### Abstract

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.

Original language | English (US) |
---|---|

Article number | 144906 |

Journal | Journal of Chemical Physics |

Volume | 143 |

Issue number | 14 |

DOIs | |

State | Published - Oct 14 2015 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*143*(14), [144906]. https://doi.org/10.1063/1.4932679

**Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions.** / Zhang, Rui; Schweizer, Kenneth S.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 143, no. 14, 144906. https://doi.org/10.1063/1.4932679

}

TY - JOUR

T1 - Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions

AU - Zhang, Rui

AU - Schweizer, Kenneth S.

PY - 2015/10/14

Y1 - 2015/10/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84944271153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944271153&partnerID=8YFLogxK

U2 - 10.1063/1.4932679

DO - 10.1063/1.4932679

M3 - Article

AN - SCOPUS:84944271153

VL - 143

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

M1 - 144906

ER -