how this is related

to the maximum value for a Newtonian fluid. Using data l'rom this study: for 3mm bail,

40mm gap, polybutene, lI) = 13.2 s (a1ready corrected for the standardized distance of

6.5mm)

S 6.5mmV=-= =0.492mm/s

1%J 13.2s

Faxen correction: VIX) = V . le =O.492mm 1S· 4.0 19 == 1.979mm / s

rl'niL\( == Va) = 0.66s-1 (Newtonian equations)d

rMm == C Va) = 0.858s-1 when c = 1.3d

•18

3.532.521.510.5o

3

2 -t--------i------;.~~------~----~ --------1

1 -t------i-------~~~-~-------~

o

3.5

-cercle i

~shear rate of-50 1

"""'-shear rate of-4O 1

i--"'-shear rale or-30 1

2.5 -t------+------+----+--~~--------Jl-shear rate of-20

~shearrateo~10

~shear rate=O

"""'-shear rate of1 0

0.5 -I-----+----+-----H~l__-~---~------__t

1.5

•

x

Figure 3.6. Shear rate distribution around the bail.

•

•CHAPTER 3: METHOOS OF MEASURING VISCOSITY AT LOW SHEAR RATE

Value calculated by the MVM software: YMVM == O.864s- '

3.2.2 PeaklPeak Measurement

19

For this technique, the time required for the ball to tàll from one peak ta the other is

measured (see figure 3.7). Knowing the viscosity ofa calibration substance (8), the viscosity of

the unknown tluid can he detennined as foUows:

•

V,,(B)'1 == 'lB V"

One can also calculate the viscosity direetly from the faIling time:

II) K'1='1B'--= '/,r,,(B)

'18where K =ln (B)'

(3-22)

(3-23)

The constant K is determined for a gravitationai field alone and tor defined spacings

between the magnets. Between these spacings, K is calculated by linear interpolation. and tàr

longer spacings, by extrapolation.

The temperature dependence of the bail detection system is taken into account by

correcting the measured falling time ofthe ball to a standardized measuring distance of6.5mm.

When the temperature rîses, the distance between the two colis (peaks) increases, and it is

corrected using the cell constants A and B.

•/

t =---<Il A+B.T

where ta == falling rime for standard distance

(3-24)

u

•o

t

20

•

•

J~ ~ f •r s. s

Bali startsfa/ling

Figure 3.7. Peak/Peak measurement evaluation, where U is thesinusoidal voltage, t, the time, te, the peak/peak falling time and Sa:, thestandardize distance.

t

r,

~ ~ . • •s

BaIl entersIinear range

Figure 3.8. Middle range measurement evaiuatioD, where U is thesinusoïdal voltage, t, the tinte, S, the distance, fI, the linear range andL\U/At. the gradient.

CHAPTER 3: METHODS OF MEASURING VISCOSlTY AT LOW SHEAR RATE

• t= measured falling time

21

3.2.3 Middle Range Measurement

For this technique, only the gradient IixJlit (x being the distance and t the time),

detennined in the linear range between the two peaks, is used ta caIculate the velocity (see

figure 3.8).

This is a useful technique for a high viscosity materiaI. because it requires a shorter

measuring rime. The ball velocity can he calculated fram:

v = / * ll,-c

C - DT iiI(3-25)

•where C and D are empirical constants, that correct for the augmentation of the distance

between the two peaks when the temperature increases, T is the measurement

temperature, and V is the bail velocity. The viscosity is then calculated as tbIlows:

"=K.~ = K ·(C +D· T}._I-~~

V A-c!I~l

(3-26)

•

The shear rate i and the shear stress rare calculated using equations 3- 14 and 3-21.

3.2.4 High-pressure cell for the Magnetoviscometer

A high-pressure cell has recendy been designed for the lVlVM by Gahleitner and

Sobczak l1 for studying the pressure dependence of viscosity. The falling ball method is

advantageous here, because there are no rotating parts(requiring seals) or pressure

gradients. The cell is hermetically sealed by means ofa gasket made of nylon or PTFE; no

supply lines to the inside of the sample cavity are therefore necessary. Heating the

specimen in the closed cell generates the required pressure~ and a cIosing screw allows the

final setting of the pressure. When the screw is tumed~ the pressure inside the cell rises

because the sample has a low compressibility. The cell can operate up to lOOO bar

(iXIOs Pa) and 523K.

The high-pressure cell has not been used in this project. but it is a very interesting

possibility for future research. It would be interesting to compare I1I1(P) data from the

MVM with lJ(r ~ p) data from the new high-pressure sliding-plate rheometer recently

developed at McGill lK•

•

•

•

CHAPTER 3: METHOOS Of MEASURING VISCOSITY AT LOW SHEAR RATE 22

•

•

•

23

CHAPTER4

EXPERIMENTAL METHüOS

4.1 Polymers Studied

The resins studied were polyethylenes made using metallocene C·single site")

catalysts. The Exact resin was made by Exxon, and Dow Chemical made the athers.

Sorne resins were received as pellets and athers in pawder form. Exact resin was chosen

ta develop and study the sample preparation technique, because in the range of shear

stresses generated by the~, this resin is in its zero-shear viscosity region. The athers

resins, 0803-1, 335A, 335B, and 335C have similar molecular weights but various degrees

ofbranching.

Table 1. List of the resins tested.

