Spectrum of light scattered from a viscoelastic gel

TLDR

Displacements of the gel fiber network generate polarized and depolarized scattered light, with longitudinal and shear moduli Gl and Gt characterizing compressional and transverse responses. The study reports measurements of the light‑scattering spectrum from thermally excited displacement fluctuations in polyacrylamide gels and presents a theory for the amplitude and time dependence of longitudinal and transverse displacements. Measurements were performed on polarized scattered light versus angle and temperature for 5 % and 2.5 % polyacrylamide gels using optical mixing spectroscopy, and the authors derived a decay‑rate expression Γ = G q²/f, measured the friction factor f and elastic moduli, and compared the theoretical predictions with experimental correlation functions. The theory predicts an exponential decay of the displacement correlation function, and the experimental data confirm the predicted decay rate and its q‑dependence, demonstrating that light‑scattering from thermal fluctuations provides a quantitative characterization of gel viscoelasticity.

Abstract

We report measurements of the spectrum of light scattered from thermally excited displacement fluctuations in polyacrylamide gels. These measurements have been carried out on the polarized scattered light as a function of scattering angle and temperature for 5% and 2.5% polyacrylamide gels using the methods of optical mixing spectroscopy. We also present a theory for the amplitude and time dependence of the thermally excited longitudinal and transverse displacements of the gel fiber network. These displacements are responsible, respectively, for the polarized and depolarized scattered light. The correlation function for the displacements having wave vector q is predicted for these gels to have the form of an exponential decay: exp(− Γt). The decay rate is given by Γ = Glq2/f or Gtq2/f, where f is the frictional force per unit volume on the fiber network as it moves with unit velocity relative to the gel liquid. Gl is the longitudinal compressional modulus for longitudinal displacements and Gt is the shear modulus for transverse displacements of the fiber network. We have measured, using macroscopic methods, the friction factor f, and the elastic moduli Gl, Gt and compared the numerical predictions of the theory with the experimental measurements of the correlation function of the scattered light intensity. The theory is quite successful in predicting the size and q dependence of the decay rate of the time correlation function of the scattered light. Conversely, these experiments demonstrate that the correlation function of the light scattered from thermal fluctuations of the gel fiber network provides a detailed quantitative characterization of the viscoelastic properties of gels.