Nanorheological AFM on Rubbers

Polymeric materials exhibit viscoelastic phenomena, which must be taken into account in designing the materials applications. For example, rubber in a tire receives stimuli over a wide frequency and temperature range from the road surface. In the case of bulk samples, the frequency and temperature can be converted mutually based on the time-temperature superposition (TTS) principle [72]. However, TTS is a kind of empirical rule and, consequently, an actual measurement method with a wide frequency and temperature range is necessary to precisely predict the properties of practical products. Various AFM-based conventional methods have been proposed to measure viscoelasticity such as lateral force microscopy (LFM) [73-75], force modulation (FM) [76-78], and contact resonance (CR) [79-81]. Even tapping mode can report energy-dissipative phenomena [44,82-84] and further offers loss tangent mapping [85,86]. 

Herein is introduced as one of the examples is a modified FV-based AFM method, hereafter called as nanorheological AFM, to measure the viscoelastic properties of polymeric materials, especially rubbers, over a wide frequency range, which was originally developed by the authors [87]. To encompass a wide-frequency range, a tiny piezoelectric actuator, measuring 3 mm x 3 mm x 2 mm, is fixed to a metallic sample holder located on the AFM scanner. The actuator is driven by the built-in oscillator of the lock-in amplifier, which is electrically isolated from all the AFM circuits. The lock-in amplifier is used to measure the amplitude and phase shift of the cantilever-deflection oscillatory signal to the drive signal. 

Note that all quantities in Equations 17.26 and 17.27 are experimentally acquired. As a viscoelastic property, the dynamic stiffness, and S are defined as 

Like in the case of static measurement, elastic moduli can be determined from stiffness if the contact radius, a, is known. Ideally, the quantity should be directly measured 

Binnig G, Rohrer H, Gerber C, Weibel E. Surface studies by scanning tunneling microscopy. Phys Rev Lett 1982 49 57-61. 

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