H. Hashemi, B. Eslami
Widener University,
United States
Keywords: SPM, AFM, Bimodal AFM, multifrequency, surface characterization, soft matter
Summary:
Atomic Force Microscopy (AFM) provides a powerful means for probing nanoscale surface morphology and mechanical response with sub-nanometer precision. Recent developments in multifrequency AFM, particularly bimodal operation, have enabled simultaneous excitation of two or more cantilever eigenmodes—offering richer contrast mechanisms that combine topographic imaging with localized material property mapping. Despite these advances, the coupled effects of drive amplitudes, tip geometry, and multimode energy distribution on the resulting viscoelastic response remain poorly understood. This study presents a comprehensive modeling and experimental framework for quantifying how amplitude ratios and geometric factors influence cantilever dynamics, energy dissipation, and tip–sample coupling in bimodal AFM. A coupled-oscillator model was developed to represent the cantilever as interacting first–second and first–third vibration modes. The simulation, implemented in C, solves the equations of motion iteratively for varying amplitude ratios (A₁/A₂ and A₁/A₃), first-mode amplitudes (50–150 nm), and tip radii (10–40 nm). The model calculates steady-state amplitude, phase, indentation depth, and maximum tip–sample force under different loading conditions. To validate simulation outcomes, experimental data were obtained from bimodal AFM imaging of polymer blends with distinct viscoelastic contrasts. The results reveal that as the cantilever approaches the surface (decreasing Z-separation), both indentation and interaction force increase sharply, transitioning from weak to strong coupling regimes. Increasing secondary-mode amplitude (A₂) enhances the energy dissipated per oscillation cycle, improving contrast in the phase channel without compromising stability in the fundamental mode. The first mode primarily governs total energy loss, reflecting overall sample damping, while higher modes capture localized viscoelastic relaxation phenomena. When the third mode (A₃) is added, the system exhibits additional high-frequency sensitivity, uncovering rapid relaxation processes that are not detectable in conventional single-mode or even second-mode operation. Parametric sweeps of the amplitude ratios demonstrate that tuning A₁/A₂ or A₁/A₃ allows deliberate control of indentation depth and contact stiffness. For smaller amplitude ratios, the tip remains in gentle-contact conditions ideal for soft or biological samples. Increasing the secondary amplitude pushes the system into stronger nonlinear coupling, where higher-frequency energy contributes to localized surface deformation and mechanical contrast enhancement. This transition, when carefully managed, enables a continuum of operational regimes—from high-sensitivity imaging with minimal perturbation to intentional nanoscale surface modification through controlled loading and energy transfer. Tip geometry plays a crucial role in determining response characteristics. Smaller radii (≈10 nm) lead to stronger force gradients and sharper phase variations, providing higher spatial resolution of near-surface mechanical heterogeneity. Intermediate radii (≈20 nm) offer balanced sensitivity and stability, while larger tips (≈40 nm) average the stress field, reducing high-mode contrast but improving imaging reproducibility. Overall, this comprehensive study highlights the interplay among amplitude ratios, drive amplitudes, and tip geometry in governing bimodal AFM performance. By unifying simulation and experimental approaches, it provides quantitative insight into optimizing bimodal excitation conditions. The resulting framework allows users to tailor operating parameters to specific objectives—whether to achieve highly sensitive imaging of viscoelastic materials or to intentionally modify and pattern surfaces through controlled tip–sample interactions. This work ultimately advances bimodal AFM toward a more predictive and application-oriented methodology for nanoscale characterization and manipulation.