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Nonlocal dielectric response of aqueous electrolytes and decay behavior of ionic correlations

Ming Chen1, Guang Feng2, Roland Kjellander3,*, and Alexei A. Kornyshev1,†

  • *Contact author: roland.kjellander@gu.se
  • †Contact author: a.kornyshev@imperial.ac.uk
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Phys. Rev. E 112, 065407 – Published 2 December, 2025

DOI: https://doi.org/10.1103/5qgc-rfvv

Abstract

We present molecular dynamics simulation results for the static nonlocal dielectric function, ɛ(k), and ion-ion correlations in aqueous electrolytes across various concentrations, analyzed within the framework of statistical mechanical theory. We investigate the complicated behavior of ɛ(k) and its influence on the screening patterns of ionic electric fields. At large to moderate values of the wave number k, ɛ(k) is primarily governed by the molecular structure of water, even at concentrations up to 1 M. However, at higher concentrations, ionic structuring begins to diminish water's influence. In agreement with the theoretical analysis presented, both Debye-type plain exponential and exponentially decaying oscillatory contributions to the electrostatic interactions are obtained for low electrolyte concentrations of NaCl in water. The latter originate from the water structure, while the former can be quantitatively described up to at least 2 M solutions by using a Debye length calculated with a concentration-dependent “dielectric constant” obtained by simulations. The theoretical basis for the use of such a “constant” is examined. At higher concentrations, there are only oscillatory contributions to the interactions. In our simulations, we do not have long-range monotonic interactions of the type reported in surface force measurements at concentrations above 1 M NaCl in water, often referred to as “anomalous underscreening.” Instead, we find a Debye-type decay, modified by an electrolyte-concentration-dependent effective dielectric constant. This behavior is seen up to at least 2 M concentrations, with decay lengths significantly shorter than those associated with underscreening.

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References (104)

  1. H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, 3rd ed. (Reinhold Publishing Corporation, New York, NY, 1958).
  2. J. Newman and N. P. Balsara, Electrochemical Systems (John Wiley & Sons, New York, NY, 2021).
  3. M. Shamsuddin and H. Y. Sohn, Role of electrochemical processes in the extraction of metals and alloys–a review, Min. Process. Extract. Metal. 132, 193 (2023).
  4. S. Porada, L. Weinstein, R. Dash, A. van der Wal, M. Bryjak, Y. Gogotsi, and P. M. Biesheuvel, Water desalination using capacitive deionization with microporous carbon electrodes, ACS Appl. Mater. Interfaces 4, 1194 (2012).
  5. B. Alberts, R. Heald, A. Johnson, D. Morgan, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (WW Norton & Company, New York, NY, 2022).
  6. D. A. McQuarrie, Statistical Mechanics (University Science Books, Melville, NY, 2000).
  7. H. L. Friedman, A Course in Statistical Mechanics (Prentice-Hall, Saddle River, NJ, 1985).
  8. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).
  9. Y. Yamada and A. Yamada, Review—Superconcentrated electrolytes for lithium batteries, J. Electrochem. Soc. 162, A2406 (2015).
  10. M. Amiri and D. Bélanger, Physicochemical and electrochemical properties of water-in-salt electrolytes, ChemSusChem 14, 2487 (2021).
  11. K. Qian, R. E. Winans, and T. Li, Insights into the nanostructure, solvation, and dynamics of liquid electrolytes through small-angle x-ray scattering, Adv. Energy Mater. 11, 2002821 (2021).
  12. B. Huang, L. Yun, Y. Yang, R. Han, K. Chen, Z. Wang, Y. Wang, H. Chen, Y. Du, Y. Hao, P. Lv, P. Ji, Y. Tan, L. Zheng, L. Liu, R. Li, and J. Yang, Structural study of aqueous electrolyte solution by MeV liquid electron scattering, J. Phys. Chem. B 128, 9197 (2024).
  13. T. S. Groves, C. S. Perez-Martinez, R. Lhermerout, and S. Perkin, Surface forces and structure in a water-in-salt electrolyte, J. Phys. Chem. Lett. 12, 1702 (2021).
  14. A. M. Smith, A. A. Lee, and S. Perkin, The electrostatic screening length in concentrated electrolytes increases with concentration, J. Phys. Chem. Lett. 7, 2157 (2016).
  15. A. A. Lee, C. S. Perez-Martinez, A. M. Smith, and S. Perkin, Scaling analysis of the screening length in concentrated electrolytes, Phys. Rev. Lett. 119, 026002 (2017).
