We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a “slaved” or “constraint release” fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values.
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21 May 2017
Research Article|
May 18 2017
Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions
Rui Zhang
;
Rui Zhang
a)
1Department of Materials Science,
University of Illinois
, Urbana, Illinois 61801, USA
2Frederick Seitz Materials Research Laboratory,
University of Illinois
, Urbana, Illinois 61801, USA
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Kenneth S. Schweizer
Kenneth S. Schweizer
a)
1Department of Materials Science,
University of Illinois
, Urbana, Illinois 61801, USA
2Frederick Seitz Materials Research Laboratory,
University of Illinois
, Urbana, Illinois 61801, USA
3Department of Chemistry,
University of Illinois
, Urbana, Illinois 61801, USA
4Department of Chemical and Biomolecular Engineering,
University of Illinois
, Urbana, Illinois 61801, USA
Search for other works by this author on:
a)
Electronic addresses: [email protected] and [email protected]
J. Chem. Phys. 146, 194906 (2017)
Article history
Received:
February 22 2017
Accepted:
April 26 2017
Citation
Rui Zhang, Kenneth S. Schweizer; Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions. J. Chem. Phys. 21 May 2017; 146 (19): 194906. https://doi.org/10.1063/1.4983224
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