Abstract
In qPlus atomic force microscopy the tip length can in principle approach the length of the cantilever. We present a detailed mathematical model of the effects this has on the dynamic properties of the qPlus sensor. The resulting, experimentally confirmed motion of the tip apex is shown to have a large lateral component, raising interesting questions for both calibration and force-spectroscopy measurements.
Highlights
From imaging of individual chemical bonds [1] to subatomic resolution of the structure of the tip apex [2], many experiments have demonstrated the ability of qPlus atomic force microscopy (AFM) to produce unprecedented imaging resolution
The tip connected to the tine, with mass mtip and moment of inertia about the point of rotation of the tip (A stylised is used to differentiate between moments of inertia and moments of area I), will produce a resulting force of and torque of
We have shown that using a simple Euler–Bernoulli model for the tine of a qPlus sensor, and inserting boundary conditions that account for both the moment of inertia and mass of the tip, we were able derive analytical results for a range of dynamic sensor properties
Summary
From imaging of individual chemical bonds [1] to subatomic resolution of the structure of the tip apex [2], many experiments have demonstrated the ability of qPlus atomic force microscopy (AFM) to produce unprecedented imaging resolution. In this paper we go further, providing a detailed analytical solution for the deflection, elastic potential energy, and spring constant of the tine of a qPlus sensor, for an arbitrary tip geometry.
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