Paschen–Back effect modulation of SO₄^2- hydration in magnetized electrolyte toward dendrite-free Zn-ion batteries

Abstract

Tuning anionic solvation structures and dynamic processes at solid–liquid interfaces is critical yet challenging for stabilizing Zn metal negative electrodes in Zn-ion batteries, particularly due to the issue of dendrite formation and hydrogen evolution reaction. Here, we show that highly hydrated SO₄^2- can be effectively modulated under a strong magnetic field via the Paschen–Back effect on O-H vibrations, which reorients individual water molecules to manipulate Zn²⁺ solvation and protonated water clusters (H₃O⁺). Molecular dynamics simulations and in situ Raman spectroscopy reveal that the hydrated SO₄^2-–H₂O complexes promote Zn²⁺ nucleation and deposition on the (002) plane, with preferential oxygen adsorption inhibiting two-dimensional Zn²⁺ diffusion. Moreover, magnetizing the electrolyte disrupts the Grotthuss proton-transfer pathway, suppressing H₂ evolution and further reducing dendrite formation. By employing inexpensive permanent magnets without external power, this magnetization strategy offers a practical, energy-efficient route to enhance both the stability and performance of zinc-based rechargeable batteries.

Introduction

Among the candidates for next-generation large-scale energy storage devices, rechargeable batteries based on the Zn metal chemistry in neutral aqueous electrolytes stand out because of their high theoretical capacity (820 mAh g⁻¹), low potential (−0.762 V) vs. standard hydrogen electrode (SHE), high ionic conductivity, and environmental friendliness^1,2. However, the Zn metal negative electrodes in aqueous zinc-ion batteries (AZIBs) face substantial stability issues caused by Zn dendrite growth, which leads to side reactions such as the hydrogen evolution reaction (HER) and Zn corrosion³.

The primary driver of Zn dendrite growth is the Zn²⁺–H₂O solvation structure, which causes uneven Zn deposition^4,5,6,7. This structure introduces a high energy barrier for desolvation and deposition of Zn²⁺ due to strong Zn²⁺–H₂O interactions that ionize water molecules in its vicinity. The electric field generated by Zn²⁺ facilitates electron transfer from water molecules to Zn²⁺, weakening O–H bonds and promoting the HER^2,8. In AZIBs, the HER mainly arises from water decomposition during Zn deposition, which produces H₃O⁺ in the mildly acidic electrolyte. This phenomenon accelerates Zn corrosion and compromises the reversibility of the negative electrode^9,10,11. Uneven Zn²⁺ deposition at the electrode/electrolyte interface fosters dendrite growth, whereas the OH⁻ generated from water decomposition often forms Zn(OH)₂, which is converted to electrochemically inactive ZnO. Strongly bound zincate complexes further exacerbate dendrite formation^12,13,14. These side reactions stem from the high reactivity of water molecules in aqueous electrolytes, which poses a critical challenge for developing stable Zn metal negative electrodes.

Much progress has been made in addressing water-related challenges in AZIBs by investigating nonaqueous solvents such as dimethyl sulfoxide (DMSO) and dimethyl carbonate (DMC)^{7,15,16,17,18,19,20}. These solvents are primarily aimed at disrupting hydrogen-bonded water structures, limiting water activity in zinc solvation sheaths, or excluding water molecules from the electric double layer (EDL), thereby improving the stability of the zinc negative electrode by suppressing side reactions. Despite these advancements, the interactions between water and anions remain a critical factor that cannot be overlooked. For example, Chen et al. ²¹ demonstrated that zinc phenol sulfonate (Zn(PS)₂), with its bulky and conjugated anion, effectively modulates the zinc-ion solvation chemistry by reducing the coordination number of water molecules. Similarly, Qiu et al. ²² classified the effects of ions on the water structure into “structure-making” and “structure-breaking” effects, identifying SO₄²⁻ as a strong “structure-maker” that stabilizes nontetrahedral hydrogen-bonded water structures. Additionally, Lu et al. ²³ emphasized the desolvation and proton-storage capabilities of anionic groups in natural and synthetic polymers, highlighting their role in enhancing Zn negative electrode stability. These findings underscore the critical need for strategies that leverage coordination chemistry to modify the anionic solvation structures and dynamic processes at solid‒liquid interfaces. Such approaches could greatly improve Zn negative electrode reversibility while reducing the reliance on specific organic solvents.

One way to enhance the stability and reversibility of the zinc negative electrode is to regulate the water molecule dynamics. The application of a magnetic field represents a promising strategy for regulating the water molecule dynamics through the magnetohydrodynamic effect, driven by the Lorentz force²⁴. However, the influence of magnetic field on hydrogen-bond (HB) networks in water remains a subject of debate. HB interactions create diverse local environments for water molecules, which can be classified into five structures: single donor–double acceptor (DAA), double donor–double acceptor (DDAA), double donor–single acceptor (DDA), single donor–single acceptor (DA), and free water. The primary differences among these configurations arise from the orientation of individual water molecules, which affects their HB connections²⁵. Toledo et al. ²⁶ reported that magnetic treatment weakens intracluster HBs while strengthening intercluster HBs, resulting in smaller water molecule clusters. In contrast, Gu et al. ²⁷ reported that a magnetic field increases the number of water molecules participating in hydration, thereby expanding the dynamic hydration layer in salt solutions. Similarly, Cai et al. ²⁸ proposed that a magnetic field induces the formation of new HBs, leading to larger water molecule clusters. In addition, Speake et al. ²⁹ demonstrated that increased charge density at higher field strengths is the primary system response to a magnetic field, rather than direct strengthening of HBs. These findings highlight that a magnetic field-induced modulation of the water molecule orientation, influenced by intermolecular interactions, could play a pivotal role in shaping the coordination chemistry and solvation structure of anions. Understanding these effects is essential for enhancing the stability and performance of Zn metal negative electrodes in AZIBs.

In this study, to enhance the stability of Zn negative electrodes, we employed an adjustable external magnetic field applied perpendicular to the electrolyte flow, through which the electrolyte was pretreated, to effectively suppress dendrite growth in Zn metal negative electrodes. Under a strong magnetic field (3 T), the HB network is modulated via the Paschen–Back effect on the O–H symmetric stretching mode, impacting the ion solvation structure and protonated water clusters, H⁺(H₂O)_n. The Lorentz force disrupts the DDAA water structure, redistributes charge, and localizes excess charge on SO₄²⁻, thereby stabilizing the DDA water structure. This behavior is corroborated by Raman spectroscopy results, molecular dynamics (MD) simulations, and ¹⁷O/¹H nuclear magnetic resonance (NMR) analyses. Notably, the enhanced intermolecular HB (H–O–H⋯OSO₃²⁻) and the modulation of the Zn²⁺ and H⁺ solvation chemistry greatly improve the thermodynamic stability of the Zn/water interface. Density functional theory (DFT) calculations and in situ Raman spectroscopy further reveal that highly hydrated SO₄²⁻ promotes dendrite-free Zn deposition and minimizes side reactions on Zn metal surfaces. This study demonstrates that water molecules can be effectively reoriented by modulating the solvation chemistry through highly hydrated SO₄²⁻, thus enhancing the stability of Zn metal negative electrodes. This approach holds promise for inspiring future advancements in optimizing other solid‒liquid interfaces through magnetic pretreatment.

