The analysis of AFM nanoindentation curves from soft materials: An iterative method for optimizing the combined determination of contact point and elastic indentation modulus.

Abstract

The atomic force microscope (AFM) is often used for nanoindentation experiments to mechanically characterize soft, hydrated materials due to its ability to nondestructively and sensitively probe delicate samples under physiological conditions. It can be challenging, however, to analyze the resulting nanoindentation force curve due to the gradual and sometimes noisy increase in the force signal, which obscures the contact point (CP). Since accurate determination of the CP is critical for reliable calculation of the elastic indentation modulus (E_ind), its misidentification can lead to substantial variability in E_ind. Existing CP determination approaches vary in robustness, often require careful selection of material-dependent parameters, are sensitive to noise, or lack applicability across a broad range of materials. To address some of these issues, we developed a combinative, iterative, and systematic analysis method to enhance the accuracy and reliability of CP and E_ind determination. We started by integrating the strengths of two existing algorithms (the ratio of variances and goodness of fit) then added iterative elements to remove the dependence of CP determination on fitting parameters. Finally, a statistical analysis was used to select an E_ind that is unaffected by variations associated with overly shallow indentation depths. In a performance comparison against multiple other methods, we found that our method balances CP accuracy and E_ind fit quality, producing consistent results. We finally tested the robustness of our method in the analysis of nanoindentation curves from a range of hydrogels proving its ability to analyze diverse data sets with little to no parameter tuning.