The identification of frequency dependent material property at nanoscale has been extensively studied and played an important role in the failure analysis of materials, wound healing, and polymer formation mechanism. In this dissertation, the development of a suite of control tools to nanoscale broadband viscoelastic spectroscopy is presented. The combination of novel iterative control techniques with the integration of system identification and optimal input design techniques together can enable rapid measurement of nanomechanical properties of soft materials over a broad frequency band. SPM and nanoindenter have become enabling tools to quantitatively measure the mechanical properties of a wide variety of materials at nanoscale. Current nanomechanical measurement, however, is limited by the slow measurement speed: the nanomechanical measurement is slow and narrow-banded and thus not capable of measuring rate-dependent phenomena of materials. As a result, large measurement (temporal)

errors are generated when material undergoes dynamic evolution during the measurement. The low-speed operation of SPMis due to the inability of current approaches to (1) rapidly excite the broadband nanomechanical behavior of materials, and (2) eliminate the convolution of the hardware adverse effects with the material response during high-speed measurements. These adverse effects include the hysteresis of the piezo actuator (used to position the probe relative to the sample); the vibrational dynamics of the piezo actuator and the cantilever along with the related mechanical mounting; and the dynamics uncertainties caused by the probe variation and the operation condition. Motivated by these challenges, this dissertation is focused on the development of novel control and system identification tools for rapid broadband nanomechanical measurement.

The first proposed approach utilizes the recently developed model-less inversion-based iterative control (MIIC) technique for accurate measurement of the material response to the applied excitation force over a broad frequency band. In the proposed approach, an input force signal with dynamic characteristics of band-limited white-noise is utilized to rapidly excite the nanomechanical response of materials over a broad frequency range. The MIIC technique is used to compensate for the hardware adverse effects, thereby allowing the precise application of such an excitation force and measurement of the material response (to the applied force). The proposed approach is illustrated by implementing it to measure the frequency-dependent plane-strain modulus of poly(dimethylsiloxane) (PDMS) over a broad frequency range extending over 3 orders of magnitude (∼ 1 Hz to 4.5 kHz).

To further attenuate the dynamics convolution effect, a model-based approach to compensate for the dynamics convolution effect in nanomechanical property measurements is proposed In this dissertation. In the indentation-based nanomechanical property measurement of soft materials, an excitation force consisting of various frequency components needs to be accurately exerted to the sample material through the probe, and the indentation of the probe into the sample needs to be accurately measured. However, when the measurement frequency range increases close to the bandwidth of the instrument hardware, the instrument dynamics along with the probe-sample interaction dynamics can be convoluted with the mechanical behavior of the soft material, resulting in distortions in both the force applied and the indentation measured, which, in turn, directly lead to errors in the measured nanomechanical property (e.g., the creep compliance) of the material. In this dissertation, the dynamics involved in indentation-based nanomechanical property measurements is analyzed to reveal that the convoluted dynamics effect can be described as the difference between the lightly-damped probe-sample interaction dynamics and the over-damped nanomechanical behavior of soft materials. Thus, these two different dynamics effects can be decoupled via numerical fitting based on the viscoelastic model of the soft material. The proposed approach is illustrated by implementing it to compensate for the dynamics convolution effect in a broadband viscoelasticity measurement of a Polydimethylsiloxane (PDMS) sample using scanning probe microscope.

This dissertation also presents an optimal input design approach to achieve rapid broadband nanomechanical measurements of soft materials using the indentation-based method for the investigation of fast evolving phenomenon, such as the the crystallization process of polymers, the nanomechanical measurement of live cell during cell movement, and force volume mapping of nonhomogeneous materials. The indentation-based nanomechanical measurement provides unique quantification of material properties at specified locations. The measurement, however, currently is too slow in time and too narrow in frequency (range) to characterize time-elapsing material properties during dynamic evolutions (e.g., the rapid-stage of the crystallization process of polymers). These limits exist because the excitation input force used in current methods cannot rapidly excite broadband nanomechanical properties of materials. The challenges arise as the instrumental hardware dynamics can be excited and convoluted with the material properties during the measurement when the frequencies in the excitation force increase, resulting in large measurement errors. Moreover, long measurement time is needed when the frequency range is large, which, in turn, leads to large temporal measurement errors upon dynamic evolution of the sample. In this dissertation, we develop an optimal-input design approach to tackle these challenges. Particularly, an input force profile with discrete spectrum is optimized to maximize the Fisher information matrix of the linear compliance model of the soft material. Both simulation and experiments on a Poly(dimethylsiloxane) (PDMS) sample are presented to illustrate the need for optimal input design, and the efficacy of the proposed approach in probe-based nanomechanical property measurements.