A Microscopic Model of the Stokes-Einstein Relation in Arbitrary Dimension

Abstract

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.

20 pages

References in corpus (4)

• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Glass transition of hard spheres in high dimensions
• Dimensional study of the dynamical arrest in a random Lorentz gas

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• Generalized Mode-Coupling Theory for Mixtures of Brownian Particles
• Unveiling the anatomy of mode-coupling theory
• Tagged-particle motion of Percus-Yevick hard spheres from first principles