Viscoelastic properties of semiflexible filamentous bacteriophage fd

The cytoskeletal protein filament F-actin has been treated in a number of recent studies as a model physical system for semiflexible filaments. In this work, we studied the viscoelastic properties of entangled solutions of the filamentous bacteriophage fd as an alternative to F-actin with similar physical parameters. We present both microrheometric and macrorheometric measurements of the viscoelastic storage and loss moduli, $G^{\prime }\left(f\right)$ and $G^{″}\left(f\right),$ respectively, in a frequency range $0.01<f<\mathrm{}4\mathrm{}\mathrm{Hz},$ for fd solutions in the concentration range $5<c<\mathrm{}15\mathrm{}\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{l}.$ The onset of a narrow and slanted plateaulike region of $G^{\prime }\left(f\right)$ is located at around 2 Hz. The variation of the plateau modulus with concentration obeys a power law $G_N^{\prime }\propto c^{1.4\pm 0.3},$ similar to that found for entangled solutions of F-actin. In the low-frequency regime, the frequency dependence of the viscoelastic moduli can be described by power laws $G^{\prime }\left(f\right)\propto f^{0.9–1.2}$ and $G^{″}\left(f\right)\propto f^{0.7–0.9},$ which deviate significantly from the simple theoretical predictions of $G^{\prime }\left(f\right)\propto f^2$ and $G^{″}\left(f\right)\propto f^1.$ The latter behavior cannot yet be understood within the framework of current theories of semiflexible filament networks. For the dynamic viscosity at the low shear rate limit, a concentration dependence of ${\eta }_0\propto c^{2.6}$ was found. Finally, a linear scaling of the terminal relaxation time with concentration, ${\tau }_d\propto c,$ was observed.