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We have developed a new technique to measure viscoelasticity in softmaterials such as polymer solutions, by monitoring thermal fluctuations ofembedded probe particles using laser interferometry in a microscope.Interferometry allows us to obtain power spectra of fluctuating beads from 0.1Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear responsetheory, we determined the frequency-dependent loss and storage shear moduli upto frequencies on the order of a kHz. Our technique measures local values ofthe viscoelastic response, without actively straining the system, and isespecially suited to soft biopolymer networks. We studied semiflexible F-actinsolutions and, as a control, flexible polyacrylamide (PAAm) gels, the latterclose to their gelation threshold. With small particles, we could probe thetransition from macroscopic viscoelasticity to more complex microscopicdynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11+/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close tothe onset of the elastic plateau, and scaling behavior consistent with G(omega)as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateaumoduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5%concentration (weight/volume) respectively, in agreement to within a factor oftwo with values obtained from conventional rheology. We also found evidence forscaling of G(omega) as \omega^(1/2), consistent with the predictions of theRouse model for flexible polymers.Comment: 16 pages, with 15 PostScript figures (to be published in  Macromolecules

Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations