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Melt fracture behaviour of molten polypropylenes Kazatchkov, Igor B. 1994

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MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENESbyIGOR B. KAZATCHKOVDip. Chem. Eng., Moscow Institute of Chemical Technology, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREEOF MASTER OF APPLIED SCIENCEinthe Faculty of Graduate StudiesDepartment of Chemical EngineeringWe accept this thesis as conforming to the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJune 1994° 1994 Igor B. KazatchkovIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives, It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission._____________________Department of (Itk1/v6e’e/AJ6The University of British ColumbiaVancouver, CanadaDate Atq.ct 2, /4DE-6 (2/88)MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENESABSTRACT/ xperiments were carried out in both sliding plate and capillaryI rheometers with two polypropylene resins to determine the conditionsfor the onset of slip, surface and gross melt fracture. It was found thatthere was no distinction between surface and gross melt fracture, which iscommonly observed in the case of polyethylenes. Furthermore, the flow curvesdetermined by using capillaries having various diameters are diameter independent,implying the absence of slip. However, performing experiments with slit dieshaving rough surfaces suggested the presence of wall slip. Further analysis hasshown that the effect of viscous heating masks the detection of slip from thediameter dependency of the flow curves. The effect of presence of a thin layer offluoropolymer (Teflon® PA and Viton®, DuPont) on the critical shear stress for theonset of wall slip and melt fracture as well as on the relationship between the wallslip and the shear stress were also examined. It was found that the presence of suchlayers increases the slip velocity while decreases the critical shear stress for theonset of slip. Surprisingly, this reduction in the wall shear stress had no effect onthe critical shear rate for the onset of melt fracture.MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENESTABLE OF CONTENTSLIST OF TABLES vLIST OF FIGURES viACKNOWLEDGEMENTS ix1. INTRODUCTION I2. LITERATURE REVIEW 42.1 Chemical structure of polypropylene and its applications 42.2 Viscometric flows 52.2.1 Flow in a circular channel 52.2.2 Flow in a rectangular channel 82.2.3 Flow in a sliding plate rheometer 102.3 Wall slip and slip velocity measurements 122.4 Melt fracture 142.5 Melt fracture in polypropylene extrusion 152.6 Pressure effects 172.7 Temperature effects — time-temperature superposition 182.8 Viscous heating 193. OBJECTIVES 214. WALL SLIP AND MELT FRACTURE OF MOLTEN POLYPROPYLENES:CAPILLARY RHEOMETER STUDIES 224.1 Experimental 224.2 Raw data 234.3 Entrance effects 24MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES iv4.4 Flow curves 284.5 WaIl slip 344.6 Viscous heating 404.7 Rabinowitsch correction 464.8 Melt fracture 494.9 Effects of surface coating 515. WALL SLIP AND MELT FRACTURE OF MOLTEN POLYPROPYLENE5:SLIDING PLATE RHEOMETER STUDIES 565.1 Experimental 565.2 Raw data 565.3 Flow curves 615.4 Viscosity measurements 625.5 Effects of surface coating 646. CONCLUSIONS 68Recommendations for future work 68REFERENCES 70NOTATION 73MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES vLIST OF TABLESTable 4-1. Circular dies used. 22Table 4-2. Slit dies used. 22Table 4-3. Properties of a typical PP at 473 K. 41MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES viLIST OF FIGURESFig. 2-1. Types of polypropylene 4Fig. 2-2. Pressure distribution in a reservoir and capillary 7Fig. 2-3. Bagley plot (schematic) 8Fig. 2-4. Simple shear and related equations 10Fig. 2-5. Velocity profiles in a sliding plate rheometer under no-slip (left) and slipconditions (right). 10Fig. 2-6. Schematic diagram ofthe shear stress transducer. 11Fig. 2-7. Flow curves under slip conditions (schematic) 13Fig. 2-8. A typical apparent flow curve for a linear polyethylene and extrudatedistortions. 14Fig. 4-1. Typical responses obtained in a steady-shear experiment in a capillaryrheometer. 24Fig. 4-2. Bagley plot for polypropylene at 200 °C. 25Fig. 4-3. Bagley corrections determined by using various capillaries for polypropyleneat 200 °C. 26Fig. 4-4. Bagley corrections determined by using various capillaries for Profaxpolypropylene at 200 °C. 26Fig. 4-5. Bagley corrections for three different temperatures (200, 230 and 260 °C). 27Fig. 4-6. Apparent flow curves for polypropylene at 200 °C determined by usingcapillary dies having various L/D ratios. 28Fig. 4-7. Apparent flow curves for polypropylene at 230 °C determined by usingcapillary dies having various L/D ratios. 29Fig. 4-8. Apparent flow curves for polypropylene at 260 °C determined by usingcapillary dies having various L/D ratios. 30Fig. 4-9. The pressure-corrected apparent flow curves ofFig. 4-5. 31Fig. 4-10. The pressure-corrected apparent flow curves ofFig. 4-6. 32Fig. 4-11. The pressure-corrected apparent flow curves ofFig. 4-7. 32MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES viiFig. 4-12. Apparent flow curves for PP Profax at 200 °C determined by using capillarydies having various L/D ratios. 33Fig. 4-13. The pressure-corrected apparent flow curves ofFig. 4-11. 34Fig. 4-14. Apparent flow curves for polypropylene at 200 °C with a constant LID andvarious diameters to detect the presence of slip. 35Fig. 4-15. Apparent flow curves for polypropylene at 230 °C with a constant LID andvarious diameters to detect the presence of slip. 36Fig. 4-16. Apparent flow curves for polypropylene at 260 °C with a constant L/D andvarious diameters to detect the presence of slip. 36Fig. 4-17. A typical schematic of the slit dies used. 37Fig. 4-18. Change of slope of the flow curves. 38Fig. 4-19. The effect of the wall roughness on the flow curve in slit extrusion. 38Fig. 4-20. Flow curves at various temperatures using the time-temperaturesuperposition principle. Note that the superposition is very poor at wallshear stresses in the melt fracture region. 40Fig. 4-2 1. Case study: calculated average temperature rise for polypropylene at 200 °Cin slit extrusion for slits having various heights and a constant length-to-height ratio. 42Fig. 4-22. Case study: flow curves with viscous heating under no-slip conditions. 43Fig. 4-23. Case study: slip velocity function (Eq. 4-4). 44Fig. 4-24. Case study: flow curves with slip and without viscous heating. 45Fig. 4-25. Case study: flow curves with viscous heating and slip. 46Fig. 4-26. The viscosity of polypropylene at various temperatures using the time-temperature superposition principle. 47Fig. 4-27. The viscosity ofProfax polypropylene at 200 °C. 48Fig. 4-28. Various samples produced by extrusion ofPP from a circular die having D0.762mm andL/D20 at 200 °C. 49Fig. 4-29. Critical shear stresses for the onset of melt fracture as a function ofL/D andtemperature. 50MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES viiiFig. 4-30. Samples ofPP produced at a fixed shear rate in circular dies with differentL’Dat200°C. 51Fig. 4-31. Apparent flow curves for polypropylene at 200 °C determined by using a slitdie with H = 0.254 mm. 52Fig. 4-32. Apparent flow curves for polypropylene at 200 °C determined by using a slitdie withH 0.508 mm. 53Fig. 4-33. The effect of a Teflon® coating on the shear stress in the continuousextrusion of polypropylene. 54Fig. 5-1. Typical responses obtained in a steady-shear experiment in a sliding-platerheometer (small shear rates). 57Fig. 5-2. Typical responses obtained in a steady-shear experiment in a sliding-platerheometer (medium shear rates). 57Fig. 5-3. Typical responses obtained in a steady-shear experiment in a sliding-platerheometer (large shear rates). 58Fig. 5-4. Typical responses obtained in a steady-shear experiment in a sliding-platerheometer (large shear rates, smaller gap). 58Fig. 5-5. Check for the displacement transducer linearity (smaller gap). 59Fig. 5-6. Check for the displacement transducer linearity (larger gap). 60Fig. 5-7. Flow curves obtained in the sliding plate rheometer for polypropylene withdifferent gap spacings. 61Fig. 5-8. Flow curves obtained in the sliding plate rheometer for PP Profax withdifferent gap spacings. 62Fig. 5-9. The viscosity of polypropylene. 63Fig. 5-10. Comparison of capillary and sliding plate data for PP Profax. 64Fig. 5-11. Flow curves obtained in the sliding plate rheometer with clean and Teflon®coated plates. 65Fig. 5-12. Responses obtained in a steady-shear experiment with Teflon®coatedplates. 66Fig. 5-13. Flow curves obtained in the sliding plate rheometer with clean and Viton®coated plates. 67MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES ixACKNOWLEDGEMENTSJ[ wish to express my sincere gratitude and appreciation to my supervisor Dr. SavvasG. Hatzikiriakos for his skillful guidance, support and encouragement during thecourse of this work.This work was supported by the Natural Sciences and Engineering Research Councilof Canada. An additional financial support and the materials were provided by E. I.DuPont de Nemours & Co., Wilmington, DE, USA.MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 11. INTRODUCTIONhe increasing role of synthetic polymers as materials of construction hasprompted the study of their processing properties. It is known that the rate ofproduction in such processes as extrusion, film blowing and moulding is limitedby the onset of flow instabilities, which results in the deterioration of the surfaceappearance and lead to commercially unacceptable products. Most of the previous studieson melt fracture (surface and gross distortions) of polymers have essentially examined thebehaviour of various types of polyethylenes (high density polyethylene, low densitypolyethylene and linear low density polyethylene), but very little is known about thisphenomenon in the processing of polypropylene resins.In the extrusion of polymer melts, below certain shear rates the emerging extrudateshave smooth surface. As the rate increases, small amplitude periodic distortions appear onthe surface (sharkskin melt fracture). As the rate increases further, the extrudate becomesseverely distorted (gross melt fracture). In capillary flow of certain polymers (e.g. highdensity polyethylene [Hatzikiriakos and Dealy (1992b)], linear low density polyethylene[Ramamurthy (1986)] and fluorinated polyethylene/polypropylene [Rosenbaum et al.(1994)]) under constant piston speed, the pressure drop has been found to be a double-valued function of apparent shear rate over a limited range of apparent shear rates. As theextrusion rate is increased, a point is reached at which the pressure jumps between lowerand higher critical values, while the extrudate appearance changes from smooth toalternating distorted and smooth portions due to these pressure oscillations. Thus, ahysteresis loop is obtained over a certain range of apparent shear rates. This finding isusually interpreted in terms of “slip”, i.e., it is implied that the velocity of the fluid at theboundary is not zero as normally assumed.For Newtonian fluids the assumption of zero velocity at the fluid-wall interface leadsto a very good agreement with experimental observations. However, in the case of manyCHAPTER 1 - INTRODUCTIONMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 2polymer melts this assumption ceases to be valid. For example, in the flow of linearpolymers through cylindrical dies, the flow curve (shear stress versus apparent shear rate)has been found to depend on the diameter of the die once the wall shear stress rises above acritical value. This is consistent with the assumption of slip and, if it is assumed that slipoccurs at the interface, the data can be superposed. Mooney (1931) derived explicitrelations for the slip velocity that can be used to calculate the slip velocity as a function ofwall shear stress.Melt fracture has been the subject of many investigations over the past decades.Numerous experimental, theoretical and computational studies have been reported, aimedat determining the origin and nature of flow instabilities in polymer melts and solutions.Some workers attributed the onset of melt fracture to pressure fluctuations resulting fromthe flow irregularities in the entrance region of the capillary due to the contraction flow[Weill (1980), Bergem (1976)], while others related it to slip at the wall [Kraynik andSchowalter (1981), Kalika and Denn (1987)]. Many terms have been used in the literatureto describe this phenomenon: “melt fracture”, “sharkskin”, “waviness”, “ripple”, “bambooeffect”, “sausage link”, etc. For polyethylene, the distinction is usually made betweensurface melt fracture (or “sharkskin”), when the distortions are relatively small and affectonly a thin layer on the surface, and gross melt fracture, with the extrudate appearanceranging from helical screw thread to severe irregular distortions. If the shear rate isincreased further, some materials (e.g. linear polyethylene, tetrafluoroethylenehexafluoropropylene copolymer) exhibit a second stable flow regime in which the extrudateis again smooth [Tordella (1969)]. Polymers such as branched polyethylene, polypropyleneand polystyrene do not appear to have a second stable regime.Polypropylene is a material of great industrial importance, as it has found manyapplications, e.g. in fibre production, injection moulding, and film extrusion industry. Theprocessing implications of this polymer have not been investigated to the same extent asthose of polyethylenes. In this work, the melt fracture behaviour of two moltenCHAPTER 1 - INTRODUCTIONMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 3polypropylenes is studied. Wall slip, which is believed to be related to the melt fracture,was also examined. Finally, Teflon® PA and Viton® were used to study the effect ofinterfacial conditions on wall slip and melt fracture of these resins.CHAPTER 1 - INTRODUCTIONMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 42. LITERATURE REVIEWressure driven flow through tubes, slits and other types of channels is of centralimportance in experimental rheology and in polymer processing. This flow isused as the basis for the most popular type of melt rheometer, and it is a flowthat occurs often in melt processing, for example in an extrusion die or in the runnerfeeding of an injection mould. In this chapter the basic equations for flow in tubes and slitsare presented, and it is shown how these can be used to interpret rheometer data. Inaddition, the melt fracture and wall slip phenomena are described and some previousknowledge on these phenomena for polypropylenes are reviewed.2.1 Chemical structure of polypropylene and its applicationsPolypropylene (PP) has the following structure:The monomer for PP is propylene. This material is predominately produced by low-pressure processes based on Ziegler-Natta catalysts. The vast majority (over 90 percent) ofthe polymer is in the isotactic form (Fig. 2-1). Isotactic polypropylene crystallizes in ahelical form whereby there are three monomer units per turn of the helix./ c ci- ci- c/ Polypropylene has a wide range of-_ .... -so ac IC applications, ranging from fiber and filamentsto films and extrusion coatings. PP fibers areSyndiatactic manufactured by an oriented extrusionprocess. Two important advantages ofAtactic polypropylene are its inertness to water andmicroorganisms and it is a low cost polymerFig. 2-i. Types of polypropyleneCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 5(around $0.66 per kg). Typical applications include carpet backing, upholstery fabrics,carpet yarn, and interior trim for automobiles.2.2 Viscometric flowsSimple shear flow is generated by the rectilinear motion of one flat plate relative toanother, where the two plates are parallel and the gap between them is constant with time.Steady simple shear is a simple shear flow that has been carried out at a constant shear ratefor a sufficient length of time that the stresses in the material are functions only of theshear rate.Steady simple shear is a uniform deformation, i.e., each fluid element undergoesexactly the same deformation, and the stresses are independent of position in space. Thereare also nonuniform flows for which the three material functions, viscosity and normalstress differences, govern the behaviour of the fluid. Such deformations are called“viscometric flows.” While different fluid elements in the field of flow may be subject todifferent shear rates, the shear rate experienced by any particular fluid element is constantwith time. Three types of viscometric flows that were used in this work, viz., steady tubeflow, steady slit flow, and steady simple shear flow, are discussed below.2.2.1 Flow in a circular channelCapillary flow is an example of a partially controllable flow. Far from the entrancewhere the flow is fully developed, the streamlines are parallel to the channel axis, but thevelocity profile depends on the rheological nature of the fluid. Unless a specificconstitutive equation is known to be valid for the fluid, as in the case of a Newtonian fluidor a power-law fluid, special computational techniques are required to calculate shearstress, shear rate and viscosity.For the steady flow of an incompressible fluid in a tube of radius R, the absolute valueof the shear stress at the wall a, is:CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 6-AP•R?TIrR= 2L(2-1)where Al’ is the pressure drop over a length of tube, L.For a Newtonian fluid, the velocity distribution is parabolic and the shear rate at thewall is given by:-= (2-2)dTr=R 7rRFor non-Newtonian fluids, if a specific constitutive equation is assumed, one canderive equations analogous to those valid for Newtonian fluids. For example, if the powerlaw given by=Ky (2-3)it can be shown that the wall shear rate is given by:= 3n +1 4Q3 1 (2-4)4n TRJThe quantity in brackets, which is equal to the wall shear rate in the case of a Newtonianfluid, no longer has this significance when the fluid is non-Newtonian. It is, however,referred to as the “apparent shear rate”,‘ A•Using Eq. 2-2, 2-3, and 2-4, it can be shown that= K(3n±l j” j = K [3n±l j (2-5)Therefore, a plot of log(o-) versus log(’) will be a straight line for a power-law fluid,and the constants K and n can be determined from the slope and the intercept. However,even if there is no constitutive equation relating the shear stress to the shear rate, a specialtechnique can be used to determine the true wall shear rate and the viscosity for any nonNewtonian fluid. This technique requires pressure drop data for a number of flow rates. ItCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 7can be shown that these data should fall on a single curve when a plot of log(cr) versuslog(’y) is made. The shear rate at the wall is given by3+b 4Q 3+b.7W= 4 irR3 =(2-6)where b is the Rabinowitsch correction given by(2-7)d1ogoThis correction term is a measure of the deviation of a polymeric fluid from Newtonianbehaviour. It equals unity for a Newtonian fluid and 1/n for a power-law fluid.In a capillary rheometer there is a largepressure drop associated with the flow in theentrance region, and this must be taken intoaccount if the reservoir pressure is thequantity measured to determine the wallshear stress. Moreover, it has been proposedthat the excess pressure drop at the entranceto a capillary is itself a useful quantity thatcan be used to characterize polymers. ThereFig. 2-2. Pressure distribution in a reservoir and capillaryalso appears to be a small residual pressureat the exit of the capillary. Wall pressuresmeasured at various axial locations in a reservoir and capillary have been reported by Han(1976) for molten polymers. A typical result is shown in Fig. 2-2. The total pressure dropfor flow from a reservoir, through a capillary and out to the ambient pressure can bethought to consist of three components:= APentrance + ZkPcap + LPg = APend + APcap (2-8)Distance from entranceCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 8The end cOrrect Ofl, tPend, can be determined by Pdusing a technique outlined by Bagley (1931). Hemeasured the driving pressure, d, for variousvalues of the flow rate using a variety ofcapillaries having different lengths. For each = constvalue of YA the driving pressure is plottedFendversus LID and a straight line is drawn throughL/Dthe points. Extrapolating the lines correspondingFig. 2-3. Bagley plot (schematic)to various values of to LID =0, an endcorrection is obtained, which is often called“Bagley correction” (Fig. 2-3). Thus, the true wall shear stress which is obtained overmost of the length of the capillary (except in the entrance) can be calculated as follows:0w (Pd— Pend) / (4LID) (2-9)In general, one should expect some curvature of the Bagley plot, which may indicatedependence of viscosity on pressure, slip at the wall [Hatzikiriakos and Dealy (1992a)] orviscous heating.2.2.2 Flow in a rectangular channelWhen a fluid flows through a rectangular channel in which the width, W, is muchlarger than the thickness, H, the edges make a negligible contribution to the pressure dropand this geometry can effectively be used for rheological measurements. The basicequations and entrance correction procedures are similar to those for capillary flow, but thedifference in geometry has certain experimental advantages: flush-mounted wall pressuretransducers can obviate the need for end corrections; two dimensional flow field facilitatesthe observation of flow.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 9For the steady flow of an incompressible fluid in such a channel, the absolute value ofthe shear stress at the wall, cr4,, is given by:= —tiP H / 2L (2-10)where tiP is the pressure drop over a length of channel, L.The apparent shear rate in a slit, which is the true wall shear rate for a Newtonianfluid is given by:‘YA (2-11)For non-Newtonian fluids the wall shear rate is given by:• 2+b[6Q 1 (2-12)W IH2WJwhere b is the Rabinowitsch correction given byd log’yb = A (2-13)d1ogcrAs in the case of circular channels, a plot of log(u) versus log(’f) reveals the behaviourof the fluid. If all the data fall on a straight line with a slope of one, then Newtonianbehaviour is obtained. If they fall on a straight line but the slope is not equal to one, thenpower-law behaviour is exhibited, with n = 1/b. Curvature indicates general non-Newtonian behaviour.For a power-law fluid the wall shear stress is as follows:(2n +11’=Kt I 7A (2-14)I. 3n jThe procedure for determination of the end effects is analogous to the one used for circularchannels.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 102.2.3 Flow in a sliding plate rheometerThe laboratory procedure thatmost closely approximates simple_______shear is to place a thin layer of fluidF between two flat plates, clamp one ofthe plates in place, and translate thesecond plate at a constant velocity, asshown in Fig. 2-4. Under no-slipconditions the actual shear rate, ‘i’, isequal to the nominal shear rate, ‘Fig. 2-5. Velocity profiles in a sliding plate rheometer under no-slip (left) and slip conditions (right).The advantages of the sliding plate geometry over the other two geometries discussedabove are that there are no effects of pressure on measurements, and that the edge effectscan be eliminated by measuring the shear stress locally (using flush-mounted shear stresstransducer). If a sliding plate rheometer is used to study viscous Newtonian liquid, thefluid itself serves to maintain the plate spacing. However, if the first normal stressDisplacement:Strain:Nominal shear rate:Stress:21Xy=zlX/h= u/hc= F/A The wall shear stress can bedetermined by measuring the forceFig. 2-4. Simple shear and related equationsrequired to drive the motion of themoving plate and dividing it by the wetted area of the plates. When slip is present, the trueshear rate is less than the nominal shear rate, as illustrated in Fig. 2-5.U UUsCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENEs 11difference N1 — 22 is positive, which seems to be the case for molten polymers, thenthe shearing deformation will result in a force tending to separate the plates, and some waymust be found to maintain the gap without introducing a significant frictional force.For this work a sliding plate rheometer with a flush-mounted shear stress transducerwas used [Giacomin et al. (1989)]. The basic features of the transducer are shown in Fig.2-6. An end plate is acted on by the shearr To amplifier stress generated by the fluid and transmits theMovingplate Probe Beam resulting moment to the cantilever beam. Toavoid the melt penetration into the gapSample around the end plate, the deflection of thelatter must be limited to very small levels.NEIidpIe That is why a capacitance system was used,Fixed platewhere a capacitor is formed by the probeFig. 