Results

The Paschen–Back effect modulates SO₄ ^{2 −} hydration

To determine if the stability of Zn negative electrodes could be enhanced by applying a magnetic field [overall aim], we first aimed to determine the effect of a magnetic field on water via free-energy calculations. In water, the center of mass is close to the O atom, resulting in minimal atomic displacement of the O atom during molecular rotation. To examine the impact of a magnetic field on the HB network, as presented in Supplementary Note 1, we first calculated the transitions of hydrogen atoms under various magnetic field intensities (Supplementary Figs. 1–3). Theoretically, Supplementary Note 2 demonstrates that an applied magnetic field of 3 T effectively disrupts spin–orbit coupling, inducing ${}^{3}S_{1}{\to }^{3}\,{P}_{0}$ transitions in hydrogen atoms and triggering the Paschen–Back effect (Fig. 1a). Under these conditions, the z-axis of H₂O undergoes rapid vibrational motion, causing the rotational dynamics to become more restricted at 3 T than at weaker fields. This restriction arises from the faster rotational motions of H atoms influenced by the Paschen–Back effect³⁰.

Fig. 1: Lorentz-force-induced O‒H stretching weakens intracluster HBs and modulates SO₄²⁻ hydration.

a A magnetic field of 3 T overcomes spin‒orbit coupling. b Induced magnetic moment vs. temperature of the ZnSO₄ electrolyte magnetized in a perpendicular magnetic field of 3 T. c Dipole moments (T = 298 K) of the ZnSO₄ electrolyte magnetized in a perpendicular magnetic field of 3 T. d Diverse water coordination structures and ion interactions in the ZnSO₄ aqueous electrolyte. e Magnetic field (3 T)-induced enhancement of the symmetric O–H stretching vibration. f Magnetic field intensity-dependent population of hydrated ions according to the Raman spectra. g ¹H NMR spectra of the magnetized ZnSO₄ electrolyte. h Normalized ¹⁷O NMR spectra of the magnetized ZnSO₄ electrolyte. i ¹⁷O NMR spectra of neat D₂O and the electrolyte showing (inset) a new peak at −70 to −30 ppm in the electrolyte that corresponds to SO₄²⁻–H₂O. j Magnetic field intensity dependence of H₃O⁺, where r, a, and b represent the frustrated rotation, asymmetric O–H stretching, and H–O–H bending of H₃O⁺, respectively.

To investigate the magnetic response mechanisms of this vibrational motion, we calculated the free energy of a water molecule as a function of temperature under various applied magnetic fields using Equation to determine the dipole moment (µ) (1)³¹.

$$\Delta {{{\rm{A}}}}=-kT{\sum }_{n}\,{{\mathrm{ln}}}\{1+\exp [-({E}_{n}-{E}_{\mu })/{{{\rm{K}}}}T]\}+N\mu$$

(1)

Here, k represents Boltzmann constant (1.38 × 10⁻²³ J K⁻¹), T represents absolute temperature in kelvin (K), K represents the unit of the Kelvin scale, μ represents the dipole moment (C m), ${E}_{n}$ represents the eigenenergy of the magnetized electrolyte in an applied field B, and ${E}_{\mu }$ represents the chemical potential. The magnetic moment of the magnetized electrolyte was calculated using Eqs. (2) and (3).

$$M={\left(\frac{\partial A({{{\bf{B}}}},\,T)}{\partial {{{\bf{B}}}}}\right)}_{{{{\bf{B}}}}=3}-{\left(\frac{{\partial }^{2}A({{{\bf{B}}}},\,T)}{\partial {{{{\bf{B}}}}}^{2}}\right)}_{{{{\bf{B}}}}=3}$$

(2)

$${M}_{m}=4\mu$$

(3)

The first term in Eq. (2) accounts for the magnetic moments associated with the orbital spin of electrons, whereas the second term considers the diamagnetism arising from the shielding effect on the nucleus due to the applied magnetic field. Using these equations, we calculated the magnetic and dipole moments at T = 298 K for all the ZnSO₄ electrolytes magnetized under magnetic field strengths of B = 0–3 T (Fig. 1b, c). The dipole moment was subsequently expanded in dimensionless normal coordinates based on both Cartesian and internal coordinate systems. A reduced-dimensional model was applied to describe the out-of-plane bending mode in the complex under the magnetic field, with particular emphasis on the two-dimensional O–H stretch vibrations (illustrated in Fig. S4). These two normal modes correspond to the displacement of the O–H bond vector in either the Cartesian (y, z) or internal (r, θ) coordinate space (Supplementary Note 3). The Hamiltonian governing this system is expressed as:

$$H=\,\frac{{\hslash }^{2}}{2{\mu }_{{{{\rm{OH}}}}}}\left(\frac{{\partial }^{2}}{\partial {y}^{2}}+\frac{{\partial }^{2}}{\partial {z}^{2}}\right)+V(\, y,z)$$

(4)

$${\mu }_{yy}{\Delta }_{y}^{2}\approx \left(\frac{{\mu }_{r}}{{r}_{e}}\Delta r+\frac{{\mu }_{\theta \theta }}{2{r}_{e}^{2}}\right)\Delta {\theta }^{2}$$

(5)

Here, ${r}_{e}$ represents the equilibrium O–H bond length, and µ denotes the magnetic moment of the system. The first term in Eq. (5) indicates that slow displacement of the hydrogen atom perpendicular to the plane results in an increased O–H bond length due to asymmetric stretching under 1 T and 2 T magnetic fields. This elongation reduces the vector sum of the dipoles of the associated water molecules. Conversely, fast displacement induces a decrease in the O–H bond length via symmetric stretching under a 3 T magnetic field, thereby enhancing the dipole moment along the y-axis. When the hydrogen atom moves perpendicular to the plane, the O–H bond is stretched. The second term in Eq. (5) captures the effect of the motion of the hydrogen atom on disrupting the hydrogen-bonded water structure, as described in the first term of Eq. (4). This disruption leads to a redistribution of charges, localizing the excess charge on the ions. The magnetic field-induced charge redistribution in individual water molecules results in different HB partners for the five distinct structural configurations. Site-specific Raman spectral signatures, which are highly sensitive to changes in molecular dipole moments, provide insights into the coordination of these structures with ions.

