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Nonlocal electrostatics in ionic liquids: the key to an understanding of the screening decay length and screened interactions

Journal article
Authors Roland Kjellander
Published in Journal of Chemical Physics
Volume 145
Issue 12
Pages 124503
ISSN 0021-9606
Publication year 2016
Published at Department of Chemistry and Molecular Biology
Pages 124503
Language en
Links dx.doi.org/10.1063/1.4962756
https://gup.ub.gu.se/file/200877
Keywords Liquid state theory, statistical mechanics, electrolytes, ionic liquids, screened electrostatics, ion-ion correlations, dielectric properties, intermolecular interactions
Subject categories Statistical physics, Liquid physics, Surface and colloid chemistry, Chemical physics, Solution chemistry, Electrochemistry, Statistical mechanics

Abstract

Screened electrostatic interactions in ionic liquids are investigated by means of exact statistical mechanical analysis combined with physical arguments that enhance the transparency and conceptual accessibility of the analysis and results. The constituent ions and immersed particles in the liquid can have arbitrary shapes and any internal charge distributions. The decay of the screened electrostatic potential and the free energy of interaction in ionic liquids can be exponentially damped oscillatory (like in molten simple salts) as well as plain exponential and long-ranged (like in dilute electrolyte solutions). Both behaviors are in agreement with the exact statistical mechanical analysis and reasons for their appearances are investigated. Exact but surprisingly simple expressions for the decay parameter κ of the screened electrostatics are obtained, which replace the classical expression for the Debye-Hückel parameter κDH (the reciprocal Debye length). The expressions are applicable both for cases with plain exponential and oscillatory behaviors. The key importance of nonlocal electrostatics is thereby demonstrated explicitly. Dielectric properties of ionic liquids and other electrolytes are investigated, in particular the static dielectric function ε(k) and some effective relative permittivities (Ereff and Er*), which take roles that the dielectric constant εr has for polar liquids consisting of electroneutral molecules. The dielectric constant in the latter case, which is the limit of ε(k) when the wave number k → 0, can be expressed solely in terms of dipolar features of the molecules. In contrast to this, the effective dielectric permittivities of ionic liquids have contributions also from quadrupolar, octupolar and higher multipolar features of the constituent ions. The "dielectric constant" of electrolytes does not exist since ε(k) → ∞ when k → 0, a well-known effect of perfect screening. The effective relative permittivities Ereff and Er* of ionic liquids are obtained from the non-diverging part of ε(k), but not as a k → 0 limit. Influences of ion associations, especially pairing, are investigated for screened electrostatics and these permittivities. A general, multipolar expansion of ε(k) is derived and used to analyze dielectric properties of ionic liquids and other electrolytes.

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