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How charge frustration causes ion ordering and microphase separation at surfaces

Nature Materials (2026)Cite this article

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Abstract

Ion interactions with charged surfaces are fundamental to electrochemical, geochemical and biological systems, yet the impact of charging on interfacial structure and dynamics is poorly understood. Here we investigate the adsorption and precipitation of multivalent ions on mica using molecularly resolved atomic force microscopy. Although divalent ions form continuous hydroxide monolayers in a manner consistent with classical models, trivalent ions adopt complex states associated with strong overcharging, including ordered ion networks, cluster arrays and microphase-separated films not predicted by those models. Monte Carlo simulations show that such states emerge from charge frustration arising when restrictions on repelling charges prevent the minimization of electrostatic forces. Due to their universal nature across cation types, the results provide general principles underlying charge-driven nanostructure formation and insights for using electric fields to direct materials synthesis.

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Fig. 1: Evolution of the ordered ion arrays at mica–AlCl3 interfaces.
Fig. 2: Interfacial structure of mica in electrolytes containing trivalent ions.
Fig. 3: Charge-frustrated lattice simulations of ion adsorption.
Fig. 4: Interfacial structure of mica in electrolytes containing divalent ions.
Fig. 5: Schematic of the interfacial structure of mica in electrolytes containing multivalent ions.

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All data in this paper are presented in the Article and its Supplementary Information. Source data are provided with this paper. Additional data are available from the corresponding authors upon request.

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The code that supports the results within this Article and the other findings of this study are available from the corresponding authors upon request.

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Acknowledgements

We thank E. Nakouzi (Pacific Northwest National Laboratory (PNNL)) for helpful discussions on the 3D AFM data. We thank G. E. Johnson (PNNL) for help with the SPA measurements. This work was primarily supported by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES), Division of Materials Science and Engineering (MSE), Synthesis and Processing Science Program, PNNL, through FWP-67554. PNNL is a multiprogram national laboratory operated for the DOE by Battelle under contract number DE-AC05–76RL01830. Initial development of the charge-frustrated Monte Carlo model to predict the ion configurations at mica interfaces was supported by DOE BES MSE under FWP-77246 at PNNL. SPA measurements for AlCl3 solutions were supported by the DOE, BES, Geosciences Program under award numbers DE-SC-00021389 and DE-AC02-05CH11231 at the University of California, Riverside. SPA measurements for MgCl2 and other electrolyte solutions were supported by he US DOE, BES, Chemical Sciences, Geosciences and Biosciences Division, Separation Science program, through FWP-81462 at PNNL. BES-FWP-67554: to M.Z., B.A.L., B.A.H., P.J.P., C.J.M. and J.J.D.Y. BES-FWP-77246: to M.Z., B.A.L. and J.J.D.Y. BES-DE-SC-00021389: to Y.Z., R.K.Y., M.I. and Y.M. BES-FWP-81462: to S.T. and V.P.

Author information

Author notes

  1. Benjamin A. Helfrecht

    Present address: Laboratory of Computational Science and Modeling, EPFL, Lausanne, Switzerland

Authors and Affiliations

  1. Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA

    Mingyi Zhang, Benjamin A. Legg, Benjamin A. Helfrecht, Shuai Tan, Venkateshkumar Prabhakaran, Peter J. Pauzauskie, Christopher J. Mundy & James J. De Yoreo

  2. Department of Chemical and Environmental Engineering, University of California, Riverside, Riverside, CA, USA

    Yuanzhong Zhang, Rae Karell Yodong, Monica Iepure & Younjin Min

  3. Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA

    Ying Xia, Peter J. Pauzauskie & James J. De Yoreo

  4. Materials Science and Engineering Program, University of California, Riverside, Riverside, CA, USA

    Younjin Min

  5. Department of Chemical Engineering, University of Washington, Seattle, WA, USA

    Christopher J. Mundy

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Contributions

M.Z., B.A.L. and J.J.D.Y. conceived and designed the study. M.Z. performed the AFM experiments with the help of B.A.L. and Y.X. M.Z., Y.Z., S.T., R.K.Y. and M.I. performed the SPA measurements with the help of V.P. and Y.M. B.A.L. developed the charge-frustrated model. M.Z., B.A.L., B.A.H. and C.J.M. performed the Monte Carlo simulations. M.Z. and B.A.L. conducted the AFM data analysis with the help of P.J.P. M.Z., B.A.L. and J.J.D.Y. wrote the manuscript with input from other authors.

