Dynamic light scattering by nonergodic media: Brownian particles trapped in polyacrylamide gels

Dynamic light scattering (DLS) is used to study the diffusional behavior of polystyrene latex spheres incorporated in polyacrylamide gels. It is shown that the gel systems exhibit nonergodic features, implying that the time-averaged intensity correlation function (ICF), the quantity obtained from a single DLS experiment, is not equal to the ensemble-averaged ICF. It is demonstrated that the theory of Pusey and van Megen [P. N. Pusey and W. van Megen, Physica A 157, 705 (1989)] on DLS by nonergodic media can be used to extract dynamic structure factors from single DLS experiments. It appears from this analysis that large values of the diffusion coefficient of the tracer particles, which would have been obtained in a classical analysis, do not imply rapid particle motions but result simply from an incorrect analysis of the data. The initial decay of the dynamic structure factor gives a short-time diffusion coefficient of the particles that hardly depends on the degree of cross-linking. We also show that a proper analysis of the data results in a dynamic structure factor that develops a nondecaying component. This component is a measure for the fraction of frozen-in fluctuations resulting from constrained diffusion of the tracer particles. From the nondecaying component in the dynamic structure factor, a distribution of root-mean-square displacements of the particles is calculated that appears to be an exponential distribution of which the decay length decreases with increasing degree of cross-linking. Although the scattering from the systems with probes is much higher than that of the matrix, we cannot neglect the gel scattering completely. We present theoretical expressions allowing corrections for gel scattering.