2-6. Schematic diagram of the shear stress acting as one of the plates, and the beam astransducer.the second plate.There are many advantages associated with the direct measurement of the shear stress:• Uncontrolled flow at the edges of the sample does not affect the determination ofthe shear stress, ailowing tests with large and rapid deformation to be carried out;• Degradation occurring as a result of contact between the exposed edges of thesample and the environment does not affect the measurement;• The exact size and shape of the sample need not to be known, and this greatlysimplifies sample loading;• Tests can be carried out with only a few grams of sample;• Bearing friction has no effect on the measured shear stress, as long as it does notintroduce mechanical noise.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 122.3 WaIl slip and slip velocity measurementsFor wall shear stresses greater than a critical value, o, it has been observed that themelt loses its adhesion at the wall (or cohesion near the wall) and that the no-slip boundarycondition is no longer valid.The question of slip was first addressed by Mooney and Black (1952), who usedcapillaries of different radii to determine the flow curve of raw rubbers. They found thatthe flow curves depended on the radius of the capillary, once the stress exceeded a criticalvalue. Mooney (1931) derived an explicit relation for determining the slip velocity as afunction of wall shear stress by assuming that the wall shear stress, slip velocity andpressure gradient are all constant along the entire length of the capillary. This expressionfor the case of circular channels is as follows:‘YA YA,s +8- (2-15)where‘ A is the apparent shear rate, ‘‘ is the apparent shear rate corrected for slip, u isthe slip velocity, and D is the diameter of the capillary. For a constant wall shear stress,and thus a constant‘A’ a plot of ‘‘A versus lID should result in a straight line with aslope equal to 8u, if the slip velocity is solely a function of the wall shear stress. To applythis technique one requires o versus- A data from at least three capillaries of variousdiameters.If it is known that a material follows power-law behaviour, then the slip velocity canbe calculated from a single apparent flow curve. For a power-law fluid A can be replacedby /A.s in Eq. 2-5, and by solving for the slip velocity the following equation can beobtained:8-=)’A — 4n (2-16)D 3n+1IKJCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 13Thus, if the power-law constants have been determined in experiments in which slip didnot occur (e.g. at low shear rates), they can be used to calculate the slip velocity from ameasured value of o for any given value of‘‘ A•Making the same assumptions as for the capillaries and neglecting the edge effects,Eq. 2-15 can be written for a slit as follows:7A A,s +6 (2-17)Thus, if the slip velocity is solely a function of wall shear stress, a plot of‘A versus 1/Hfor constant o4, will give a straight line with a slope equal to 6u8.For a sliding plate rheometer under slip conditions it can be easily shown that‘y, =y+25 (2-18)with the assumption of equal slip velocities on both plates. Figure 2-7 illustrates the use ofthe Mooney technique for the case of sliding plate rheometer. At low shear rates the flowcurves (wall shear stress versus nominal shear rate) for different gap spacings, h1 to h3,_________________________superpose, which indicates that there is no slip.(1w However, for higher shear rates the flow curves starth1to diverge above a certain value of the wall shearh3stress. From Equation 2-18 it follows that the slip> >has a greater effect on the flow curve obtained withthe smallest gap spacing. The slip velocity as afunction of the shear stress can be calculated bytaking two points for different h at a constant shearFig. 2-7. Flow curves under slip conditions(schematic) stress and solving Equation 2-18 for u.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 142.4 Melt fractureA principal problem in the extrusion of polyolefms is the phenomenon of extrudatedistortion commonly known as melt fracture. This usually appears when the wall shearstress exceeds a critical value [Ramamurthy (1986)]. The flow instabilities are reflected inthe apparent flow curve (a plot of o, versus’s’ A) A typical apparent flow curve for a linearpolymer such as a high density polyethylene (HDPE) or a linear low density polyethylene(LLDPE) is shown in figure 2-8, where six distinct flow regions can be identified. Atextremely low shear rates (below 1 1) the wall shear stress is proportional to the shearrate, and the fluid behaves as a Newtonian fluid. In this region the viscosity of the fluid isconstant, and the apparent shear rate,‘‘ A’ is equal to the true wall shear rate, ‘‘ . Thesecond region is the transition from Newtonian behaviour to power-law behaviour. In thepower-law region (#3) the viscosity decreases with shear rate, and the o, — relationshipis given by Eq. 2-3. All these flow regions are stable, the extrudates are smooth (sampleA), and the no-slip boundary condition is consistent with experimental observations.However, when the wall shear stress is greater than a critical value o, the extrudateExtrudate appearance FlowregionA-smooth__________1-3B-sharksldn iIF] 4C - oscillating 5D-withkinks U I] 6E-waiy 6Apparent shear rateFig. 2-8. A typical apparent flow curve for a linear polyethylene and extrudate distortions.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 15loses its glossiness, which is accompanied by a noticeable change in the slope of theapparent flow curve. This region (#4) is known as the sharkskin flow region due to the factthat small amplitude periodic distortions appear on the surface of the extrudate (sample B).In addition, the apparent flow curve is diameter-dependent — an observation that isconsistent with the assumption of a slip boundary condition.At shear rates greater than a second critical value and within a certain range ofapparent shear rates, the flow ceases to be stable (region #5). The pressure drop oscillatesbetween two extreme values, and this fact causes a discontinuity in the apparent flowcurve. The periodic variations of the pressure and apparent shear rate define a hysteresisloop that connects the two branches of the apparent flow curve. The extrudate appearance(sample C) follows the oscillations, with the smooth portion associated with the descendingpart of the flow curve and the fractured portion associated with the ascending one. If therate is increased further, the gross fracture flow regime (#6) starts where the extrudate isinitially smooth with some kinks (sample D), then it becomes grossly distorted (sample E).In this flow regime the extrudate appearance depends on the type of polymer used and thedesign details of the die.2.5 Melt fracture in polypropylene extrusionWhile different flow regimes and types of distortion obtained in polyethylene extrusionhave been studied extensively and are essentially well documented, very little informationcan be found for polypropylene (PP) on these phenomena. In this section some of theprevious work related to the melt fracture of PP is reviewed.Bartos (1964) studied the melt fracture behaviour of a series of polypropylenes toexamine the critical conditions for the onset of extrudate distortions. He found that meltfracture occurs at a critical value of a “melt fracture” number, NMF = 8.5 MPa, which isCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 16defined as N o’ /j, where i7 is the zero-shear viscosity, ‘‘ is the critical shear ratefor the onset of melt fracture, and I is the polydispersity. Kamide et al. (1966) found acritical value of 10.9 MPa while Barnett (1967) a critical value of 10.4 MPa for otherseries of polypropylenes. It would be desirable to have this information in terms of acritical shear stress, which unfortunately is lacking in these papers.Middleman (1977) has noted that linear polypropylene did not show the flowdiscontinuity when exhibiting melt fracture, and the severity of the melt fracture of linearpolymers increased as the die was lengthened. He argued that the criteria for determiningthe onset of melt fracture was the recoverable shear defined as SR (11-2) / 2z-12, wherer and 2 are the normal stresses, and v is the shear stress. The critical value of 5R wasfound to be about 2.6.Ui et a!. (1964) have also studied the melt fracture behaviour of a number of differentpolymers at various temperatures, including polypropylene. The flow curves obtained weresmooth without any discontinuity. Discontinuities are commonly observed in the flowcurves of high density and linear low density polyethylenes [Ramamurthy (1986), Kalikaand Denn (1987), Hatzikiriakos and Dealy (1992a)]. The type of melt fracture obtainedwas fairly regular with a sharp transition from a smooth to a gross fracture appearance.Thus, small amplitude periodic distortions which are obtained in the extrusion of linear lowdensity polyethylenes were not obtained. Finally, they found that melt fracture occurs at acritical value of the wall shear stress in the range of 0.1-0.13 MPa, independently oftemperature (in the range of 180-260° C).Athey et a!. (1986) and Rudin et a!. (1985) studied the melt fracture of a moltenpolypropylene and used a small amount of fluoropolymer additive to the resin to suppressthis phenomenon. They found that this additive provided some benefits in the extrusionprocess, such as reduction in power and die pressure. Other references addressing the meltfracture of PP include Akay (1983) and Fujiyama and Kawasaki (1991). They havereported critical shear stresses for the onset of melt fracture ranging from 0.13 to 0.2 MPa.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 17All the existing studies of polypropylene resins can be summarized as follows:• There is no sharkskin region. As the shear rate increases, the extrudate appearancesuddenly changes from smooth to gross melt fracture;• Melt fracture occurs at a critical value of the wall shear stress of about 0.15 MPa;• No previous work has examined wall slip.2.6 Pressure effectsLarge pressure gradients are typical in the processing of molten polymers. Thecompressibility of these materials in a molten state is quite high, and the effect of pressureon the viscosity cannot be neglected. It is known from experiments [Rauwendaal andFernandez (1985), Kalika and Denn (1987)1 that the apparent flow curves do not superposefor capillaries of different LID ratios. Instead, the apparent flow curves shift to highervalues of the wall shear stress with increase of the LID ratio and therefore, pressure. Thepressure dependence of viscosity is typically represented by an exponential function (firstorder approximation) which for a given temperature can be written as= i°exp(aP) (2-19)where if is the viscosity at ambient pressure, a is the pressure coefficient of viscosity andP is the absolute pressure.It has been proven that pressure has also an effect on the slip velocity. Hatzikiriakosand Dealy (1992a) studied the slip behaviour of several high density polyethylene blends atvarious pressures and temperatures. They have found that the slip velocity decreases withincrease in pressure and this effect saturates at very high pressures. Therefore, as thepressure drops along the capillary, the slip velocity increases and the fluid accelerates nearthe exit of the capillary. This gives rise to a high extensional rate which may be theprimary cause of the surface melt fracture (sharkskin) [}{atzikiriakos (1994)].CHAPTER 2- LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 18Another effect of pressure is that the viscosity increases with pressure, which results inthe formation of a “prestress zone” at the die entrance [Mounihan (1990)1. Therefore, itcan be argued that the melt fracture occurs in the entrance region where a material passesthrough a maximum in the wall shear stress.2.7 Temperature effects — time-temperature superpositionRheological properties are usually highly temperature dependent. This means that toobtain a complete picture of the behaviour, experiments must be carried out at severaltemperatures. It is often found that data taken at several temperatures can be broughttogether on a single master curve by means of “time-temperature superposition.” Thisgreatly simplifies the description of the effect of