Corresponding authors

Correspondence to Benjamin A. Legg or James J. De Yoreo.

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Extended data

Extended Data Fig. 1 Evolution of an ordered ion network at the mica-AlCl3 interface revealed by in-situ AFM.

a-f, A time series showing the mica surface in a 1 mM AlCl3 solution at pH 3.9 is shown at various time points: (a) t0, (b) t0 + 65.5 s, (c) t0 + 131.0 s, (d) t0 + 196.5 s, (e) t0 + 262.1 s, (f) t0 + 495 s. The small light spots, corresponding to hydrolyzed Al ions, cover the entire surface, forming a network. Additionally, some larger particles can be seen fluctuating on top of the network.

Extended Data Fig. 2 Dynamics of the interfacial structure on mica surface in 1 mM AlCl3 at mild pH conditions (pH 4 to pH 5) revealed by in-situ AFM.

a, At pH 3.9, an ordered ion network forms. b, As the pH reaches 4, the ions begin to crosslink, forming small clusters and breaking the initial symmetry. c, Above pH 4, these clusters transition into a microphase separated monolayered Al(OH)3 film with a network of gaps. Insets display autocorrelation patterns to illustrate the symmetry of the surface structure. d,e, High resolution AFM images of the structure of the lamella patterned microphase separated Al(OH)3 films. f-j, in-situ AFM images show the transition from Al ion clusters to discontinuous Al(OH)3 films. k-n, in-situ AFM images show the coarsening of the films with increasing pH, where the average size of the islands increases from 2.36 to 60.5 nm2. o, An AFM image shows the monolayered Al(OH)3 films after a week of incubation.

Extended Data Fig. 3 Dynamics of the interfacial structure on mica surface in 1 mM AlCl3 at high pH conditions (above pH 5) revealed by in-situ AFM.

a, b, The growth of the upper layered Al(OH)3 films on the top of the first layer at pH 5.1 and at pH 6.9. c, At higher pH levels (above PZC), these films begin to dissolve. d, e, A high-resolution AFM image and FFT pattern reveal that these upper-layered films are well crystalline with a lattice structure consistent with gibbsite. f-j, in-situ AFM images capture the nucleation of the upper-layered films. k-o, in-situ AFM images capture the growth of the upper-layered films. These films exhibit distinct dynamics compared to the first layer and follow the expectations by the classical nucleation model.

Extended Data Fig. 4 Zeta potential of mica in various electrolytes measured by SPA.

a-f, Zeta potential of mica surface at (a) 1 mM KCl, (b) 1 mM FeCl3, (c) 1 mM CrCl3, (d) 0.1 mM NiCl2, (e) 1 mM CoCl2, (f) 1 mM ZnCl2. g-i, Proposed models of the zeta potential versus pH on mica in different electrolytes. Both divalent and trivalent ions reverse the zeta potential, but the potentials in trivalent ion electrolytes can be 10-fold higher than in divalent ion electrolytes. Additionally, the potential is strongly correlated with the interfacial structure. For divalent ions, the overcharging at high pH is related to the formation of hydroxide films. For trivalent ions, the strong overcharging is associated with the observed ordered ions/clusters and microphase separation phenomena. Data are presented as mean ± one standard deviation, each derived from three independent measurements.

Source data

Extended Data Fig. 5 Dynamics of the interfacial structure on mica surface in 1 mM CrCl3 at various pH values.

a, b, AFM images display the adsorption of Cr3+ ions/clusters on the mica surface into ordered patterns at pH 2.1 and pH 3.1. c, At pH 4.5, the clusters cross-link and form a discontinuous film with nanometer-sized gaps in between. The insets in each image show autocorrelation patterns, revealing that the clusters exhibit near-hexagonal symmetry, which breaks when the films form. d, 1D autocorrelation plots, indicating that the distance between clusters and nearby films is consistently 2.5 to 3 nm during the transition. e-i, in-situ AFM images of the dynamics of Cr3+ clusters on mica at pH 3, with an averaged frame in (j). k-o, in-situ AFM images of the dynamics of the Cr(OH)3 films at pH 4.5, with an averaged frame in (p).

Source data

Extended Data Fig. 6 Phase diagrams in q-µ space at various J values simulated by the Charge-Frustrated Model.

a–e, 2D phase diagrams show the change of surface coverage as a function of q and µ is plotted at J = 4 kT, J = 0 kT, J = -4 kT, J = -8 kT, J = -12 kT. f-j, 2D phase diagrams show the change of surface potential as a function of q and µ is plotted at J = 4 kT, J = 0 kT, J = -4 kT, J = -8 kT, J = -12 kT. k-m, Three groups of the simulated interfacial structure at J = 0 kT, J = -4 kT, and J = -10 kT, respectively.

