We report on a technique that simultaneously quantifies the contact stiffness and dissipation of an AFM cantilever in contact with a surface, which can ultimately be used for quantitative nanomechanical characterization of surfaces. The method is based on measuring the contact resonance frequency using dual AC resonance tracking (DART), where the amplitude and phase of the cantilever response are monitored at two frequencies on either side of the contact resonance. By modelling the tip-sample contact as a driven damped harmonic oscillator, the four measured quantities (two amplitudes and two phases) allow the four model parameters, namely, drive amplitude, drive phase, resonance frequency and quality factor, to be calculated. These mechanical parameters can in turn be used to make quantitative statements about localized sample properties. We apply the method to study the electromechanical coupling coefficients in ferroelectric materials and the storage and loss moduli in viscoelastic materials.
We demonstrate the accurate nanoscale mapping of near-surface loss and storage moduli on a polystyrene-polypropylene blend with contact resonance force microscopy (CR-FM). These viscoelastic properties are extracted from spatially resolved maps of the contact resonance frequency and quality factor of the AFM cantilever. We consider two methods of data acquisition: (i) discrete stepping between mapping points and (ii) continuous scanning. For point mapping and low-speed scanning, the values of the relative loss and storage modulus are in good agreement with the time-temperature superposition of low-frequency dynamic mechanical analysis measurements to the high frequencies probed by CR-FM.
The storage modulus (E′) and loss modulus (E″) of polyolefin blends have been mapped on the nanoscale with contact resonance atomic force microscopy (CR-FM), a dynamic contact mode of atomic force microscopy (AFM). Modulus values measured on various components within a blend of polyethylene, polypropylene, and polystyrene compared favorably with expected moduli of individual pure components at the contact resonance frequency that were calculated from bulk dynamic mechanical analysis (DMA) measurement results. Absolute storage modulus values were in good agreement with DMA results, while the loss modulus values obtained from CR-FM were consistently lower than those acquired from DMA. Application of CR-FM to an elastomercontaining blend resulted in moduli map artifacts due to the elastomer's high adhesion and low storage modulus, illustrating its limitation in quantifying viscoelastic properties of soft elastomers. In spite of this current limitation, the results presented in this paper demonstrate the potential of contact resonance methods for quantifying nanoscale viscoelastic properties of certain thermoplastic polymers.
Piezoresponse force microscopy (PFM) has emerged as the tool of choice for characterizing piezoelectricity and ferroelectricity of low-dimensional nanostructures, yet quantitative analysis of such low-dimensional ferroelectrics is extremely challenging. In this communication, we report a dual frequency resonance tracking technique to probe nanocrystalline BiFeO(3) nanofibers with substantially enhanced piezoresponse sensitivity, while simultaneously determining its piezoelectric coefficient quantitatively and correlating quality factor mappings with dissipative domain switching processes. This technique can be applied to probe the piezoelectricity and ferroelectricity of a wide range of low-dimensional nanostructures or materials with extremely small piezoelectric effects.
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