Identification of Nanoscale Dissipation Processes by Dynamic Atomic Force Microscopy

Identification of energy-dissipation processes at the nanoscale is demonstrated by using amplitude-modulation atomic force microscopy. The variation of the energy dissipated on a surface by a vibrating tip as a function of its oscillation amplitude has a shape that singles out the dissipative process occurring at the surface. The method is illustrated by calculating the energy-dissipation curves for surface energy hysteresis, long-range interfacial interactions and viscoelasticity. The method remains valid with independency of the amount of dissipated energy per cycle, from 0.1 to 50 eV. The agreement obtained between theory and experiments performed on silicon and polystyrene validates the method.

Figure 1

(a) Dynamic-dissipation curves for different nonconservative interactions (simulations). Energy-dissipation values are calculated per oscillation cycle. Triangles are for surface energy hysteresis; squares for a (noncontact) interfacial interaction, and the solid line is for viscoelasticity. Each curve has been normalized with respect to its respective maximum, $E_{\mathrm{dis}}(\max )=9.2$, 1.4, and 50 eV, respectively. (b) Derivative with respect to the amplitude ratio of the curves shown in (a).

Figure 2

Measured and simulated dynamic-dissipation curves. (a) On a Si surface when there is not mechanical contact between tip and surface; $A_0=6.6\mathrm{nm}$, $k=2\mathrm{N}/\mathrm{m}$. (b) On silicon when there are surface energy hysteresis and long-range interfacial interactions; $A_0=32.5\mathrm{nm}$, $k=2\mathrm{N}/\mathrm{m}$. (c) On a PS region (cross in the inset) of PS/PB blend, $A_0=15\mathrm{nm}$. (d),(e),(f) The derivatives of the normalized energy-dissipation curves shown in (a),(b),(c), respectively. The insets show the energy-dissipation images taken on Si, Figs. 2a (attractive) and 2b (repulsive), and on a PS region [Fig. 2c]. The steplike discontinuities observed in Fig. 2b mark the transition between attractive and repulsive interaction regimes.