Analysis of nanoindentation of soft materials with an atomic force microscope
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Nanoindentation is a popular experimental technique for characterization of the mechanical properties of soft and biological materials. With its force resolution of tens of pico-Newtons, the atomic force microscope (AFM) is well-suited for performing indentation experiments on soft materials. However, nonlinear contact and adhesion complicate such experiments. This paper critically examines the application of the Johnson-Kendall-Roberts (JKR) adhesion model to nanoindentation data collected with an AFM. The use of a nonlinear least-square error-fitting algorithm to calculate reduced modulus from the nanoindentation data using the JKR model is discussed. It is found that the JKR model fits the data during loading but does not fit the data during unloading. A fracture stability analysis shows that the JKR model does not fit the data collected during unloading because of the increased stability provided by the AFM cantilever.
I. INTRODUCTION
In recent years, the importance of the mechanical characterization of biological materials has become evident in the field of mechanobiology, ranging from the diagnosis of diseases like cancer1 and malaria2 to the understanding of mechanisms in cell biology such as cell growth3 and locomotion.4,5 Biological materials are commonly soft and inhomogeneous in nature, which can make them difficult to characterize using traditional mechanical experiments. Additionally, biological specimens such as thin protein films and cells often have small sizes or volumes. When mechanical properties of such biological specimens are of interest, nanoindentation provides a means to characterize the mechanical behavior of these specimens. Several studies have been performed detailing the use of a commercial nanoindenter to mechanically characterize biological specimens such as skin6 and cartilage.7 An alternative instrument to the nanoindenter is the atomic force microscope (AFM), and a nanoindentation experiment with an AFM is shown in Fig. 1(a). The AFM offers several advantages over the nanoindenter: it is a more common instrument; use of different types of cantilevers gives the AFM more flexibility in indenter shape, size, and surface functionalization; and most commercial AFMs come with a fluid cell for experiments with hydrated specimens. Possibly the biggest advantage of the AFM is that unlike a nanoindenter, the AFM does not require a load cell to measure the indentation load. Instead, the indentation force is measured in an AFM by multiplya)
Address all correspondence to this author. e-mail: [email protected]. DOI: 10.1557/jmr.2011.252 J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012
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ing the measured deflection of the cantilever with the cantilever’s stiffness. Compared to the nanoindenter, which has a resolution of approximately 100 nN, the AFM can measure forces in the range of pico-Newtons to hundreds of micro-Newtons by simply changing the stiffness of the cantilever. The superior force resolution of the AFM makes it particularly suitable for na
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