Extracting Active Fluctuating forces from Fluctuating motions of an active particle in a viscoelastic medium in a quadratic confinement*

Fluctuating motions of active Brownian particles are produced by a combination of active and passive forces; However, active force, carrying the origin and the mechanisms of how they are generated, are difficult to separate from the Brownian motion. Extracting the active forces from the fluctuating motions of an active particle is nontrivial because the motions produced by the two different forces are convoluted. However, if the active Brownian particle in aqueous is confined in a quadratic potential, the histogram of the pure active fluctuation can be extracted from known histograms of the total fluctuating position and that of the Brownian fluctuations by deconvolution. Whether and how deconvolution can work for active particle motions in viscoelastic media is of current interest. This study uses two different wavelength lasers to create an optical trap and to serve as a tracking beam. Viscoelastic properties of a PEG-based hydrogel over an extended frequency range (1–6000 Hz) are measured using active microrheology. Motions of active particles, i.e., electroosmosis-driven metallic Janus particles, embedded in the hydrogel in an optical trap are measured by the tracking laser beam. Mean square displacements, power spectral densities, and particle position histograms of the same experimental data are analyzed to compare the limitations of each analytical method.