Figure 8.

Results of energy dissipation when a tip interacts with a Nafion model under a numerically simulated trajectory. (a) Shows force distance curves for tips driven at different eigenfrequencies (color coded). The inset in (a) shows the behavior of dissipation as the frequency increases, and each color coded line relates to a specific amplitude setpoint (A₁/A₀₁). (b) shows dissipation vs amplitude setpoint (A₁/A₀₁) curves, where each color coded line corresponds to a specific eigenfrequency. The inset in (b) shows the slope of the curves in (b) near the range where the slopes cross the x-axis in order to easily locate the maxima of the curves in (b). (c) shows the response of the surface and dashpots of the Nafion model for two cases at different cantilever eigenfrequencies. The parameters for the cantilever dynamics were the same as in Figure 6 and Figure 7. The sample parameters were: k_e = 20 N/m, k₁ = 10 N/m, k₂ = 5 N/m, c₁ = 0.5 × 10⁻⁵ N·s/m, and c₂ = 100.0 × 10⁻⁵ N·s/m. Time normalization has been carried out in (c) with respect to the fundamental period for ease of comparison.