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

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

• an excitation electronic circuitry configured to generate an excitation force signal that includes multiple sinusoidal signals having respectively-corresponding distinct frequencies covering at least one decade in a frequency space, wherein amplitudes of said multiple sinusoidal signals are varied between a maximum value and a minimum value, each of the maximum and minimum values being the same for all of said multiple sinusoidal signals;
• a position-detecting system configured to detect a deflection of a cantilever of a cantilevered probe of the AFM hardware and to generate data representing the deflection;
• a feedback electronic circuitry operably connected with the position-detecting system and configured to monitor both a mean value of said excitation force signal and an oscillatory component of said first excitation force signal and to generate a feedback output representing both a mean value of said excitation force signal and an oscillatory component of said first excitation force signal;
• an electro-mechanical sub-system cooperated with the excitation electronic circuitry and the feedback electronic circuitry and configured:
• when the cantilever is deflected by a pre-determined amount from a nominal orientation thereof, to cause a mechanical oscillation between the sample and the probe in response to the excitation force signal transferred from the excitation electronic circuitry;
• and
• upon receiving the feedback output, to maintain said one of the sample and the probe in a position, with respect to the other of the sample and the probe, in which an area of contact between a tip of the probe and a surface of the sample is kept substantially constant during said mechanical oscillation;
• a programmable processor in operable communication with at least position-detecting system and programmed:
• to suspend an operation of the electro-mechanical sub-system for a relaxation period of time sufficient for relaxation of a creep of a surface of the sample that is caused by repositioning of said one of the sample and the probe with respect to the other of the sample and the probe;
• and
• to acquire said data from the position-detecting system to determine a viscoelastic parameter after the relaxation period of time has lapsed.