We heuristically formulate a microscopic, force level, self-consistent nonlinear Langevin equation theory for activated barrier hopping and non-hydrodynamic diffusion of a hard sphere penetrant in very dense hard sphere fluid matrices. Penetrant dynamics is controlled by a rich competition between force relaxation due to penetrant self-motion and collective matrix structural (alpha) relaxation. In the absence of penetrant-matrix attraction, three activated dynamical regimes are predicted as a function of penetrant-matrix size ratio which are physically distinguished by penetrant jump distance and the nature of matrix motion required to facilitate its hopping. The penetrant diffusion constant decreases the fastest with size ratio for relatively small penetrants where the matrix effectively acts as a vibrating amorphous solid. Increasing penetrant-matrix attraction strength reduces penetrant diffusivity due to physical bonding. For size ratios approaching unity, a distinct dynamical regime emerges associated with strong slaving of penetrant hopping to matrix structural relaxation. A crossover regime at intermediate penetrant-matrix size ratio connects the two limiting behaviors for hard penetrants, but essentially disappears if there are strong attractions with the matrix. Activated penetrant diffusivity decreases strongly with matrix volume fraction in a manner that intensifies as the size ratio increases. We propose and implement a quasi-universal approach for activated diffusion of a rigid atomic/molecular penetrant in a supercooled liquid based on a mapping between the hard sphere system and thermal liquids. Calculations for specific systems agree reasonably well with experiments over a wide range of temperature, covering more than 10 orders of magnitude of variation of the penetrant diffusion constant.
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14 October 2015
Research Article|
October 13 2015
Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions
Rui Zhang
;
Rui Zhang
Department of Materials Science and Frederick Seitz Materials Research Laboratory,
University of Illinois
, 1304 West Green Street, Urbana, Illinois 61801, USA
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Kenneth S. Schweizer
Kenneth S. Schweizer
a)
Department of Materials Science and Frederick Seitz Materials Research Laboratory,
University of Illinois
, 1304 West Green Street, Urbana, Illinois 61801, USA
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J. Chem. Phys. 143, 144906 (2015)
Article history
Received:
July 28 2015
Accepted:
September 24 2015
Citation
Rui Zhang, Kenneth S. Schweizer; Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions. J. Chem. Phys. 14 October 2015; 143 (14): 144906. https://doi.org/10.1063/1.4932679
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