temperature. Furthermore, it makespossible the display on a single curve of material behaviour covering a much broader rangeof time or frequency than can ever be measured at a single temperature. Materials whosebehaviour can be displayed in this way are said to be “thermorheologically simple” [Dealyand Wissbrun (1990)1.It was found that data for different temperatures can often be superposed byintroducing a shift factor, a’., determined empirically. Thus, if one makes a plot of arheological property versus time, a is obtained from the horizontal shift necessary to bringthe data for any temperature T onto the same curve as data for temperature T0. Forexample, flow curves (shear stress vs. shear rate) will be plotted as shear stress versus‘a. Note that no shift factor is required for quantities not containing units of time. Thisimplies that a plot of one such quantity versus another will be temperature independent.The shift factor is a function of temperature, and the WLF equation has been founduseful [Tanner (1985)]:-c10(T-T)1og(a)€2 +(T — T)(2-20)CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 1 9where C1° and C2° are constants determined at T0 for each material.2.8 Viscous heatingIn high speed processing operations, such as extrusion, viscous heating is inevitablebecause of the high viscosity of the polymeric liquids and because of the large velocitygradients. Moreover, because of the low thermal conductivity of polymers, temperatureincreases due to the viscous heating can be considerable and very non-uniform. A reliableestimation of viscous heating effects and local temperatures is of particular interest inpolymer flow problems because of their strong influence on the properties of polymers,such as viscosity and rate of chemical degradation.Cox and Macosco (1974) observed large temperature rises in capillary extrusion ofacrylonitrile butadiene styrene (ABS) which can be as high as 70 K for apparent shear ratesof the order of s. Shidara and Denn (1993) have discussed the effect of viscousheating for a molten polystyrene in slit extrusion. To explain their result they assessed thiseffect to be significant. They also pointed out that a numerical solution of the full field incapillary/slit flow incorporating pressure and temperature effects is needed. One normallyexpects that the effect of viscous heating is less significant for high density polyethylene,and increases in significance for linear low density polyethylene, polypropylene andpolystyrene respectively. This can be determined by examining the values of thetemperature-dependency coefficient of viscosity FIJi et a?. (1964), Van Krevelen (1990)].A review of approximate analytical solutions to the flow of power-law fluids incircular channels with viscous heating is given by Bird et al. (1987). These are seriessolutions that exist for certain values of the power-law constant (Eq. 2-3) and constantvalues of thermophysical properties. To make the calculations in order to assess viscousheating effects, it is necessary to make an assumption for boundary conditions at the wallof the capillary, and two limiting cases are usually considered. In the isothermal case, theCHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 20wall is assumed to be at a uniform temperature, and in the adiabatic case, it is assumed thatthere is no heat transfer at the wall. In the first case, the temperature profile asymptoticallyreaches a fully developed profile, while in the second case a continuous, infinitetemperature rise is predicted. The real conditions in the extrusion of polymer melts aresomewhere between these limiting cases. It is also important to note that, according tothese solutions, the temperature rise is higher for longer capillaries having a largerdiameter. Thus, length and diameter of capillaries or length and height of slits areimportant parameters which should be taken into account.CHAPTER 2 - LITERATURE REVIEWMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPyLENES 213. OBJECTIVEShe primary objective of this work is to study the origins of extrudate distortionin the extrusion of polypropylene resins. Due to the fact that extrudatedistortion of polyethylenes (high density and linear low density polyethylene) isaccompanied by wall slip, a comprehensive study of slip is also needed. Moreover, it is notknown whether these two phenomena, melt fracture and wall slip, are linked together forpolypropylenes.It is known that a thin layer of fluoropolymers, acting as a slip promoter, suppressesthe surface melt fracture of polyethylenes and allows to decrease the wall shear stress andconsequently the driving pressure required to extrude the material. Therefore, it isnecessary to check if the slip promoters have a similar effect on the processing behaviourof polypropylenes.The objectives can be summarized as follows:1. To determine the critical wall shear stresses for the onset of wall slip andmelt fracture as functions of:• Temperature• Pressure• Interface conditions2. To study the effect of interface conditions on slip velocity and extrudatedistortion by application of processing aids (mainly fluoropolymers) to thesolid walls.CHAPTER 3 - OBJECTIVESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROpYLENES 224. WALL SLIP AND MELT FRACTURE OF MOLTEN POLYPROPYLENES:CAPILLARY RHEOMETER STUDIESJr n this chapter the behaviour of two polypropylene resins is examined in capillaryextrusion to determine the critical conditions for the occurrence of wall slip and meltfracture. To determine the flow curves from capillary data, the entrance effects arefirst assessed by using orifice dies and consequently the Rabinowitsch correction is used todetermine the viscosity. To determine the wall slip, viscous heating should be taken intoaccount and a critical discussion for its effects is presented. Finally, effects of processingaids on melt fracture and wall slip of polypropylene are examined.4.1 ExperimentalThe experiments were carried out on Instron Model 1123 constant-speed piston-drivencapillary rheometer. Circular dies of various diameters, D, and length to diameter ratios(LID) were used to examine possible effects of pressure on viscosity and slip velocity. Todetermine the Bagley correction with accuracy, capillary dies having a length-to-diameterratio of zero were also used for each series of dies. All the circular dies had a 900 entranceangle. The dimensions of all capillary dies used in this work are listed in Table 4-1.Slit dies (having a rectangular cross-section) were also used in order to examine theeffect of surface coating on extrudate distortion and wall slip. These slit dies wereconstructed of two pieces so that the inside surface could be exposed, and the wall coatingDiameter, mm LID0.508 (0.02”) 0, 40, 1000.762 (0.03”) 0, 10, 20, 40, 70, 1001.27 (0.05”) 0, 40, 70Table 4-1. Circular dies used. Table 4-2. Slit dies used.Height, mm LIH WIH0.254 100 10.10.508 60 9.8CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 23could be applied on the surface. The dimensions of all slits used are listed in Table 4-2(height, H; width, W; and length, L). More details on the method of applying the coatingonto the slits and their schematic diagram are given below.As previously discussed, the resins used in this work were two polypropylenes (PPs).The experiments for the first PP were carried out at three temperatures: 200, 230 and260 °C, while those for the other resin (PP Profax) were done at 200 °C only. Theaverage molecular weights, M, of the resins were 510,000 and 550,000 kg/kmol. Thesewere determined from zero-shear viscosity (j0) data, making use of a correlation betweenM and i for other linear polypropylenes [Hingmann and Marczinke (1994)].Teflon PA in the form of solution, provided by DuPont, was used to coat the surfaceof slits. Some additional experiments using Viton® as a processing aid were also carried outto determine its effects on wall slip and extrudate distortion of polypropylene. Viton® isavailable in the form of pellets and a 2% acetone solution was prepared. A certain amountof the solution was applied on the surface and enough time was allowed for the solvent toevaporate, which resulted in a uniform coating on the surface.4.2 Raw dataFigure 4-1 shows some typical responses obtained in the capillary rheometer. It can beseen that the time required to reach a steady state depends on the shear rate and geometriccharacteristics of the capillary. The curve levels off slower for longer capillaries and lowershear rates. At small rates the materials behave as viscous fluids (no overshoot), however,as the shear rate increases the response becomes more elastic and thus overshoots appear inthe shear stress response. This behaviour is due to the viscoelastic nature of the material.CHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 24L/D= 100, ‘=13.9sUD=20,=104s110z________LID20,13.9s1>.c0Polypropylene, 200 °CI Capillary rheometerD = 0.762 mm0 10 20 30 40Time, mmFig. 4-1. Typical responses obtained in a steady-shear experiment in a capillary rheometer.4.3 Entrance effectsTo determine the pressure drop associated with changes in the velocity disthbutionnear the entrance and exit of the capillary, a technique outlined by Bagley (1957) wasemployed. Figure 4-2 plots the driving pressure, d, as a function of the LID ratio forseveral values of the apparent shear rate, ‘‘A = 4Q / 2rR3, where Q is the volumetric flowrate and R is the capillary radius. The Bagley correction, send, can be found byextrapolating the data to zero LID. It can be seen from Fig. 4-2 that the data do not fall onstraight lines even for the smaller values of the apparent shear rate. This implies that theviscosity is a function of pressure. To extrapolate to zero LID, a quadratic function wasfitted to the data, a technique previously used by Laun (1983) and Hatzikiriakos and Dealy(1992a).I,CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 256050040Cl)Cl)00)>20100100L/DFig. 4-2. Bagley plot for polypropylene at 200 °C.Another method of determining the Bagley correction is to make use of orificecapillaries (LID = 0). The Bagley corrections obtained with such capillaries and thosedetermined by extrapolation from the Bagley plot are compared in Fig. 4-3. Most of thedata points fall approximately on the same line. A degree of scatter exhibited by the dataparticularly at the smaller values of wall shear stress can be attributed to the experimentalerror. The same agreement for the Bagley corrections determined independently using twodifferent methods can be observed for another type of polypropylene (Fig. 4-4), designatedhere as “PP Profax”. This good agreement indicates that the obtained Bagley correctionsare accurate enough to allow for an accurate determination of the flow curves.0 20 40 60 80CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 2610.0 -(Ua0a)I.0.1 -0.01Wall shear stress, MPaFig. 4-3. Bagley corrections determined by using various capillaries for polypropylene at 200 °C.10.0(Ua00a)II001.00)(U0.10.01 0.10Wall shear stress, MPaFig. 4-4. Bagley corrections determined by using various capillaries for Profax polypropylene at 200 °C.0CPolypropylene, T = 200LID = 0, 0 = 0.508 mmLID = 0, D = 0.762mmLID = 0, D = 1.27mmFrom Bagley plot0.10PP Profax, T = 200 °C CCo LID=0,D=O.508mmC LID=0,D=0.762mm‘ LID=0,D=1.27mmC O• From Bagley plotSD•C0CCHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 2710.0Cu0C0.00.10.01 0.10Wall shear stress, MPaFig. 4-5. Bagley corrections for three different temperatures (200, 230 and 260 °C).It is interesting to note that the dependence of the Bagley correction on the wall shearstress does not seem to be affected by temperature. Figure 4-5 compares the Bagleycorrections versus wall shear stress, obtained at three different temperatures. The dataessentially defines a single line on a log-log plot. It is noted that no trends are observed asfar as the dependency of the Bagley correction on temperature is concerned.Polypropylene—LJD=O• T=200°C• T=230°CA T=260°C•.%•A • AA•A AAAACHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROpyLENES 284.4 Flow curvesUsing the Bagley corrections determined in the previous section, one may determinethe apparent flow curves (wall shear stress vs. apparent shear rate) for various values ofcapillary diameter and LID ratios. The wall shear stress, O4 is assumed to be uniformalong the capillary and is defmed as:= (Pd - Fend) / (4LID) (41)0.4 I I IPolypropylene, T = 200 °CD=.508 mm: • LJD= 40LJD=100 AD=.762mm: L/D=10L/D=200.3 - • LJD=40 IL/D=70L/D=100 AD=1.27mm: LJD=40v LJD=70 A.1a).c IU) $=CUmelt fracturev.z0.1 -0.0 I I I I10 100 1000 10000Apparent shear rate, s-1Fig. 4-6. Apparent flow curves for polypropylene at 200 °C determined by using capillary dies having various LIDratios.