To investigate the effect of a magnetic field on the HB network in ZnSO₄ electrolytes, we employed an adjustable external magnetic field (0 T, 1 T, 2 T, and 3 T) aligned parallel to the circulation velocity to modulate ion‒water interactions (Supplementary Fig. 5). A circulatory system with a flow rate of 100 mL/min and a magnetic pretreatment duration of 25 min was used. Based on the water molecule structures shown in Fig. 1d, the absorbance bands in the 2800–3800 cm⁻¹ region for the magnetized electrolyte correspond to O–H stretching vibrations³². Specifically, variations in the 3050–3200 cm⁻¹ range reflect substantial contributions from symmetric O–H stretching vibrations associated with hydrogen-bonded patches of core water, whereas higher-frequency peaks represent asymmetric O–H stretching vibrations characteristic of interfacial water (Supplementary Fig. 6)³³. Within the strongly hydrogen-bonded region, the low-wavenumber component is indicative of Zn²⁺ hydrated water (Zn·H₂O), which is characterized by a Fermi resonance. In contrast, the peak observed at 3200 cm⁻¹ corresponds to the collective in-phase vibrations of DDAA water molecules. As illustrated in Fig. 1e, f, the HB network is substantially disrupted under a magnetic field, as evidenced by the emergence of a peak at 3400 cm⁻¹, which is attributed to the out-of-phase vibrations of nontetrahedral structures (DDA + DAA). This distinction highlights the structural heterogeneity within the strongly hydrogen-bonded region³⁴. Under magnetic field treatments of 1 T and 2 T, the 3030 cm⁻¹ peak shifts to higher frequencies, suggesting reduced orientation of water molecules due to changes in their dipole moments. This shift indicates the formation of hydration shells around Zn²⁺ ions. Concurrently, the 3400 cm⁻¹ peak gradually shifts to higher frequencies, likely due to enhanced molecular asymmetric stretching and increased Fermi resonance. As the magnetic field intensity increases, the peak at 3400 cm⁻¹ increases in intensity at the expense of the 3200 cm⁻¹ peak, indicating disruption of the DDAA structure. Following magnetic field pretreatment at 3 T, the 3030 cm⁻¹ peak blueshifts, signifying enhanced HB interactions within core water molecules and a reduction in Zn²⁺ hydration. At this stage, the 3400 cm⁻¹ peak shifts to a lower frequency, suggesting that the enhanced O–H stretching vibrations of DDA water molecules significantly strengthen the HB network between the hydrogen atoms of water molecules and the SO₄²⁻ groups. The proportion of these interactions increases from 53.55% to 71.70%. This observation aligns with the trends observed in both the ¹H and ¹⁷O NMR spectra of D₂O and the ZnSO₄ electrolyte. ¹H NMR spectroscopy confirms that water molecules are influenced by their surrounding environment in the magnetized ZnSO₄ electrolyte. As shown in Fig. 1g, water protons resonate at ~4.716 ppm for pure water but exhibit a significant upfield shift to ~4.702 ppm in the ZnSO₄ electrolyte, indicating an increased electron density around water protons compared with that in pure water. Electron-rich groups such as SO₄²⁻ increase the electron density around water protons during interactions, resulting in proton shielding. This shift highlights the strong HB interactions between SO₄²⁻ and water, both within the solvation sheath of SO₄²⁻ and among the DDA water molecules outside this structure. Notably, the NMR spectra show distinct shifts for magnetic pretreatments at 1 T and 3 T. For 1 T pretreatment, the Zn²⁺–H₂O interaction ionizes water molecules, with the magnetic field inducing electron transfer from coordinated water to the empty orbitals of Zn²⁺, leading to substantial formation of DAA water molecules. This results in a notable downfield shift to ~4.832 ppm in the ZnSO₄ electrolyte. In contrast, at 3 T, water protons exhibit a significant upfield shift to ~4.701 ppm, indicating a gradual increase in the electron density due to intensified dipole‒dipole interactions between DDA water molecules and SO₄²⁻ (Supplementary Fig. 7)³⁵. These strong interactions between SO₄²⁻ and H₂O partially cancel the polarization effect, thereby inhibiting the Zn²⁺–H₂O interaction. Consequently, the Zn²⁺–H₂O peak shifts upfield to ~4.793 ppm at 3 T, reflecting a weakened Zn²⁺–H₂O interaction (Supplementary Fig. 8). This weakened interaction indicates that a magnetic field of 3 T can reduce side reactions in ZnSO₄ electrolytes. The smallest full width at half maximum (FWHM) of the Zn²⁺–H₂O ¹⁷O NMR peak at 3 T further indicates improved desolvation of solvated Zn²⁺, which results in enhanced conductivity (Supplementary Fig. 9). The shift in the water proton resonance frequency underscores the strong dipole‒dipole interactions between SO₄²⁻ and DDA water molecules. In aqueous ZnSO₄ electrolytes, the hydrogen nucleus experiences deshielding under the influence of the more electropositive Zn²⁺, reflecting the presence of strong H–O–H‧‧‧OSO₃²⁻ bonds. This interaction disrupts the HBs of DDAA water molecules, enhancing the deshielding effect around the oxygen atom (Fig. 1h). The downfield shift of the ¹⁷O NMR signals following ZnSO₄ electrolyte pretreatment further suggests enhanced deshielding at 3 T, with the ¹⁷O resonance frequency shifting downfield (Fig. 1i). The water molecules adjacent to SO₄²⁻ form a higher-density, nontetrahedral structure (DDA) dominated by noncollective vibrations. This configuration indicates strong electrostatic interactions between tetrahedral SO₄²⁻ and DDA water molecules, driven by symmetric O–H stretching vibrations. The dipole moment calculations shown in Fig. 1c support these findings, demonstrating that the dynamic dipole—defined as the change in the dipole moment during molecular rotation—increases due to intramolecular polarization. Consequently, the magnetic field selectively manipulates DDAA water molecules and the SO₄²⁻ solvation structure. These two competing factors nearly cancel each other out, contributing to the electrical anharmonicity calculated in Cartesian coordinates. This effect, driven by ionic HB motion that displaces the hydrogen atom away from the X–O bond axis, is observed in the ~2200 cm⁻¹ band³². This band corresponds to a resonance state of DDA asymmetric O–H stretching in H₃O⁺ as well as combination tones of the frustrated rotational vibration of H₃O⁺ (${\nu }_{{H}_{3}{O}^{+}}^{a,r}$)³⁶. This observation aligns with the frustrated rotation peak at ~800 cm⁻¹ attributed to the libration of three neighboring DDA-type neutral water molecules surrounding surface-bound H₃O⁺ (${\nu }_{{H}_{3}{O}^{+}}^{r}$) in the DDA configuration. In the original ZnSO₄ electrolyte, protons tend to concentrate at the water interface (Fig. 1j), readily integrating into the interfacial HB network as hydrated ions (H₃O⁺ (${\nu }_{{H}_{3}{O}^{+}}^{s}$,${\nu }_{{H}_{3}{O}^{+}}^{a}$)). These hydrated ions impact the interfacial spectra through their O–H stretching vibrations and the reorientation of individual water molecules under the surface field they generate. Consequently, the disappearance of H₃O⁺ is attributed to the Lorentz force, which disrupts the hydrogen-bonded water structure and induces charge redistribution to SO₄²⁻ due to electrical anharmonicity³⁷. The data in Fig. 1 demonstrate that a magnetic field selectively modulates anion and cation hydration by regulating ion-water interactions, providing insights into magnetic field effects and a basis for optimizing electrolyte design and electrochemical performance.

Magnetic field modulates the configuration of water molecules and strengthens HB (H–O–H‧‧‧OSO₃ ^{2 −})

