A mode of atomic force microscopy (AFM) is demonstrated where an oscillating AFM cantilever having linear response is driven with two frequencies in the vicinity of a resonance. New frequencies in the response, known as intermodulation products, are generated when the linearity of the cantilever response is perturbed by the nonlinear tip-surface interaction. A rich structure of the intermodulation products is observed as a function of the probe-surface separation, indicating that it is possible to extract much more detailed information about the tip-surface interaction than is possible with the standard amplitude and phase imaging methods.

Ferroelectric materials exhibit a phase transition to a paraelectric state driven by temperature - called the Curie transition. In conventional ferroelectrics, the Curie transition is caused by a change in crystal symmetry, while the material itself remains a continuous three-dimensional solid crystal. However, ferroelectric polymers behave differently. Polymeric materials are typically of semi-crystalline nature, meaning that they are an intermixture of crystalline and amorphous regions. Here, we demonstrate that the semi-crystalline morphology of the ferroelectric copolymer of vinylidene fluoride and trifluoroethylene (P(VDF-TrFE)) strongly affects its Curie transition, as not only a change in crystal symmetry but also in morphology occurs. We demonstrate, by high-resolution nanomechanical measurements, that the semi-crystalline microstructure in the paraelectric state is formed by crystalline domains embedded into a softer amorphous phase. Using in situ X-ray diffraction measurements, we show that the local electromechanical response of the crystalline domains is counterbalanced by the amorphous phase, effectively masking its macroscopic effect. Our quantitative multi-scale characterisations unite the nano- and macroscopic material properties of the ferroelectric polymer P(VDF-TrFE) through its semi-crystalline nature.

We present a method to reconstruct the nonlinear tip-surface force and extract material properties from a multifrequency atomic force microscopy (AFM) measurement with a high-quality-factor cantilever resonance. In a measurement time of $\sim${}2 ms, we are able to accurately reconstruct the tip-surface force-displacement curve, allowing simultaneous high-resolution imaging of both topography and material properties at typical AFM scan rates. We verify the method using numerical simulations, apply it to experimental data, and use it to image mechanical properties of a polymer blend. We further discuss the limitations of the method and identify suitable operating conditions for AFM experiments.

Intermodulation atomic force microscopy is used to quantitatively determine both viscous and elastic parameters of a soft material interface. A model of the tip surface interaction is introduced, taking in to account the dynamics of both cantilever and viscoelastic surface.

Nonlinear systems can be probed by driving them with two or more pure tones while measuring the intermodulation products of the drive tones in the response. We describe a digital lockin analyzer which is designed explicitly for this purpose. The analyzer is implemented on a field-programmable gate array, providing speed in analysis, real-time feedback, and stability in operation. The use of the analyzer is demonstrated for intermodulation atomic force microscopy. A generalization of the intermodulation spectral technique to arbitrary drive waveforms is discussed.