Ionic Transport in Non-Aqueous Electrolyte Solutions - (ii) Monte-Carlo Simulation Based on Lattice Gas Model
Authors: Kiyobayashi Tetsu , Ozaki Hiroyuki , Uchida Satoshi , Sano Hikaru 
Published: December 2020

Transport phenomena in electrolyte solutions have a century-long history of research. Yet its mechanism is still somewhat unclear at the salt concentration C of ca. 1 mol L−1 or higher, at which many electrochemical devices function, such as Li-ion battery. Behind the difficulty in understanding the phenomena lies a fact that at high concentrations the ionic transport is significantly dominated by the inter-ionic interactions that are trivial in a dilute solution. Taking the specific conductivity σ as an example, it marks a maximum σmax at a certain salt concentration C
∗, at which the positive contribution from the increase in the charge carrier with the increase in C is counter-balanced by the correlation between ions dragging or repulsing each other. Another trade-off situation is that, while one may expect that a higher valence of the charge carrier (e.g., Li+ → Mg2+) would be beneficial in increasing the conductivity, its stronger interaction would at the same time dampen the ionic movement.
We have put forward a simple (and hence abstract) lattice gas model to explain the ionic conductivity and viscosity of the electrolyte solution at high concentrations.[1,2] This model successfully describes the maximum in σmax and the steep increase in the viscosity with concentration in terms of the strong repulsion between ions with identical sign. It also explains how the dielectic constant of the solvent plays the role in determining these transport properties.
Based on the experimental data for the divalent systems added anew— the preceding presentation by Sano et al., the present paper deals with our model to discuss how σmax is scaled by the valence of the charge carrier z
± and ε. We found that, if other conditions are identical, σ is proportional to the “harmonic mean valence” z
h of the salt, where 1/z
h ≡ (1/z
++1/|z
−|)/2, while at the same time σ and C
∗ are scaled by the factor exp(−az
+|z
−|u/ε) where a is a constant and u is a parameter that represents the strength of the Coulombic interaction between two single charges. As a result, the fact that despite the higher valence of MgA2 (z
h = 4/3) than LiA or NaA (z
h = 1), σ
max of the divalent system is smaller than the monovalent counterparts
(σmax(MgA2) < σmax(LiA) or σmax(NaA)) is explained by the greater argument in the exponentially decaying function (i.e., z
+|z
−| = 2 for MgA2 while z
+|z
−| = 1 for LiA or NaA), which significantly attenuates the conductivity. The relation to the viscosity will also be addressed on site.

References

[1] H. Ozaki, K. Kuratani and T. Kiyobayashi, J. Electrochem. Soc., 163(7), H576-H583 (2016).
[2] H. Ozaki, K. Kuratani, H. Sano and T. Kiyobayashi, J. Chem. Phys.,147, 034904 (2017).

Figure Caption

Simulated specific conductivity σ vs. the number density of ions C. z
h: harmonic mean valence (1/z
h = (1/z
++1/|z
−|)/2), Bσ
: constant defined in the theory (the explanation omitted in this abstract), u: strength of the Coulombic interaction between two single charges, εh: relative dielectric constant of the solvent, k: Boltzmann’s constant and T: absolute temperature.

Figure 1