Browsing by Author "Charbonneau, Benoit"

Now showing 1 - 4 of 4

Open Access
A microscopic model of the Stokes-Einstein relation in arbitrary dimension.
(The Journal of chemical physics, 2018-06) Charbonneau, Benoit; Charbonneau, Patrick; Szamel, Grzegorz
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.
Open Access
Dimensional dependence of the Stokes-Einstein relation and its violation
(Journal of Chemical Physics, 2013-10-28) Charbonneau, Benoit; Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco
We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension d u = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.
Open Access
Geometrical frustration and static correlations in hard-sphere glass formers.
(J Chem Phys, 2013-03-28) Charbonneau, Benoit; Charbonneau, Patrick; Tarjus, Gilles
We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.
Open Access
High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas.
(Physical review. E, 2021-08) Charbonneau, Benoit; Charbonneau, Patrick; Hu, Yi; Yang, Zhen
The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization transition at the void percolation threshold is not well controlled analytically nor computationally. A recent study [Biroli et al., Phys. Rev. E 103, L030104 (2021)2470-004510.1103/PhysRevE.103.L030104] of the caging behavior of the RLG motivated by the mean-field theory of glasses has uncovered physical inconsistencies in that scaling that heighten the need for guidance. Here we first extend analytical expectations for asymptotic high-d bounds on the void percolation threshold and then computationally evaluate both the threshold and its criticality in various d. In high-d systems, we observe that the standard percolation physics is complemented by a dynamical slowdown of the tracer dynamics reminiscent of mean-field caging. A simple modification of the RLG is found to bring the interplay between percolation and mean-field-like caging down to d=3.