Resin Manufacturer Density (glcmJ) ~Iw LCD Comonomer

Exact EXXON 0.9100 119400 No Butene

0803-1 Dow Chemical 0.9374 100900 No Butene

335A Dow Chemical 0.9592 88900 Yes None

335B Dow Chemical 0.9583 92600 Yes None

335C Dow Chemical 0.9575 93400 Yes None

The resins that were received in powder form had to be transtàrmed into pellets.

Powder is a problem when one applies vacuum to the press for molding, because it gets

aspirated by the vacuum pump. Here, the resins were molded into a rectangular sheets

with dimensions of 4 X 6 ~ X 0.025 inches using a Carver press. The mold was a

stainless steel plate with a reetangular hole in it. In compression malding, this mold is

filled with polyrner and sandwiched between two Mylar sheets and two steel plates, to

allow easy removal of the cooled product. The press is then heated until it reaches

thermal equilibrium at 150°C. The mold and the pawder are placed in the press, and a low

pressure from 0 to 5 metric tons is applied for five minutes in arder [0 force out trapped

air and promote complete melting of the powder. Then the pressure is increased ta 15

tons in two steps of 5 metric tons at 5 minutes intervals. This is ta remove any remaining

air and ensuring good sample consistency. Finally, the mold is coaled to roam

temperature by circulating water through the press for 15 ta 20 minutes. The sample is

then removed, and using a blade or scissors, it is eut into small pieces. The pieces should

be less than 4mm in size in order ta fit into the MVM press.

•

•

CHAPTER4: EXPERIMENTAL METHODS 24

•

4.2 Sampie Preparation Technique

4.2. 1 Design of the press

[t was tirst necessary ta design and construct a press to make samples for the

MVM. The required sample size is about 3cm3• The "'mother cell" (an inner mold) used

ta produce cylindrical samples of 6.9mm inside diameter and of 25mm in length, is shawn

in the Fig. 4.1 (see also figure 4.2). The mother cell is different from the measuring cell

mainly in that it has a magnet at its bottom ta ensure that the iron bail stays at the center

of the sample during molding. There are two types of mother cell: one for peak/peak

measurements and one for middJe range measurements. The peak/peak cell bas an angle

Figure 4.1 a) Mother cell for peak/peak measurements, b)Mother cell for middle range measurement.

•

•

•

30

a)

r11CV'8t

6.9

b)

25

•

•

26

•

Figure 4.2. Picture of the cells: the measuring cells are on the left andthe mother cell is on the right.

at the bottom of 1500, and the middle range cell has an angle of 1780

• The angle in the

cells is very important. The angle in the peak/peak cell allows the bail to center itself for

the next experiment. This is not needed for the middle range, since the ball does not reach

the bottom of the cell. The bail starts further up and stops near the second peak as

explained in section 3.2.3. Both are made of stainless steel as opposed to the Hmeasuring

cells" which are made of brass. The mother cell needs to be strong to support the

pressure in the press. They are made of brass, mainly because it is cheap. SA if the

material under study is hard to remove (for example a highly viscous ail), one can simply

discard the cell.

Figure 4.3 shows the important features of the lVlVM press (see also figure 4.4). It

has a I200W, 120V heater band, which is controlled by the temperature controller. The

hydraulic cylinder has a maximum capacity of 10 000 psi (6. 9X 10'Pa). [t has a plunger a

diameter of 1mm and long enough to eject the mother cell. It has a copper seaI support a

vacuum inside the press and to keep the resin inside. The mold is water-cooled. There is

aIso a hole for connection to a vacuum pump to prevent the tormation ofair bubbles in the

sample. A vacuum of 26 ioches of Mercury (660 mm Hg) can be generated. The press

aIso has a screw at the bottom of the mold to release the mother cell.

•

•

CHAPTER 4: EXPERIMENTAL METHOOS 27

•

4.2.2 Procedure for Sample Preparation

The molding procedure that was developed is as follows. First, a release agent is

applied to the mother cell inner surface if the resin tends to stick ta the mold. Then an

iron ball (2 or 3 mm diameter) is placed inside. The bail is centered by the magnet. The

screw is put in its position, and the cell is pushed to the bottom of the mold with the help

•28

hydraulic cylinder

•

secl

~plunger

tovacuum

........----n- heating coil

-+'---....coollng

•

Figure 4.3. Design of the MVM press.

of the piston. The pellets are poured ~ up to the vacuum hole. The mold is then sealed

by the pisto~ and the vacuum pump is tumed on. A vacuum of about 660 mm Hg is

maintained for 10 min at room temperature. At this point, the heater is tumed on for 20

to 30min. A pressure of 1500 ta 2000 lbs (680-910 kg) is then applied for 5 to la min. It

is important that the pressure not exceed la 000 psi. because this would damage the

copper seaI. \Vhile \vaiting, the vacuum pump is tumed off. since the vacuum hole is

blocked.

Ta cool the mold, the heater is tumed off, and the water valve is opened. It

normally takes fram 2 ta 5 min ta cool the mold ta a temperature of 3DoC. To remove the

sample, the pressure is released, the screw is removed. and the cell is pushed out of the

cylinder using the piston. The sample shauld then come out of the cell easily.

Finally, the sample needs ta be eut ta fit in the measuriog cell. The first eut is

made at ISmm from the bottom (see figure 4.5a). When doing a middle range experiment,

the sample has to be eut again at 4.5mm. Theo the segment eontaining the baIl is tumed

180° (see figure 4.5b.). The sample and segments are placed in the measuring cell, and the

cap is screwed on.

