Correlated two-particle diffusion in dense colloidal suspensions at early times: Theory and comparison to experiment

Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations

Correlations of the displacement field in a two-dimensional model colloidal liquid are studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as 0.5. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect.

Dynamic cross-correlations between entangled biofilaments as they diffuse

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 10⁴ times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

Anisotropy and memory during cage breaking events close to a wall

The slow dynamics in a glassy hard-sphere system is dominated by cage breaking events, i.e. rearrangements where a particle escapes from the cage formed by its neighboring particles. We study such events for an overdamped colloidal system by the means of Brownian dynamics simulations. While it is difficult to relate cage breaking events to structural mean field results in bulk, we show that the microscopic dynamics of particles close to a wall can be related to the anisotropic two-particle density. In particular, we study cage-breaking trajectories, mean forces on a tracked particle, and the impact of the history of trajectories. Based on our simulation results, we further construct two different one-particle random-walk models-one without and one with memory incorporated-and find the local anisotropy and the history-dependence of particles as crucial ingredients to describe the escape from a cage. Finally, our detailed study of a rearrangement event close to a wall not only reveals the memory effect of cages, but leads to a deeper insight into the fundamental mechanisms of glassy dynamics.