To investigate the structural evolution of the HB network under the influence of the magnetic field and to elucidate the magnetic field-regulation mechanism of ion-water interactions, we increased the magnetic pretreatment time at 3 T from 0 min to 100 min. Infrared (IR), Raman, and attenuated total reflectance infrared (ATR-IR) spectra, which probe the fundamental molecular vibrations in liquid water, provided evidence that the local molecular structure is particularly sensitive to a strong magnetic field. Upon analysis of the ATR-FTIR spectra, we observed a shift in the ~600 cm⁻¹ band over time (Fig. 2a). Initially, from 0 to 25 min, the band shifts to higher frequencies, but from 25 to 100 min, it gradually shifts to lower frequencies. This shift is primarily due to the enhancement of intermolecular HBs, which leads to a high-frequency shift and narrowing of the molecular vibration band on the low-frequency side³⁸. The decreased band intensity over time suggests that the intermolecular charge flux and related cross terms are reduced, in which the typical solvation structure of the [Zn(OH₂)₆]²⁺ complex is notably suppressed. The low-frequency Raman spectrum of the ZnSO₄ electrolyte in Fig. 2b, which reflects the solvation structure, exhibits a distinct shoulder peak at 385 cm⁻¹ assigned to the symmetric stretching mode of octahedral [Zn(OH₂)₆]²⁺, which can appear in both inner-sphere and outer-sphere ion pairs. This result further indicates that Zn²⁺ generally exists in the form of a hexahydrate solvate^39,40. With the enhancement of intermolecular HBs, the [Zn(H₂O)₆]²⁺ peak slightly blueshifts and broadens, consistent with the dehydration of [Zn(OH₂)₆]²⁺ due to the formation of more SO₄²⁻–H₂O complex ions. This result aligns well with the results obtained from ATR-IR analyses. When polyatomic anions such as SO₄²⁻ enter the first hydration shell of Zn²⁺, significant spectral changes occur in the ligated sulfate bands, enabling distinction between ligated and unligated sulfates⁴¹. Under a 3 T magnetic field application for 25 min, the formation of strong HBs between DDA water molecules and SO₄²⁻ anions significantly reduces Zn²⁺ hydration, leading to the emergence of various contact ion pairs (CIPs). This results in a remarkable shift in the ν-SO₄²⁻ band to a higher frequency ( ~ 981.5 cm⁻¹), indicating the development of a unique solvation structure. In this structure, Zn²⁺ is strongly coordinated with anions, forming a tightly bound [Zn²⁺–SO₄²⁻] ion association (Fig. 2c). This coordination decreases the symmetry of SO₄²⁻, as evidenced by a blueshift in the v-SO₄²⁻ band positions. Conversely, in the electrostatic double layer formed by cations attracted to the negatively charged layer of anions, the ν (SO₄²⁻) stretching vibration observed in the ATR-IR spectra at ~980 cm⁻¹, corresponding to the solvent-separated ion pairs (SSIPs), shifts to lower wavenumbers with increasing magnetic pretreatment time^42,43. This phenomenon is further corroborated by the Raman spectra (Fig. 2d), in which the ν (SO₄²⁻) antisymmetric stretching vibration, located at ~1079.2 cm⁻¹ in the raw ZnSO₄ solution, exhibits a consistent shift under varying magnetic field treatment duration. These spectral changes provide compelling evidence of the altered solvation structure driven by enhanced intermolecular HBs under the magnetic field. As shown in Fig. 2e, the O–H stretching vibrations associated with HB networks can be classified into weak HBs (3085 cm⁻¹), medium HBs (3338 cm⁻¹), and strong HBs (3554 cm⁻¹)⁴⁴. After 25 min of magnetic treatment, a pronounced absorption band emerges at ~3414 cm⁻¹, near the strong HB peak at 3554 cm⁻¹. This peak at 3414 cm⁻¹ corresponds to long-range HBs (S=O‧‧‧H–O), indicating the enhanced hydration ability of SO₄²⁻ ions through interactions with four neighboring DDA-type water molecules. The symmetric O–H stretching vibrations facilitate the rupture of DDAA-type water molecules, resulting in the formation of DDA-type water molecules. The donor-bonded OH groups of DDAA water molecules at the interface orient their stretch dipole moments toward the liquid, whereas covalent O–H bonds, which are typically oriented away from cations, position their associated hydrogen atoms farther from the charges. This finding aligns with the Raman spectra, which primarily highlight anionic interactions³⁴. As nonpolarizable SO₄²⁻ ions migrate to the water interface, the number of solvent molecules present increases, minimizing the vector sum of their dipole moments². This displacement of SO₄²⁻ leads to reorganization of interfacial water molecules, with the extent of the effect governed by the hydration dynamics. Prolonged magnetic treatment further transforms DDA-type hydrogen bonds into weaker DA-type hydrogen bonds. Crucially, this phenomenon is driven by dipole moment transitions under a magnetic field, which are attributed to quantization effects arising from the vibrational Stark effect (VSE) of the O–H stretching mode under the magnetic field-induced electric field, as described by Eq. (6)⁴⁵.

$$\nu -{\nu }_{0}=-\Delta \overrightarrow{\mu }\cdot {{{\bf{F}}}}$$

(6)

Fig. 2: Magnetic field-induced highly hydrated SO₄²⁻ reorients and stabilizes interfacial water.

a Change in the ATR-FTIR spectrum of the high-frequency librational motion with the magnetic pretreatment time. b Raman peaks representing Zn²⁺ solvation configurations. c FTIR spectrum of a series of SO₄²⁻ structures. d Raman spectra of a series of ν-SO₄²⁻ antisymmetric stretching vibrations. e Change in the FTIR spectrum between 2600 and 4000 cm⁻¹ with the magnetic pretreatment time. f ¹H chemical shift of H₂O. g ESP mapping of the original Zn²⁺‒H₂O, Zn²⁺‒6H₂O, H⁺‒6H₂O, and SO₄²⁻‒4H₂O solvation structures. h Mulliken charges of Zn²⁺‒H₂O and Zn²⁺‒6H₂O. i Binding energies of Zn²⁺‒H₂O, H⁺‒H₂O, Zn²⁺‒6H₂O, the DDAA water structure and SO₄²⁻‒H₂O. j O‒H bond lengths of Zn²⁺‒H₂O, the DDAA water structure, H⁺‒H₂O, Zn²⁺‒6H₂O, and SO₄²⁻‒H₂O.

The vibrational frequencies ν and ν₀ represent specific molecular vibrational modes with and without an external electric field, respectively. The electric field force F is expressed as F = qϑ × B where q is the charge, ϑ is the charge velocity, B is the magnetic field intensity, and E is the electric field strength dependent on the change in B. The dipole moment difference Δ$\overrightarrow{\mu }$ (also known as the Stark tuning rate) plays a crucial role. As the magnetic treatment time increases, the average number of HBs (H–O–H‧‧‧OSO₃²⁻) initially increases to 25 min and then decreases. This behavior is due to the Lorentz force in the x-direction, which affects the intermolecular electrostatic interactions. Water molecules typically adopt a tetrahedral arrangement, with two hydrogen atoms and two lone pairs of electrons on the oxygen atom forming connections. However, after approximately 50 min of magnetic field treatment, the role of the Lorentz force transitions from predominantly inducing symmetric O–H stretching vibrations to activating bending modes. For samples treated for 50, 75, and 100 min, this vibrational shift inadvertently facilitates the rapid interaction and association of Zn²⁺ and H⁺ ions with DA-configured water molecules. This phenomenon is corroborated by proton (¹H) NMR spectra, which sensitively reflect changes in molecular dipole moments (Fig. 2f). The shift of the ¹H NMR signal to higher magnetic fields after 25 min of magnetic treatment indicates an enhanced shielding effect in SO₄²⁻–H₂O complex ions. The hydrogen bonds formed between anions and water molecules are stronger than those formed among water molecules, and extended magnetic treatment promotes the formation of more DA-type water molecules, thereby weakening the electron shielding around the atomic nucleus (Fig. 2g). Similarly, the dominant vibration of Zn²⁺–H₂O at ~1600 cm⁻¹ shifts to lower wavenumbers in the presence of high concentrations of SO₄²⁻–H₂O complex ions, reflecting a suppressed stretching mode. This shift arises as Zn²⁺ is excluded from the water interface (Supplementary Fig. 10), confirming that the magnetic field weakens the strong but short-range Coulombic interactions between Zn²⁺ and DAA- or DA-type water molecules. The modulation of the water molecule dipole moments by the magnetic field, particularly in the context of intermolecular interactions between DDA water molecules and SO₄²⁻–H₂O, enhances the dehydration of Zn²⁺. Consequently, a more pronounced negative charge distribution forms at the water interface, with the negative pole of the water dipole shifting closer to the molecular center relative to the positive pole. Under a magnetic field intensity of 3 T, the orientation of the O–H bond shifts away from the SO₄²⁻ geometry, leading to a stronger electrostatic potential (ESP) being experienced by anions at the water molecule surface compared to that experienced by cations.

