Decoupling of rotational and translational diffusion in supercooled colloidal fluids

Abstract

We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion. R apidly cooling a glass-forming liquid fundamentally changes the nature of fluid transport at a molecular scale (1-7). For a tracer in a continuum fluid, the translational and rotational diffusion coefficients D T and D R , respectively, depend on temperature T and viscosity η as D ∝ T/η. Therefore, the ratio D T /D R is a constant that is independent of both T and η. However, this relationship breaks down in the deeply supercooled regime near the glass transition, according to experiments with molecular glass formers and also molecular dynamics simulations (1)(2)(3)(8)(9)(10)(11)(12)(13)(14).Experiments with glass-forming materials find that rotational diffusion remains strongly coupled with viscosity, where D R ∝ η −1 , whereas translational diffusion decouples, developing a fractional dependence on η where D T ∝ η −ξ with ξ < 1 (2, 8, 15). Near the glass transition, D T can be enhanced by two orders of magnitude over what would be calculated from the material's viscosity. The rotational diffusion coefficients from these experiments are inferred from measurements related to molecular rotations, and are evaluated using the "Debye model" due to an inability to directly observe molecular rearrangements in a material's bulk (3, 8-10, 16, 17). This experimental limitation has inspired computational studies where diffusion can be calculated using the Debye model and also a complementary method, the "Einstein formulation," which is more directly related to the trajectories of the diffusing objects. These simulations studied pure systems of water (9), ortho-terphenyl (10), and hard dumbbell particles (11). Intriguingly, the simulations found that decoupling depends qualitatively on the analysis method: They find rotational motion is enhanced over translational motion when quantified with the Einstein formulation, with the opposite being true in the Debye formulation. The results from these simulations raise the need for a critical reexamination of our current understanding of the relationship between translational and rotational diffusion, and only through direct observation can these differences be add...

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