Measurement of the loss tangent of low-density polyethylene with a nanoindentation technique
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W.C. Oliver and B.N. Lucas MTS Systems Corporation, Nano Instruments Innovation Center, 1001 Larson Drive, Oak Ridge, Tennessee 37830 (Received 23 September 1999; accepted 28 February 2000)
This paper describes experimental measurements of the linear viscoelastic behavior of the surface of low-density (LD) polyethylene in contact with a pyramidal Berkovich diamond indenter. The experiments were carried out at two different temperatures, 15.9 and 27.2 °C, between frequencies of 0.1 and 800 Hz. Using the shift of the loss tangent between the two temperatures at frequencies lower than 20 Hz and an Arrhenius equation, an activation energy of 105 ± 2 kJ/mol was obtained. This value is in good agreement with the bulk value of the ␣ relaxation of LD polyethylene reported in the literature.
I. INTRODUCTION
The viscoelastic behavior of surfaces is fundamental in fields dealing with interfaces, such as adhesion, polymer blending, composite materials, and tribology. There has been considerable recent effort devoted to investigating the viscoelastic properties of thin films using surface apparati (SFA) 1–5 and atomic force microscopy (AFM).6,7 One of the most advanced techniques available for the measurement of spatially resolved mechanical properties of solids is the depth-sensing indentation technique. Both static and dynamic mechanical properties can be measured using this technique. In addition to hardness, techniques for measuring the elastic modulus are well documented.8–10 Recently, there has been much progress in the development of techniques for measuring time-dependent properties. The strain rate sensitivities and apparent activation energies for indentation creep11–13 for a number of materials were accurately measured. The results compared well with more conventional measurements. Furthermore, recent results indicate that both the storage and loss modulus can also be measured.14 Specifically, it was shown that it is possible to measure the linear viscoelastic properties of an unvulcanized, natural rubber using small, oscillatory motions of the indenter, yielding a shear field in the material from which the complex elastic modulus (G*) of this tacky polymer could be deduced. The goal of this work is to extend the dynamic indentation technique to the measurements of the loss tangent of a nonadherent solid polymer, low-density (LD) polyethylene. This study will be conducted as a function of frequency and temperature to determine if an activation J. Mater. Res., Vol. 15, No. 5, May 2000
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energy for the indentation process can be deduced this way. The value obtained for the small surface volume will then be compared to the one obtained with conventional bulk mechanical techniques.
II. EXPERIMENTAL
Two different samples were analyzed, fused silica and LD polyethylene. Fused silica is a bulk specimen of a few millimeters in thickness. It is an optically flat substrate material. It is known to have low internal mechanical losses15 and is the sample usually taken a
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