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Nanoindentation of Polymers

Reconstructed AFM tip

Nanoindentation of Polymers with the AFM

AFM Indentation Basics

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Depth-Sensing Indentation

The atomic force microscope (AFM) has become an increasingly popular tool for characterizing surfaces and thin films of many different types of materials.  Recent developments have led to the utilization of the AFM as a nanoindentation device.  During operation of the AFM in force mode, the probe tip is first lowered into contact with the sample, then indented into the surface, and finally lifted off the sample surface.  Concurrently, a measurement of the probe tip deflection is produced through an optical lever detection system, in which a laser beam is reflected off the top of the probe and onto a segmented photodiode.  A plot of this tip deflection signal as a function of the vertical displacement of the piezo scanner is called a force curve.  AFM software has been modified and diamond-tipped stainless steel probes have been developed specifically for indenting and scratching materials with nanoscale spatial resolution.  The software modification allows the surface to be imaged in tapping mode immediately before and after indentation, which is particularly important for soft engineering materials that can be damaged easily by contact mode AFM.  Thus, we now have the ability to image the surface in tapping mode, perhaps utilizing phase contrast imaging, indent (or scratch) at specified points, and then image the residual impressions.

Technical Barriers

When performing indentation with an AFM cantilever probe, lateral motion of the probe tip occurs as the cantilever bends.  This motion causes the tip to deform a larger area of the sample as the tip shifts to the left.  Also, a lateral force constraining this motion will build up and produce a moment that bends the cantilever in a direction opposing the bending due to the lateral contact force.  To compensate for this effect and create "true" vertical motion of the probe tip, a lateral motion factor is incorporated in the AFM indentation software.  This factor is input as an angular measurement in degrees, the tangent of which is equal to the ratio of x-motion to z-motion.  Images of the residual impressions left after indenting an epoxy sample using two different types of probes are shown below.  In both cases, increasing the amount of compensation (from left to right) produces a smaller indent.  The amount of compensation will depend largely on the ratio of tip height to cantilever length, and thus is larger for the diamond-tipped probe.

Series of indents on epoxy with a diamond-tipped probe showing the effect of lateral motion compensation Series of indents on epoxy with a silicon probe showing the effect of lateral motion compensation

Left -- a diamond-tipped stainless steel cantilever probe is used and the dents from left to right were taken using compensation angles of 0, 10, 20, 30, 35, 40, 45, and 50 degrees; Right -- an ultra-stiff silicon probe is used and the dents from lower left to upper right were taken using compensation angles of 0, 5, 10, 15, 20, and 25 degrees (the image was captured with a 45 degree scan angle). 

In practice, complete compensation for the lateral tip motion during indentation is difficult to achieve, so the objective of lateral compensation becomes one of minimizing experimental uncertainties.   Other experimental uncertainties that limit the use of the AFM as an indentation device include nonlinearity, hysteresis, and creep of the piezoelectric scanners and nonlinearity of the photodetector.   Despite these technical barriers, achieving quantitative indentation measurements of polymers with nanoscale spatial resolution can be achieved when operational settings are chosen to correctly minimize uncertainties.  However, these measurements are generally relative measurements because the probe tip shape and, in some cases, the probe spring constant are typically unknown or known only within large uncertainties.  Current research efforts are aimed at overcoming these technical barriers.

References:

Application to Polymers

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Depth-Sensing Indentation

Research at the University of Delaware by VanLandingham et al. was the first of its kind to utilize the AFM to measure the indentation response of polymers in a quantitative fashion (see references below).  This research established the procedural and analytical methods for making quantitative indentation measurements with an AFM cantilever probe while also identifying the sources and levels of experimental uncertainties and the extent to which those uncertainties limit the use of the AFM as an indentation device (see previous section).  In the following references, numerous applications of AFM nanoindentation to polymeric materials can be found, including the identification of phases in polyethylene blends, the characterization of a skin-core phenomena in a polydimethylsiloxane (PDMS), and elevated- temperature measurements of polymeric composite interphases.

References:

Recent Research

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Depth-Sensing Indentation

For reliable indentation measurements, knowledge of the shape of the indenter tip is required.  For indentation measurements involving sub-micrometer scale contacts, accurate characterization of the tip shape is difficult.  In our current research efforts, we are utilizing a technique referred to as blind reconstruction to measure the tip shapes of AFM indentation probes through collaborations with Dr. John S. Villarrubia of the Precision Engineering Division of NIST's Manufacturing Engineering Laboratory.  This method has the potential for material independent calibration of indenter tips used with the AFM as well as those used with depth-sensing indentation.  Below, results from blind reconstruction are used to determine the elastic modulus, E, of a polymeric material as a function of the contact depth, hc. In these results, a commercial mathematical software package was used to fit smooth spline curves to the unloading data and provide estimates of the contact stiffness, S.  An average value of E of 5.1 GPa ± 0.8 GPa was calculated, with no discernable increasing or decreasing trend in E as a function of hc.  From tensile tests on this polymer film, a modulus of 2.9 GPa was measured.  Thus, the AFM indentation measurement of E is significantly higher than this bulk tensile test measurement.  The discrepancies between these values of E are likely due to a combination of experimental uncertainties, the important deviations in behavior due to viscoelasticity relative to the elasticity-based analysis, and the non-ideal tip shape of the AFM probe near its apex, as shown in the lower left figure.  Note, however, that using a relatively stiff probe (k = 120 N/m ± 10 N/m), maximum indentation loads as low as 1.4 mN were used that created maximum penetration depths as low as 25 nm with residual plastic depths of < 2 nm (compares favorably to current capabilities of depth-sensing indentation).  Use of more sensitive probes (lower values of k) results in enhanced load sensitivity for more compliant materials.

indents on polymer indentation load-penetration curves

Left -- AFM topographic image of 3 rows of indents made at 8 different load levels (total height scale in the image is 20 nm from black to white); Right -- 8 indentation load- penetration curves correponding to one of the rows in the image.

3D representation of reconstructed tip shape modulus measured as a function of contact depth using the blind reconstruction area function

Left -- 3D representation of reconstructed tip shape for the AFM diamond-tipped probe used in indentation study above; Right -- Modulus, E, measured as a function of contact depth, hc, using the blind reconstruction area function.

This study was done through collaborations with Dr. John S. Villarrubia of the Precision Engineering Division of NIST's Manufacturing Engineering Laboratory and Dr. Greg F. Meyers of The Dow Chemical Company.

References:

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Date created: 4/01/2000
Last updated: 2/27/2003