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Dimensional dependence of the Stokes-Einstein relation and its violation
Benoit Charbonneau1, Patrick Charbonneau, Yuliang Jin
1Mathematics Department, St. Jerome's University in the University of Waterloo, Waterloo, Ontario N2L 3G3, Canada.
The Journal of Chemical Physics
|November 5, 2013
Summary
This study generalizes the Stokes-Einstein relation (SER) to higher dimensions, finding that SER violations in hard sphere glass formers disappear above 8 dimensions. The critical exponent
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Materials science
Background:
- The Stokes-Einstein relation (SER) connects diffusion and viscosity.
- Understanding SER violations is crucial for glass transition theories.
- Previous studies focused on lower dimensions.
Purpose of the Study:
- Generalize the Stokes-Einstein relation (SER) and diffusivity corrections to higher spatial dimensions.
- Investigate the dimensional dependence of high-density SER violations in hard sphere systems.
- Benchmark theoretical predictions against numerical simulations.
Main Methods:
- Generalization of theoretical relations to arbitrary spatial dimensions.
- Numerical simulations of hard sphere systems.
- Analysis of the critical exponent of SER violation.
Main Results:
- The Stokes-Einstein relation (SER) and its corrections were generalized to higher dimensions.
- A dimension-dependent SER violation was observed in hard sphere glass formers.
- The SER violation disappears above dimension d=8.
- The critical exponent's linear dependence on (8-d) was observed, but with an inconsistent coefficient.
Conclusions:
- The dimensional dependence of SER violation provides a new benchmark for theoretical models.
- The disappearance of SER violation above 8 dimensions is a significant finding.
- Discrepancies in the critical exponent suggest limitations in current theoretical frameworks.
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