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High sensitivity measurements of normal force under large amplitude oscillatory shear

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Abstract

The two aims of this publication are to introduce a new and rheometer-independent rheometric tool for measuring the axial normal force in oscillatory shear rheology and to study the normal forces of polyolefin melts under large amplitude oscillatory shear (LAOS). A new plate geometry with an incorporated highly sensitive piezoelectric normal force sensor was designed for a rotational rheometer. The new geometry was used to investigate normal forces of polyethylene (PE) melts under LAOS. The resulting stress and normal force data was compared with the data from measurements in commercial high performance rotational rheometers. The stress and the normal force response were Fourier-transformed and their resulting spectra were analysed. The non-linear contributions to the FT-magnitude spectra (i.e. the intensities of the higher harmonics) were analysed using the framework of the Q-parameter, \(Q=I_{3/1}/{\gamma ^{2}_{0}}\) for both the stress spectrum and the normal force spectrum, resulting in the strain-dependent \(Q\left (\gamma _{0}\right )\) and \(Q_{NF}\left (\gamma _{0}\right )\), respectively. The newly designed normal force geometry had a sensitivity in the measurement starting from \(5\times 10^{-5}\) N up to 20 N, and respectively a signal-to-noise ratio (SNR) of \(1:\) 16.000, which is about a factor of 1.8 times better than the best performing commercial rheometers. The new geometry was used to determine \(Q\left (\gamma _{0}\right )\) and \(Q_{NF}\left (\gamma _{0}\right )\), to characterize the shear rheological behaviour of the PE melts. Even rather simple rheometers, those without normal force detection, can be extended utilizing the here presented tools for high sensitive FT-rheology analysing the normal forces.

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Notes

  1. More details about polymer topology, and the detection of branching can be found in, e.g. the book of Strobl (2007), or in articles like Gahleitner (2001), Vega et al. (2002), and Klimke et al. (2006).

  2. It was first commercialised with the ARES G2 from TA-instruments.

  3. See for more details also Giacomin and Oakley (1992), Hatzikiriakos and Dealy (1991), Jeyaseelan and Giacomin (1993), and Oakley and Giacomin (1994).

  4. This depends strongly on the sample type and the concentration.

  5. The torque sensitivity is specified by the manufacturer to be between 0.002 - 200 mNm; respectively 5 decades.

  6. The normal force is specified by the manufacturer to be between 0.02 - 20 N; respectively 3 decades.

  7. Torque sensitivity as specified by the manufacturer: 0.05 μNm - 200 mNm; respectively 6 decades. Normal force sensitivity as specified by the manufacturer: 0.001 N - 20 N; respectively 4 decades.

  8. \(\overline {M}_{w}\): weight averaged molecular weight, \(\overline {M}_{n}\): number averaged molecular weight, PDI: polydispersity index, \(T_{m}\): melting temperature

  9. In a second design, the amount of screws was reduced to three to reduce weight and assembly work.

  10. In the following the term time-dependent shear stress is shortened to shear stress, because no other dependence was studied in this article. A similar abbreviation is used for the time-dependent normal force.

  11. This is known under the term of oversampling and is a crucial tool to significantly improve the signal to noise ratio.

  12. The definition of \(Q_{NF}\) will be given later in this article (“Non-linear parameters from the FT-measurement”).

  13. The excitation frequency is identical with the frequency of the first harmonic of the Fourier transform spectrum, ν0 ≡ ν1 = n ⋅ ν0,for n = 1. In the following equations and data analysis the angular frequency \(\omega \) is substituted by \(\nu \times 2\pi \), because \(\nu \) uses the units of 1/s instead of rad/s.

