N. Zimron-Politi, R.C. Tung
University of Nevada, Reno,
United States
Keywords: contact-resonance AFM, viscoelasticity, damping, loss tangent, high-loss materials
Summary:
Contact-resonance atomic force microscopy (CR-AFM) enables nanoscale mechanical characterization by tracking the resonance response of a cantilever in contact with a sample of interest. The use of CR-AFM for mechanical characterization of viscoelastic samples was introduced by Dupas and Rabe, and later evolved into the techniques commonly used in CR metrology. Over the past two decades, small damping was assumed to simplify the post-processing procedure for the data acquired using CR-AFM on viscoelastic samples. In a damped vibrational response, the eigenfrequencies of the system can be represented using complex eigenvalues, where the real and imaginary parts are calculated using experimentally measured properties for each mode. The small-damping simplification was examined for cases where the ratio between the imaginary and real parts of the eigenvalues is less than 0.05. Studies for the range where this ratio is greater than 0.05, where dissipation dominates the response, are missing. In this work, we show that by mathematically manipulating the contact resonance viscoelastic characteristic equation, we eliminate the need to assume small damping of the sample in the solution procedure and obtain improved prediction accuracy of both viscous and elastic properties of the sample. The prediction for the loss tangent of the sample is also improved using the proposed method. The proposed method allows us to examine responses that are in the range where the ratio between the imaginary and real parts of the eigenvalues is greater than 0.05. We use a numerical experiment and implement a multi-modal (“mode-crossing”) data processing approach to find the unknown system parameters and compare them with the assigned values. In our multi-modal approach, unknown parameters are restricted to physically meaningful values. Using the proposed method, not only is the accuracy improved, but the prediction range for which physically meaningful results are obtained is significantly increased. Numerical experiment results on representative high-loss materials indicate that neglecting damping can lead to large errors in sample stiffness, damping, and loss tangent. By explicitly accounting for dissipation within the characteristic equation and leveraging multiple modes, CR-AFM can quantify nanoscale mechanical loss alongside stiffness without prior sensor-geometry knowledge, improving nano-mechanical characterization accuracy for samples where energy dissipation dominates the response. These findings advance CR-AFM toward routine, quantitative mapping of viscoelastic losses in polymers, hydrogels, and biomaterials. We employ our findings to inform practical choices of mode order and operating conditions for high-damping measurements, aligning with the original vision of contact resonance for viscoelastic loss tangent metrology.