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 29Figure 4-6 shows apparent flow curves obtained with dies having a constant diameterand various LID ratios at 200 °C. It can be seen that the data does not fall on a singlecurve. Instead, the apparent flow curves shift to higher values of the wall shear stress withincrease of the LID ratio, thus pressure. This implies that the viscosity of polypropylene isa function of pressure. This was also concluded from the Bagley plot (Fig. 4-2) asdiscussed in the previous section. Similar effects were obtained at the other twotemperatures, i.e. at 230 and 260 °C. As seen in Fig. 4-7 and 4-8, the data does not fall ona single curve indicating an effect of pressure on the viscosity of the melt.0.3 I I I IPolypropylene, T 230 °CD=.508 mm: • L/D= 40L/D= 100D=.762 mm: LID= 10LJD=20• LJD=40 A° LJD=700.2 LID=l00D=1.27mm: LID=40 •• Av L/D=70 °CO AL_. VO. Vci)V(0 • melt fractureA0.10.0 I10 100 1000 10000Apparent shear rate, s1Fig. 4-7. Apparent flow curves for polypropylene at 230 °C determined by using capillary dies having various LIDratios.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 300.3 I I I IPolypropylene, T = 260 °CD=.508 mm: LID= 40UD=100D=.762 mm: A LID= 10UD=20Cu • UD=40° UD700.2 a UD=100 -C D=1.27 mm: LID= 40UD70V A.Cl) AS.- VCuCl) A= melt fractureV AV.1aV• VA0.0 I10 100 1000 10000Apparent shear rate, s1Fig. 4-8. Apparent flow curves for polypropylene at 260 °C determined by using capillary dies having various LIDratios.The pressure dependence of viscosity is typically represented by an exponentialfunction, Eq. 2-19. The value of the pressure coefficient of viscosity, a, required tosuperpose the data reasonably well was found to be in the range 5.9 x iO to i(Y Pa1,increasing with temperature. The free volume increases with temperature, and thuspressure has a higher effect on the viscosity at a higher temperature. The values of adetermined in this work are higher than those reported in the literature for polyethylenes:e.g., Kalika and Denn (1987) reported the pressure coefficient of viscosity for a LLDPE tobe 5 x i0 Pa1, while for HDPE a is believed to be less than 0.52 x i0 Pa’CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 31[Rauwendaal and Fernandez (1985)]. Using Eq. 2-19 a pressure correction can be appliedto the flow curve. The resulting pressure-corrected flow curves are shown on Fig. 4-9, 4-10 and 4-11 for the three temperatures. A reasonable superposition of the data for wallshear stresses less than about 0.18 MPa is obtained. Note that a semi-log plot was used toshow clearly the superposition of the data.0.4 I I I IPolypropylene, T = 200D=.508 mm: L/D= 40• LJD=100- D=.762 mm: A [JD= 10 ALJD=200.3 • UD=40° LJD=70° LJD=l00 xx0= 1.27 mm: LJD= 40Co UD70 $—ACu V0.2 •;U)IU) S4o IC-).p.o.i2Q0correction = 5.9*109 Pa0.0 I I I10 100 1000 10000Apparent shear rate, s1Fig. 4-9, The pressure-corrected apparent flow curves of Fig. 4-5.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 320.3 IPolypropylene, T = 230 °CD=.508mm: • LID=40• L/D=IOO0.762 mm: A LID= 10of LiD=20• LID=400 L1D70LID=1000.2D1.27 mm: A L!D 40 •.=LID=70—•L.•.2. A0.1=U)Cl)8)I0correction = 1.0*10.8 Pa0.0---•- --.-.,-. I ........ I10 100 1000 10000Apparent shear rate, s1Fig. 4-10. The pressure-corrected apparent flow curves of Fig. 4-6.0.3 IPolypropylene, T = 260 °C(0 D.508mm: • L/D40• L/D=100D=.762 mm: A LIO= 10CO ‘ LID=20• LID=400 LID=700 LID=1000.2D=1.27 mm: A LID= 40LID=70—V.•A••o 00•0.1I— IU)0correction = 8.8*10.9 Pa0.0 I I I10 100 1000 10000Apparent shear rate, s1Fig. 4-11. The pressure-corrected apparent flow curves of Fig. 4-7.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 33Cl)CoI-Cu 0.2a)U)0.1A similar approach was used to apply the pressure correction to the apparent flowcurves obtained for Profax polypropylene (Fig. 4-12). The shaded area corresponds to therange of shear stresses where the onset of melt fracture was observed. Again, the apparentflow curves shift to higher values of the wall shear stress with increase of the LID ratio.The value of the pressure coefficient of viscosity was found to be about 1.0 x Parn’which is close to that for the other polypropylene used in this study. The resultingpressure-corrected flow curves are shown in Fig. 4-13.0.4 V IPP Profax, T = 200 °CD=.508mm: • LJD=40D=.762mm: A LJD=10LJD=20• LJD=40• LJD=70• LJD=100D=1.27 mm: LJD= 40AVA.VVA•Ieonset of melt fracture0.0 I I I I10 100 1000 10000Apparent shear rate, s1Fig. 4-12. Apparent flow curves for PP Profax at 200 °C determined by using capillary dies having various LID ratios.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 340.4 I I I IPP Profax, T = 200 °C0D=.762mm: • L/D=10• LID=20$ 0.3 A LJD=40LID=70• L/D=100civo2 AG)I.- . I8 1.(1) V(i)V.Ia)correction = 1.0100.0 I I10 100 1000 10000Apparent shear rate, s1Fig. 4-13. The pressure-corrected apparent flow curves of Fig. 4-11.4.5 Wall slipTo calculate the slip velocity as a function of wall shear stress one may use theMooney (1931) technique. According to this technique the flow curves determined with aseries of capillaries having different diameters diverge at the critical shear stress for theonset of slip. In addition, to eliminate the effects of pressure on viscosity and slip velocityone should keep the LID ratio constant. This technique was used in the past for a series ofHDPE’s and it was found that these polymers slip at critical shear stresses in the range of0.1-0.18 MPa depending on the molecular weight and polydispersity of the resinCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 35CuaU)U)a)IU)(Ua)-cC’)[Hatzikiriakos and Dealy (1992a)]. Ramamurthy (1986) also determined critical shearstresses in the same range for LLDPE’s.Polypropylene, LID =40L/D = 40, T = 200 °C• D=.508mm• D=.762mm0.2 - A D=1.27mm0.1-LIII1 10 100 1000Apparent shear rate, s1Fig. 4-14. Apparent flow curves for polypropylene at 200 °C with a constant LID and various diameters to detect thepresence of slip.Figures 4-14, 4-15 and 4-16 show the apparent flow curves of PP determined with dieshaving different diameters but constant LID ratio, for three different temperatures. Notethat a semi-log plot is used to show clearly any divergence of the flow curves. It can bemelt fractureCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 36Polypropylene, L/D = 400.25LID = 40, T = 230 °C• 0.508mm• D.762mm0.20 D = 1.27 mm0.15U) melt fracture0.100.051 10 100 1000 10000Apparent shear rate, sFig. 4-15. Apparent flow curves for polypropylene at 230 °C with a constant LID and various diameters to detect thepresence of slip.0.25 I IPolypropylene, L/D 40LID = 40, T 260 OC0.20 • 0 = .508 mm I• D=.762mmD=1.27mm0.15melt fracturea)0.1o0.050.00 I I I1 10 100 1000 10000Apparent shear rate, sFig. 4-16. Apparent flow curves for polypropylene at 260 °C with a constant LID and various diameters to detect thepresence of slip.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 37with smooth surfaces and subsequently the walls ofseen that these flow curves show no divergence for wall shear stresses less than about 0.2MPa, implying the absence of slip. One could conclude that the data for 260 °C diverge inthe pre-fracture region (the points for a smaller diameter fall below others), but thedifference is to small and too close to the experimental error to consider this as anindication of slip. These observations are in agreement with the data obtained byHatzikiriakos (1991) for Profax 6631 polypropylene using both a sliding plate rheometerwith various gap spacings and a capillary rheometer with capillaries of various diametersand LID ratios. He found that Profax 6631 PP does not slip for wall shear stresses less thanabout 0.16 MPa in capillary flow.However, in view of theexperimental observations discussed below that this resin fracturesat shear stresses greater than 0.12MPa, and that there is a changeof slope of the flow curves on alog-log plot (Fig. 4-18), oneusually anticipates the presence ofslip. This was investigated furtherby using the slit dies describedabove. A typical schematic of aFig. 4-17.slit die is shown in Fig. 4-17.Experiments were initially carried outthe slit were roughened by sandblasting. To detect any changes of the slit height resultingfrom the roughening procedure, the walls were polished again and the experiments wererepeated.A typical schematic of the slit dies used.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 38CU0.011Fig. 4-18. Change of slope of the flow curves.CU0Cl,Cl,1)4-.U,I-CUC’,0.200.100.090.080.07Apparent shear rate, s1100100001000Apparent shear rate, sFig. 4-19. The effect of the wall roughness on the flow curve in slit extrusion.. .Polypropylene, L/D = 40• T=230°C• T=260°C.•melt fracture10 100 1000Polypropylene, T = 200 °CH = 0.254 mm, L/H = 100, W/H = 10• Clean surface• RoughA PolishedI••I•1ICHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 39The results are plotted m Fig. 4-19. Three apparent flow curves appear labelled as: “cleansurface” (cleaning the surface by using normal procedures; the presence of oxides whichlower substantially the surface energy cannot be excluded [Fowkes (1964)]; “rough”surface using sandblasting; and “polished” (polishing the surface has possibly increased thesurface energy compared to the normal “clean surface”). The experimental error has alsobeen assessed, indicating reproducibility of the results over a long period of time. It canclearly be seen that the data for “rough surface” fall above the other two sets. These datasuggest that slip is present and that the flow curves are affected by the surface roughness.White et al. (1991) used grooved and smooth surfaces to assess the slip behaviour ofrubber. They found that the shear stresses obtained with grooved surfaces were higher thanthose with smooth surfaces, indicating that grooved surfaces decrease wall slip. The samewas observed for PVC by Chauffoureaux et a!. (1979).As discussed above, the experiments were carried out at three different temperatures.A technique known as “time-temperature superposition” or “method of reduced variables”is often employed in rheological measurements to obtain values of a material function overa wide range of shear rates (see Chapter 2). It is based on the observation that temperaturedoes not affect the functional dependence of that property. In case of viscosity, thetemperature merely alters the zero-shear-rate viscosity and the shear rate at which thetransition from constant viscosity to power-law behaviour occurs. In the absence of slip,application of the time-temperature superposition principle on the apparent flow curves forseveral temperatures should result in a reasonable superposition. This is done in Fig. 4-20where it can be seen that the superposition is reasonable up to shear stresses of about 0.13MPa. It is noted that for shear stresses greater than this critical value melt fracture occurs.It can also be seen that for shear stresses greater than 0.13 MPa the curves do notsuperpose well but rather diverge. It is believed that this is due to the effect of slip. Ingeneral, the slip velocity increases with temperature [Hatzikiriakos and Dealy (1992a)].Thus, as the temperature increases, one expects that the part of the flow curve beyond theCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 40critical stress would shift toward the lower values of shear stress, exactly as obtained inFig. 4-20.0.35 IPolypropylene0.. 030Capillaries, D = 0.762 mm:• T200°C0.25 • T = 230 °C, T = 0.45 $A T=26O°C,xT=O.270.20Cu..I• I.—A13 0.15S0C.)melt fracture0.100.050.00 ,,..,, I I1 10 100 1000 10000Shear rate * sFig. 4-20. Flow curves at various temperatures using the time-temperature superposition principle. Note that thesuperposition is very poor at wall shear stresses in the melt fracture region.4.6 Viscous heatingBased on the results discussed in the previous section, it is believed that slip is present.However, one should explain why a diameter dependence is not obtained for the flowcurves in Figures 4-14, 4-15 and 4-16. It is believed that the effect of viscous heatingmasks the determination of slip velocity by using the Mooney method (diameterdependency of flow curves determined with capillaries having a fixed LID ratio). TheCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 41effect of viscous heating on rheological measurements in capillary/slit flow was discussedby many workers in the past [Bird (1955), Cox and Macosko (1974)].To calculate the temperature rise in a capillary or slit flow, it is necessary to make anassumption about the boundary conditions for the energy equation. There are two limitingcases which are usually considered. In the isothermal case, the wall is assumed to be at auniform temperature, and in the adiabatic case, it is assumed that there is no heat transferat the wall. Ybarra and Eckert (1980) obtained an approximate solution of the energyequation for the slit flow of a power-law fluid. Using their numerical results a case studyfor the slit flow of PP is presented here.According to the series solution for the slit flow of a power-law fluid, the temperaturerise is a function of thermophysical properties and power-law constants of the fluid andgeometrical characteristics of the slit. This function is rather complex, but a simplerelationship can be derived: for constant L/H in the isothermal case the temperature rise isproportional to B”, where H is the slit height, L is the slit length, and n varies from 0 to 2for 0 < L < . It is clear that the effect of the slit height on the temperature rise may bequite strong, and this point is demonstrated on a numerical example for polypropylene.The thermophysical properties and power-law constants of a typical PP were obtainedfrom Van Krevelen (1990) and theseare summarized in Table 4-3. Figure4-21 plots the average temperaturerise as a function of the apparentshear rate in slits having a fixedlength-to-height ratio of 40 and threedifferent heights for the case ofTable 4-3. Properties of a typical PP at 473 K.isothermal walls.Heat capacity, c,,Heat conductivity, kensity,pPower-lawexponent, nPower-law consistency, K2450 J/kg K0.15 W/mK800 kg/rn0.30.0278 MPa s7’CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 4287a,U)1.a)0E4a)4-4)0)a,2I05000Fig. 4-21. Case study: calculated average temperature rise for polypropylene at 200 °C in slit extrusion for slits havingvarious heights and a constant length-to-height ratio.It is noted that the calculated temperature rise is much higher for the case of adiabaticwalls. It can be seen from Fig. 4-21 that the effect of viscous heating is more significant inslit dies having a larger height. If one assumes the absence of slip then, according to thisresult, one expects to obtain a height dependence for the flow curves. Temperaturedependence of the viscosity was determined by a vertical shift of the flow curvescorresponding to different temperatures and is usually represented by an exponentialrelationship:-A(T -r,)w,T = W.T0 e (4-2)0 1000 2000 3000 4000Apparent shear rate, s’CHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 430.3(aI:__100Apparent shear rate, s1Fig. 4-22. Case study: flow curves with viscous heating under no-slip conditions.where ci w,T and ci are wall shear stresses at the corresponding temperatures, T and T0.The value of the temperature coefficient of viscosity, A, was found to be about 0.015 K’.Equation 4-2 indicates that the higher the temperature, the lower the viscosity, thus theflow curve for a slit having a larger height shifts to lower values of shear stress, asillustrated by Fig. 4-22. The solid line is a power law with parameters from Table 4-3; it isthe flow curve without slip and without viscous heating.Polypropylene, 200 °CL/H = 4010H=0.508mmH= 0.762 mmH= 1.27 mmpower-law1000CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 4440If slip is present, itwill affect the flow30 curves in a differentway: the flow curve forC.)020 a slit having a smaller0.height shifts to lower10 values of shear stress.To estimate the effect of0 slip, a relation for the0.0 0.1 0.2 0.3slip velocity must beShear stress, MPaassumed. Due to theFig. 4-23. Case study: slip velocity function (Eq. 4-4).absence of experimentaldata for wall slip ofpolypropylene, it is reasonable to take the available data for high density polyethylene.Hatzikiriakos and Dealy (1992a) reported that the slip velocity of HDPE can be fitted to apower-law equation:u =ao (4-3)It is applicable for o, > o, where o is the critical shear stress for the onset of slip. Forpolyethylene crc, was found to be about 0.1 MPa. More realistic behaviour of the slipvelocity at very low shear stresses can be attained by introducing one more parameterwhich zeroes the u for 04, < o, (Fig. 4-23):_____mu=ao (4-4)U.wCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPyLENES 450.3-1/7Polypropylene, 200 °C 14L/H = 40 ft::/..I—a).=‘I)= //A... H = 0.508 mm0.1- ......—..—.. H=0.762mm• ———-H=1.27mmpower-lawI I I I lIP1 I I I liii I I10 100 1000Apparent shear rate, sFig. 4-24. Case study: flow curves with slip and without viscous heating.Using Eq. 4-4 with parameters a = 2.58 MPC’ mis, o = 0.1 MPa, m = 3.4,together with Eq. 2-3 and 2-17, the slip can be imposed on the flow curves. Figure 4-24shows the effect of slip on flow curves in the case when there is no viscous heating.Therefore, a height dependence of the flow curves is obtained which is opposite from whatone gets if only viscous heating is taken into account. In a similar way, the effect of slipcan be applied to the flow curves with viscous heating and the results are plotted in Fig. 4-25. Now, with viscous heating and wall slip acting in the opposite directions, the flowcurves show almost no divergence.CHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 460.3Cua020.1100Apparent shear rate, s’Fig. 4-25. Case study: flow curves with viscous heating and slip.From the case study discussed above it is clear that with certain values of parametersaffecting viscous heating and wall slip, the flow curves for a given material can besuperposed and lead us to wrong conclusions. This seems to be the case for capillary flowas the data of Fig. 4-14, 4-15 and 4-16 indicate. Normally, one expects that capillary datawould not be much different than slit data. Therefore, it is the combined effect of slipvelocity and viscous heating that superposes the data.4.7 Rabinowitsch correctionOnce the slip effects are determined, one may calculate the viscosity. To do this, theRabinowitsch correction should be applied, which for circular dies is given by:Polypropylene, 200 °CL/H = 4011=0.508mmH= 0.762 mm1.27 mmpower-law10 1000CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 4710000 IPolypropylene008. 1000-> Capillaries, D = 0.762 mm: A• T=200°C• T=230°C,=O.45A T:260C,cz.1.=0.2710 100Shear rate * &.t, sFig. 4-26. The viscosity of polypropylene at various temperatures using the time-temperature superposition principle.13+lInL7W [ 4 J7A (4-5)where n is the power-law exponent, given by the slope of log(cr) versus log(-),assuming that the material under study is a power-law fluid. In fact, the graph of log(u)vs. log(’’A) exhibits a slight curvature, and the local value of the slope was used to applythe Rabinowitsch correction along the entire curve. Due to the uncertainty of wall slip forwall shear stresses greater than about 0.13 MPa only data in the fracture-free region areconsidered in calculating the viscosity. The resulting viscosity values have been correctedCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 48for the effects of pressure and these are plotted in Fig. 4-26. The data for the other twotemperatures, 230 and 260 °C, using the time-temperature superposition principle are alsoplotted.10000 IPP Profax, T = 200 °C,10000>U)0C.)Cl)WA100 VD=.762 mm: • UD= 10W LID=20A LID=40V IJD=70• L/D=1001010 100 1000 10000Shear rate, sFig. 4-27. The viscosity of Profax polypropylene at 200 °C.The agreement between the data obtained using various capillaries is also verified forProfax polypropylene by plotting the viscosity data (Fig. 4-27). Again, the pressure andRabinowitsch corrections were applied to the capillary data. A reasonable superposition isobtained for shear stresses not exceeding the onset of gross melt fracture (about 0.14MPa).CHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 494.8 Melt fractureSamples of polypropylene extrudates produced at various shear rates using a capillaryhaving a length-to-diameter ratio of 20 and diameter of 0.762 mm are shown in Fig. 4-28.It can be observed that there is a sudden transition from a smooth extrudate to a grosslydistorted one. The types of gross distortions range from a helical screw thread appearanceto severe irregular distortions. For polyethylenes, surface melt fracture (sharkskin) usuallyoccurs before gross melt fracture [Ramamurthy (1986)]. However, this type of distortiondoes not occur in the case of polypropylene and the transition from a smooth surface to agrossly distorted one is rather abrupt.Fig. 4-28. Various samples produced by extrusion of PP from a circular die having D = 0.762 mm and LID = 20 at200 °C.CHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 500.30 -_____________PolypropyleneD = 0.762 mm0.25 -0.20 -U)Cl)a)0.15 —0.10 -• 200°C0.05-• 230°CA 260°C0.00- I I I I I20 40 60 80 100LIDFig. 4-29. Cñtical shear stresses for the onset of melt fracture as a function of LID and temperature.The onset of gross melt fracture was detected to occur at critical shear stresses in therange of 0.12-0.15 MPa for capillary dies having LID ratios from 10 to 100 andindependent of temperature (Fig. 4-29). These values of o agree with those reported byother researchers. For example, Fujiyama and Kawasaki (1991) averaged their capillaryrheometer data for isotactic PP obtained with capillaries having LID ratios in the rangefrom 2 to 10 to give a value of 0.13 MPa for the onset of fracture. Ui et a!. (1964) foundthe critical shear stresses for the onset of melt fracture for a series of polypropylenes to bein the range between 0.1-0.13 MPa.ACHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 51Fig. 4-30. Samples of PP produced at a fixed shear rate in circular dies with different LID at 200 °C.It was also observed that the severity of extrudate distortion increases with LID ratio ata given apparent shear rate, as illustrated in Fig. 4-30. This finding is rather surprising, asan increase of the LID ratio and hence, of pressure, has been found to suppress theextrudate distortion in some cases in the extrusion of polyethylene/polypropylene blends[Vinogradov and Ivanova (1967)1. However, at a given apparent shear rate, the wall shearstress at the entrance of the die is higher for a longer capillary due to the effect of pressureon viscosity. This possibly gives an explanation as to why the LID ratio has an effect onthe severity of melt fracture.4.9 Effects of surface coatingCoating the die walls with a fluoropolymer can provide the same benefits as using thefluoroelastomer as additive to the resin. For example, Hatzilcirialcos et a!. (1993) foundCHAPTER 4- CAPILLARY RHEOMETER STUDiESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 52that processing aids such as Viton® and Teflon® PA (DuPont) could significantly lower thecritical shear stress for the onset of slip. Using these fluoropolymers, they coated thesurface of the plates in a sliding plate rheometer. They found that the critical shear stressfor the onset of slip could be as low as 0.027 MPa with a Teflon® coating. In addition, inslit extrusion with Viton® coated surface, a reduction of the wall shear stress was obtainedranging from 20 to 50%, depending on the extrusion rate.0.25 IPolypropylene, T = 200 °CH = 0.254 mm, L/H = 100, W/H = 10.1.0.20 -• Clean surface• Viton coating.Cl)U) -U)IU)I.U) .a,.U).0.l0 .•..0.05 ••0.0010 100 1000Appa rent shear rate, s’Fig. 4-31. Apparent flow curves for polypropylene at 200 °C determined by using a slit die with H = 0.254 mm.The polymer-metal interface in the slit dies was modified by applying a Teflon®coating in order to examine its effect on the processing of PP and the critical conditions forCHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 53the onset of wall slip. The procedure used to coat the dies is as follows: the solution wasapplied to the surface at 160 °C and enough time was allowed for the solvent to evaporateand for the resulting film to stabilize. Viton® coating was obtained by dissolving the pelletsin acetone and applying the solution at room temperature.0.25 I I IPolypropylene, T = 200 °CH = 0.508 mm, L/H = 60, W/H = 9.80.20•• Clean surface• Viton coatingU)0.15.010 -....