DOI: 10.1063/1.439430. Macroscopic model for solvated ion dynamics

Macroscopic model for solvated ion dynamics

10.1063/1.439430

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A macroscopic treatment of solvated ion dynamics is developed and applied to calculate the limiting (zero concentration) conductance of cations in several aprotic solvents. The theory is based on a coupled set of electrostatic and hydrodynamic equations for the density, flow, and polarization fields induced in the polar solvent by a moving ion. These equations, which are derived by the Mori projection technique, include crucial local solvent structure (ion solvation) effects through solvent compressibility, and local constitutive parameters. If solvent structure is suppressed, the equations reduce to those derived previously by Onsager and Hubbard [J. B. Hubbard and L. Onsager, J. Chem. Phys. 67, 4850 (1977)]. The macroscopic equations are approximately decoupled into electrostatic and hydrodynamic parts. The decoupled equations are solved assuming a step density, viscosity, and dielectric constant model for the local solvent structure and dynamics. This yields analytic expressions for the viscous, ζV, and dielectric ζD, contributions to the ion friction coefficient. These expressions generalize, respectively, the Stokes and Zwanzig results for the (slip) viscous and dielectric friction so as to account for ion solvation effects. The friction coefficients involve a desolvation function Δ which depends on the local structure (density) and dynamics of the solvent. The drag coefficient results reduce in form to those of Zwanzig (within a flow gradient correction factor of 2/3) and Stokes for both weak (Δ→1) and strong (Δ→0) ion–solvent interaction. For Δ→1 the true ionic radius Ri appears in the drag formulas while for Δ→0 a renormalized solvated ion radius σ=Ri+2Rs (where Rs=solvent molecule radius) appears. The theory is fit to experimental cation conductances in pyridine, acetone, and acetonitrile by representing Δ by a two parameter switching function. Agreement between the model and experiment is satisfactory for all three solvents. Moreover dielectric friction is found to have a negligible effect on ion mobility in these solvents.

Bibliography

Chen, J.-H., & Adelman, S. A. (1980). Macroscopic model for solvated ion dynamics. The Journal of Chemical Physics, 72(4), 2819â2831.

Authors 2

J. -H. Chen (first)
S. A. Adelman (additional)

References 31 Referenced 57

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Dates

Type	When
Created	22 years, 6 months ago (Feb. 28, 2003, 3 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 3:51 p.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 8:44 a.m.)
Issued	45 years, 6 months ago (Feb. 15, 1980)
Published	45 years, 6 months ago (Feb. 15, 1980)
Published Print	45 years, 6 months ago (Feb. 15, 1980)

Funders 0

None

BibTeX

@article{Chen_1980, title={Macroscopic model for solvated ion dynamics}, volume={72}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.439430}, DOI={10.1063/1.439430}, number={4}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Chen, J. -H. and Adelman, S. A.}, year={1980}, month=feb, pages={2819–2831} }

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  "abstract": "<jats:p>A macroscopic treatment of solvated ion dynamics is developed and applied to calculate the limiting (zero concentration) conductance of cations in several aprotic solvents. The theory is based on a coupled set of electrostatic and hydrodynamic equations for the density, flow, and polarization fields induced in the polar solvent by a moving ion. These equations, which are derived by the Mori projection technique, include crucial local solvent structure (ion solvation) effects through solvent compressibility, and local constitutive parameters. If solvent structure is suppressed, the equations reduce to those derived previously by Onsager and Hubbard [J. B. Hubbard and L. Onsager, J. Chem. Phys. 67, 4850 (1977)]. The macroscopic equations are approximately decoupled into electrostatic and hydrodynamic parts. The decoupled equations are solved assuming a step density, viscosity, and dielectric constant model for the local solvent structure and dynamics. This yields analytic expressions for the viscous, \u03b6V, and dielectric \u03b6D, contributions to the ion friction coefficient. These expressions generalize, respectively, the Stokes and Zwanzig results for the (slip) viscous and dielectric friction so as to account for ion solvation effects. The friction coefficients involve a desolvation function \u0394 which depends on the local structure (density) and dynamics of the solvent. The drag coefficient results reduce in form to those of Zwanzig (within a flow gradient correction factor of 2/3) and Stokes for both weak (\u0394\u21921) and strong (\u0394\u21920) ion\u2013solvent interaction. For \u0394\u21921 the true ionic radius Ri appears in the drag formulas while for \u0394\u21920 a renormalized solvated ion radius \u03c3=Ri+2Rs (where Rs=solvent molecule radius) appears. The theory is fit to experimental cation conductances in pyridine, acetone, and acetonitrile by representing \u0394 by a two parameter switching function. Agreement between the model and experiment is satisfactory for all three solvents. Moreover dielectric friction is found to have a negligible effect on ion mobility in these solvents.</jats:p>",
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