Active Microrheology of Networks Composed of Semiflexible Polymers. II. Theory and comparison with simulations

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Building on the results of our computer simulation (ArXiv cond-mat/0503573)we develop a theoretical description of the motion of a bead, embedded in a network of semiflexible polymers, and responding to an applied force. The theory reveals the existence of an osmotic restoring force, generated by the piling up of filaments in front of the moving bead and first deduced through computer simulations. The theory predicts that the bead displacement scales like x tᵃlfa with time, with alfa=0.5 in an intermediate- and alfa=1 in a long-time regime. It also predicts that the compliance varies with concentration like c(-4/3) in agreement with experiment.