Hidden Information in Force Curves: Transient- and Brownian-Driven Dynamics

Abstract

Force distance curves (FCs) are direct probes of tip sample interactions in atomic force microscopy, but their dynamic content is often suppressed by filtering, averaging and quasistatic analysis. Indeed, in the forty years since the invention of the AFM, this hidden dynamic signal has been largely ignored, with exceptions restricted to the large oscillations associated with relatively large adhesive separations (snap from contact) or to time averaged approaches that carry their own challenges. Using high bandwidth interferometric detection, we directly measure fast FCs, including short lived cantilever oscillations during snap in, contact and pull off. Two excitation mechanisms coexist: thermal fluctuations and transients generated by rapid changes in the tip sample boundary condition. Cycle resolved frequency and amplitude estimators provide time local observables of the evolving cantilever and sample system within single FCs, creating a pixel by pixel mechanical contrast channel that requires no external broadband excitation, resonant tracking or multi pass imaging. A state dependent harmonic oscillator model incorporating van der Waals attraction, hysteretic capillary bridge formation and rupture, hydration mediated damping and repulsive contact stiffness partitions each FC into five interaction regimes and reproduces the observed responses. In repulsive contact, frequency shifts yield stiffness maps consistent with contact-mechanics estimates, enabling high throughput stiffness mapping and localization of transient tip sample events from individual pixels. More broadly, this hitherto hidden signal may pave the way for new ways of studying and exploiting Brownian motion in a variety of systems, providing the capability to follow time resolved (non) Markovian and (non) ergodic dynamics mediated by the tip sample interaction, including single event dynamics.