Comment on “A symmetrical method to obtain shear moduli from microrheology” by K. Nishi, M. L. Kilfoil, C. F. Schmidt, and F. C. MacKintosh, Soft Matter, 2018, 14, 3716

Abstract

Nishi et al. have presented a new analytical method for transforming the time-dependent materials' compliance into their frequency-dependent complex shear modulus, without the need of a preconceived fitting function nor the use of Kramers–Kronig transformations. They claim that their method significantly improves the accuracy of the outcomes, especially at high frequencies, up to “almost” the Nyquist frequency. Here, I corroborate that their method is actually able to provide a close estimation of the materials' complex shear modulus over the ‘entire’ range of explored frequencies (i.e. beyond the Nyquist frequency), as long as the compliance values are linearly spaced in the time-domain and its value at time zero is included as the first data point in the input file. Moreover, as a means of comparison, I employ the analytical method introduced by Tassieri et al. [New J. Phys., 2012, 14, 115032] for performing the Fourier transform of any generic time-dependent function that vanishes for negative times, is sampled at a finite rate, need not be equally spaced and extends over a finite time window. This existing method does not need preconceived fitting functions nor the use of Kramers–Kronig transformations; yet it shows a higher degree of accuracy compared to the one proposed by Nishi et al.