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, 7 (8), 650-4

Noncontact Microrheology at Acoustic Frequencies Using Frequency-Modulated Atomic Force Microscopy

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Noncontact Microrheology at Acoustic Frequencies Using Frequency-Modulated Atomic Force Microscopy

Núria Gavara et al. Nat Methods.

Abstract

We report an atomic force microscopy (AFM) method for assessing elastic and viscous properties of soft samples at acoustic frequencies under non-contact conditions. The method can be used to measure material properties via frequency modulation and is based on hydrodynamics theory of thin gaps we developed here. A cantilever with an attached microsphere is forced to oscillate tens of nanometers above a sample. The elastic modulus and viscosity of the sample are estimated by measuring the frequency-dependence of the phase lag between the oscillating microsphere and the driving piezo at various heights above the sample. This method features an effective area of pyramidal tips used in contact AFM but with only piconewton applied forces. Using this method, we analyzed polyacrylamide gels of different stiffness and assessed graded mechanical properties of guinea pig tectorial membrane. The technique enables the study of microrheology of biological tissues that produce or detect sound.

Conflict of interest statement

COM PETIN G FIN ANCI AL INTERESTS

The authors declare no competing financial interests.

Figures

Figure 1
Figure 1
Concept of FM-AFM to measure mechanical properties of soft samples. (a) A hydrodynamic reaction force will emerge when a sphere is forced to oscillate close to a surface (left). This effect will lessen when the sphere is far from the surface (middle) or when the surface is compliant (right). (b) Sketch of a typical AFM setup; a cantilever with a bead attached to its end is used to probe the sample. A laser beam is focused onto the tip of the cantilever, and the reflected light is measured by a photodetector. Vertical oscillations of the cantilever and its height with respect to the sample are controlled with a piezo. (c) The thin gap assumption of our theory requires bead-sample gaps (hm) much smaller than the bead size (a0) and oscillation amplitudes much smaller than the bead-sample gap.
Figure 2
Figure 2
Estimation of mechanical properties through measurement of frequency shifts. (a) Shifts observed on the phase-frequency curves recorded around fπ/2 when the oscillating sphere is moved closer to the sample’s surface. Dotted line shows π/2 phase intercept. Estimated E value of the gel was 50 kPa. Inset, fπ/2 was computed by fitting a subset of points around the π/2 intercept with a second-order polynomial. (b) Representative examples of single measurements performed at one gel location for gels of different stiffness. Fitted lines correspond to the frequency shifts predicted by our theoretical results, with a 1/3 exponent with increasing bead-sample distance. (c) Acoustic values of E computed using the measured frequency shifts versus quasistatic values of E computed using force-displacement curves and the Hertz contact model. Plotted are mean E values for five different gels. Error bars, s.d. (n = 5). Dotted line is the identity line. Data points above the dotted line display stiffening at acoustic frequencies, and data points below the dotted line exhibit softening.
Figure 3
Figure 3
Effective probe area of pyramidal-probe C-AFM versus FM-AFM. (a) Topography along a line crossing the highest part of a 10-µm latex bead, obtained with a pyramidal tip in C-AFM (top). The gel surface was fitted with a solid line, whereas the bead surface was fitted with a 10 µm diameter circle. E value obtained with a pyramidal tip in C-AFM along the crossing line (middle) and with FM-AFM at the same locations as above (bottom). The shaded area corresponds to the region of the bead emerging from the gel, as determined by the topographic measurements. (b) Averaged E values over the gel or the bead obtained with C-AFM and FM-AFM. Values are mean ± s.d. (n = 22 over gel, n = 7 over bead).

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