Correlations from Ion Pairing and the Nernst-Einstein Equation

We present a new approximation to ionic conductivity well suited to dynamical atomic-scale simulations, based on the Nernst-Einstein equation. In our approximation, ionic aggregates constitute the elementary charge carriers, and are considered as noninteracting species. This approach conveniently captures the dominant effect of ion-ion correlations on conductivity, short range interactions in the form of clustering. In addition to providing better estimates to the conductivity at a lower computational cost than exact approaches, this new method allows us to understand the physical mechanisms driving ion conduction in concentrated electrolytes. As an example, we consider ${\mathrm{Li}}^{+}$ conduction in poly(ethylene oxide), a standard solid-state polymer electrolyte. Using our newly developed approach, we are able to reproduce recent experimental results reporting negative cation transference numbers at high salt concentrations, and to confirm that this effect can be caused by a large population of negatively charged clusters involving cations.

Figure 1

Schematic presenting fundamental differences between the exact (Einstein) approach, the cluster Nernst-Einstein, and the standard Nernst-Einstein equation. Dashed lines represent the interactions taken into account—black lines are short-range intracluster interactions. Green arrows correspond to the quantities sampled during an actual dynamical simulation.

Figure 2

Noninteracting toy model. (a) Cluster population, (b) ionic conductivity over lag time obtained using the three different approaches. Conductivities are normalized using the average converged Einstein conductivity.

Figure 3

PEO results. (a) Cluster population statistics, and (b) ionic conductivity over lag time obtained through the Einstein, Nernst-Einstein, and ${\mathrm{cNE}}_0$ approaches. The cNE conductivity is also shown.