•

•

CHAPTER -l: EXPERIMENTAL METHOOS 30

•

4.3 Magnetoviscometer operation

The settings of the MVM eontroller were the same for ail measurements. The

middle range arm was used, with a fibergIass caver avec it ta ensure that the temperature

inside was constant and uniform. The instrument cao be operated from room temperature

up to 300°C. The distance between the two magnets cao range from 36mm to SOmm.

•31

then• - """"

---------_-'_---1---

18mm 18mm

..... .. .4.5

Figure 4.5. a) cut for a peak/peak measurement, b) cuts for a middlerange measurements.•

a) b)

•

Based on experience with ather instruments~ measurements were delayed for about 15 min

ta ensure that the sample had reached the set temperature.

Ta make a test~ a measuring cell is Ioaded into the arm, and the tiberglass caver is

slid inta place. The parameters chosen for the test are entered, and the computer contrais

the operation.

Ta clean the ceU~ it is taken out of the arm, the cap is unscrewed, and a

screwdriver is inserted in the sample. The cell is then caoled with water ta room

temperature, and the polymer is taken out by pulling on the screwdriver.

•

•

•

CHAPTER4: EXPERIMENTAL METHOOS 32

•

•

•

33

CHAPTER5

RESULTS AND DISCUSSION

S.l Temperature in MVM

The distribution of the temperature in the MVM arms was measured to learo if

there was a temperature gradient in the sample and if it was affected by the surroundings.

This study was done to ensure that there was no temperature gradient inside the sample.

It is known that a temperature variation of 1°C, depending of the material used't can cause

variations in viscosity of 5 to 10%. A special cap was fabricated ta make it possible ta

insert a thermocouple inside the sample. Two hales were made: one in the center (which

was an enlargement of the hale already existing) and one at the edge. [\Ileasurements were

made at four points as shown in Fig. 5. 1: two from the center hole (one at the center and

one at the bottom), and two from the hole on the edge (one at the center and one at the

bottom). A caver made of fiberglass fabric was used ta provide additional insulation for

the arm.

• •

Figure S.L Temperature in MVM.

A J-type thermocouple was used, the set temperature was 130°C. and the Exact•CHAPTER 5: RESULTS AND DISCUSSION 34

•

•

resin was used. The data were collected after 45min for the peak/peak arm.. and these are

shawn in table 2. One can see that when there was no caver. the variation in the

temperature was ±O.6°C, and when there was a caver" the variation fell to ±O.3°C. The

fiberglass caver was therefore used for aIl the experiments.

Table 2. Temperature in the MVM peak/peak arm, with and \vithout cover.

No Caver With CaverA 136.2°C 137.6°C8 136.3°C 137.6°CC 136.S0C 137.9°CD 136.SoC 137.SoC

At the beginning ofthis research, the MVM was install in a room \vere there was

an air conditioner with an ON/OFF controller. Every 15 min or so.. there was a sudden

draft of cool air. Since there was a significant variation in the room temperature near the

MVM arm (due ta the convection of the air and its temperature) (see figure 5.2), [ tracked

the variation of temperature at the center of the sample. [t varied between 136.2°C to

135.SoC when the air conditioner went ON or OFF with no cover on the peak/peak arm.

A cardboard box was placed aver the apparatus ta see the effeet of reducing the

forced convection. As shawn in Figure 5.2, the box damped the variation of temperature

near the arm, implying a reduced variation in sample temperature.

For the experiments whose data are reported here, the MVM was moved ta

another laboratory in which there was no major variation in temperature near the arm. It

was thus not necessary to use the box.

•35

24.5 .,.----------------------------..

•

24 .

23.5 .

o 23Ga!œ" 22.5 .-!:2

! 22Ga~

E~ 21.5 .

21 -

20.5 -

......­.....- ,···,·,·······,··,·,. ,. ,, .

~ ,·.• t1 •, r·.·.o.o •.,~

••••• 'without the box:

-with the box

2:302:001:301:000:3020 ~.-----.....----.......----------------....

0:00

lime (hrs)

Figure 5.2. Variation of the room temperature near the MVM arm:effect of air conditioning.

•

A temperature calibration was done ta ensure the comparability of data with thase•CHAPTER 5: RESULTS AND DISCUSSION

from other instruments in the laboratory.

5.2 Effect of sample preparation technique on the zero-shear viscosity

measurements

36

•

•

A series of tests were carried out ta see if the sample preparation technique had an

effect on the viscosity measured by the MVM. A one-haif traction of the 2'~ design was

used ta set the parameters for the operation of the press. With this type of design.. one can

use 8 samples instead of 16 ta compare the interactions of the parameters \vith each other.

Table 3 shows the parameter values used. [n the table.. a --+'" indicates the maximum

value of the pararneter, and a···" indicates the minimum value.

Table 3. One-half fraction of the 2k design.

Run P T HP HT1 - - . -2 + . - +3 - + - +4 + + - -5 - . + +6 + - + -7 . + + -8 + + + +

Where the minimum and maximum values are:

Min (-) Max(+)P (pressure) 1500-2000 lbs 3000-3500 lbsT (temperature) I50aC I8SaCHP (compression time) Smin 10 minKT (bestiol( time) 20mîn 30 min

The vacuum was constant at 26"Hg, and the cooling time was bet\veen 2 and 5 min. The•CHAPTER 5: RESULTS AND DISCUSSION 37

•

ball diameter was 3mm, and the Exact resin was used.

