Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations

We have developed a new technique to measure viscoelasticity in soft materials such as entangled polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, with subnanometer spatial resolution. Using Linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kilohertz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible poly(acrylamide) (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G' = 0.11 +/- 0.03 and 0.17 +/- 0.07 Pa for 1 and 2 mg/mL actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G(*)(omega) similar to omega(3/4) at higher frequencies. For poly(acrylamide) we measured plateau moduli of 2.0, 24, 100, and 280 Pa for cross-linked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of 2 with values obtained from conventional theology. We also found evidence for scaling of G(*)(omega) similar to omega(1/2), consistent with the predictions of the Rouse model for flexible polymers.