# Traceable stiffness calibration of colloidal AFM probes for biomechanical measurements

## TL;DR

This paper introduces a new model and experimental method to accurately calibrate colloidal AFM probes by accounting for friction effects, improving the reliability of biomechanical measurements.

## Contribution

A new analytical model and experimental validation method for colloidal AFM probe stiffness calibration that accounts for frictional contact effects.

## Key findings

- The proposed model showed good agreement with a validated system, with deviations within 1.5%.
- Frictional contact was confirmed to cause a transition phase in unloading curves of large-sphere colloidal probes.
- Friction coefficients for four tip-surface combinations were experimentally determined and found broadly applicable.

## Abstract

The accurate calibration of bending stiffness of colloidal atomic force microscopy (AFM) probes is essential for reliable nanomechanical measurements, especially when large micro-spheres are used in biological applications. This study investigates the influence of frictional contact between an AFM spherical tip and the load button on stiffness measurements obtained via bending tests and proposes a new analytical model to account for this effect. Finite element simulations of frictional sliding contact between colloidal spheres and load button were conducted to validate the proposed model. A proof-of-principle experimental setup was developed to traceably acquire force-deflection curves of several typical colloidal AFM probes, and results showed good agreement (within 1.5 % deviation) with a validated stiffness calibration system. Experimental data for large-sphere colloidal probes confirmed the presence of a transition phase in the unloading curve due to frictional contact and demonstrated that accurate stiffness results can be obtained when friction is properly considered. Additionally, friction coefficients for four tip-surface material combinations were experimentally determined, providing broadly relevant data that can be effectively applied in AFM nanomechanics, especially in investigations of tip-sample interactions.