Evaluation from force-distance data

An expression for elastic modulus evaluation from force-distance data can be derived from (7) taking into account condition (6) ... 

By combining optimal cantilever parameters and experimental conditions one can obtain reliable force distance data which is appropriate for further contact mechanics analysis for a wide selection of polymeric materials. Both Sneddon s and Hertzian models of elastic contact give consistent results in the range of indentation depth up to 100 nm. Close correlation is observed between elastic moduli determined by SFM in compression mode (approaching cycle) and measured values for bulk materials. As shown, for elastic materials force-distance curves can be used for evaluation of tensile elastic moduli from retracing cycle. For rubber material, the latest is in a good agreement with measuremente in compression mode. 

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

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