Reciprocal Space Study of Brownian Yet Non-Gaussian Diffusion of Small Tracers in a Hard-Sphere Glass

Abstract

The simultaneous presence of normal (Brownian) diffusion and non-Gaussian statistics of particle displacements has been identified as a recurring motif for a broad spectrum of physical and biological systems. While not yet fully understood, it is generally accepted that a key ingredient for observing this Brownian yet non-Gaussian (BNG) diffusion is that the environment hosting the particles appears stationary and homogenous on the small length and time scales, while displaying significant fluctuations on larger distances and/or longer time scales. To date, most of the experimental studies on systems displaying BNG diffusion have been performed in direct space, usually via a combination of optical microscopy and particle tracking to quantify the particle’s self-diffusion. Here, we demonstrate that a reciprocal space analysis of the density fluctuations caused by the particle motion as a function of the wave vector enables the investigation of BNG diffusion in situations where single-particle tracking is impossible. To accomplish this aim, we use confocal differential dynamic microscopy (ConDDM) to study the BNG dynamics of diluted sub-resolution tracers diffusing in a glassy matrix of larger hard spheres. We first elucidate the nontrivial connection between the tracer self-diffusion and collective relaxation of the resulting density fluctuations. We find that the experimentally determined intermediate scattering functions are in excellent agreement with the recent predictions of a “diffusing diffusivity” model of BNG diffusion, whose analytical predictions are available only in reciprocal space. Our results show that studying BNG diffusion in reciprocal space can be an invaluable strategy to access the fast, anomalous dynamics occurring at very small scales in crowded environments.

Detecting temporal correlations in hopping dynamics in Lennard–Jones liquids

“…Recent experiments and extensive numerical simulations have pointed out that a BnG regime is clearly displayed by glass-forming systems [33][34][35], as well as by small tracers diffusing in glassy colloidal matrices [3,36]. Moreover, a similar behaviour has also been observed in experimental studies of suspension of colloidal beads under the action of a static and spatially random optical force [37,38], a system that display a single-particle motion qualitatively similar to the intermittent single-particle dynamics of glassy system.…”

Quantitative rheo-microscopy of soft matter

“…For both types of perturbation, distributions exhibits marked exponential tails. This combination of non-Gaussian statistics of the displacement and linear (Fickian) scaling of the MSD with time has been found to be a recurring feature of particles moving in heterogeneous environments [37,38]. Remarkably, for the same measured strain amplitude (same color on the plot) distributions are sensibly larger for sinusoidal stress application.…”

Protein Sizing with Differential Dynamic Microscopy

“…10 This approach, named differential dynamic microscopy (DDM), relies on a fully automated and operator-independent procedure that calculates simultaneously for different wavevectors q the temporal correlations of the spatially Fourier-transformed sample images. 11 DDM has been successfully demonstrated in a wide range of applications including the characterization of the Brownian dynamics of diluted 10,12 and concentrated 13,14 colloidal suspensions, the microrheology of complex fluids, 15−17 the active motion of swimming microorganisms 13,18,19 and crawling cells, 20 the protein absorption on functionalized nanoparticles, 21 and the diffusive behavior of large protein clusters. 22 The close formal correspondence with DLS enabled expanding the range of applicability of DDM by directly exploiting or adapting both well-established experimental geometries (like depolarized 23,24 or wide-angle scattering 25 to measure the rototranslational dynamics of anisotropic particles) and analytical tools (like cumulant expansions 22,24 to estimate polydispersity or even more refined inversion schemes, like CONTIN, 26 to access the particle size distribution).…”

“…This approach, named differential dynamic microscopy (DDM), relies on a fully automated and operator-independent procedure that calculates simultaneously for different wavevectors q the temporal correlations of the spatially Fourier-transformed sample images . DDM has been successfully demonstrated in a wide range of applications including the characterization of the Brownian dynamics of diluted , and concentrated , colloidal suspensions, the microrheology of complex fluids, – the active motion of swimming microorganisms ,, and crawling cells, the protein absorption on functionalized nanoparticles, and the diffusive behavior of large protein clusters …”