The test conditions were kept constant.. and the middle range measurement was

adopted with the fiber glass caver in place. The magnetic field was used with a distance

between the poles of 36mm. The test temperature was 130°C at the middle of the sample,

and the equilibration time was 800s. The sample was cut as èxplainèù in sèction 4.2.2.

A separate study was done to evaluate the noise level in the data. The experiment

design is shawn in table 4. Ten samples were made.. and aIl were used. even if they had

defects (such as aif bubbles before or after the measurement. baIl not centered. white

spots, etc.) (see figure 5.3" run 9). Eliminating the samples with defects left 4 samples

(see figure 5.4, run 9). Those samples had an average measured viscosity of2.6IXIO~

Pa·s, and the variation was ±2%.

Table 4. Evaluation of the noise.

RUD

9

p T+

HP+

UT+

•

About 4 samples were made for each experimental condition for a total of 28

samples (see figure 5.3). Ali the samples were used even if they had detècts. Eliminating

the samples with defects left ID (see figure 5.4). These samples had an average measured

viscosity of 2.64XI04 Pa·s" and the variation coefficient was ±3%. [t was concluded that

the effect ofvariation in sample preparation technique is negligible. because the variation

coefficient is below the reproducibility of the MVMÎ, which is about 5%. The only factor

i From the technical Specifications orthe MVM

•38

28000 ~--------------------.,

27000 - 0 0~

00 0 0

10 §826000 -

0 0 ~0 80 0 ~~ 25000 - ~enni 0Q. 0'-'"

~ 24000 - 0 0en0uen

• :> 23000 - 0

22000 -

21000 - 0

10o20000 -+------"r------r--1---r--1---.,.....1-----i

246 8

Runs number

Figure 5.3. Parameter Analysis, before elimination of defective samples.

•

•39

28000 -r------------------------,

21000 -

10o20000 -+-------,.I------,I...-----..--I---~I----f

246 8

Run number

Figure 5.4. Parameter Analysis, defective samples eliminated.

•

that has an appreciable effect on the measurement of the viscosity is the presence of air

bubbles. Ifair bubbles are presence, the measured viscosity is lower than the true value.•CHAPTER 5: RESULTS AND DISCUSSION 40

•

•

5.3 MVM versus RDA II values

Another set of experiments was done to compare the results of the MVM with

low-frequency dynamic data. The resins used were 0803-1. 335A. 3358. 335C. and the

test temperature was 150°C. The ball diameter and the distance bet\veen the magnets

were varied to obtain a wide range of shear rates. The nominal shear rate (the value

indicated by the MVM) is dependent on the falling time. sa ta get a curve of viscosity

versus nominal shear rate.. the distance between the magnets is varied. (Using a smaller

ball diameter also extends the range, because the force applied varies \vith the mass of the

ball, but it was found that the 2mm baIl diameter could not be used tor the middle range

experiments.) Middle range experiments are usually used for high viscosity resins.. which

require a high magnetic force. High forces can only be achieved using "vith the 3mm ball.

(The 2mm baIl has not been calibrated for use with that arm. ) For middle range

measurements.. the gradient ôxlÔl must be known ta calculate viscosity.. which means

that the amplitude of the signal (voltage in mV) must be knO\vn. but this had been

adjusted for the 3mm ball. For this reason viscosities determined using the 2mm ball

were not valid and have been excluded from the following analysis.

The low-frequency dynamic data were obtained using a Rheometrics Dynamic

Analyser II (RDA), a controlled strain rotational rheometer. By using the Cox-Merz

Rule, which is always valid in the limit of very low frequencies.. one can convert the

complex viscosity into a steady-shear viscosity. Each of the RDA curves is the average

of at least 5 runs. The MVM curves show data for 4 or 5 samples. Viscosities were

determined at several force levels (distances between magnets) using a 3mm baIl. In this

way, it was possible ta get a curve ofviscosity versus nominal shear rate.

Figure 5.5 shows the viscosity as a function of shear rate tor the 0803-1 resin.

This figure is particularly interesting, because it was possible to rncasure the true zero­

shear viscosity using the RDA. This value was 5.78X103 Pa·s. The average of the MVM

data was 6.70X103 Pa·s. These include repetitions of the 5 samples. The points to the

right were obtained using the 36mm gap between the magnets. and the points situated

between 2.5XIO·2 and 6.5XIO-2S·I were obtained using variOlls gaps between the

magnets. The shear rate decreases as the distance between the magnets increases. The

three points situated around 2.0X10-3S·l were obtained using the gravitational tield. The

difference between the two curves is about 15.90/0. It is possible that ail the data coming

from the RDA were measured, in faet, at 151°C instead 0 f 150e C. which would lower the

value of the viscosity. This was found after the resins (OS03-L 335A. 3358, and 335C)

were tested, when a temperature calibration of the RDA was carried out. The effect of

temperature would be different for each resin tested~ since each has a different shift

factor, aT. It would be interesting to measure these shifts to see the etfect on the figures,

but this was not within the scope ofthe present project.

Figure 5.6 shows the viscosity versus shear rate for polymer 335A. The MVM

data are for 4 samples and the average values are shown in table 5. In this case, for this

material, this is the value from the RDA curve. The difference between the two is about

1%.