To verify the electron delocalization in the designed molecular systems, the ESP was calculated to assess the intrinsic electronic properties (Fig. 2g, see Supplementary Data 1). The results reveal a systematic decrease in ESP values across the solvation states of H⁺–H₂O, Zn²⁺–6H₂O, Zn²⁺–H₂O, and SO₄²⁻–4H₂O. Among these, H⁺ has the most significant influence on the ESP. Regions with higher ESP values are more susceptible to nucleophilic reactions, whereas those with lower ESPs favor electrophilic interactions⁴⁶. Notably, the SO₄²⁻–4H₂O solvation state demonstrates a lower ESP and a more uniform surface charge distribution compared to H⁺–H₂O, Zn²⁺–6H₂O, and Zn²⁺–H₂O, which is attributed to the symmetric arrangement of water molecules, and this SO₄²⁻–4H₂O solvation structure is more beneficial for enhancing water molecule stability. Preliminary calculations suggest that electron delocalization significantly reduces electrostatic repulsion between water molecules, thereby enhancing the stability of DDA water structures. For Zn²⁺, the electrostatic interaction in the Zn²⁺–H₂O complex is weaker than that in Zn²⁺–6H₂O. This weaker interaction results in a higher Mulliken charge of 1.590 for the zinc atom in Zn²⁺–H₂O (Fig. 2h), indicating enhanced Zn²⁺ migration and transport. These findings were corroborated through quantitative electrochemical characterization using electrochemical impedance spectroscopy (EIS). To delve deeper into the influence of ions on their coordinated water molecules, the binding energies for Zn²⁺–6H₂O, Zn²⁺–H₂O, DDAA water molecules, SO₄²⁻–4H₂O, and H⁺–H₂O were calculated: −20.41, −5.17, −3.32, −2.99, and −0.82 eV, respectively (Fig. 2i). These results indicate that the electrostatic interaction strength between SO₄²⁻ ions and water molecule lies between the strong interactions of Zn²⁺ ions with DDAA water molecules and the weak interactions of H⁺ ions with water molecules. Furthermore, the binding energy of Zn²⁺–H₂O in the solvation shell is lower than that of Zn²⁺−6H₂O, which is attributed to the increased electron density of the water molecules⁴⁷, consistent with the NMR and FTIR analysis results. The differences in binding energies further suggest that disruption of the tetrahedral HB network generates DDA-type water molecules, which preferentially redistribute charges to SO₄²⁻ ions. This charge redistribution ultimately leads to the disappearance of H₃O⁺. The high polarity and electron-rich regions of SO₄²⁻ promote the formation of strong solvation structures, which interact with DDA-type water molecules and alter the O‒H bond length (Fig. 2j, see Supplementary Data 1). Notably, the O–H bond length in the SO₄²⁻–4H₂O system is significantly shorter than that in the other solvation states, indicating that the stretching of the O–H bond disrupts DDAA water molecules and generates DDA water molecules. This interaction also reduces the coordination between water molecules and Zn²⁺ ions, leading to shorter O‒H bonds within the coordination sphere and a reduction in water activity. Furthermore, this interaction is corroborated by the blueshift in the O–H stretching vibration wavenumber observed in the Raman spectra under a 3 T magnetic field compared with 0 T. This blueshift, accompanied by an increase in the number of proton donor components, reflects the stabilization of the HB network^39,48. Therefore, magnetic field modulation of the HB network reduces HB acceptors and strengthens SO₄²⁻–DDA water interactions, mitigating Zn²⁺ hydration with DAA/DA water molecules.

Magnetic-driven modulation of hydrated SO₄ ^{2 −} suppresses Zn dendrites and HER

Given that the configuration of water molecules governs their hydration interactions with specific ions, understanding how water molecule reorientation influences electrodeposition behavior within the interfacial nanolayer is critical, the Zn‒O (H₂O) and Zn‒H (H₂O) distances were analyzed using MD simulations (Fig. 3a–e, see Supplementary Data 2). Considering that dendrite growth predominantly occurs at the electrode‒electrolyte interface, the Zn‒H distance on different crystal planes was examined and found to be 2.74 Å on the zinc (101) crystal plane, which is shorter than that on the zinc (100) (3.43 Å) and zinc (002) (3.52 Å) crystal planes, as illustrated in Fig. 3d. Conversely, the Zn‒O distance progressively decreases from the zinc (101) to zinc (100) and zinc (002) crystal planes (Fig. 3e). A partially enlarged snapshot reveals the interaction between DAA water molecules and Zn²⁺ alongside the conformations of H₃O⁺ and DDA water molecules. The SO₄²⁻ ion interacts with DAA water molecules, where DAA has a dangling OH group pointing toward the vapor phase, whereas DDA water molecules have their oxygen atoms facing the vapor side. This observation aligns with the general trend observed in the Raman spectra for O–H stretching vibrations and frustrated rotation. These findings demonstrate that the abundant anionic functional groups within water molecules exhibit a high adsorption energy for the Zn (002) crystal plane, with horizontal alignment. This result suggests that a synergistic inhibition mechanism works within hydrated SO₄²⁻, facilitating an equilibrium ion flux and promoting the preferred growth of Zn crystals on the Zn (002) crystal plane, thereby cooperatively regulating Zn deposition. Additionally, hydrogen atoms within the O‒H bonds of water molecules tend to accumulate at the Zn (101) interface, leading to significant orientation of these weakly hydrogen-bonded water molecules in the interfacial region. The preferential adsorption of oxygen atoms increases the interfacial tension between the bare Zn electrode and the magnetized electrolytes, as shown in Fig. 3f. By combining the SO₄²⁻ solvation structure with Young’s equation:

$${\gamma }_{{{{\rm{SL}}}}}={\gamma }_{{{{\rm{SV}}}}}-{\gamma }_{{{{\rm{LV}}}}}\,\cos \theta$$

(7)

where ${\gamma }_{{{{\rm{SL}}}}}$ is the interfacial tension, ${\gamma }_{{{{\rm{SV}}}}}$ is the free energy, ${\gamma }_{{{{\rm{LV}}}}}$ is the surface tension and θ is the contact angle, the interfacial tension of the solid‒liquid interface can be calculated if the population and stability of the SO₄²⁻ solvation structure are known. Notably, for the 25-min treatment, through the calculation of interfacial tension, it was found that the work of adhesion at the solid-liquid interface is greater than that for the other treatment times, causing the interfacial DDA water molecules to orient with their H → O bonds toward the Zn electrode interface. This leads to significant alignment of these negative water molecules in the interfacial region, confining water into three-dimensional nanodomains. However, with extended magnetic pretreatment, the magnetic field enhances the formation of DA water whiskers and disrupts the hydrated SO₄²⁻–4H₂O complex. The free O–H stretch water molecules tend to directly form H⁺–H₂O and Zn²⁺–6H₂O complexes, with the H atoms of the O–H bonds in the water molecules accumulating at the Zn electrode interface. As shown in Fig. 2e, the FTIR spectra progression between 2600 and 4000 cm⁻¹ with increasing magnetic pretreatment time demonstrates a distinct enhancement at 3414 cm⁻¹, attributed to hydrated SO₄²⁻–4H₂O complexes. This enhancement correlates with an increase in interfacial tension. Thus, we conclude that the interfacial water consists of hydrated SO₄²⁻–4H₂O complexes. The wettability of the magnetized electrolyte was evaluated through water contact angle measurements. The results reveal that the contact angle decreases as the hydrated SO₄²⁻–4H₂O content increases in the magnetized electrolyte (Fig. 2m). After 25 min of magnetic treatment, the contact angle reaches a minimum value of 33.28°, which can be attributed to the higher concentration of HBs (H–O–H‧‧‧OSO₃²⁻) in the surface layer than in the bulk. The improved wettability of the magnetized electrolyte with the increased amount of hydrated SO₄²⁻–4H₂O is related to the hydrophilicity of the electrolyte due to the presence of hydroxyl or oxygen moieties as terminal groups⁴⁹. This property results in lower internal ionic resistance in batteries and extends electrolyte retention at the Zn electrode. Consequently, the contact angle and interfacial tension can be concluded to be closely related to the reorientation of the HB network between the electrolyte and the Zn electrode.

