(195f) Frequency Dependence of Ionic Conductivity in Concentrated Electrolytes

The transport of ions in a confined environment underlies a number of important technologies that utilize separations, electrochemistry, and energy storage and delivery. [1, 2] The motion of ions in an electrolyte solution is described by the specific conductivity. The conductivity quantifies to what extent the collective net motion of ions responds to the presence of an electric field. At low concentrations and/or low ionic strengths, the motion of a central ion can be assumed to be uncorrelated with its neighboring species. In this regime, the conductivity is well explained by the classical transport theories by Debye, Hükel and Onsager.[3] However, at high concentrations and/or high ionic strengths, the screening length acquires values in the order of the ion’s diameter, and the inter-ionic correlations become significant, noticeably increasing the complexity of the physical problem. While the ideality assumptions initially introduced by Debye and Hükel can be extended to concentrated electrolytes by introducing molecular scale correlations between the ions, and paired ions can be treated as paired species, a fully molecular theory which is valid in this regime has yet to be developed. [4, 5]

Alternating fields are commonly used in experiments to measure electrical conductivity and relaxation phenomena in electrolytes and electrolyte interfaces.[1] The motion of ions due to a time-varying field is usually described by the frequency-dependent conductivity. Studies of the frequency-dependent conductivity were performed by Debye and Falkenhagen.[6, 7] In their studies, the authors took into account the effect of the dynamic relaxation of the atmosphere on the motion of the ion. When ions move in an electrolyte solution, the atmosphere is unable to instantaneously move with a central ion and it becomes asymmetric, leading to an increase in the electrolyte friction and, in consequence, a decrease in the conductivity. This asymmetry is reduced in the presence of an alternating field, allowing for increased conductivity at low frequencies. At high frequencies, ions oscillate so quickly that their motion in the direction of the field is less than that seen in the presence of a static field.

Here we use Brownian Dynamics coupled with Poisson’s equation to investigate the response of ions to a time-dependent electric field. The analysis is performed over a large range of ionic concentrations, extending from the very dilute regime up to the regime where cross-correlations and important packing effects arise. The simulation takes advantage of an optimally windowed chirp previously used for rheological measurements, [8] in which an exponentially varying frequency sweep windowed by a cosine tampering function is applied.[9] The response of the electrolyte is then analyzed in Fourier space. We show that this novel approach enables the computation of the full frequency spectrum of the conductivity, and we demonstrate that at high concentrations far from the dilute regime, the frequency-dependent conductivity cannot be explained by simple single-mode models.

References

[1] W. B. Russel, D. A. Saville and W. R. Schowalte, Colloidal dispersions, Cambridge Monographs on Mechanics.

[2] J. N. Israelachvili, Intermolecular and surface forces, 2nd ed. (Academic Press London; San Diego, 1991).

[3] M. Cetin, "Electrolytic conductivity, debye-huckel theory, and the onsager limiting law", Phys. Rev. E 55, 2814-2817 (1997).

[4] A. Chandra, D. Wei, and G. N. Patey, "The frequency dependent conductivity of electrolyte solutions", The Journal of Chemical Physics 99, 2083-2094 (1993).

[5] A. Chandra and B. Bagchi, "Frequency dependence of ionic conductivity of electrolyte solutions", The Journal of Chemical Physics 112, 1876-1886 (2000).

[6] P. Debye and H. Falkenhagen, Physikalische Zeitschrift 121, 401 (1928).

[7] K. Ibuki and M. Nakahara, "Effect of relaxation of ionic atmosphere on the short-time dynamics of diffusion-controlled reaction", The Journal of Chemical Physics 92, 7323-7329 (1990).

[8] M. Bouzid, B. Keshavarz, M. Geri, T. Divoux, E. Del Gado, and G. H. McKinley, "Computing the linear viscoelastic properties of soft gels using an optimally windowed chirp protocol", Journal of Rheology 62, 1037-1050 (2018).

[9] M. Geri, B. Keshavarz, T. Divoux, C. Clasen, D. J. Curtis, and G. H. McKinley, "Time resolved mechanical spectroscopy of soft materials via optimally windowed chirps", Phys. Rev. X 8, 041042 (2018).