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A microscopic model of the Stokes-Einstein relation in arbitrary dimension.

Benoit Charbonneau1, Patrick Charbonneau2, Grzegorz Szamel3

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Deviations from the Stokes-Einstein relation (SER) in liquids, particularly for self-solvation, are explained by a generalized statistical mechanics model. This work revisits Masters and Madden

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Area of Science:

  • Physical Chemistry
  • Statistical Mechanics
  • Liquid State Theory

Background:

  • The Stokes-Einstein relation (SER) is a cornerstone in liquid theory, relating diffusion coefficients to viscosity.
  • Standard hydrodynamic derivations of SER fail to explain observed deviations, especially in self-solvation dynamics.
  • Masters and Madden previously explored a statistical mechanics model for SER using projection operator formalism.

Purpose of the Study:

  • To investigate the microscopic origins of deviations from the Stokes-Einstein relation.
  • To generalize the statistical mechanics model of SER to various spatial dimensions and solvent structures.
  • To explore the validity of SER in idealized fluid systems.

Main Methods:

  • Revisiting and generalizing the statistical mechanics model developed by Masters and Madden.
  • Applying the projection operator formalism to analyze liquid dynamics.
  • Extending the analysis to arbitrary spatial dimensions and partially structured solvents.
  • Investigating the exact dynamics of infinite-dimensional fluids.

Main Results:

  • Identified a potential microscopic origin for deviations from the Stokes-Einstein relation.
  • Successfully generalized the statistical mechanics model to include dimensionality and solvent structure.
  • Reproduced SER-like behavior from the exact dynamics of infinite-dimensional fluids.

Conclusions:

  • The generalized statistical mechanics model provides insights into the microscopic basis of SER deviations.
  • Dimensionality and solvent structure play crucial roles in the validity of the Stokes-Einstein relation.
  • Infinite-dimensional fluid dynamics offer a theoretical framework for understanding SER.