• .0.05.N0.00 I I1 10 100 1000Apparent shear rate, s1Fig. 4-32. Apparent flow curves for polypropylene at 200 °C determined by using a slit die with H = 0.508 mm.The flow curves obtained using the two slit dies (#1 and 2, Table 4-2) with Viton®coating are shown in Fig. 4-31 and Fig. 4-32, respectively. It can be observed that thecoating has a dramatic effect on the flow curves for a wide range of wall shear stresses upto 0.16 MPa. Beyond that point the flow curves come close to each other, andsimultaneously the flow curve for clean surface starts to bend down, considerably deviatingCHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 54from the power law. This observation may serve as another proof that polypropylene slipsat a certain value of shear stress not far below 0.16 MPa.0.100.0800.06U,Ia,a)-cU)0.040.020.00Fig. 4-33. The effect of a Teflon® coating on the shear stress in the continuous extrusion of polypropylene.Figure 4-33 shows the dependence of the shear stress response in slit extrusion onsurface conditions as a function of time. The data was obtained by using a slit die #2. Eachcurve represents the extrusion of a fixed amount of the polymer (one full load of thebarrel). After the response for the clean surface was obtained, the Teflon® coating wasapplied only once for all subsequent runs 1 to 6. It can be seen that the presence of Teflon®significantly decreases the shear stress, resulting in easier processing. As more polymer isextruded over the same coating, a further decrease in the shear stress is obtained. Thisindicates that initially the resulting coating is not as smooth as with further treatment.Some mechanical interlocking of the polypropylene molecules within the micropores of the0 20 0 20 40 60 80 100 120Time, mmCHAPTER 4- CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 55coating initially occurs. However, as extrusion continues the Teflon® coating becomessmoother and as a result the wall shear stress decreases. One could conclude that a steady-state had been reached in run #3. However, as runs 5 and 6 indicate, a further decrease inwall shear stress was obtained. It is not known with certainty if these values represent thefinal steady-state values. This is the main reason why flow curves with a Teflon® coatedsurface have not been plotted.As it was mentioned above, a thin layer of fluorocarbons, acting as a slip promoter,suppressed the surface melt fracture of polyethylenes. However, experiments with the twopolypropylenes used in this work have shown that the presence of a Teflon® or Viton®coating had no effect on the critical shear stress for the onset of melt fracture and did notallow elimination of the extrudate distortions or delay of the onset of these distortions tohigher shear rates. An explanation of the behaviour of PPs in capillary extrusion withcoated surfaces which is different from that of PEs is currently lacking, but of course it hasto do with the molecular architecture of the two types of polymers.CHAPTER 4 - CAPILLARY RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 565. WALL SLIP AND MELT FRACTURE OF MOLTEN POLYPROPYLENES:SLIDING PLATE RHEOMETER STUDIEShis chapter is devoted to the analysis of the data for the two polypropylenesobtained from a sliding plate rheometer. The flow curves, viscosity andoccurrence of slip are determined and compared with the capillary rheometerdata. Effects of processing aids on wall slip of polypropylene are also examined.5.1 ExperimentalA sliding plate rheometer (Interlaken Series 3200) was used to determine the viscosityof the materials and compare it with data obtained from the capillary rheometer. This pieceof equipment was also used to determine the onset of slip at smaller shear rates for Teflon®and Viton® coated surfaces. The rheometer’s design allowed for two different gapspacings, 0.45 and 0.20 mm. The same resins as in the capillary rheometer studies wereused. The experiments were carried out at 200 °C only.5.2 Raw dataFigure 5-1 shows the response of the stress transducer at very low shear rates when thesteady state is reached at small strains, with no or very small overshoots at the beginning.If the shear rate is increased, the overshooting becomes stronger (Fig. 5-2) and largerstrains are required to reach a steady state. At very large shear rates over- and undershootsappear in the curves (Fig. 5-3). Analogous curves were obtained with a smaller gapbetween the plates (Fig. 5-4). This behaviour is due to the viscoelastic nature of thematerials under study. At small rates the materials behave as viscous fluids (no overshoot),however, as the shear rate increases the response becomes more elastic and thus overshootsand undershoots appear in the shear stress response. These observations are typical forviscoelastic fluids.CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESa(0(0I—CoCua)(0(U80a)II-(Ua)-C(040MELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 5730 -25 -20 -15 -10 -5-0-Polypropylene, 200 °CGap = 0.45 mm2.0 s1I 1 .1 s-II,1/0.56 sIi ‘‘ —- —‘ —‘ 0.28 s10.11 .10 2 4 6 8Displacement, mmFig. 5-1. Typical responses obtained in a steady-shear experiment in a sliding-plate rheometer (small shear rates).1002000 2 4 6 8 10 12 14Displacement, mmFig. 5-2. Typical responses obtained in a steady-shear experiment in a sliding-plate rheometer (medium shear rates).CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 58CUa1CUCD.C’,160140CU0120I-CUa)Co16014012010080600 5 10 15 20Displacement, mmFig. 5-3. Typical responses obtained in a steady-shear experiment in a sliding-plate rheometer (large shear rates).10080600 5 10Displacement, mmFig. 5-4. Typical responses obtained in a steady-shear experiment in a sliding-place rheometer (large shear rates,smaller gap).CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRAcTuRE BEHAVIOUR OF MOLTEN POLYPROPYLENES 591.0. 0.4Q0.20.00.0 0.2 0.4 0.6 0.8 1.0Dimensionless timeFig. 5-5. Check for the displacement transducer linearity (smaller gap).For an accurate determination of a steady-state value of the shear stress it is importantto ensure that the sliding plate travels at a constant speed. Figures 5-5 and 5-6 plot thedimensionless shear rate (shear rate at a given time divided by a programmed shear rate)versus dimensionless time (scaled with respect to the total duration of each run) for anumber of shear rates. It can be seen that in the case of 0.20 mm gap (Fig. 5-5) the platereaches a constant speed at the beginning of the experiment even for the high values of theshear rate.462 s1128 s1Sliding plate rheometerGap = 0.20 mmCHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 601.0I::. 0.40.20.00.0Fig. 5-6. Check for the displacement transducer linearity (larger gap).However, in the case of 0.45 mm gap (Fig. 5-6) the plate inertia starts to affect its motion,and for higher shear rates the programmed value is not reached at all. Therefore, only thelast 10% of the shear rate curve were considered for those shear rates, and appropriatecorrections were made for the values of nominal shear rates that were used in thesubsequent calculations. The nominal shear rates were calculated by differentiating thedisplacement data. The “jitter” in these graphs is explained by the fact that the data wasgenerated by an analogue-digital converter used to process the signal coming fromdisplacement transducers.0.2 0.4 0.6 0.8 1.0Dimensionless timeCHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 615.3 Flow curvesFigures 5-7 and 5-8 show the flow curves (steady-state shear stresses from Fig. 5-1 —5-4 versus nominal shear rate) obtained in the sliding plate rheometer with two differentgap spacings for the two polypropylene resins. It can be seen that these flow curves showno divergence for wall shear stresses less than about 0.13 MPa, implying the absence ofslip in the pre-fracture region. These observations are in agreement with the data obtainedby Hatzikiriakos (1991) for Profax 6631 polypropylene using both a sliding platerheometer with various gap spacings and a capillary rheometer with capillaries of variousdiameters and LID ratios. He found that Profax 6631 did not slip for wall shear stressesless than about 0.16 MPa.Polypropylene, T = 200 °CSliding plate, 0.45 mm0.10 • Sliding plate, 0.20 mm.•.•‘Cu ..11.Cl)Cl).•..a)(I)= ••U.0.01U•.•.0.1 1.0 10.0 100.0Shear rate, s1Fig. 5-7. Flow curves obtained in the sliding plate rheometer for polypropylene with different gap spacings.CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 62PP Profax, T = 200 °CSliding plate: • 0.45 mm• 0.20mm0.10Cu ...•U)••UCoI.Cua)•U)= ••U0.01..U.0.1 1.0 10.0 100.0Shear rate, s-’Fig. 5-8. Flow curves obtained in the sliding plate rheometer for PP Profax with different gap spacings.5.4 Viscosity measurementsViscosity is frequently used to characterize thermoplastic resins. It is a function offlow conditions (shear rate, temperature, pressure) and resin composition (chemicalstructure, molecular weight distribution, presence of long chain branches, nature andconcentration of additives) [Dealy and Wissbrun (1990)]. Steady shear experiments areused to determine the dependence of viscosity on various parameters.The viscosity values for polypropylene at 200 °C are plotted in Fig. 5-9, along withthe viscosity data obtained from the capillary rheometer at three temperatures. Thecapillary data have been corrected for the effects of pressure and the time-temperaturesuperposition principle was applied to the data for the other two temperatures, 230 andCHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 63260 °C. Note the excellent agreement between the data obtained from the two instruments.Due to the uncertainty of wall slip for wall shear stresses greater than about 0.13 MPa onlydata in the fracture-free region are considered in calculating the viscosity.The agreement between the data obtained in the two rheometers is also verified byplotting the viscosity data for Profax polypropylene (Fig. 5-10). Again, the pressure andRabinowitsch corrections were applied to the capillary data. A reasonable superposition isobtained for shear stresses not exceeding the onset of gross melt fracture (about 0.14MPa).I I I IPolypropyleneVVVVV10000 7VVVLVCapillaries, D = 0.762 mm: v8 • T=200°C• T=230°C,XT= 0.45A T=260°C,cL =0.27 ‘11000 TSliding plate:V Gap =0.45mm,T=200°C0.1 1.0 10.0 100.0Shear rate * T’ SFig. 5-9. The viscosity of polypropylene.CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 6410000010000(0(U1000C.,U)>100100.1 1.0 10.0 100.0 1000.0 10000.0Shear rate, s1Fig. 5-10. Comparison of capillary and sliding plate data for PP Profax.5.5 Effects of surface coatingThe sliding plate rheometer which made it possible to carry out steady shearexperiments at extremely low shear rates was used to determine the critical shear stress forthe onset of slip with fluoropolymer-treated surfaces. Hatzikiriakos et al. (1993) used asimilar sliding plate rheometer to study the effect of processing aids such as Viton® andTeflon® PA (DuPont) and found that they could significantly lower the critical shear stressfor the onset of slip.The procedures used to coat the surface of one of the plates with Teflon® and Viton®are the same as in the case of slit dies (see section 4-1). Figure 5-11 shows the flow curvesobtained with clean and Teflon®-coated surfaces. It can be seen that the onset of slip can beas low as about 0.01 MPa, and above that point the flow curves for coated plates fallPP Profax, T = 200 °CSliding plate: • 0.20 mm• 0.45 mmD=.762 mm: • L/D 10• L/D=20A L/D40V LID 70• L/D100CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEI-IAVIOUR OF MOLTEN POLYPROPYLENES 65below those for untreated surfaces. A region of flow instabilities can be observed atintermediate values of shear stress, where there is a considerable scatter in the data points.The responses for this region are shown in Fig. 5-12. It can be seen that no steady state isreached, and the shear stress for higher shear rates may be lower than that for lower shearrates. It is believed that the data points for Teflon®-coated surfaces for higher shear ratesshown in Fig. 5-11 do not represent steady-state values. In section 4-9 it was shown that avery long time is required for the Teflon® coating to stabilize, and during that period theshear stress continues to drop, reaching values that are 50% below of those obtained withclean surfaces.I I IPolypropylene, T = 200 °C100Sliding plateAAV..a_ V.