R.C. Tung, N. Zimron-Politi
University of Nevada, Reno,
Keywords: contact resonance, AFM, nanomechanics
Summary:In this work, we present theoretical and experimental methods for Contact Resonance spectroscopy using non-traditional sensor tips. In Contact Resonance (CR) Atomic Force Microscopy (AFM), the coupled sensor-sample system’s natural frequencies are measured and processed using a theoretical model to estimate the sample's stiffness. To-date, CR spectroscopy has been limited to traditional cantilever AFM probes due to the dynamic effects present when using advanced sensors. The use of an advanced nano-needle sensor was successfully demonstrated to allow imaging of biological samples in their natural liquid environment, while the sensor's body remains outside of the liquid environment to minimize hydrodynamic effects. Furthermore, the use of a quartz tuning fork with an added tungsten tip was demonstrated in dynamic AFM measurements and may soon be used for CR-AFM. The dynamic effects resulting from the additional mass, rotational inertia, and tip length were incorporated into a new CR theoretical model, and experimentally validated here. Additionally, we further extend the theoretical model to include effects from the tip's flexibility. For both new CR models, the freely vibrating sensor eigenfrequencies are used to estimate the unknown system parameters: the nondimensional added mass and rotational inertia, a parameter encapsulating beam properties (which is also used to relate the experimental eigenfrequencies to the eigenvalues of the system), and a nondimensional dynamic factor relating the tip and cantilever dynamics for the flexible tip case. The complex dynamics of a sensor with a long, massive tip show unprecedented experimental measurements of the 1st eigenmode with a CR frequency higher than the freely vibrating 2nd eigenmode. To the best of our knowledge, this is the first time in-contact spectra are measured at a higher frequency than the immediately subsequent out-of-contact eigenmode for cantilevers with long tip geometry. Such behavior contradicts with conventional, simple, single-spring CR models, that predict an upper bound for the in-contact eigenfrequency that is lower than the immediately subsequent eigenmode free frequency, nevertheless, such behavior is well-described by both new models. We discuss the lower and upper theoretical bounds of the analytical eigenfrequencies for both new models and compare to a traditional CR model.