•

•

•

CHAPTER 5: RESULTS AND DISCUSSION 41

•42

1.00E+04 -r------..,...-----~-----------------..,

o MVM. P6

A MVM. P7

C MVM. P9

+ MVM. P11

MVM. P13

- • - • RDA approx

• RDA

E:I

t

1

1

1

11

IVlscosity Avetctge values:~mm: 6.70e03 Pa.sRDA: 5.78eo3j Pa.5

•1.00E+011.00E+OO1.00E-02 1.00e-C1

Shear Rate (5-1)

1.00E.Q31.00E+03 .....-----......-----....-----------------....

1.00e-04

Figure S.S. Viscosity curves for 0803-1 at a temperature of 150C C.

•

•43

1.00E+05 r-------..,..------~--------------...

1

!R. _. - -_. _. - -1-· _. _. _ ...........~~::..i.:.

- -------~--

-;;

~~ 1.00E+04 t---------+--- ----<.__~___a:=~

';io~>

• <> MVM, A1

X MVM.A5

o MVM.A7

a MVM.A8

- - - - RDA approx1 RDA

1.00E+OO1.00E-011.00E-02

Shear Rate (5-1)

1.00E.Q31.00E+03 .....------........------......---------------'

1.00E-04

Figure 5.6. Viscosity curves for 335A at a temperature of 150°C.

•

•44

1.00E+OS ,...-------~------~--------------- ...

• MVM. B1

Il MVM. B2 '1

C MVM. B4Z MVM, B6 1

- • - • RDA approx 1

1

---RDA :

1.~._.~.~.~.~._.-.-.~

ü!..e:.~ 1.00E+Q4 I---------.........--------.-;.--~-~~-~~--.--::~-_tlito~>

•1.00E+OO1.aOE-011.00E-02

Shear Rate (5-1)

1.00E-031.00E+03 ....-------~----------------------...

1.00E-04

Figure 5.7. Viscosity curves for 3358 at a temperature of I50aC.

•

•45

1.00E+05 ,.....------..."...------~--------------....

1

, Il ~,• __ • _ • _ • -. • .-. -. - -- • _ • _ 0-. • .-.j. ~ .. ~ • _ • _ • ~ _ ~ .. .- • _ • _ •

o MVM. Cl

a MVM. C2

Z MVM. CS

o MVM. C6

• RDA

- - - - RDA approx

-;riiie:.~ 1.00E+Q4 1-- ---4--- , '1fto~~•

1.00E+OO1.00E-Dl1.00e-D2

Shear Rate (5-11

1.00E-D31.00E+03 ....------.....------....---------------'"

1.00E-D4

Figure S.S. Viscosity curves for 335C at a temperature of 150°C.

•

•CHAPTER 5: RESULTS AND DISCUSSION

Table 5: Viscosity of resins 335A~ 335B. and 335C

nMVM.avl! 11 RDA. av!!

335A 1.18XIO" Pa·s 1.17Xl04 Pa·s335B 3.93XIO" Pa·s 3.16Xl04 Pa·s335C 6.35XIO" Pa·s '&:65XI04 Pa·s

46

•

•

Figures 5.7 and 5.8 show data for polymers 335B and tor 335C. and the averages

are tabulated in table 5. For resin 335B, the difference is 19.70/0. For resin 335C. the

difference is 10.9%. For these two polymers't the RDA value for the zero-shear viscosity

was estimated as it was not possible to get a low enough frequencies ta measure the true

zero-shear viscosity. [t is possible that the estimation gives a value of 110 that is tao low,

which would expIain at least partly the discrepancy between the values.

One can say that the comparison between the MV~l and RDA is reasonably good

when one consider the effect of the temperature on the RDA curves and the approximate

value of the RDA zero-shear viscosity.

5.4 Reprodueibility

There are two types of reproducibility: hetween sample and within sample. The

between sample reproducibility is shawn by Fig. 5.4. Since it was shawn that there is no

appreciable variation due to sample preparation, it is assumed that aIl he sarnples are the

same. The average for all samples is 2.62XIO" Pa·s, and the variation coefficient is ±3%.

Fig. 5.9 shows the reproducibility within a sample. A PDMS sample was studied

at 30°C using the peak/peak test. The measurement was repeated ten times with a 3mm

balL The average value was 2.70XI04 Pa·s, and the variation coefficient \vas ±4%. Since

both types of reproducibility are within the value given by the technical specification of

precision of the MVM, which is ±5%, one can say that the MVM gives the specified

precision as long as the sample selection criteria is follow..

•

•

•

CHAPTER 5: RESULTS AND DISCUSSION 47

•48

2.85E+04 -,.-------------------------.

2.75E+04 -I---------~----I---'---.

2.80E+04 -+----------------:------------1

2.S0E+04 -I----Jf-----\---f-----V----~\.-j~~

2.S5E+04 -I---~------------~

.-ent 2.7DE+04 -I-----_a__---II----,---J.--\_.

~

a­oc;;

o:;I2.65E+04 -1------f--1k----f----\--f----+--1-

>

•108642

2.S0E+04 ------~---.......-------------.......

anumber of repetitions

Figure 5.9. PDMS at 30°C. The average is 2.669X 104 Pa·s and thevariation coefficient is 4.0%.

•

•

•

•

49

CHAPTER6

SUMMARY AND RECOMMENDATIONS

A special press was designed and fabricated to produce samples tor the MVM.