Fig. 3: Magnetic field-induced highly hydrated SO₄²⁻ facilitates interfacial Zn²⁺ transport and leads to homogenization of the Zn²⁺ distribution.

a 3D snapshot presenting the orientation and conformation of interfacial water molecules at a zinc (101) crystal plane interface. b 3D snapshot presenting the orientation and conformation of interfacial water molecules at a zinc (100) crystal plane interface. c 3D snapshot presenting the orientation and conformation of interfacial water molecules at a zinc (002) crystal plane interface. d Distance between Zn and the H atom of a water molecule at different zinc crystal plane interfaces. e Distance between Zn and the O atom of a water molecule at different zinc crystal plane interfaces. f Interfacial tension of a series of magnetized electrolytes. g Data are presented as mean ± SD. Contact angles of electrolytes magnetized for various durations were analyzed (n  =  3). *p  <  0.05; **p  <  0.01; ***p  <  0.001. h i-t curves of Zn‒Zn symmetric cells in the magnetized ZnSO₄ electrolyte, where “3D” indicates two-dimensional planar Zn deposition and “3D” represents three-dimensional dendritic Zn growth. i Nyquist plots of a Zn electrode in the magnetized ZnSO₄ electrolyte. j Cyclic voltammograms (CVs) of Zn||Ti cells in electrolytes with different magnetic pretreatment times. k Linear polarization curves of fresh Zn electrodes (commercial Zn foils with the same surface conditions and effective surface areas) in electrolytes with 0 T and 3 T magnetic field intensity collected at a scanning rate of 0.1 mV s⁻¹ using a three-electrode cell. All experiments were conducted at 298 K.

To further verify that highly hydrated sulfate ions inhibit the two-dimensional diffusion of Zn²⁺ ions, we performed chronoamperometry (CA) tests and analyzed the Zn deposition behavior in a 2 M ZnSO₄ electrolyte (T = 298 K) subjected to magnetic treatment. The electrochemical performance was further evaluated using CA, in which the variation in the deposition current over time under a constant potential provided sensitive insights into the nucleation dynamics and surface modifications^42,50. With the unmagnetized electrolyte (0 T), the deposition current gradually increases within 50 s, indicating pronounced 2D diffusion and uneven Zn deposition (Fig. 3h). During this process, desolvated Zn²⁺ ions adsorb onto the Zn metal surface, laterally diffusing along the surface to locate preferred sites that minimize the surface energy. As a result, the Zn²⁺ ions tend to aggregate and grow at protrusions, accelerating dendrite formation. In stark contrast, when the electrolyte is magnetized at 3 T for 25 min, nucleation and 3D diffusion are observed within 50 s, followed by stable 3D diffusion, with a relatively constant current density of −18.5 mA cm⁻². This behavior suggests a homogenized Zn²⁺ distribution and consistent nucleation, promoting smooth Zn deposition. During this phase, the interactions between SO₄²⁻ and DDA water molecules significantly improve electrolyte retention at the Zn electrode. The electrolyte magnetized at 3 T for 25 min also demonstrates remarkable stability, with no observable current density decay during 3600 s of electrolysis at an applied potential of -1.6 V versus Ag/AgCl on a bare Zn electrode. Instead, a 4% increase in the current density is recorded, likely due to the rapid diffusion of Zn²⁺ ions.

EIS was employed to further elucidate the interfacial dynamics of the desolvated Zn²⁺ ions. Figure 3i and Table S1 reveal that the electrolyte magnetized at 3 T for 25 min exhibits significantly lower interfacial impedance, consistent with desolvated Zn²⁺ having a larger Mulliken charge. This result suggests that the strong interfacial adsorption of hydrated SO₄²⁻ facilitates Zn²⁺ transport and homogenizes the Zn²⁺ distribution at the interface. Moreover, Zn²⁺ ions begin being reduced to Zn⁰ at −0.0704 V (vs. Zn/Zn²⁺), and metallic Zn dissolution occurs at approximately 0.39 V. The nucleation of Zn in the electrolyte treated for 25 min results in a larger polarization voltage than that in the original ZnSO₄ electrolyte (|PP|= 44 mV) (Fig. 3j), primarily due to fast Zn²⁺ transport and relatively negative interfacial water potentials. This results in homogeneous deposition, yielding a smooth, fine-grained Zn plating surface. Additionally, a lower oxidation potential on the Ti substrate of 0.39 V is observed with the magnetized electrolyte compared with the value of 0.50 V observed with the 2 M ZnSO₄ electrolyte. These findings highlight the unique properties of the magnetized electrolyte treated at 3 T for 25 min, which promote zinc deposition. The stability of Zn electrodes was assessed using linear polarization curves (Fig. 3k). Compared with Zn electrodes in the original electrolyte, the corrosion potential of the Zn electrode in the 25-min-treated electrolyte increases from −0.959 V to −0.956 V (vs. Ag/AgCl)⁵¹. Furthermore, the electrolyte treated for 25 min exhibits a significantly lower corrosion current of 37.12 µA compared with the value of 211.67 µA in the original electrolyte, indicating the enhanced anticorrosion properties of the magnetized electrolyte, which are attributable to the orientation of interfacial DDA water molecules (H → O) toward the Zn electrode interface. This orientation, along with the highly hydrated SO₄²⁻–4H₂O structures, suppresses side reactions and reduces the corrosion rate of Zn negative electrodes, improving the stability and uniformity of Zn electrode deposition, thereby inhibiting dendrite formation.

The effectiveness of the magnetized electrolyte strategy in suppressing H₂ coevolution was verified using linear sweep voltammetry (LSV), as shown in Fig. 4a. The H₂ coevolution behavior was first examined in a commonly used mildly acidic electrolyte. During LSV measurements, the cathodic current exhibits an exponential increase from −0.35 V to −0.60 V (all potentials in the LSV tests were normalized to the Ag/AgCl scale at 0.210 V vs. SHE), which is attributed to the reduction of free protons (Eq. (9)) generated from hydrolysis of water by the bivalent Zn²⁺ cation (Eq. (8)). Beyond −0.7 V, both the polarization current and H₂ evolution sharply increase due to the direct reduction of H₂O (Eq. (10))⁵². In contrast, the proton reduction current is significantly reduced in the electrolyte magnetized at 3 T for 25 min, with H₂ evolution initiating at −0.8 V. Water reduction commences at −0.99 V, accompanied by a decrease in the polarization current. The strengthened HBs (H–O–H‧‧‧OSO₃²⁻) simultaneously reduce the onset potentials for proton reduction, water reduction, and O₂ evolution compared with the electrolyte solution treated at 0 T (Fig. 4b). These results confirm that highly hydrated SO₄²⁻ effectively suppresses H₂ evolution by shortening the O‒H bond length and breaking the Grotthuss proton-transport mechanism^53,54, as shown in Fig. 4c, d.

