Heterodyne force microscopy of PMMA/rubber nanocomposites: nanomapping of viscoelastic response at ultrasonic frequencies

Abstract

We present measurements of the nanoscale elastic and viscoelastic properties of samples of poly(methylmetacrylate) (PMMA)/rubber nanocomposites. For these studies we have used a new technique based on atomic force microscopy (AFM) with ultrasonic excitation, heterodyne force microscopy (HFM), which provides a means of testing the viscoelastic response of polymeric materials locally (in tip-probed regions) at MHz frequencies. Phase-HFM contrast distinguishes local differences in the dynamic response of PMMA/rubber composites. Comparison of HFM with other AFM-based techniques (ultrasonic force microscopy, friction force microscopy and force modulation microscopy), while imaging the same surface region, emphasizes the unique capabilities of HFM for these kinds of studies, and reveals key nanostructural characteristics of the composites. Some of the toughening particles appear to be broken down, with areas of PMMA detached from the surrounding matrix.

Beating beats mixing in heterodyne detection schemes

“…Although beating and mixing are two intrinsically different effects that are classified by the type of mixer and their Fourier analyses, we will fully counterintuitively demonstrate that beating even dominates mixing, if the mixer is of higher order than quadratic! To illustrate the importance of beating in heterodyne measurements, we use the example of heterodyne force microscopy (HFM) [8][9][10] , as it represents a model system with a highly nonlinear mixing element (much higher order than quadratic). HFM enables the non-destructive imaging below a surface with nanometre resolution using an atomic force microscope [11][12][13][14][15][16][17][18][19] .…”

Near-Field Ultrasonic Imaging: A Novel Method for Nondestructive Mechanical Imaging of IC Interconnect Structures

“…The tip piezo amplitude was held constant at 2.0v. The increase is approximately monotonic which implies a nonlinear viscoelastic response, or a strongly varying coupling between the tip and sample which shifts the heterodyne oscillation [5]. The operational parameters of the piezoelectric ceramics used here restricts the voltage to values below 10v to prevent damage.…”

“…The heterodyne nature of this deflection is illustrated by assuming a weak nonlinearity represented by a nonvanishing 2 nd order susceptibility, χ 2 , above. Assuming that the high-frequency response of the cantilever vibrations is beyond the temporal resolution of the SPM photodiode, the average deflection is simply calculated to be [5]:…”

“…Each technique is traditionally sensitive to the static elastic properties of the sample surface. Recently, a high spatial resolution phase-sensitive technique has been demonstrated which employs an ultrasonic heterodyne methodology for imaging elastic as well as viscoelastic variations across a sample surface [5]. So-called heterodyne force microscopy (HFM) uses a near-field approach to measure time-resolved variations in ultrasonic oscillations at a sample surface.…”

Image contrast reversals in contact resonance atomic force microscopy

“…[13][14][15][16] Moreover, by modulating the tip-sample interaction at a frequency close to one of the contact resonance frequencies while scanning the sample surface, or by recording contact resonances point-by-point across the scan area and calculating subsequently, semi-quantitative or even quantitative mapping of the mechanical properties of the sample surface can be realized. [17][18][19][20][21][22] However, the material properties, contact conditions, loading forces, excitation amplitudes and the operating frequency can affect the final results. Therefore, an in-depth analysis of the effects of these factors is urgently needed for better image interpretation.…”