聚合物中聚合物拉伸黏度检测方案(流变仪)

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PN002 The ARES-EVF： Option for Measuring Extensional Viscosity ofPolymer Melts A. Franck， TA Instruments Germany INTRODUCTION The roots of extensional rheometry are to befound at the very beginning of the 20th century. Itwas Trouton， who when experimenting with pitchand shoemaker’s wax， subjected these materials to“torsion”and“traction”deformations. He discoveredthrough his ingenious experiments， that the uniaxialextension viscosity is three times the shearviscosity."....A variety of pitch which gave bytraction method =4.3 x1010 poise was found bytorsion method to have a viscosity u=1.4 x 10poise... F.T. Trouton (1906)”/1/ Despite these early experiments， the developmentsin elongational rheometry were few until the end ofthe sixties. In 1955 Bueche /2/ reported onelongation measurements performed with PMMA.Karam et al./3/， Ballman /4/ and Cogswell /5/ in1969 published results on PS， obtained on homebuilt elongation rheometers. The exciting phase inelongation rheometry started in 1969 with Meissner/6/ and Vinogradov etal./7/. Whereas all experimentalapproaches up to this date were based on pulling arod like sample apart by the ends， Meissnerintroduced a novel idea， which changed the field ofelongation rheometry. He replaced the movingclamps with fixed mounted rotating clamps. Thesample is held between two pairs of rotating spurgears pulling the sample and expelling the materialfrom the fixed test section. The advantage of thistechnique is -first， the total elongation is not limitedby the apparatus size and second， by expelling thesample out of the test section， necking or end effectsat the clamps are removed continuously. Theconcept introduced by Meissner is also used in theExtensional Viscosity Fixture (EVF) introduced Figure 1： Cauchy or engineering strain Figure 2： Hencky strain and Hencky rate later in this presentation. Why are elongation experiments important andwhy has so much effort been put into the designand manufacturing of elongational rheometers，while rheological measurements in shear usingrotational rheometers are so much easier to perform?The number one reason is that extensionaldeformations play a significant role in manyprocessing operations. Fiber spinning， film blowing，blow molding， thermoforming etc. are essentiallydominated by extensional flow. Most process flowshowever are mixed flows， such as convergingregions in dies， or coating processes. In manyprocesses extensional flows are essential. Ex-tensional material functions are needed to modelthe flow and since extensional flows are strong Figure 3： Elongational stress and viscosity in an uniaxialelongation experiment flows，consi/derably orienting molecules， asymmetricparticles or the dispersed phase in blends， the finalproduct properties are strongly effected. The secondreason to perform elongational measurements isrelated to the sensitivity of these flows to molecularstructure， such as branching. The elongationalviscosity at large strains is more sensitive tovariations in long chain branching than the linearviscoelastic shear properties. The third reason isacademic. Since elongation properties differ somuch from shear properties， the elongationexperiments are ideal to test constitutive equationsand flow models. THE ELONGATION STRAINRATE(HENCKY STRAIN) The most common elongation measurement isthe engineering strain or Cauchy strain， defined asthe increase in length AL divided by the initial lengthL (Figure 1). The Cauchy strain is a deformationmeasure valid for small deformations. For largedeformations (AL>>L)， the Cauchy strain isreplaced by the Hencky strain. The Hencky rate isrelated to the velocity of a particle along thedeformation axis v =(de/dt)x (Figure 2). In aconstant rate experiment (two ends moving at thesame speed)， the particle in the center of the rodhas a velocity zero and the particle velocity increaseswith the distance from the center. The rotating clamptechnique deforms the material at constant Henckyrate by expelling the material at a fixed distance x=L /2 from the sample center with a constantvelocity vapplied by the rotating clamps. In atraditional elongation experiment， with the samplevolume constant， the sample ends must thereforemove at a speed v=(L/2)de/dt. Integrating fromL to the final length L，leads to an exponentialincrease of the sample length over time L(t)=L exp[(de/dt)t]. The final strain thus can beexpressed as s =ln[L/L] The elongation viscosity nis defined as thestress divided by the elongation rate. The stressis the force divided by the surface area normalto the direction of deformation. For an in-compressible material， the volume is conservedand the surface area must decrease exponentiallyas A(t)=A exp{(de/dt)t} with the sample length1ncreasing(Figure 3) while the experimentproceeds. THE ARES-EVF The EVF concept The ARES-EVF design (patent pending) is basedon the original Meissner concept and elongates thesample within a confined space by expelling thesample with rotary clamps. Instead of the rotaryclamps， two cylinders are used to wind up the·onsample； one cylinder is rotating， the other measuringthe force. In order to wind up the sample equally