  16. A. M. Smith, A. A. Lee, and S. Perkin, Switching the structural force in ionic liquid-solvent mixtures by varying composition, Phys. Rev. Lett. 118, 096002 (2017).
  17. Y. K. C. Fung and S. Perkin, Structure and anomalous underscreening in ethylammonium nitrate solutions confined between two mica surfaces, Faraday Discuss. 246, 370 (2023).
  18. P. Cats, R. Evans, A. Härtel, and R. van Roij, Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations, J. Chem. Phys. 154, 124504 (2021).
  19. T. Xiao and X. Song, A molecular Debye-Huckel theory and its applications to electrolyte solutions, J. Chem. Phys. 135, 104104 (2011).
  20. G. Monet, F. Bresme, A. Kornyshev, and H. Berthoumieux, Nonlocal dielectric response of water in nanoconfinement, Phys. Rev. Lett. 126, 216001 (2021).
  21. Y. Avni, R. M. Adar, and D. Andelman, Charge oscillations in ionic liquids: A microscopic cluster model, Phys. Rev. E 101, 010601 (2020).
  22. R. Kjellander, Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions (CRC Press, Boca Raton, FL, 2020), Chaps. 6-8, Vol. I.
  23. R. Kjellander, Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions (CRC Press, Boca Raton, FL, 2025), Chaps. 12–14, Vol. II.
  24. T. A. Pham, Ab initio simulations of liquid electrolytes for energy conversion and storage, Int. J. Quantum Chem. 119, e25795 (2019).
  25. I. Nezbeda, M. Filip, and W. R. Smith, Recent progress in molecular simulation of aqueous electrolytes: Force fields, chemical potentials and solubility, Mol. Phys. 114, 1665 (2016).
  26. Y. Shao, H. Gudla, J. Mindemark, D. Brandell, and C. Zhang, Ion transport in polymer electrolytes: Building new bridges between experiment and molecular simulation, Acc. Chem. Res. 57, 1123 (2024).
  27. J. P. Heindel, K. M. Herman, and S. S. Xantheas, Many-body effects in aqueous systems: Synergies between interaction analysis techniques and force field development, Annu. Rev. Phys. Chem. 74, 337 (2023).
  28. S. W. Coles, C. Park, R. Nikam, M. Kanduč, J. Dzubiella, and B. Rotenberg, Correlation length in concentrated electrolytes: Insights from all-atom molecular dynamics simulations, J. Phys. Chem. B 124, 1778 (2020).
  29. J. Zeman, S. Kondrat, and C. Holm, Ionic screening in bulk and under confinement, J. Chem. Phys. 155, 204501 (2021).
  30. J. G. Hedley, H. Berthoumieux, and A. A. Kornyshev, The dramatic effect of water structure on hydration forces and the electrical double layer, J. Phys. Chem. C 127, 8429 (2023).
  31. A. A. Kornyshev, Nonlocal screening of ions in a structurized polar liquid—New aspects of solvent description in electrolyte theory, Electrochim. Acta 26, 1 (1981).
  32. R. J. F. Leote de Carvalho and R. Evans, The decay of correlations in ionic fluids, Mol. Phys. 83, 619 (1994).
  33. R. Kjellander and D. J. Mitchell, Dressed ion theory for electric double layer structure and interactions: An exact analysis, Mol. Phys. 91, 173 (1997).
  34. R. Kjellander and D. J. Mitchell, An exact but linear and Poisson—Boltzmann-like theory for electrolytes and colloid dispersions in the primitive model, Chem. Phys. Lett. 200, 76 (1992).
  35. G. R. Elliott, K. P. Gregory, H. Robertson, V. S. J. Craig, G. B. Webber, E. J. Wanless, and A. J. Page, The known-unknowns of anomalous underscreening in concentrated electrolytes, Chem. Phys. Lett. 843, 141190 (2024).
  36. A. Härtel, M. Bültmann, and F. Coupette, Anomalous underscreening in the restricted primitive model, Phys. Rev. Lett. 130, 108202 (2023).
  37. The term “regular underscreening” has sometimes been used for the oscillatory ion-ion correlations beyond the Kirkwood crossover point, which has a decay length greater than the Debye length. This terminology will not be used here because the concept of “underscreening” is reserved for a large decay length of a monotonic long-range tail.
  38. J. Zeman, S. Kondrat, and C. Holm, Bulk ionic screening lengths from extremely large-scale molecular dynamics simulations, Chem. Commun. (Camb.) 56, 15635 (2020).
