Viscoelastic properties of semiflexible filamentous bacteriophage fd

Abstract

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, ${G}^{\ensuremath{'}}(f)$ and ${G}^{\ensuremath{''}}(f),$ respectively, in a frequency range $0.01<f<4\mathrm{Hz},$ for fd solutions in the concentration range $5<c<15\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{l}.$ The onset of a narrow and slanted plateaulike region of ${G}^{\ensuremath{'}}(f)$ is located at around 2 Hz. The variation of the plateau modulus with concentration obeys a power law ${G}_{N}^{\ensuremath{'}}\ensuremath{\propto}{c}^{1.4\ifmmode\pm\else\textpm\fi{}0.3},$ 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 ${G}^{\ensuremath{'}}(f)\ensuremath{\propto}{f}^{0.9--1.2}$ and ${G}^{\ensuremath{''}}(f)\ensuremath{\propto}{f}^{0.7--0.9},$ which deviate significantly from the simple theoretical predictions of ${G}^{\ensuremath{'}}(f)\ensuremath{\propto}{f}^{2}$ and ${G}^{\ensuremath{''}}(f)\ensuremath{\propto}{f}^{1}.$ 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 ${\ensuremath{\eta}}_{0}\ensuremath{\propto}{c}^{2.6}$ was found. Finally, a linear scaling of the terminal relaxation time with concentration, ${\ensuremath{\tau}}_{d}\ensuremath{\propto}c,$ was observed.