onboth sides， the rotating cylinder moves on a circularorbit around the force measuring cylinder whilerotating around its own axis at the same time (Figure4). Since the force measuring cylinder is fixed inspace it can be directly coupled with the torquetransducer of the ARES. All the motion of therotating cylinder is generated by the ARES actuator.As such the force measurement is decoupled fromall the moving parts and consequently friction andinertia contributions are not affecting the materialresponse， namely the force signal. Figure 4： The eccentric drum rotates around the fixed drumwhile spinning around its own axis Figure 5： Schematic of the EVF (ExtensionalViscosityFixture) The ARES transducer measures a torque. Theforce at the sample can be easily calculated fromthe measured torque divided by the cylinder radius.The strain rate applied is the velocity at the cylinder，divided by the sample length L which is equivalentto the separation of the center axes of the twocylinders. The velocity is given by the product ofthe angular rotation speed Q(t) and the cylinderradius Dr /2. Since the sample is elongated at both Figure 6： EVF installed on the ARES rheometer ends， the Hencky rate applied by the actuator is theproduct of angular rotation speed and cylinderdiameter divided by the distance of the twocylinders. The EVF design A schematic of the Extensional Viscosity fixture(EVF) is given in Figure 5. Motor and transduceraxis are aligned， and the rotating drum is mountedeccentric at a distance (center to center) of 12.7 mm.In order to rotate thedrum， a fixed hollow shaft，ending as a spur gear at the top， is mounted aroundthe motor shaft to the ARES frame. As the eccentricmounted drum is orbiting around the transducer Figure 7： Sample stiffness in the RME and the ARES-EVF drum， the spur gear drives the rotation around itsown axis. The EVF is designed to fit into thestandard ARES oven. The diameter of each drum is10.3 mm and the clearance between the drums is2.4 mm. Figure 6 shows the EVF option， installedon the ARES rheometer. Since the cylindrical drums are mountedvertically， the sample is also loaded vertically ontothe drums and attached with two tiny clips. Sample support a must or not necessary? The RME (Rheometric Melt Elongation rheo-meter) and the original Meissner elongationrheometer used a support medium to prevent themolten sample from sagging. The sample wasfloating on oil or on air during the experiment. Inthe RME， the belt carriers， which apply theelongation deformation to the sample are mountedhorizontally. The rectangular shaped sampleconsequently is in an horizontal position. On theEVF， the samples are mounted vertically and thesample length L is reduced from 40 mm (RME) to12.7mm (EVF). These two changes increase theeffective stiffness increase of a sample by a factor Figure 8： Recorded force during an elongation experimentat constant Hencky rate (Lupolen 1810H) of 1 million (Figure 7). This is a key advantage ofthe EVF because materials with a shear viscosityabove 1000 Pa s do not significantly sag under thegravity force during loading and testing. Due to thesmall sample size required for the EVF and the fastheating rate of the ARES oven， the waiting timeafter loading the sample is less than 3 minutes， thuspreventing creep in the sample. EXPERIMENTALForce and stress results The response of the material to a constantdeformation rate is the stress.During the experimentthe reactive force at the transducer is measured as afunction of time or deformation. In a typical forcecurve， shown in Figure 8， the force grows from zeroas the stress builds up in the sample with time. Aftera short period， the force goes through a maximumand decreases from then on continuously more orless exponentially. The reason for the force decreaseis the exponentially decreasing cross section of thesample with increasing total deformation. Thecorresponding viscosity， the ratio of force F andsample cross section A(t) divided by the rateincreases strongly at the start up and then levels offto a steady state. (see Figure 8). Effective strain rate， minimum andmaximum values A key feature of the rotating clamp concept isthe prevention of sample necking at the clamp bycontinuously removing it out of the measuring zone.This ensures a nice， uniform rectangular sampleshape throughout the experiment with minimum boundary effects. This feature is essential whenreducing the sample size to a minimum like in theEVF. The polymer melt sample adheres to the drumat test temperature. For a sample thickness of lessthen 0.8 mm， the variation of the sample velocity atthe drum due to the variation of the radius (samplethickness changes) is negligible. As such， thenominal elongation rate varies very little with theaverage rate applied during the experiment. In orderto verify this “non slip”condition， a section ofknown length can be cut from the remaining samplestrand at the end of the test. From the weight andthe density at test temperature， an average samplecross section can be determined and subsequentlyan average Hencky elongation rate. Although thetheoretical upper limit in elongation rate for theARES at 100 rad/s is 81 s-l， 10 sl is the practicallimit； a Hencky strain