  14. The quantities obtained from the measurement of the time-dependent behaviour are, e.g. moduli, viscosity or torque.

  15. The manufacturer (TA-Instruments) claims only a sensitivity of \(10^{-3}\) N.

References

  • Baek S-G, Magda JJ (2003) Monolithic rheometer plate fabricated using silicon micromachining technology and containing miniature pressure sensors for N1 and N2 measurements. J Rheol 47(5):1249–1260

    Article  CAS  Google Scholar 

  • Bracewell RN (1965) The Fourier transform and its applications. McGraw-Hill, New York

    Google Scholar 

  • Carotenuto C, Grosso M, Maffettone PL (2008) Fourier transform rheology of dilute immiscible polymer blends A novel procedure to probe blend morphology. Macromolecules 41(12):4492–4500

    Article  CAS  Google Scholar 

  • Cziep MA, Abbasi M, Heck M, Arens L, Wilhelm M (2016) Effect of molecular weight, polydispersity, and monomer of linear homopolymer melts on the intrinsic mechanical nonlinearity \({~}^{3}\!\text {q}0(\omega )\) in MAOS. Macromolecules 49(9):3566–3579

    Article  CAS  Google Scholar 

  • Debbaut B, Burhin H (2002) Large amplitude oscillatory shear and fourier-transform rheology for a high-density polyethylene: experiments and numerical simulation. J Rheol 46(5):1155–1176

    Article  CAS  Google Scholar 

  • Dodge JS, Krieger IM (1971) Oscillatory shear of nonlinear fluids I. preliminary investigation. Trans Soc Rheol 15(4):589–601

    Article  Google Scholar 

  • Doeblin EO, Manik DN (2011) Measurement systems. Tata McGraw-Hill, New Delhi

    Google Scholar 

  • Gahleitner M (2001) Melt rheology of polyolefins. Prog Polym Sci 26(6):895–944

    Article  CAS  Google Scholar 

  • Giacomin AJ, Oakley JG (1992) Structural network models for molten plastics evaluated in large-amplitude oscillatory shear. J Rheol 36(8):1529–1546

    Article  CAS  Google Scholar 

  • Giacomin AJ, Jeyaseelan RS, Samurkas T, Dealy JM (1993) Validity of separable BKZ model for large-amplitude oscillatory shear. J Rheol 37(5):811–826

    Article  CAS  Google Scholar 

  • Gleissle W (1974) Schub- und Normalspannungsmessungen an silikonölen bei hohen Schergefällen mit einem neuen Kegel-Platte-Rheometer. Colloid Polym Sci 252(10):848–853

    Article  CAS  Google Scholar 

  • Gleissle W, Ohl N (1990) On the relaxation of shear and normal stresses of viscoelastic fluids following constant shear rate experiments. Rheol Acta 29(4):261–280

    Article  CAS  Google Scholar 

  • Gleissle W, Reichert H (1973) Kurzzeit-Rotations-Rheometer zur Messung von hohen Schub- und Normalspannungen bei grossen Schergefällen. Rheol Acta 12(4):572–577

    Article  Google Scholar 

  • Graham MD (1995) Wall slip the nonlinear dynamics of large amplitude oscillatory shear flows. J Rheol 39 (4):697–712

    Article  CAS  Google Scholar 

  • Hatzikiriakos SG, Dealy JM (1991) Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies. J Rheol 35(4):497–523

    Article  CAS  Google Scholar 

  • Heymann L, Peukert S, Aksel N (2002) Investigation of the solid–liquid transition of highly concentrated suspensions in oscillatory amplitude sweeps. J Rheol 46(1):93–112

    Article  CAS  Google Scholar 

  • Hyun K, Kim W (2011) A new non-linear parameter Q from FT-rheology under nonlinear dynamic oscillatory shear for polymer melts system Korea-Australia. Rheol J 23(4):227–235

    Google Scholar 

  • Hyun K, Wilhelm M (2008) Establishing a new mechanical nonlinear coefficient Q from FT-rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules 42(1):411–422

    Article  Google Scholar 

  • Hyun K, Wilhelm M (2010) Non-linear rheology of entangled linear and branched polymer melts under large amplitude oscillatory shear. Kautsch Gummi Kunstst 4:123–129

    Google Scholar 

  • Hyun K, Wilhelm M, Klein C, Cho KS, Nam JG, Ahn KH, Lee SJ, Ewoldt RH, McKinley GH (2011) A review of nonlinear oscillatory shear tests Analysis and application of large amplitude oscillatory shear (LAOS). Prog Polym Sci 36(12):1697– 1753

    Article  CAS  Google Scholar 

  • Jeyaseelan RS, Giacomin AJ (1993) Best fit for differential constitutive model parameters to nonlinear oscillation data. J Non-Newtonian Fluid Mech 47:267–280

    Article  CAS  Google Scholar 

  • Kempf M (2011) Synthesis and rheology of model comb polymer architectures. PhD thesis, Karlsruhe Institute of Technology (KIT)

  • Kempf M, Barroso VC, Wilhelm M (2010) Anionic synthesis and rheological characterization of poly(p-methylstyrene) model comb architectures with a defined and very low degree of long chain branching. Macromol Rapid Commun 31(24):2140–2145

    Article  CAS  Google Scholar 

  • Klein C (2005) Rheology and fourier-transform rheology on water-based systems. PhD thesis, Johannes Gutenberg University Mainz

  • Klein C, Naue IFC, Nijman J, Wilhelm M (2009) Addition of the force measurement capability to a commercially available extensional rheometer (caBER). Soft Mater 7(4):242–257

    Article  Google Scholar 

  • Klimke K, Parkinson M, Piel C, Kaminsky W, Spiess H-W, Wilhelm M (2006) Optimisation and application of polyolefin branch quantification by melt-state \(_{13}\)C NMR spectroscopy. Macromol Chem Phys 207(4):382–395

    Article  CAS  Google Scholar 

  • Komatsu H, Mitsui T, Onogi S (1973) Nonlinear viscoelastic properties of semisolid emulsions. Trans Soc Rheol 17(2):351–364

    Article  CAS  Google Scholar 

  • Kröger M (2004) Simple models for complex nonequilibrium fluids. Phys Rep 390(6):453–551

    Article  Google Scholar 

  • Laun HM (1978) Description of the non-linear shear behaviour of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17(1):1–15

    Article  CAS  Google Scholar 

  • Liu J, Lou L, Yu W, Liao R, Li R, Zhou C (2010) Long chain branching polylactide: structures and properties. Polymers 51(22):5186–5197

    Article  CAS  Google Scholar 

  • Lodge AS (1989) An attempt to measure the first normal-stress difference N1 in shear flow for a polyisobutylene/decalin solution D2b at shear rates up to 106 \(s^{-1}\). J Rheol 33(6):821–841

    Article  CAS  Google Scholar 

  • Lohse DJ, Milner ST, Fetters LJ, Xenidou M, Hadjichristidis N, Mendelson RA, Garcia-Franco CA, Lyon MK (2002) Well-defined, model long chain branched polyethylene. 2. melt rheological behavior. Macromolecules 35(8):3066–3075

    Article  CAS  Google Scholar 

  • Matsumoto T, Segawa Y, Warashina Y, Onogi S (1973) Nonlinear behavior of viscoelastic materials. III. The method of analysis and temperature dependence of nonlinear viscoelastic functions. Trans Soc Rheol 17(1):47–62

    Article  CAS  Google Scholar 

  • Merger D, Wilhelm M (2014) Intrinsic nonlinearity from LAOStrain experiments on various strain- and stress-controlled rheometers: a quantitative comparison. Rheol Acta 53(8):621–634

    Article  CAS  Google Scholar 

  • Münstedt H, Laun HM (1979) Elongational behaviour of a low density polyethylene melt. Rheol Acta 18 (4):492–504

    Article  Google Scholar 

  • Münstedt H, Laun HM (1981) Elongational properties and molecular structure of polyethylene melts. Rheol Acta 20(3):211–221

    Article  Google Scholar 

  • Nam JG, Hyun K, Ahn KH, Lee SJ (2008) Prediction of normal stresses under large amplitude oscillatory shear flow. J Non-Newtonian Fluid Mech 150(1):1–10

    Article  CAS  Google Scholar 

  • Nam JG, Ahn KH, Lee SJ, Hyun K (2010) First normal stress difference of entangled polymer solutions in large amplitude oscillatory shear flow. J Rheol 54(6):1243–1266

    Article  CAS  Google Scholar 

  • Neidhöfer T, Wilhelm M, Debbaut B (2003) Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions. J Rheol 47(6):1351–1371

    Article  Google Scholar 

  • Oakley JG, Giacomin AJ (1994) A sliding plate normal thrust rheometer for molten plastics. Polym Eng Sci 34(7):580–584

    Article  CAS  Google Scholar 

  • Onogi S, Masuda T, Matsumoto T (1970) Non-linear behavior of viscoelastic materials. I. disperse systems of polystyrene solution and carbon black. Trans Soc Rheol 14(2):275–294