$${{{{\rm{Zn}}}}}^{2+}+n{{{{\rm{H}}}}}_{2}{{{\rm{O}}}}\to {[{{{\rm{Zn}}}}{({{{\rm{OH}}}})}_{n}]}^{2-n}+n{{{{\rm{H}}}}}^{+}$$

(8)

$${{{{\rm{H}}}}}^{+}+{{{{\rm{e}}}}}^{-}\to \tfrac{1}{2}{{{{\rm{H}}}}}_{2}\,{E}^{\theta }=-0.225\,{{{\rm{V}}}}\,{{{\rm{\nu }}}}{{{\rm{s}}}}.\,{{{\rm{Ag}}}}/{{{\rm{AgCl}}}}$$

(9)

$${{{{\rm{H}}}}}_{2}{{{\rm{O}}}}+{{{{\rm{e}}}}}^{-}\to \tfrac{1}{2}{{{{\rm{H}}}}}_{2}{+{{{\rm{OH}}}}}^{-}\,{E}^{\theta }=-1.050\,{{{\rm{V}}}}\,{{{\rm{\nu }}}}{{{\rm{s}}}}.\,{{{\rm{Ag}}}}/\,{{{\rm{AgCl}}}}$$

(10)

Fig. 4: Magnetic field-induced highly hydrated SO₄²⁻ reduces the onset potential for both proton reduction and water reduction.

a Cathodic stability and H₂ coevolutionary behavior of the magnetized ZnSO₄ electrolyte determined by LSV. b O₂ coevolution behavior of the magnetized ZnSO₄ electrolyte determined by LSV. The measurements were performed in a three-electrode cell consisting of a Pt foil working electrode, a Zn counter electrode, and an Ag/AgCl reference electrode at a scan rate of 1 mV s⁻¹ at ~298 K. c Schematic illustration of proton transport via the Grotthuss mechanism in the ZnSO₄ electrolyte. d Schematic illustration of the transport limitation for protons and water in the magnetized ZnSO₄ electrolyte.

Magnetic field-enhanced hydrated SO₄ ^{2 −} for dendrite-free Zn negative electrodes

Zn deposits in ZnSO₄ electrolytes are known to exhibit a hexagonal-platelet morphology, primarily due to the high activation energy associated with Zn dissolution on the Zn (002) crystal plane⁵⁵. To understand how magnetic pretreatment of the electrolyte influences Zn electrodeposition, we analyzed the structure of Zn deposits obtained from electrolytes at a concentration of 2 mol/L treated for 0, 25, 50, 75, and 100 min using X-ray diffraction (XRD). This analysis was conducted at a fixed current density of 10 mA cm⁻² to assess the texturing and orientation anisotropy of the thin films. Notably, the Zn deposits obtained from the electrolyte treated for 25 min exhibit a dominant (002) peak with minimal byproduct peaks, as shown in the zoomed-in inset of Fig. 5a, indicating a high degree of preferred orientation for Zn²⁺ deposition. The findings suggest that the interfacial water in the 25-min-treated electrolyte predominantly consists of SO₄²⁻–4H₂O hydrated complexes. Furthermore, the work of adhesion at the solid‒liquid interface in the electrolyte treated for 25 min is greater than that observed in the electrolytes subjected to magnetic pretreatment for other durations. This increased work of adhesion reduces the onset potentials for proton and water reduction, thereby inhibiting the formation of Zn₄(OH)₆SO₄·xH₂O (Fig. 5a and Supplementary Fig. 11). Extended magnetic pretreatment times lead to disruption of the HB network, causing free O–H stretch water molecules to form direct Zn²⁺–6H₂O complexes. The electric field generated by Zn²⁺ induces electron transfer from coordinated water to the vacant orbitals of Zn²⁺–H₂O, significantly weakening the O‒H bonds of water molecules and promoting the formation of Zn₄(OH)₆SO₄·xH₂O. These findings indicate that dendrite formation is significantly suppressed in the highly hydrated SO₄²⁻ electrolyte, which also inhibits the formation of Zn₄(OH)₆SO₄·xH₂O in the Zn||Ti asymmetric cell.

Fig. 5: The magnetized ZnSO₄ electrolyte enables a dendrite-free performance for Zn deposition.

a XRD patterns of Zn deposits (we disassembled the Zn||Ti cell after charging it for 4 h at a current density of 10 mA cm⁻², removed the Ti electrode, and collected the deposited Zn metal on the Ti electrode) in electrolytes with different magnetic pretreatment times. b AFM images of Zn deposits from the Ti electrodes of Zn||Ti cells subjected to a fixed current density of 10 mA cm⁻² in the original electrolyte. c AFM images of Zn deposits from the Ti electrodes of Zn||Ti cells subjected to a fixed current density of 10 mA cm⁻² in the electrolyte treated for 25 min. d AFM images of Zn deposits from the Ti electrodes of Zn||Ti cells subjected to a fixed current density of 10 mA cm⁻² in the electrolyte treated for 50 min. e, f In situ Raman spectra showing interfacial water (SO₄²⁻–H₂O, ~3400 cm⁻¹) on Ti electrodes from Zn||Ti cells subjected to linear sweep voltammetry in electrolytes pretreated at (e) 0 T and (f) 3 T. The measurements were conducted at a scan rate of 1 mV s⁻¹ and a temperature of 298 K. g Current-dependent in situ Raman spectra illustrating interfacial water (SO₄²⁻–H₂O, ~3400 cm⁻¹) on Ti electrode, correlated with nucleation dynamics. h OH stretching frequency shifts of SO₄²⁻–H₂O in Raman spectra: original solution vs. 3 T magnetic field pretreatment. i SEM and EDS images of Zn deposits on Ti electrodes from Zn||Ti cells subjected to linear sweep voltammetry in electrolytes pretreated at 0 T. j SEM and EDS images of Zn deposits on Ti electrodes from Zn||Ti cells subjected to linear sweep voltammetry in electrolytes pretreated at 3 T. k, l SEM images of Zn deposits on Ti electrodes formed at a constant potential of −1.6 V vs. Ag/AgCl in electrolytes pretreated at (k) 0 T and (l) 3 T.

To further elucidate the different plating patterns in the cation/anion solvation structure electrolytes, we examined the morphology of the Zn deposits in the electrolytes subjected to various magnetic pretreatment times. The normalized Zn (002) XRD peaks of the five samples are shown in Supplementary Fig. 12. The shift of the Zn (002) XRD peak in the pattern of the electrolyte treated for 25 min suggests enhanced crystallinity or the formation of larger Zn grains, consistent with the enlarged Zn grains observed in the atomic force microscopy (AFM) images. The AFM images (Fig. 5b–d and Supplementary Fig. 13) reveal that the Zn deposits obtained in the ZnSO₄ electrolyte form hexagonal platelets, with the thickness of the platelets increasing as the magnetic pretreatment time increases. The electrolyte treated for 25 min exhibits a significantly smoother Zn deposition surface than those treated for 0 and 50 min, for which the Zn deposits show a rough and undulating morphology. Figure 5b shows the morphological evolution of the Zn deposits in the untreated electrolyte. After 4 h, Zn nucleation is uneven and spottily distributed, with Zn nuclei reaching a vertical height of approximately 1.9 µm. The concentrated Zn²⁺ flux at the tips of the Zn nuclei, driven by the strong electric field around the sharp edges, causes the Zn nuclei to grow along the vertical axis into dendrites. This dendritic growth promotes the formation of Zn₄(OH)₆SO₄·xH₂O due to contact with DAA water molecules. In contrast, during Zn nucleation in the electrolyte treated for 25 min, the Zn nuclei exhibit a uniform plane-distributed morphology with a slice thickness of approximately 153.6 nm. As Zn plating progresses, planar Zn horizontally extends and grows due to the increased interfacial tension and equilibrium coverage, which limits vertical growth according to Eq. (11). Consequently, Zn deposits obtained from the electrolyte treated for 25 min are characterized by hexagonal platelets and a nondendritic morphology.