The sample preparation takes about 35 min to 50 min, and it can produce samples with no

air bubbles. This sample preparation technique has no effeet on the measurement of the

viscosity. The only factor that causes an appreciable effect is the presence of air bubbles

which causes the rneasured viscosity to be lower than the true value.

A fiberglass caver was made for the MVM arm ta reduce variations in sample

temperature due to conduction in the arm, and variation of air temperature.

The MVM results obtained by varying the gap between the magnets compared

reasonably well with dynamic data, and the sample to sarnple and ron-to-run variation of

in the measurements is near 5%.

The prototype MVM has severa! limitations. The maximum viscosity that can be

measured is 5XI0s Pa·s, and this is insufficient for sorne polymers. For example, sorne

high-density polyethylenes have viscosities above 5X106 Pa·s. The maximum viscosity

depends on the falling lime; the more viscous the fluid~ the longer the tàlling time. The

sinus curve used to calculate the falling lime becomes thick and (ess precise.. until the

signal is mostly noise. It would be interesting to explore the possibility of using stronger

magnets.

The MVM moving parts (the arm and the magnets) should be placed inside a box

to protect them from variations in room air temperature.

It would also be advantageous to merge the twa arrns into one to avoid the use of

different calibrations for each. For example~ the temperature distributions are not the

same in the two arms.

[t would be advantageous to use the 2mm baIl for middle range measurements~ as

this would broaden the available range of shear rate. Sometimes the resin under study is

not in the 10\\1- shear rate Newtonian region when one is using th~ 3n1111 bail. This was the

case for a HDPE. MH07 (for a spacing of 46mm~ T=180°C. 'l=1.926XIOs Pa·s and the

shear rate was 8.663XIO"" S-l). It would have been interesting to see the results with the

2mm, which would have extended the measurements to lower shear rates __

[t will also be interesting ta do sorne experiments with the high pressure cell

described in section 3.2.4 and to compare the results with those l'rom the high pressure

sliding plate rheometer recently developed at McGill.

•

•

•

CHAPTER6: SUMMARY AND RECOMMENDATIONS 50

•

•

•

51

REFERENCES

1 Dealy, J.M., Wissbnm, K.F., ~'Melt Rheology and its Role in Plastic Processing", VanNostrand Reinhold, New York (1990)

2 Wood-Adams, P., Dealy, lM., "'Use of rheological measurements to estimate themolecular weight distribution of linear polyethylene'\ 1. Rheal. 40(5)~ p.761-778 (1996)

3 Park, N.A., Irvine, T.F.Jr., '~The Falling Needle Viscometer: A new technique forviscometry measurements", American Laboratory, Nov. 1988

4 HappeI, l, Brenner, H., ÔI.Low Reynolds number hydrodynamics'~~ Martinus NijhoffPublisher, p.318 (1986)

~ Bohlin, T., 1.·0n the drag on a rigid sphere moving in a viscous liqllid [nside a cylindricaltube'\ Transactions ofthe Royal Institute ofTechnology.. (Stockholm).. 155, (1960)

6 Becker, L.E., McKinley, G.H., Rasmussen, H.K., Hassager.. O.~ "The llnsteady motion ofa sphere in a viscoelastic fluid".. 1. Rhea!., 38 (2), p.377-403 (1994)

7 Arigo, M.T., McKinley, G.H., '"The etfects ofviscoelasticity on the transient motion ofasphere in a shear-thinning fluid".1. Rheo/... 41 (1), p.l 03-128 (1997)

IC Park, N.A., [rvine, T.F.Jr... ~~Measurements of rheological nuid properties with thefalling needle viscometer", Rev. Sci. /nstnlm., 59(9), p.2051-8 (1988)

9 Zheng, R., Phan-Thien, N." Hic, V., ·'Falling Needle Rheometry for G~neral ViscoelasticFluids", J Fluids Eng., 116, p.619-624 (1994)

10 Chu, B., Wang, 1., Tuminello.. W.H., ·'Fast Determination of Polymer Melt Viscosity byOptical Falling Needle Viscometer", 1. Applied Polym. Sei., 49~ p.97-101 (1993)

II Linliu, K., Yeh, F., Shook, J.W., Tuminello, W.H., Chu. B... ··Development of acentrifuge baIl viscometer for polymer melts", Rev. Sci. Inslrum.~ 65( 12).. p.3823-8 (1994)

12 Herman,W., Sobczak, R., "Falling Sphere Viscometry in Gravitational and MagneticFields", Monatsheftefür Chemie, 117/6-7, p.753 (1986)

1] Gahleitner, M., Sobczak, R., "The Magnetoviscometer: From an idea to a RheologicalInstrument", Rhea/ogy 91, p.236..240, Dec. 1991

14 Ringhofer, M., Gahleitner, M., Sobczak, R., ~I.Low frequency/shear rate measurementson polymer melts with a novel rheometer", Rheal Acta 35 (1996)

15 Sobczak, R., "Viscosity measurement by sphere falling in a magnetic field", RheologicaActa, 25:p.l75-179 (1986)

•

•

•

52

REFERENCES

16 Gahleitner, M., Sobczak, R., ~"Viscosity measurements ,vith a magnetoviscometer in thezero-shear and transition region ofpolypropylenes". Rheologie"l Acta. 26~ p.371-374(1987)

17 Sobczak" R., Mattischek" J.-P." ·"High pressure cell tor measuring the zero-shearviscosity ofpolymer meits", Rev. Sei. /nstrum., 68(5)., p.2101-21 05 (1997)

18 Koran" F., Dealy, 1., ··Determination ofviscosity and \vaU slip of molten polymers athigh pressure." To he published.

• APPENDIX A: EXPERIMENTAL DATA

Faxen correction for ditTerent order.

