Loss Tangent Atomic Force Microscopy of Polymer Materials

One of the main challenges associated with quantitative nano-mechanical measurements is calibration.  Calibration of the spring constant, detector sensitivity and the tip shape to mention only three parameters are all critical to accurate nano-mechanical properties measurements.  Yet, one does not need to go far in the literature to find ~50-100% uncertainties in these parameters. 

Since the first phase images of wood pulp were presented at a Microscopy and Microanalysis meeting over fifteen years ago, phase imaging has become a mainstay in a number of AFM application areas, most notably for polymers where the phase channel is often capable of resolving fine structural details and providing contrast that is not present in the topography channel. Interpreting the phase of amplitude-modulated AFM(AM-AFM or Tapping mode) in terms of the mechanical and chemical properties of the surface has seen some progress, for example relating the phase shifts to energy dissipation.  Even with these advances, however, obtaining accurate quantitative mechanical or chemical properties remains problematic for the reasons mentioned above.

In this work, we derive an expression for loss tangent measurement of a surface in amplitude modulation atomic force microscopy that only depends on the cantilever phase and the normalized cantilever amplitude.  This provides a direct, nearly calibration-free measurement of compositional information of the surface in contrast to conventional phase imaging, and incorporates both the lost and stored energy into one term that represents a new interpretation of the phase signal in amplitude modulation imaging.  The simplified expression for the loss tangent agrees with numerical solutions over a wide range of the amplitude values, implying that the loss tangent is a robust and precise signal, independent of the particular set-point chosen by the user.

We will report results from ongoing quantitative experimental AFM measurements on various model Polyolefin-Polystyrene and Polymer-elastomer blends that have also been characterized by Dynamic Mechanical Analysis (DMA).  The experimental AFM results show excellent qualitative agreement and, subject to some experimental criteria that will be discussed, quantitative agreement with the bulk DMA data.