  39. I. Skarmoutsos and S. Mossa, Length scales in electrolytes, J. Chem. Phys. 163, 054502 (2025).
  40. K. Komori and T. Terao, Cluster-size distribution of ions in concentrated aqueous NaCl solutions: Molecular dynamics simulations, Chem. Phys. Lett. 825, 140627 (2023).
  41. A. K. Giri and E. Spohr, Cluster formation of NaCl in bulk solutions: Arithmetic vs. geometric combination rules, J. Mol. Liq. 228, 63 (2017).
  42. S. Weerasinghe and P. E. Smith, A Kirkwood–Buff derived force field for sodium chloride in water, J. Chem. Phys. 119, 11342 (2003).
  43. A. A. Kornyshev and G. Sutmann, Nonlocal dielectric saturation in liquid water, Phys. Rev. Lett. 79, 3435 (1997).
  44. M. V. Fedorov and A. A. Kornyshev, Unravelling the solvent response to neutral and charged solutes, Mol. Phys. 105, 1 (2007).
  45. H. Berthoumieux and F. Paillusson, Dielectric response in the vicinity of an ion: A nonlocal and nonlinear model of the dielectric properties of water, J. Chem. Phys. 150, 094507 (2019).
  46. R. Kjellander and D. J. Mitchell, Dressed-ion theory for electrolyte solutions: A Debye–Hückel-like reformulation of the exact theory for the primitive model, J. Chem. Phys. 101, 603 (1994).
  47. R. Ramirez and R. Kjellander, Dressed molecule theory for liquids and solutions: An exact charge renormalization formalism for molecules with arbitrary charge distributions, J. Chem. Phys. 119, 11380 (2003).
  48. R. Ramirez and R. Kjellander, Effective multipoles and Yukawa electrostatics in dressed molecule theory, J. Chem. Phys. 125, 144110 (2006).
  49. R. Kjellander, Nonlocal electrostatics in ionic liquids: The key to an understanding of the screening decay length and screened interactions, J. Chem. Phys. 145, 124503 (2016).
  50. R. Kjellander, Focus article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges, J. Chem. Phys. 148, 193701 (2018).
  51. R. Kjellander, The intimate relationship between the dielectric response and the decay of intermolecular correlations and surface forces in electrolytes, Soft Matter 15, 5866 (2019).
  52. P. A. Bopp, A. A. Kornyshev, and G. Sutmann, Static nonlocal dielectric function of liquid water, Phys. Rev. Lett. 76, 1280 (1996).
  53. L. D. Landau and E. M. Lífshíts, Electrodynamics of Continuous Media (Pergamon Press, Oxford, UK, 1884), Vol. 2.
  54. A. A. Kornyshev, Nonlocal electrostatics of solvation, in The Chemical Physics of Solvation, edited by R. R. Dogonadze, E. Kalman, A. A. Kornyshev, and J. Ulstrup (Elsevier, Amsterdam, 1985), Part A, pp. 77–118.
  55. M. A. Vorotyntsev and A. A. Kornyshev, Electrostatics of a Medium with the Spatial Dispersion (Nauka, Moscow, 1993).
  56. A. A. Kornyshev and M. A. Vorotyntsev, Nonlocal electrostatic approach to the double layer and adsorption at the electrode-electrolyte interface, Surf. Sci. 101, 23 (1980).
  57. M. Vorotyntsev and A. Kornyshev, Physical significance of an effective dielectric constant that depends on the distance from the electrode, Soviet Electrochem. 15, 560 (1979).
  58. A. A. Kornyshev, On the non-local electrostatic theory of hydration force, J. Electroanal. Chem. Interfacial Electrochem. 204, 79 (1986).
  59. M. Vorotyntsev, V. Y. Izotov, and A. Kornyshev, Differential capacitance of the electric double layer in dilute solutions of surface-inactive electrolytes and upon the specific adsorption of ions: Nonlocal and nonlinear effects, Sov. Electrochem. 19, 364 (1983).
  60. O. V. Dolgov, D. A. Kirzhnits, and E. G. Maksimov, On an admissible sign of the static dielectric function of matter, Rev. Mod. Phys. 53, 81 (1981).
  61. H. Ehrenreich and M. H. Cohen, Self-consistent field approach to the many-electron problem, Phys. Rev. 115, 786 (1959).
  62. J. Lindhard, On the properties of a gas of charged particles, Dan. Mat. Fys. Medd. 28(8) (1954).
  63. R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Courier Corporation, North Chelmsford, MA, 2002).
  64. J. Barthel, H. Krienke, and W. Kunz, Physical Chemistry of Electrolyte Solutions: Modern Aspects (Springer Science & Business Media, Cham, 1998), Vol. 5.
