Nanoscale dynamic mechanical analysis via atomic force microscopy (AFM-nDMA)

An apparatus configured to determine a mechanical property of a surface of a viscoelastic sample with an atomic-force-microscope (AFM) hardware, the apparatus comprising:

• an excitation electronic circuitry configured to generate a first oscillatory signal at at least one frequency, the first oscillatory signal including any of a low frequency signal, a multi-frequency signal, and a mixed frequency signal,
• wherein the low frequency signal is a single sinusoidal signal at a frequency of up to 1,000 Hz, the multi-frequency signal is a signal at multiple frequencies, and the mixed frequency signal is a combination of multiple sinusoidal signals at corresponding distinct frequencies;
• an electro-mechanical sub-system in operable cooperation with the excitation electronic circuitry, the electro-mechanical system configured
• to reposition one of the sample and a cantilevered probe of the AFM with respect to another of the sample and the probe until a point where a cantilever of the cantilevered probe is deflected by a pre-determined amount from a nominal orientation of the cantilever;
• to maintain the probe in a position, with respect to the surface of the sample, in which at least one of
• i) an average sample-loading force, generated by the cantilevered probe, and
• ii) an area of contact between a tip of the cantilevered probe and the surface of the sample is kept substantially constant;
• and
• to cause a mechanical oscillation of one of the sample and the cantilevered probe with respect to another of the sample and the cantilevered probe by transferring said first oscillatory signal to the electro-mechanical system;
• a position-detecting system configured to detect a deflection of the cantilever as a function of at least one of a temporal factor and a spatial factor characterizing an operation of the apparatus;
• a programmable processor in electrical communication with the electro-mechanical sub-system and programmed
• to transfer the first oscillatory signal from the excitation electronic circuitry to the electro-mechanical sub-system,
• to suspend an operation of the electro-mechanical sub-system for a relaxation period of time that is sufficient for relaxation of a creep of the surface, wherein the creep has been caused by repositioning of one of the sample and the cantilevered probe of the AFM with respect to another of the sample and the cantilevered probe;
• and
• to acquire data, from the position-detecting system, to determine a viscoelastic parameter of the surface after the relaxation period of time lapsed.