# Charge Renormalization and Charge Oscillation in Asymmetric Primitive Model of Electrolytes

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## Abstract

Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of the system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upward by ionic correlations, while those of smaller ions remain approximately the same. For sufficiently high density, the system exhibits charge oscillations. The threshold ion density for charge oscillation is much lower than the corresponding values for symmetric electrolytes. Our results agree well with large-scale Monte Carlo simulations, and find good agreement in general, except for the case of small ion sizes (\(d = 4\,\AA \)) near the charge oscillation threshold.

## Keywords

Charge renormalization Primitive model Electrolyte Charging oscillation Debye charging## Notes

### Acknowledgements

We thank the NSFC (Grants Nos. 11174196 and 91130012) for their financial support. We also thank Wei Cai for interesting discussions.

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