Is It Possible to Directly Determine the Radius of a Spherical Indenter Using Force Indentation Data on Soft Samples?

An important factor affecting the accuracy of Young's modulus calculation in Atomic Force Microscopy (AFM) indentation experiments is the determination of the dimensions of the indenter. This procedure is usually performed using AFM calibration gratings or Scanning Electron Microscopy (SEM) imaging. However, the aforementioned procedure is frequently omitted because it requires additional equipment. In this paper, a new approach is presented that focused on the calibration of spherical indenters without the need of special equipment but instead using force indentation data on soft samples. Firstly, the question whether it is mathematically possible to simultaneously calculate the indenter's radius and the Young's modulus of the tested sample (under the restriction that the sample presents a linear elastic response) using the same force indentation data is discussed. Using a simple mathematical approach, it was proved that the aforementioned procedure is theoretically valid. In addition, to test this method in real indentation experiments agarose gels were used. Multiple measurements on different agarose gels showed that the calibration of a spherical indenter is possible and can be accurately performed. Thus, the indenter's radius and the soft sample's Young's modulus can be determined using the same force indentation data. It is also important to note that the provided accuracy is similar to the accuracy obtained when using AFM calibration gratings. The major advantage of this paper is that it provides a method for the simultaneous determination of the indenter's radius and the sample's Young's modulus without requiring any additional equipment.