Optimal Excitation Force Design in Indentation-Based Rapid Broadband Nanomechanical Spectroscopy: Poly(dimethylsiloxane) Example

This paper presents an optimal input design approach to achieve rapid broadband nanomechanical measurements of soft materials using indentation-based method. The indentation-based nanomechanical measurement provides unique quantification of material properties at specified locations. The measurement, however, is currently too slow 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 limitations exist because the excitation input force used in current methods cannot rapidly excite broadband nanomechanical properties of materials. The challenges arise as a result of the instrumental hardware dynamics being excited and convoluted with the material properties during the measurement when the frequencies in the excitation force increase, resulting in large measurement errors. Moreover, measurement takes a long time when the frequency range is large, which, in turn, leads to large temporal measurement errors upon dynamic evolution of the sample. In this paper, 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.