Measuring local viscoelastic properties of complex materials with tapping mode atomic force microscopy

Tapping mode atomic force microscopy is a technique to measure the topography and properties of surfaces involving a micro-cantilever with a tip at one end that is excited into an oscillation near its resonance frequency. The phase lag between the excitation signal and the observed oscillation is sensitive to local mechanical properties under certain experimental conditions. We have found that by using silicon as an internal standard reference surface we can unambiguously relate the phase lag to local viscoelastic properties of a polymeric material. A model describing this relation has been built, validated with experimental data and finally inverted such that it can be used to determine local properties. This allows us to measure high frequency local viscoelastic properties on length scales as small as several nanometers. This technique works well for relatively compliant polymer surfaces with a shear modulus less than about 1 GPa.