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

Abstract

The spatially resolved diffusive dynamic cross correlations of a pair of colloids in dense quasi-two-dimensional monolayers of identical particles are studied experimentally and theoretically at early times where motion is Fickian. In very dense systems where strong oscillatory equilibrium packing correlations are present, we find an exponential decay of the dynamic cross correlations on small and intermediate length scales. At large separations where structure becomes random, an apparent power law decay with an exponent of approximately −2.2 is observed. For a moderately dense suspension where local structural correlations are essentially absent, this same apparent power law decay is observed over all probed interparticle separations. A microscopic nonhydrodynamic theory is constructed for the dynamic cross correlations which is based on interparticle frictional effects and effective structural forces. Hydrodynamics enters only via setting the very short-time single-particle self-diffusion constant. No-adjustable-parameter quantitative predictions of the theory for the dynamic cross correlations are in good agreement with experiment over all length scales. The origin of the long-range apparent power law is the influence of the constraint of fixed interparticle separation on the amplitude of the mean square force exerted on the two tagged particles by the surrounding fluid. The theory is extended to study high-packing-fraction 3D hard sphere fluids. The same pattern of an oscillatory exponential form of the dynamic cross correlation function is predicted in the structural regime, but the long-range tail decays faster than in monolayers with an exponent of −3.

Dynamic cross-correlations between entangled biofilaments as they diffuse

“…When one considers that the dynamical structure is expected to depend weakly on concentration (because for the concentration studied ξ m =d T ∝ c -1=10 theoretically) (36,37), it is pleasing to confirm that D rr is insensitive to concentration over the range that we studied. When particles interact via conservative central forces, it is natural to expect radial correlations (D rr ) to dominate over transverse (D tt ) correlations for a nonhydrodynamic mechanism (35). Testing this proposition, our experiments indeed find that D tt << D rr on intermediate length scales less than the filament length (Fig.…”

“…predictions compare favorably to experiments with colloids (35). Here, we qualitatively extend this approach to the more complex case of entangled biopolymers and compare its predictions to our experiments to quantify nonhydrodynamic, noncontinuum crosscorrelations in long-range pair diffusion and test the proposed mechanism.…”

“…Effective incompressibility implies the emergence of a strong interpolymer spatial correlation known as the de Gennes "correlation hole" (2, 3) and an effective long-range repulsion that can induce space-time dynamic displacement correlations. We formulate this physical picture using quantitative statistical mechanics by combining the reptation-tube ideas of single polymer motion (4-6) with force-level generalized Brownian motion ideas for predicting intermolecular dynamical correlations (35,(41)(42)(43)(44)(45)(46). Here we sketch the essential elements of the model and theory and present technical details in Supporting Information.…”

Structure and Capacitance of Electrical Double Layers at the Graphene–Ionic Liquid Interface

“…What is more, Figure 6 indicates the ion-ion pair correlation functions [38] or radial distribution functions (RDF) for the [EMIM] + /[BF 4 ] − ions near the non-rough neutral electrode surface, so as to further understand the alternate stacked layers of cations and anions in the EDL, where g(r) is the probability of finding one kind of ion at a distance r from the reference ion with respect to that in the bulk phase, and where r is the distance between a pair of ions. …”

“…In addition, the rough electrode induces a wider scope of oscillations in the ion concentration profiles, implying that the ion layers can be extended deeper into the bulk electrolyte solution by the larger interaction from the rough electrode. What is more, Figure 6 indicates the ion-ion pair correlation functions [38] or radial distribution functions (RDF) for the [EMIM] + /[BF4] − ions near the non-rough neutral electrode surface, so as to further understand the alternate stacked layers of cations and anions in the EDL, where g(r) is the probability of finding one kind of ion at a distance r from the reference ion with respect to that in the bulk phase, and where r is the distance between a pair of ions. Additionally, it is worth noting from Figures 4 and 5 that even on the neutral electrode surface (σ = 0 e/atom) there also exists an obvious first layer of ions in the EDL, which is able to produce the potential on the uncharged electrode surface (as discussed in the following Section 3.2).…”