Optimal input design for indentation-based rapid broadband nanomechanical spectroscopy: Poly(dimethylsiloxane) example

This article presents an optimal input design approach to achieve rapid broadband nanomechanical measurements of soft materials using the indentation-based method. The indentation-based nanomechanical measurement provides unique quantifications of material properties at specified locations. The measurements, however, are currently 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). Such limits exist because the input force profiles used in current approaches cannot rapidly excite broadband nanomechanical properties of materials. In this article, 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 experimental results on a PDMS sample are presented to illustrate the need for optimal input design, and its efficacy in probe-based nanomechanical property measurements.