of 5 will be reached in 0.5 sand reliable force data are obtained from 100 mson. The ARES is capable of making measurementsat extremely low elongation rates， and coupled witha sensitive force rebalance transducer， a wide rangeof practical elongation rates can be realized. Reproducibility and maximum strain Figure 9 shows three experiments performed ata rate of 0.1 s-lon the reference material Lupolen1810H at 150°C. All tests were done with differentsample thickness ranging from 0.7 to 1.2 mm. Theviscosity curves overlay， proving excellent Figure 9： Reproducibility of 3 consecutive tests. Themaximum strain depends on the initial sample thickness reproducibility. During a measurement on the EVF，the sample wraps around both the fixed and rotatingdrums. After one revolution， the sample will windup on top of itself and the force signal becomesunusable. A maximum elongation 8 of 4.3 can beobtained with a sample thickness of 0.7. Sampleswith thickness >1 mm can be tested to a Henckystrain 8 of 3.4 only， because the sample at theclips of both drums will come into contact after3/4 of a revolution (Figure 9). For one experimentin figure 9 the viscosity curve can be observed tolevel off due to non-uniform sample deformationsat8=4. Comparison with Lupolen 1810H In order to validate the EVF， a series oftests wasperformed on the reference Lupolen 1810H. TheEVF data were compared to the data originallypublished by Meissner and Raible/8/. As can be seenin Figure 10， excellent agreement was obtained forresults at0.1 s. Slight differences between the EVFand Meissner data can be seen at lower rates andhigh elongations. These deviations may be attributedto sample preparation. More important to note isthat the EVF can generate data at a rate of 10 s，where neither the Meissner unit nor the RME could. APPLICATIONEXAMPLESLLDPE，HDPE，LDPE Measuring the extensional viscosity is criticalto understand processing behavior of polyolefinsStrain hardening is a desired property in filmblowing or spinning processes， as it stabilizes thefilm bubble or the free fiber during the melt Figure 10： Elongational viscosity of Lupolen 1810Hcompared with the original Meissner data /8/ Figure 11： Strain hardening in LDPE， LLDPE and HDPE elongation phase. High take up speeds are onlypossible with the right amount of strain hardeningto avoid bubble collapsing and fiber breaking.Figure 11 shows the elongation viscosity fordifferent typical representatives of polyethene，LDPE， LLDPE and HDPE. The LDPE sampleshows considerable strain hardening at highelongation strain as a result of the high content oflong chain branches. The HDPE and LLDPE， withlow long chain branching， exhibit very little strainhardening. Metallocene catalyzed long chainbranched PE Figure 12 shows elongation data of a poly-ethylene obtained by metallocene catalyse’s in theDow process. For reference LLDPE and LDPEmanufactured using the traditional technique areshown also. The metallocene catalyst controls thepolymer architecture and thus allows tailoring ofthe molecular structure and consequently thephysical properties to the required needs. The PEsynthesized in the metallocene catalized processshows elongational properties with strong strainhardening， the shape of the viscosity curve verysimilar to the one of the standard LDPE CONCLUSIONAND OUTLOOK The ARES-EVF is a new melt extensional fixturefor the ARES rheometer. It can perform uniaxialextension measurements to a Hencky strain of 4.3，elongation rates up to 10 s， to a maximumtemperature of 250°℃ (350℃ Optional). The EVFis very easy to operate and combined with the speedof the ARES oven can provide sample throughput Figure 12： PE manufactured by metallocene catalise’s incomparison to LDPE and LLDPE obtained in a traditionalmanufactured process of four to five experiments per hour. The datagenerated on the ARES-EVF show excellentagreement with the RME or the original Meissnerrotating clamp rheometer. Although the RME canachieve slightly higher total elongation comparedto the EVF， the ARES-EVF is better suited for fastelongation rates not easily accessible on theRME.The new EVF provides for an affordable wayto transform any ARES into an even more powerfulcombined shear and extensional polymer rheologyplatform. ( REFERENCES ) ( /1/Trouton， F. T. P roc. R. Soc. 77，426 (1906) ) ( /2/ Bueche， F. J. Chem.Phys， 22， 4 803 (1954) ) ( /3/Karam， H. . J. et al.. Trans， Soc. Rheol.13， 2 ，209 (1969) ) ( /4/ Ballman， R.L. Rheologica acta 4， 2 138 (1965) ) ( /5/ Cogsell， F.N. Rheologica Acta 2 187 (1969) ) ( /6/ Meissner， J. Rheologica Acta 8， 78 (1968) ) ( /7/ Vinogradov et al. J. Polym. S ci. A-28， 657 (1970) ) ( /8/ Raible， T . e t al. J. Polym. Bull. 1， 397 (1979) ) PN The roots of extensional rheometry are to be found at the very beginning of the 20th century. It was Trouton, who when experimenting with pitch and shoemaker’s wax, subjected these materials to “torsion” and “traction” deformations. He discovered through his ingenious experiments, that the uniaxial extension viscosity is three times the shear viscosity.”.…A variety of pitch which gave by traction method λ=4.3 x 1010 poise was found by torsion method to have a viscosity μ=1.4 x 1010 poise… F.T. Trouton (1906)”