53

•

•

d diD fe 1 te 3 te 5 te 6 fe 8 fe 101 0.143 1.430 1.418 1.418 1.418 1.418 1.4182 0.286 2.508 2.235 2.244 2.248 2.247 2.2473 0.429 10.194 3.809 4.019 4.161 4.086 4.1014 0.571 -4.938 5.342 7.725 12.243 7.957 9.081

d d/D (te1r 1 (fe 3r1 (te Sr1 (te Sr1(te Sr1 (te 10r1

1 0.143 0.699 0.705 0.705 0.705 0.705 0.7052 0.286 0.399 0.447 0.446 0.445 0.445 0.4453 0.429 0.098 0.263 0.249 0.2403 0.245 0.2444 0.571 -0.203 0.187 0.129 0.082 0.126 0.110

• Variation ofroom temperature near the MVM arm: effect of air conditioning.

54

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•

without the box with the boxTime (hrs) Temp.(OC) time (hrs) Temp.(OC)

0:00 22.9 0:00 23.90: Il 23 0:05 23.40:39 23.3 0:07 23.10:58 23.3 0: 12 '"'~ ~_.3 . .3

1: 12 23.3 0:27 23.81: 17 20.4 0:34 23.81:20 21.3 0:38 241:30 23 0:43 23.92:52 23.3 0:46 23.9

0:52 .,~

_.3

0:58 .,~

_.3

1:03 ., "" ""_.3 . .3

1: Il 23.51:24 23.61:30 23.61:37 .,~

_.3

1:41 22.81:50 23.11:55 ,","" ""_.3 . .J

2:03 23.42: 17 23.52:24 22.92:25 22.72:25 22.8

• Parameter Analysis data. before elimination of defective sampies.

55

Run 1 Run 2 Run3 Run4 RuoS Run6 RUB 7 RunS Run92.106e4 2.548e4 2.570e4 2.396e4 2.521e4 2.441e4 2.455e4 2.563e4 2.520e42.64ge4 2.50ge4 2.583e4 2.646e4 2.28ge4 2.570e4 2.524e4 2.591e4 2.494e42.648e4 2.404e4 2.593e4 2.676e4 2.658e4 2.623e4 2.541e4 2.613e4 2.625e42.686e4 2.840e4 2.624e4 2.633e4 2.60ge4

2.617e42.70ge42.64ge4

12.616e4

Viscosity in Pa·s 2.635e4

1 2.561e4

Parameter Analysis data. defective samples eliminated.

•RUDS Viscositv in Pa·s

1 2.64ge42 2.840e43 2.570e44 2.676e45 2.658e4 2.624e46 2.633e47 2.524e48 2.563e4 2.613e49 2.60ge4 2.617e4 2.635e4 2.S61e4

•

•

•

•

Viscosity data from MVM for 0803-1 resin•

Shear stress Shear Rate Viscosity(pa) (s~t) (Pa-s)

P6 3.88E02 S.62E-02 6.90E+03P7 3.88E02 S.40E-02 7.19E+03P9 1.66E02 2.S3E-02 6.60E+03

1.66E02 2.S0E-02 6.67E+031.59EOI 2.0SE-03 7.75E+031.66E02 2.S5E-02 6.54E+03

PlI 1.66E02 2.62E-02 6.37E+031.59EO 1 2.26E-03 7.03E+033.88E02 S.70E-02 6.81E+032.96E02 4.70E-02 6.3IE+03

PI3 1.66E02 2.S9E-02 6.44E+033.88E02 2.3IE-03 6.79E+03I.59EOI 3.86E-02 6.46E+032.49E02 6.50E-02 S.97E+03

Viscosity data from MVM for 335A resin.

Shear stress Shear rate Viscosity(pa) (S·l) (Pa·s)

Al 3.38E+02 3.IIE-02 1.2SE+043.38E+02 3.S8E-02 1.09E+042.96E+02 2.46E-02 1.21E+042.96E+02 2.60E-02 L14E+041.67E+02 1.47E-02 LI4E+04

AS 1.S9E+OI 1.20E-03 1.33E+041.67E+02 1.41E-02 1.19E+042.96E+02 2.36E-02 1.26E+04

A7 1.67E+02 1.42E-02 1.18E+041.67E+02 1.41E-02 LI8E+041.67E+02 1.44E-02 1.16E+04

AS 2.96E+02 2.64E-02 1.12E+041.67E+02 1.48E-02 1.13E+041.59E+Ol 1.18E-03 1.35E+043.88E+02 4.27E-02 9.09E+033.88E+02 3.09E-02 1.26E+04

56

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•

Viscosity data from MVM for 3358 resin.

Shear stress Shear rate Viscosity(pa) (S-l) (Pa·s)

BI 3.88E+02 9.36E-03 4.15E+043.88E+02 1.06E-02 3.66E+042.96E+02 7.54E-03 3.93E+041.67E+02 4.45E-03 3.75E+04

82 3.88E+02 9.85E-03 3.94E+042.49E+02 6.78E-03 3.68E+041.59E+O 1 3.36E-04 4. 74E+04

84 1.67E+02 4.26E-03 3.92E+042.96E+02 7.61E-03 3.89E+043.88E+02 9.02E-03 4.3IE+043.88E+02 l.04E-02 3.72E+04

86 3.88E+02 9.47E-03 4.10E+042.96E+02 8.06E-03 3.68E+041.67E+02 4.59E-03 3.63E+04

Viscosity data from MVM for 335C resin.

