A time-shift correction for extraction of viscoelastic parameters from ramp-hold AFM experiments

The stress relaxation and creep measurements are commonly implemented in AFM indentation experiments to analyze the viscoelastic properties of a sample in the time domain. The assumption of an instantaneous step load is often applied which can lead to erroneous estimation of viscoelastic parameters from the experimental data. A viscoelastic solution for the ramp-hold indentation profile might be used but requires higher computational costs. Here, we employed simulations for the ramp-hold indentations for the power-law rheology (PLR) and standard linear solid models. The error coming from the instantaneous load assumption was analyzed and a simple empirical correction for the finite ramp time was employed as a time shift of the hold region. The correction was tested in experiments on cells, in which the data from stress relaxation, creep, and force volume experiments were compared. The correction showed good applicability for the extraction of the PLR viscoelastic parameters.