Extended Data Fig. 7 Phase diagrams in J-µ space at various q values simulated by the Charge-Frustrated Model.

a-g, Heatmaps show the change of surface coverage versus J and µ at q = 0 e, q = 0.5 e, q = 1.0 e, q = 1.5 e, q = 2 e, q = 2.5 e, q = 3.0 e.

Extended Data Fig. 8 Dynamics of the interfacial structure on mica surface in 20 mM MgCl2 at various pH values.

a, b, Before pH 10, there is very weak adsorption observed on the mica surface, as shown in (a) at pH 3.4 and (b) at pH 6.9. c,d, Once the pH is raised to 10, where Mg(OH)2 becomes supersaturated, monolayered Mg(OH)2 films start to form on the mica surface. The thickness of the film is around 0.5 nm, which is close to the thickness of a layer of brucite, but the film is not well-crystalline, as shown in (d). e, A high-resolution AFM image of the mica surface in 20 mM MgCl2, where some contrasts are observed, but no obvious interfacial structure due to ion adsorption is seen, unlike in trivalent ion electrolytes. f, A time averaged image of over 100 frames (shown in Movie S5). It is likely that the brighter spots correspond to regions with a higher probability of Mg2+ adsorption. g, A space-correlated averaged image showing the mica lattice structure. h-l, A time series of the nucleation of the Mg(OH)2 films on mica in 20 mM MgCl2 at pH 10. Combined with the AFM data showing the growth kinetics in Fig. 4, the formation of these films is consistent with the prediction of classical nucleation theory for two-dimensional systems.

Extended Data Fig. 9 Interfacial structure of mica in electrolytes containing divalent cations.

a, An AFM image of the mica surface in 0.1 mM NiCl2 solution at pH = 6.8. b-d, Monolayered Ni(OH)2 films form on the mica surface when the pH is increased to 9.4. e, An AFM image show the mica surface in 1 mM CoCl2 solution at pH = 6.4. f-h, Monolayered Co(OH)2 films form on the mica surface when the pH is increased to 8.6. i, An AFM image of the mica surface in 1 mM ZnCl2 at pH 6.0. j-l, Monolayered Zn(OH)2 films form on the mica surface when the pH is increased to 7.7. All three ions show similar behaviors to Mg2+.

Extended Data Fig. 10 Speciation calculation of aqueous ions as a function of pH in bulk solutions.

The concentrations of the solution species for (a) Co(II), (b) Ni(II), (c) Zn(II), (d) Al(III), (e) Fe(III), (f) Cr(III) are plotted in solid lines while the average charge of the species is plotted in dashed lines. The calculation is based on 1 mM concentration for all ions using VisualMinteq.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–10, captions to Supplementary Videos and Text.

Supplementary Video 1

In situ AFM images show the transition from Al ion clusters to Al(OH) discontinuous films, corresponding to the interfacial structure of mica in 1 mM of AlCl from pH 4 to pH 4.4 (left, unregistered stack; right, registered stack; frame: 39.3 s).

Supplementary Video 2

In situ AFM images show the nucleation of multilayered Al(OH) films on mica (frame, 39.3 s).

Supplementary Video 3

In situ AFM images show the growth of multilayered Al(OH) films on mica (frame, 39.3 s).

Supplementary Video 4

In situ AFM images show the dynamic of Cr(OH) films on mica (frame, 39.3 s).

Supplementary Video 5

In situ AFM images show the dynamics of mica interface in 20 mM of MgCl solutions (frame, 19.7 s).

Supplementary Video 6

In situ AFM images show the nucleation of Mg(OH) films on mica (frame, 19.7 s).

Supplementary Video 7

In situ AFM images show the growth of Mg(OH) films on mica (frame, 65.6 s).

Source data

Source Data Fig. 1

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Source Data Fig. 2

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Source Data Fig. 3

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Source Data Fig. 4

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Source Data Extended Data Fig. 4

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Source Data Extended Data Fig. 5

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Source Data Extended Data Fig. 10

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Zhang, M., Legg, B.A., Helfrecht, B.A. et al. How charge frustration causes ion ordering and microphase separation at surfaces. Nat. Mater. (2026). https://doi.org/10.1038/s41563-025-02467-5

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