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^'(f) and G^''(f), respectively, in a frequency range 0.01<f<4Hz, for fd solutions in the concentration range 5<c<15mg/ml. The onset of a narrow and slanted plateaulike region of G^'(f) is located at around 2 Hz. The variation of the plateau modulus with concentration obeys a power law GN^'∝c^1.4±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^'(f)∝f0.9--1.2 and G^''(f)∝f0.7--0.9, which deviate significantly from the simple theoretical predictions of G^'(f)∝f² and G^''(f)∝f¹. 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 η₀∝c2.6 was found. Finally, a linear scaling of the terminal relaxation time with concentration, τd∝c, was observed.