Shear stress Shear rate Viscosity(pa) (fl) (Pa·s)

Cl 3.88E+02 5.99E-03 6.48E+042.96E+02 5.07E-03 5.8SE+04

C2 3.88E+02 S.74E-03 6.76E+042.49E+02 3.99E-03 6.24E+041.67E+02 2.75E-03 6.07E+04

CS 3.88E+02 5.69E-03 6.89E+042.69E+02 4.55E-03 6.51E+041.67E+02 2.64E-03 6.32E+04

C6 3.88E+02 5.91E-03 6.S7E+042.96E+02 S.05E-03 5.87E+04

57

• Viscosity data from RDA. Values are the average viscosity of 5 samples.

58

•

•

0883-1 335A 3358 335Cm Freq. Viscosity Viscosity Viscosity Viscosity

(radIs) (S-I) (Pa·s) (Pa·5) (Pa·s) (Pa·s)1.86E-02 5.93E-03 1.15E+04 3.14E+04 S.OOE+042.59E-02 8.24E-03 1.14E+04 2.96E+04 4.76E+043.60E-02 1.I5E-02 5.79E+03 1.12E+04 2.76E+04 4.48E+04S.OOE-02 1.59E-02 5.78E+03 1.IOE+04 2.66E+04 4.19E+046.95E-02 2.2IE-02 5.77E+03 I.08E+04 2.53E+04 3.88E+049.65E-02 3.07E-02 S.75E+03 I.04E+04 2.36E+04 3.S6E+041.34E-O 1 4.27E-02 5.73E+03 I.OOE+04 2.19E+04 3.23E+041.86E-O 1 S.93E-02 5.70E+03 9.6IE+03 2.00E+04 2.91E+042.59E-O 1 8.24E-02 5.66E+03 9.IIE+03 1.83E+04 2.60E+043.60E-OI l.I5E-OI 5.6IE+03 8.58E+03 1.65E+04 2.3IE+045.00E-OI 1.59E-OI 5.58E+03 8.04E+03 1.49E+04 1.04E+046.95E-OI 2.2IE-OI 5.52E+03 7.47E+03 I.J3E+04 1. 79E+049.65E-OI 3.07E-Ol S.45E+03 6.90E+03 1.18E+04 1. 57E+04I.34E+OO 4.27E-Ol 5.36E+03 6.34E+03 l.OSE+04 1.J7E+041.86E+OO 5.93E-Ol 5.26E+03 5.80E+03 9.30E+03 1.19E+042.59E+OO 8.24E-O 1 5.15E+03 5.30E+OJ 8.24E+03 1.03 E+043.60E+OO 1.15E+OO 5.0IE+03 4.83E+03 7.32E+03 9.0IE+035.00E+OO 1.59E+OO 4.85E+03 4.40E+03 6.52E+03 7. 86E+036.95E+OO 2.2IE+OO 4.66E+03 4.01E+OJ 5.82E+03 6. 87E+039.65E+OO 3.07E+OO 4.44E+03 3.65E+03 5.19E+03 6.0IE+031.34E+OI 4.27E+OO 4.20E+03 3.32E+03 4.66E+03 5.29E+03l.86E+OI 5.93E+OO 3.92E+03 3.02E+03 4.13E+03 4.62E+032.59E+OI 8.24E+OO 3.63E+03 2.74E+03 3.67E+03 4.05E+033.60E+OI 1.15E+O 1 3.31E+03 2.47E+03 3.25E+03 3.54E+035.00E+OI I.59E+OI 2.98E+03 2.22E+03 2.86E+03 3.08E+036.95E+OI 2.2IE+OI 2.65E+03 1.98E+03 2.50E+03 2.67E+039.65E+Ol 3.07E+O 1 2.J3E+03 1.75E+03 2.17E+03 2.29E+031.34E+02 4.27E+Ol 2.0IE+03 1.53E+03 1.86E+03 1.96E+OJ1.86E+02 5.93E+OI 1.72E+03 1.33E+03 1.59E+03 1.66E+032.59E+02 8.24E+Ol 1.44E+03 1. 14E+03 1.34E+03 l.39E+033.60E+02 1. 15E+02 1.20E+03 9.60E+02 1.11E+03 l. 15E+035.00E+02 1.59E+02 9.83E+02 8.02E+02 9.15E+02 9.42E+02

•

•

•

PDMS al30oe.

Test condition: peak/peak artn, 3mm ball, 36mm gap and Exact resin. No cover.

falling time shear rate Viscosity(5) (s-1 ) (Pa·s)

1 7.46E+02 1.53E..02 2.54E+042 7.93E+02 1.44E..02 2.70E+043 7.53E+02 1.52E..Q2 2.56E+044 8.12E+02 1.40E..Q2 2.77E+045 7.63E+02 1.50E..02 2.60E+046 8.21E+02 1.39E..02 2.80E+047 7.60E+02 1.50E..02 2.59E+048 8.18E+02 1.39E-02 2.78E+049 7.58E+02 1.51E-02 2.58E+0410 8.18E+02 1.39E-D2 2.78E+04

59