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

Fluctuating motions of active Brownian particles are produced by a combination of active and passive forces, however, active forces, 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 randomly fluctuating forces are convoluted. However, if the active Brownian particle in aqueous is confined in a quadratic potential, the position 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 1064nm and 980nm wavelength lasers to create an optical trap and to serve as a tracking beam, respectively. Motions of active particles, i.e., electrophoresis-driven Janus particles, embedded in a PEG-based hydrogel in an optical trap are measured by the tracking laser beam. Langevin equation-based numerical simulations are conducted to recreate the motion of the active particles in viscoelastic media for comparing with the experimental results. Mean square displacements, power spectral densities, and particle position histograms of the same experimental data are analyzed for comparing the limitations of each analytical method.