-•V.(IU)0.)vv •Cl) vCuVU) AV—VVCU A-V10Gap = 0.45 mm • Clean surfaceI • Teflon coatingI.Gap = 0.20 mm A Clean surfaceV Teflon coatingI I I0.1 1.0 10.0 100.0 1000.0Shear rate, s1Fig. 5-11. Flow curves obtained in the sliding plate rheometer with clean and Teflon® coated plates.CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 66Similar effect on the shear stress can be seen in the case of Viton®-coated surface (Fig. 5-13). The onset of slip was detected at the shear stress of 0.009 MPa, although at highershear rates the decrease in shear stress is not so significant as in the case of Teflon®coating.The effect of both coatings starts to be noticeable at very low shear stresses (about0.01 MPa), and at higher shear rates a significant decrease in the shear stress is observed.All these observations point out the benefits provided by these processing aids, i.e.decreasing the power consumption in extrusion or in other polymer processing operations.30020CoU)a)4.-4-Co4.-C’,ci).U)100Fig. 5-12. Responses obtained in a steady-shear experiment with Teflon®-coated plates.0 1 2 3 4Displacement, mmCHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 67Polypropylene, T = 200 °C100-Sliding plate, gap = 0.45 mm •.•.. N. .Ca .0...•(If . NU)•I(0 • •I. Nci).Cl)—.Ca10-I • Clean surfacei • Viton coatinga0.1 1.0 10.0 100.0 1000.0Shear rate, sFig. 5-13. Flow curves obtained in the sliding plate rheometer with clean and Viton® coated plates.CHAPTER 5 - SLIDING PLATE RHEOMETER STUDIESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 686. CONCLUSIONSA sliding plate and capillary rheometers were used to determine the conditionsfor the onset of slip, surface and gross melt fracture for two polypropyleneresins. It was found that surface melt fracture commonly observed in theprocessing of polyethylenes did not occur for these polypropylenes. Instead, a sharptransition from a smooth to a grossly distorted appearance was obtained. The onset of grossmelt fracture was detected at a critical wall shear stress in the range from 0.12 to 0.15MPa, independent of temperature and geomethc characteristics of the dies.An attempt was made to explain the diameter-independence of the flow curves ofpolypropylene in capillary flow. It was suggested that viscous heating is strong enough tomask this dependence under slip conditions and one should solve the full field equationsincluding the energy equation to definitely assess its importance.Finally, it was found that the presence of Teflon® and Viton® coatings on the polymer-wall interface significantly decreased the wall shear stress which implies that thesematerials are strong slip promoters. The onset of slip was found to occur at the criticalshear stress of about 0.01 MPa, while the decrease in shear stress can be up to 50% insome cases. This results in the reduction of the driving pressure required to extrude thematerial and therefore in energy savings.Recommendations for future workBased on the experience gained during this study, the following recommendations forfuture work can be made.• The diameter-independence of the flow curves of polypropylene in capillary flow wasexplained by viscous heating, which can be strong enough to mask the effect of wallslip. Moreover, it is still not known whether the slip occurs at the polymer-wallinterface (adhesive failure) or within the polymer but close to the wall (cohesiveCHAPTER 6 - CONCLUSIONSMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 69failure). New techniques should be devised to provide deeper insights into the natureof slip and to make its determination easier. Direct measurements of velocity profilesnear the wall of a capillary/slit would be useful to prove this point experimentally andto resolve the remaining uncertainty. The possible methods could include laservelocitometry, radioactive tracer techniques, and scanning electron microscopy.• It was shown that the effect of viscous heating was stronger in channels of a largercross-section. In this regard it would be better to perform capillary rheometerexperiments using capillaries and silts of a minimal diameter or a slit height. This willalso allow a wider range of attainable shear rates.• One of the methods used to detect the occurrence of slip in this work was rougheningof the inner surface of a slit. Taking into account that pressure has a strong effect onthe slip velocity, it would be useful to roughen plates in the sliding plate rheometer,where the sample is not subjected to an external pressure. The effect of pressure on theslip velocity results in the fluid acceleration as it approaches the exit of a capillary.This will be reflected in the local shear stress and pressure. Therefore, slits with stressand pressure transducers mounted on their walls to measure the shear stress andpressure locally would be helpful for this kind of study. Currently, such slit dies areused at McGill university to determine slip.• The resins used in this work had close values of molecular weights, while otherparameters such as molecular weight distribution, presence of chain branches, isomericconfiguration of the molecules were not known. To relate the molecular characteristicsof a resin with its rheological properties, melt fracture and slip behaviour, it isnecessary to perform similar experiments with other polypropylene resins varyingthose parameters.CHAPTER 6 - CONCLUSIONSMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 70REFERENCESAkay, G., Unstable Capillary Flow ofReinforced Polymer Melts, J. Non-Newtonian FluidMech., 13, 309-323 (1983)Athey, R. 3., R. C. Thamm, R. D. Souffle and G. R. Chapman, The Processing Behaviorof Polyolefins Containing a Fluoroelastomer Additive, ANTEC ‘86, 1149-1153 (1986)Bagley, E. B., End Corrections in the Capillary Flow of Polyethylene. 3. Appi. Phys., 28,624 (1957)Barnett, S. M., A Correlationfor Melt Fracture, Pol. Eng. Sci., 7, 168 (1967)Bartos, 0., Fracture of Polymer Melts at High Shear Stress, J. Appi. Phys., 35 (9), 2767(1964)Bergem, N., Visualization Studies of Polymer Melt Flow Anomalities in Extrusion, Proc.8th mt. Congr. Rheol., Gothenberg, p. 50 (1976)Bird, R. B., Viscous Heat Effects in Extrusion ofMolten Plastics, SPE 1., 11, 35 (1955)Bird, R. B., R. C. Armstrong and 0. Hassager, Dynamics of Polymeric Liquids, Vol. 1:Fluid Mechanics, Wiley, NY (1987)Chaufforeaux, J. C., C. Dehennau and J. Van Rijckevorsel, Flow and Thermal Stability ofRigid PVC, J. Rheol., 23, 1 (1979)Cox, H. W., and C. W. Macosko, Viscous Dissipation in Die Flows, AIChE J., 20 (4),785-795 (1974)Dealy, J. M., and K. F. Wissbrun, Melt Rheology and Its Role in Plastics Processing:Theory and Applications. Reinhold, NY, 1990Fowkes, F. M., Attractive Forces at Interfaces, md. Eng. Chem., 56 (12), 40 (1964)Fujiyama, M., and Y. Kawasaki, Rheological Properties of Polypropylene/High-DensityPolyethylene Blend Melts. I. Capillary Flow Properties, 3. Appi. Polym. Sci., 42,467-480 (1991)Giacomin, A. J., T. Samurkas and 3. M. Dealy, A Novel Sliding Plate Rheometer forMolten Plastics, Polym. Eng. Sci., 29 (8), (1989)Han, C. D., Rheology in Polymer Processing, Academic Press, NY, 1976REFERENCESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 71Hatzikiriakos, S. G., Wall Slip of Linear Polymers and its Role in Melt Fracture, Ph.D.Thesis, McGill University (1991)Hatzikiriakos, S. G., and 3. M. Dealy, Wall Slip ofMolten High Density Polyethylene. II.Capillary Rheometer Studies, 3. Rheol., 36 (4), 703-74 1 (1992a)Hatzikiriakos, S. G., and 3. M. Dealy, Role ofSlip and Fracture in the Oscillating Flow ofHDPE in a Capillary, J. Rheol., 36 (5), 845-884 (1992b)Hatzikiriakos, S. G., C. W. Stewart and J.M. Dealy, Effect of Surface Coatings on WallSlip ofLLDPE, Intern. Polymer Processing VIII, 1, 30-35 (1993)Hatzikiriakos, S. G., The Onset of Wall Slip and Sharksldn Melt Fracture in CapillaryFlow, Polym. Eng. Sci., in press (1994)Hingmann, R., and B. L. Marczinke, Shear and Elongational Flow Properties ofPolypropylene Melts, 3. Rheol., 38 (3), 573 (1994)Kalilca, D. S., and M. M. Denn, Wall Slip and Extrudate Distortion in Linear Low-DensityPolyethylene, J. Rheol., 31 (8), 815-834 (1987)Kamide, K., Y. Inamoto and K. Ono, Effect of Molecular Weight and Molecular WeightDistribution on Stretchability of Polypropylene Fiber, Intern. Chem. Eng., 6 (2), 340(1966)Kraynik, A. M., and W. R. Schowalter, Slip at the Wall and Extrudate Roughness withAqueous Solutions ofPolyvinyl Alcohol and Sodium Borate, J. Rheol., 25, 95 (1981)Kurtz, S. 3., Die Geometry Solutions to Sharkskin Melt Fracture, Advances in Rheology,ed. B. Mena, A. Garcia-Rejon, and C. Rangel Nafaile (UNAM, Mexico City, 1984),Vol. 3, p. 399Latin, H. M., Polymer Melt Rheology with a Slit Die, Rheol. Acta, 22, 171 (1983)Middleman, S., Fundamentals of Polymer Processing, McGraw-Hill, NY, 1977Mooney, M., Explicit Formulas for Slip and Fluidity, J. Rheol., 2, 210 (1931)Mooney, M., and S. A. Black, A Generalized Fluidity Power Law and Law of Extrusion,3. Colloid Sci., 7, 204 (1952)Mounihan, R. H., D. G. Baird and R. Ramanathan, Additional Observations on theSurface Melt Fracture Behavior of LLDPE, 3. Non-Newtonian Fl. Mech., 36, 255(1990)REFERENCESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 72Ramamurthy, A. V., Wall Slip in Viscous Fluids and Influence of Materials ofConstruction, J. Rheol., 30 (2), 337-357 (1986)Rauwendaal, C., and F. Fernandez, Experimental Study and Analysis of a Slit DieViscometer, Polym. Eng. Sci., 25, 765 (1985)Rosenbaum E. E., S. G. Hatzikiriakos and C. W. Stewart, Flow Implications in theProcessing of Teflon Resins, to be presented at the Soc. of Rheology meeting,Philadelphia, Oct. 2-6, 1994Rudin, A., A. T. Worm and J. E. Blacklock, Fluocarbon Elastomer Processing Aid forLLDPE, HDPE and PP Resins, Processing and Property Enhancement UtilizingModifiers and Additives in Polymers: First Intl. Conf., p.’7l-8l, Nov. 1985Shidara, H., and M. M. Denn, Polymer Melt Flow in Veiy Thin Slits, 3. Non-NewtonianFluid Mech., 48, 101-110 (1993)Tanner, R. I., Engineering Rheology, Oxford University Press, Oxford, 1985Tordella, J. P., Unstable Flow of Molten Polymers, in Rheology, Vol. 5, F. R. Eirich,ed., Academic Press, NY, 57 (1987)Ui, 3., Y. Ishimaru, H. Murakami, N. Fukushima and Y. Mori, Study of Flow PropertiesofPolymer Melt with the Screw Extruder, SPE Trans., 295 (1964)Van Krevelen, D. W., Properties Of Polymers: Their Correlation with Chemical Structure;Their Numerical Estimation and Prediction from Additive Group Contributions,Elsevier, NY, 1990Vinogradov, G. V., and L. I. Ivanova, Viscous Properties of Polymer Melts andElastomers Exempled by Ethylene-Propylene Copolymer, Rheol. Acta, 6, 209 (1967)Weill, A., About the Origin of Sharskin, Rheol. Acta, 19, 623 (1980)White, 3. L., M. H. Han, M. Nakajima and R. Brzoskowski, The influence of Materials ofConstruction on Biconical Rotor and Capillary Measurements of Shear Viscosity ofRubber and its Compounds and Considerations ofSlippage, J. Rheol., 35, 167 (1991)Ybarra, R. M., and R. E. Eckert, Viscous Heat Generation in Slit Flow, AIChE 3., 26 (5),75 1-762 (1980)REFERENCESMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 73NOTATIONA temperature coefficient of viscosity, K’a parameter in the slip velocity equation (Eq. 4-4), MPam . rn/saT shift factorb Rabinowitsch correctionc, heat capacity, J/(kg K)D capillary diameter, rnH slit height, rnh gap between plates, mI melt polydispersityK power-law consistency index, MPa• sk heat conductivity, WI(m. K)L capillary or slit length, mM weight-average molecular weight, kg/kmolm parameter in the slip velocity equation (Eq. 4-4)n power-law exponentNMF melt fracture number, MPaP absolute pressure, Pad driving pressure, Pa1end Bagley correction, PaQ volumetric flow rate, m3/sR capillary radius, mT absolute temperature, Ku melt velocity, rn/su slip velocity, m/sW slit width, mNOTATIONMELT FRACTURE BEHAVIOUR OF MOLTEN POLYPROPYLENES 74Greek Lettersa pressure coefficient of viscosity, P&1true shear rate, s17 A apparent shear rate, s1 Vapparent shear rate, corrected for slip, s1nominal shear rate, s’wall shear rate, sviscosity, Pa• S1o zero-shear viscosity, Pa• sviscosity at ambient pressure, Pa• sp density, kg/rn3o critical shear stress for the onset of melt fracture, MPaa, wall shear stress, MPaUw,T wall shear stress with viscous heating, MPaNOTATION

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