  65. M. A. Vorotyntsev and A. A. Kornyshev, Electrostatic interaction at the metal/dielectric interface, Soviet Physics—JETP 51, 509 (1980).
  66. A. M. Gabovich, M. S. Li, H. Szymczak, and A. I. Voitenko, Charge-charge interaction in three-layer systems: Classical approach, Phys. Rev. B 105, 115415 (2022).
  67. N. Kavokine, P. Robin, and L. Bocquet, Interaction confinement and electronic screening in two-dimensional nanofluidic channels, J. Chem. Phys. 157, 114703 (2022).
  68. M. Vatin, A. Porro, N. Sator, J. F. Dufrêche, and H. Berthoumieux, Electrostatic interactions in water: A nonlocal electrostatic approach, Mol. Phys. 119, e1825849 (2020).
  69. E. Haimov, J. G. Hedley, and A. A. Kornyshev, Nonlocal structural effects of water on DNA homology recognition, J. Phys. Condens. Matter 36, 40LT01 (2024).
  70. J. G. Hedley, E. Haimov, and A. A. Kornyshev, Water structural effects on DNA–DNA interactions and homologous recognition, Physica A 647, 129894 (2024).
  71. J. G. Hedley, K. Coshic, A. Aksimentiev, and A. A. Kornyshev, Electric field of DNA in solution: Who is in charge? Phys. Rev. X 14, 031042 (2024).
  72. E. H. Hwang and S. Das Sarma, Dielectric function, screening, and plasmons in two-dimensional graphene, Phys. Rev. B 75, 205418 (2007).
  73. P. A. Bopp, A. A. Kornyshev, and G. Sutmann, Frequency and wave-vector dependent dielectric function of water: Collective modes and relaxation spectra, J. Chem. Phys. 109, 1939 (1998).
  74. A. K. Soper and M. G. Phillips, A new determination of the structure of water at 25 °C, Chem. Phys. 107, 47 (1986).
  75. A. K. Soper and J. Turner, Impact of neutron scattering on the study of water and aqueous solutions, Int. J. Mod. Phys. B 07, 3049 (1993).
  76. J. L. Finney and A. K. Soper, Solvent structure and perturbations in solutions of chemical and biological importance, Chem. Soc. Rev. 23, 1 (1994).
  77. M. P. Tosi, Screening in dense ionic fluids, in Condensed Matter Physics Aspects of Electrochemistry, edited by M. P. Tosi and A. A. Kornyshev (World Scientific, Singapore, 1991), pp. 68–78.
  78. M. R. Becker, R. R. Netz, P. Loche, D. J. Bonthuis, D. Mouhanna, and H. Berthoumieux, Dielectric properties of aqueous electrolytes at the nanoscale, Phys. Rev. Lett. 134, 158001 (2025).
  79. F. O. Raineri, H. Resat, and H. L. Friedman, Static longitudinal dielectric function of model molecular fluids, J. Chem. Phys. 96, 3068 (1992).
  80. A. A. Kornyshev, Non-local dielectric response of a polar solvent and Debye screening in ionic solution, J. Chem. Soc. Faraday Trans. 2 79, 651 (1983).
  81. F. Cornu, Exact algebraic tails of static correlations in quantum plasmas at low density, Phys. Rev. Lett. 78, 1464 (1997).
  82. D. Brydges and P. A. Martin, Survey of exact results in low density Coulomb systems, J. Phys. IV France 10, Pr5-53 (2000).
  83. R. Kjellander and B. Forsberg, Ionic fluids with r−6 pair interactions have power-law electrostatic screening, J. Phys. A Math. Gen. 38, 5405 (2005).
  84. R. Kjellander, Electrostatic screening in classical Coulomb fluids: Exponential or power-law decay or both? An investigation into the effect of dispersion interactions, J. Phys. A Math. Gen. 39, 4631 (2006).
  85. R. Kjellander and R. Ramirez, Yukawa multipole electrostatics and nontrivial coupling between electrostatic and dispersion interactions in electrolytes, J. Phys. Condens. Matter 20, 494209 (2008).
  86. R. J. F. L. d. Carvalho, R. Evans, D. C. Hoyle, and J. R. Henderson, The decay of the pair correlation function in simple fluids: Long- versus short-ranged potentials, J. Phys. Condens. Matter 6, 9275 (1994).
