Semiflexible polymers are of great biological importance in determining the mechanical properties of cells. Techniques collectively known as microrheology have recently been developed to measure the viscoelastic properties of solutions of submicroliter volumes. We employ one such technique, which uses a focused laser beam to trap a micron-sized silica bead and interferometric photodiode detection to measure passively the position fluctuations of the trapped bead with nanometer resolution and high bandwidth. The frequency-dependent complex shear modulus $G^{*}\left(f\right)$ can be extracted from the position fluctuations via the fluctuation-dissipation theorem and the generalized Stokes-Einstein relation. Using particle tracking microrheology, we report measurements of shear moduli of solutions of fd viruses, which are filamentous, semiflexible, and monodisperse bacteriophages, each $0.9\mu \mathrm{m}\text{long}$, $7\mathrm{nm}$ in diameter, and having a persistence length of $2.2\mu \mathrm{m}$. Recent theoretical treatments of semiflexible polymer dynamics provide quantitative predictions of the rheological properties of such a model system. The fd samples measured span the dilute, semidilute, and concentrated regimes. In the dilute regime $G^{*}\left(f\right)$ is dominated by (rigid rod) rotational relaxation, whereas the high-frequency regime reflects single-semiflexible filament dynamics consistent with the theoretical prediction. Due to the short length of fd viruses used in this study, the intermediate regime does not exhibit a well-developed plateau. A dynamic scaling analysis gives rise to a concentration scaling of $c^{1.36}\left(r=0.99\right)$ in the transition regime and a frequency scaling of $f^{0.63}\left(r=0.98\right)$ at high frequencies.

• Received 24 February 2004

DOI:https://doi.org/10.1103/PhysRevE.70.021503