Probing length scale of dynamic correlation by particle tracking.

Abstract

Dynamic heterogeneity in complex fluids is often inferred from broad relaxation spectra or non-Gaussian probe motion, but these signatures do not by themselves identify the relevant spatial length scales or distinguish heterogeneity from inter-particle dynamic correlation. Here, we develop an analytical framework for multiparticle tracking microrheology that separates these two aspects of dynamics. The framework compares single-particle and multi-particle non-Gaussian parameters <i>α</i>sp2 and <i>α</i>mp2 to infer the accessible length-scale range of diffusivity heterogeneity, and introduces an overlap-based cross-covariance quantity, <i>χ</i>_cross, to quantify inter-particle dynamic correlation. Brownian-dynamics simulations validate the expected behavior of these estimators under simplified heterogeneous-diffusivity and correlated-motion models. The framework is then applied to two-component tetra-PEG hydrogels with symmetric and asymmetric stoichiometric ratios. In post-gel samples, <i>α</i>mp2 > 0 while <i>α</i>sp2 ≈ 0, indicating dynamic heterogeneity on length scales larger than the single-trajectory span and within the experimental field of view, on the order of tens of microns. The two gel systems exhibit distinct dynamical signatures: in the post-gel regime, the symmetric-ratio gel shows slightly smaller <i>α</i>mp2 and little detectable cross-correlation, whereas the asymmetric-ratio gel shows slightly larger <i>α</i>mp2 and significant cross-correlation. These results demonstrate that dynamic heterogeneity and dynamic correlation are not equivalent observables in particle-tracking experiments, and that their combined analysis provides a more resolved description of gelling complex fluids.