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Connection between fragility, mean-squared displacement, and shear modulus in two van der Waals bonded glass-forming liquids

Henriette W. Hansen, Bernhard Frick, Tina Hecksher, Jeppe C. Dyre, and Kristine Niss
Phys. Rev. B 95, 104202 – Published 10 March 2017
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  • INTRODUCTION
  • THE SHOVING MODEL—TWO VERSIONS
  • EXPERIMENTS AND DATA
  • TESTING THE MODELS
  • DISCUSSION AND CONCLUSION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The temperature dependence of the high-frequency shear modulus measured in the kHz range is compared with the mean-squared displacement measured in the nanosecond range for the two van der Waals bonded glass-forming liquids cumene and 5-polyphenyl ether. This provides an experimental test for the assumption connecting two versions of the shoving model for the non-Arrhenius temperature dependence of the relaxation time in glass formers. The two versions of the model are also tested directly and both are shown to work well for these liquids.

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    • Received 6 November 2016
    • Revised 18 January 2017

    DOI:https://doi.org/10.1103/PhysRevB.95.104202

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Glass transitionViscoelasticity
    1. Physical Systems
    Liquids
    1. Techniques
    Neutron scatteringRheology techniques
    Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

    Authors & Affiliations

    Henriette W. Hansen1, Bernhard Frick2, Tina Hecksher1, Jeppe C. Dyre1, and Kristine Niss1,*

    • 1“Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
    • 2Insitut Laue-Langevin, 71 Avenue des Martyrs, F-38042 Grenoble, France

    • *kniss@ruc.dk

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    Issue

    Vol. 95, Iss. 10 — 1 March 2017

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    Images

    • Figure 1
      Figure 1

      (top) The MSD of cumene as a function of temperature from IN16B (•) and old data from IN10(□). The shaded area marks the temperature interval where the shear modulus was measured. (inset) Zoom; the lines are guides to the eye to show the change in dynamics around Tg and Td≈150 K. (bottom) Loss peak of the shear modulus of cumene measured in the temperature interval 130–140 K. The inset shows the extrapolation of the loss-peak moduli according to Eq. (8) into the higher-temperature liquid range that was used for neutron scattering.

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    • Figure 2
      Figure 2

      Testing Eq. (5) for cumene in the liquid. The black data points mark temperatures at which the shear modulus was measured. Equation (5) holds until the temperature 1.2Tg where the alpha relaxation enters the neutron-scattering window.

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    • Figure 3
      Figure 3

      Fixed window scan on IN16B on cumene summed over Q. From the inelastic signal (IFWS: broken lines) we see the alpha relaxation entering the instrument window around 150 K signal (EFWS: full line). Please note the different scales between the EFWS and IFWS.

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    • Figure 4
      Figure 4

      The shoving plot with the prediction (black line), relaxation time against Gmax′′(T)TgGmax′′(Tg)T (△), and 〈u2〉g/〈u2〉(T) (×). Relaxation time for cumene is plotted against temperature for the standard Angell plot (∘).

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    • Figure 5
      Figure 5

      (top) The MSD of 5PPE as function of temperature. The shaded area illustrates the temperature interval of the measured shear modulus. (inset) Zoom; the lines are guides to the eye to show the change in dynamics around Tg and Td≈280 K. (bottom) Loss peak of the shear modulus of 5PPE measured in the temperature interval 245–265 K. Inset shows the extrapolation of the loss peak moduli into the whole liquid temperature range that was used for neutron scattering.

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    • Figure 6
      Figure 6

      (top) Testing Eq. (5) for 5PPE in the liquid. The black data points mark temperatures at which the shear modulus was measured. Equation (5) holds until 1.15Tg where the alpha relaxation enters the neutron-scattering window. (bottom) The shoving plot with the prediction (black line), relaxation time against Gmax′′(T)TgGmax′′(Tg)T (△), and 〈u2〉g/〈u2〉(T) (×). Relaxation time for 5PPE is plotted against temperature for the standard Angell plot (∘).

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