Generalizations of the Fuoss Approximation for Ion Pairing

TL;DR

This paper extends the Fuoss approximation for ion pairing probability distributions, incorporating measurable correlations and non-ionic effects, and validates these models against simulations for various electrolyte solutions.

Contribution

It introduces generalized models of the Fuoss approximation that include non-ionic interactions and solvation effects, improving accuracy for complex electrolyte solutions.

Findings

Simple generalization accurate for low concentration electrolyte solutions.

Atomically detailed models reveal solvent-separated ion pairs.

Augmented maximum entropy method improves predictions for ionic liquids.

Abstract

An elementary statistical observation identifies generalizations of the Fuoss approximation for the probability distribution function that describes ion clustering in electrolyte solutions. The simplest generalization, equivalent to a Poisson distribution model for inner-shell occupancy, exploits measurable inter-ionic correlation functions, and is correct at the closest pair distances whether primitive electrolyte solutions models or molecularly detailed models are considered, and for low electrolyte concentrations in all cases. With detailed models these generalizations includes non-ionic interactions and solvation effects. These generalizations are relevant for computational analysis of bi-molecular reactive processes in solution. Comparisons with direct numerical simulation results show that the simplest generalization is accurate for a slightly supersaturated solution of tetraethylammonium tetrafluoroborate in propylene carbonate ([tea][BF$_4$]/PC), and also for a primitive model associated with the [tea][BF$_4$]/PC results. For [tea][BF$_4$]/PC, the atomically detailed results identify solvent-separated nearest-neighbor ion-pairs. This generalization is examined also for the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF$_4$]) where the simplest implementation is less accurate. In this more challenging situation an augmented maximum entropy procedure is satisfactory, and explains the more varied near-neighbor distributions observed in that case.