  87. Due to the presence of 1/r6 dispersion interactions, the poles of the electrostatic potential and distribution functions in Fourier space always have both real and imaginary parts [84]. Therefore, no purely imaginary pole k=iκ with real κ appears, which would have given rise to a monotonic Yukawa function [86]. Instead, the poles give oscillatory Yukawa function, but the poles that are purely imaginary in the absence of the dispersion interaction, usually have small real parts in its presence, so the wavelength of the oscillation is very long compared to the decay length. In practice the functions therefore decay like monotonic Yukawa functions. Mathematically, this feature is caused by the contribution C/r6 in the interparticle interactions that gives rise to a term Cπ2k3/12 in Fourier space (the term is −Cπ2k3/12 when the real part of k is negative). Due to this contribution, odd-powered k-terms appear, for instance in the denominator of the electrostatic potential in k space. While (iκ)2ν for real κ is a real number (ν= an integer), the terms with (iκ)2ν+1 are imaginary, so no purely imaginary pole can exist. If the 1/r6 interaction is truncated and is put to zero beyond a finite but arbitrarily large distance, then the odd-powered terms vanish, and monotonic Yukawa functions appear.
  88. J. Ennis, R. Kjellander, and D. J. Mitchell, Dressed ion theory for bulk symmetric electrolytes in the restricted primitive model, J. Chem. Phys. 102, 975 (1995).
  89. C. W. Outhwaite, in Statistical Mechanics (Specialist Periodical Reports) edited by K. Singer, 1st ed. (Royal Society of Chemistry, London, UK, 1975), Vol. 2.
  90. J. G. Kirkwood, Statistical mechanics of liquid solutions, Chem. Rev. 19, 275 (1936).
  91. J. G. Kirkwood and J. C. Poirier, The statistical mechanical basis of the Debye–Hüekel theory of strong electrolytes, J. Phys. Chem. 58, 591 (1954).
  92. B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, GROMACS 4:  Algorithms for highly efficient, load-balanced, and scalable molecular simulation, J. Chem. Theory Comput. 4, 435 (2008).
  93. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, The missing term in effective pair potentials, J. Phys. Chem. 91, 6269 (1987).
  94. W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc. 118, 11225 (1996).
  95. See Supplemental Material at http://link.aps.org/supplemental/10.1103/5qgc-rfvv for additional simulation details, figures, and data supporting this work.
  96. G. Nienhuis and J. M. Deutch, Comparison of two theories for the two particle distribution function of polar fluids, J. Chem. Phys. 56, 5511 (1972).
  97. J. S. Ho/ye and G. Stell, Statistical mechanics of polar systems. II, J. Chem. Phys. 64, 1952 (1976).
  98. Recall that Eq. (29) is applicable only for electrolytes, but Eq. (28) is valid in general and for polar fluids it reads [k2ɛreg(k)]k=iκν=−κν2E*(κν)=0.
  99. I. Y. Shilov and A. K. Lyashchenko, The role of concentration dependent static permittivity of electrolyte solutions in the Debye–Hückel theory, J. Phys. Chem. B 119, 10087 (2015).
  100. A. C. Tikanen and W. R. Fawcett, Application of the mean spherical approximation and ion association to describe the activity coefficients of aqueous 1:1 electrolytes, J. Electroanal. Chem. 439, 107 (1997).
  101. J. Ulander and R. Kjellander, The decay of pair correlation functions in ionic fluids: A dressed ion theory analysis of Monte Carlo simulations, J. Chem. Phys. 114, 4893 (2001).
  102. A. P. Abbott, R. Atkin, D. W. Bruce, P. Carbone, G. Damilano, R. A. W. Dryfe, J.-F. Dufrêche, K. J. Edler, Y. K. C. Fung, K. Goloviznina, M. C. Gomes, A. Grimaud, T. S. Groves, J. M. Hartley, J. D. Holbrey, C. Holm, P. Illien, R. Kjellander, A. Kornyshev, K. R. J. Lovelock et al., Ionic fluids at equilibrium: Thermodynamics, nanostructure, phase behaviour, activity: General discussion, Faraday Discuss. 253, 289 (2024).
  103. A. Härtel and R. Kjellander, On the strength of underscreening, in Ref. [102], pp. 293–295.
  104. A. A. Kornyshev and G. Sutmann, The shape of the nonlocal dielectric function of polar liquids and the implications for thermodynamic properties of electrolytes: A comparative study, J. Chem. Phys. 104, 1524 (1996).

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Phys. Rev. E 112, 065407– Published 2 December, 2025
  • Received 12 June 2025
  • Accepted 17 October 2025
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