Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids.
In this Letter, we present a novel method for measuring the linear viscoelastic properties of a complex fluid over an extended range of frequencies. We show that the response of the fluid to thermal fluctuations, as probed by the average motion of small particles dispersed within the fluid, provides a close representation of the response of the bulk fluid to an imposed shear strain. The essential physics of this approach is that the bulk mechanical susceptibility of the fluid determines the response of a small particle excited by the thermal stochastic forces which lead to Brownian motion. We use dynamic light scattering to measure the mean square displacement of a probe particle, kDr 2 stdl, and relate this to G p svd by describing the motion of the particle with a generalized Langevin equation, incorporating a memory function to account for the viscoelasticity. We compare this G p svd to that measured by conventional mechanical means. Remarkably good agreement is found. We demonstrate the flexibility of this new technique by measuring the moduli of a variety of complex fluids, and illustrate its potential to determine new behavior. We describe the motion of a small, neutrally buoyant particle dispersed in a complex fluid by means of generalized Langevin equation [2,3],