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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.

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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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