Quantitative subsurface contact resonance force microscopy of model polymer nanocomposites.

We present experimental results on the use of quantitative contact resonance force microscopy (CR-FM) for mapping the planar location and depth of 50 nm diameter silica nanoparticles buried beneath polystyrene films 30-165 nm thick. The presence of shallowly buried nanoparticles, with stiffness greater than that of the surrounding matrix, is shown to locally affect the surface contact stiffness of a material for all depths investigated. To achieve the necessary stiffness sensitivity, the CR-FM measurements are obtained utilizing the fifth contact eigenmode. Stiffness contrast is found to increase rapidly with initial increases in force, but plateaus at higher loads. Over the explored depth range, stiffness contrast spans roughly one order of magnitude, suggesting good depth differentiation. Scatter in the stiffness contrast for single images reveals nonuniformities in the model samples that can be explained by particle size dispersity. Finite element analysis is used to simulate the significant effect particle size can have on contact stiffness contrast. Finally, we show how measurements at a range of forces may be used to deconvolve particle size effects from depth effects.