    Article  CAS  Google Scholar 

  • Philippoff W (1966) Vibrational measurements with large amplitudes. J Rheol 10(1):317–334

    CAS  Google Scholar 

  • Sagis LMC, Ramaekers M, van der Linden E (2001) Constitutive equations for an elastic material with anisotropic rigid particles. Phys Rev E 63(5):051504

  • Schweizer T (2002) Measurement of the first and second normal stress differences in a polystyrene melt with a cone and partitioned plate tool. Rheol Acta 41(4):337–344

    Article  CAS  Google Scholar 

  • Schweizer T (2003) Comparing cone-partitioned plate and cone-standard plate shear rheometry of a polystyrene melt. J Rheol 47(4):1071–1085

    Article  CAS  Google Scholar 

  • Schweizer T, Bardow A (2006) The role of instrument compliance in normal force measurements of polymer melts. Rheol Acta 45(4):393–402

    Article  CAS  Google Scholar 

  • Shaw MT (2012) Introduction to polymer rheology. Wiley, Hoboken

    Google Scholar 

  • Sim HG, Ahn KH, Lee SJ (2003) Three-dimensional dynamics simulation of electrorheological fluids under large amplitude oscillatory shear flow. J Rheol 47(4):879–895

    Article  CAS  Google Scholar 

  • Strobl G (2007) The physics of polymers: concepts for understanding their structure and behaviour. Springer, Berlin

    Google Scholar 

  • Tee T-T, Dealy JM (1975) Nonlinear viscoelasticity of polymer melts. Trans Soc Rheol 19(4):595–615

    Article  CAS  Google Scholar 

  • van Dusschoten D, Wilhelm M (2001) Increased torque transducer sensitivity via oversampling. Rheol Acta 40(4):395–399

  • Vega J, Aguilar M, Peon J, Pastor D, Marnez-Salazar J (2002) Effect of long chain branching on linear-viscoelastic melt properties of polyolefins. e-Polymer 2:624

    Article  Google Scholar 

  • Vittorias IA (2006) Fourier-transform rheology applied on homopolymer melts of different architectures- experiments and finite element simulation. PhD thesis, TUD - Technical University Darmstadt

  • Wagner MH, Bastian H, Bernnat A, Kurzbeck S, Chai CK (2002) Determination of elongational viscosity of polymer melts by rme and rheotens experiments. Rheol Acta 41(4):316–325

    Article  CAS  Google Scholar 

  • Wilhelm M (2002) Fourier-transform rheology. Macromol Mater Eng 287(2):83–105

    Article  CAS  Google Scholar 

  • Wilhelm M, Maring D, Spiess H-W (1998) Fourier-transform rheology. Rheol Acta 37(4):399–405

    Article  CAS  Google Scholar 

  • Wilhelm M, Reinheimer P, Ortseifer M (1999) High sensitivity fourier-transform rheology. Rheol Acta 38:349–356

    Article  CAS  Google Scholar 

  • Wilhelm M, Reinheimer K, Kübel J (2012) Optimizing the sensitivity of FT-rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer. Z Phys Chem 226:547

    Article  CAS  Google Scholar 

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Acknowledgments

The authors want to thank Dr. C.O. Klein for his preliminary work with the CaBER, see Klein et al. (2009) and D. Zimmermann for his support at the ARES measurements. Furthermore, the authors want to thank, Dr. I. Vittorias from LyondellBASELL, Dr. S.A. Filipe from Borealis and Prof. H. Münstedt for providing some of the samples. The authors are grateful to Dr. D. Merger, Dr. M. Abbasi and, especially, Dr. J. Kübel for proofreading the manuscript.

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  1. Karlsruhe Institute of Technology - KIT, Engesserstr. 18, 76131, Karlsruhe, Germany

    Ingo F. C. Naue & M. Wilhelm

  2. Department of Industrial and Materials Science, Chalmers University of Technology, SE-41296, Gothenburg, Sweden

    Roland Kádár

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  1. Ingo F. C. Naue
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Correspondence to Roland Kádár.

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Naue, I.F.C., Kádár, R. & Wilhelm, M. High sensitivity measurements of normal force under large amplitude oscillatory shear. Rheol Acta 57, 757–770 (2018). https://doi.org/10.1007/s00397-018-1111-y

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