$${\gamma }_{{{{\boldsymbol{S}}}}{{{\boldsymbol{L}}}}}=\,{{\mathrm{ln}}}\left(\frac{K}{\omega }\right)\left(\frac{1}{h}\right)\,(\rho nFRT{\eta }_{{{{\rm{c}}}}}/-{{{\rm{\pi }}}}LA)$$

(11)

where$\omega$ represents the nucleation rate, K denotes the pre-exponential factor, h represents the height of the 2D cylindrical nucleus, ${\gamma }_{{{{\boldsymbol{S}}}}{{{\boldsymbol{L}}}}}$ represents the interfacial tension between the nucleus and the solution, L represents Avogadro’s constant, A represents the relative atomic mass of the deposited metal, ρ represents the density of the deposited metal, n represents the valence of the metal ions, F represents the Faraday constant, R represents the universal gas constant, and${\eta }_{{{{\rm{c}}}}}$ represents the overpotential. As shown in Fig. 5a, the nondendritic morphology gradually decreases with increasing interfacial tension. The three-dimensional AFM height images of the electrolyte treated for 50 min clearly highlight the differences in Zn deposition across the three electrolytes. The surface of the Zn foil in the 50-min-treated electrolyte exhibits numerous prominent, sharp zinc dendrites. These zinc dendrites were confirmed to be Zn₄(OH)₆SO₄·xH₂O, corroborated by the XRD patterns. Therefore, the Paschen–Back-effect-driven coordination modulation of H–O–H‧‧‧OSO₃²⁻, achieved via a magnetized electrolyte at 3 T for 25 min. In situ Raman spectroscopy further confirms the crucial role of interfacial water molecules (SO₄²⁻–H₂O) in controlling the morphological evolution of Zn deposits. As shown in Fig. 5e, f, the OH stretching peaks were deconvoluted into two distinct components: symmetric hydrogen-bonded water molecules at 3270 cm⁻¹ (DDAA) and asymmetric hydrogen-bonded water molecules at 3450 cm⁻¹ (SO₄²⁻–H₂O). As depicted in Fig. 5g–h, substantial shifts in the -OH stretching vibration peaks occur under increasingly negative electrode potentials. The 3450 cm⁻¹ peak gradually intensifies, while the 3270 cm⁻¹ peak notably diminishes, indicating a reduction of DDAA water and an increase in SO₄²⁻–H₂O configurations. Peak deconvolution reveals that the proportion of SO₄²⁻–H₂O increases from 38.47% at −1.0 V vs. Ag/AgCl to 49.46% at −1.6 V, clearly indicating strengthened interactions between the electrode and SO₄²⁻–H₂O at lower potentials. Correspondingly, the proportion of DDAA decreases from 61.53% to 50.54%. The associated vibrational frequency shifts further elucidate the dynamic reorganization of the HB network. Specifically, the SO₄²⁻–H₂O vibration frequency undergoes a distinct red shift from 3458.10 cm⁻¹ at −1.0 V vs. Ag/AgCl to 3447.12 cm⁻¹ at −1.6 V, while the DDAA vibration frequency shifts from 3269.29 cm⁻¹ to 3245.91 cm⁻¹, highlighting the gradual replacement of DDAA water molecules by hydrated cations⁵⁶. Upon application of a 3 T magnetic field, the interactions between the electrode and SO₄²⁻–H₂O become further enhanced, as evidenced by a more pronounced red shift in the SO₄²⁻–H₂O vibration frequency from 3448.72 cm⁻¹ at −1.0 V vs. Ag/AgCl to 3431.99 cm⁻¹ at −1.6 V. These spectral shifts clearly demonstrate that the magnetic field drives significant reconfiguration of the HB network and hydration shell structures. Notably, the magnetic field significantly restructures SO₄²⁻ solvation and further enhances HB interactions, increasing the SO₄²⁻–H₂O proportion from 48.05% at −1.0 V vs. Ag/AgCl to 61.17% at −1.6 V. These findings illustrate that the magnetic field strengthens electrostatic interactions between interfacial water molecules and the electrode surface, optimizing HB network ordering. Consequently, interactions between SO₄²⁻ and DDA water molecules are enhanced, significantly accelerating nucleation and promoting uniform 3D Zn diffusion, which inherently results in a reduced current density. Furthermore, as illustrated in Fig. 5i–l, Zn deposits obtained from electrolytes pretreated at 3 T exhibit a distinct platelet-like morphology compared to those formed in the original solution, indicating that the magnetic field preferentially promotes the exposure of the densely packed (002) crystal plane in hexagonal close-packed (hcp) Zn. Combined insights from MD simulations and in situ Raman spectroscopy further confirm that interfacial water predominantly consists of the SO₄²⁻–H₂O configuration. The magnetic field precisely modulates molecular configurations and HB networks through the Paschen–Back effect, facilitating dendrite-free Zn growth while effectively suppressing HER. This molecular-level modulation strongly inhibits H₂ coevolution, prevents dendritic and dead Zn formation, and enhances corrosion resistance. After magnetic field pretreatment, the O wt% proportion decreases by 4.20% (Fig. 5i, j and Fig. S14a, b). Furthermore, Zn deposits formed in electrolytes pretreated at 0 T (Fig. 5k) exhibit a randomly oriented structure, whereas those deposited under a 3 T field (Fig. 5l) display a well-directed growth pattern, demonstrating a locked orientation relationship with highly hydrated SO₄²⁻–4H₂O configurations. and substantially improves reaction kinetics, as summarized schematically in Fig. 6.

Fig. 6: Schematic illustration of Paschen–Back-effect-driven coordination modulation of SO₄²⁻ hydration for dendrite-free Zn-ion batteries.

The Paschen–Back effect disrupts the HB network (DDAA), reduces H₃O⁺-mediated proton transfer, and regulates ion solvation. This promotes DDA-type water cluster formation and enhances SO₄²⁻ hydration, facilitating Zn(002) preferential growth, reducing H₃O⁺ concentration, and improving Zn stripping efficiency. These modifications effectively suppress dendrite growth and HER, and enhance electrode corrosion resistance through interfacial repulsion.

To systematically assess the long-term stability of Zn deposition under magnetic field treatment, extended Zn plating/stripping tests were performed on Zn||Zn symmetric cells using different electrolyte conditions. The voltage profiles show that cells employing a 2 M ZnSO₄ blank electrolyte exhibit increasingly irregular voltage fluctuations over time, indicative of Zn dendrite formation and side reactions that undermine Zn plating/stripping stability. In contrast, cells with the magnetized electrolyte maintain stable and narrow voltage profiles for over 400 h, demonstrating markedly enhanced Zn plating/stripping durability (Fig. 7a, b). Furthermore, galvanostatic Zn plating/stripping at current densities of 1, 2, 5, and 10 mA cm⁻², with corresponding areal capacities of 1, 2, 5, and 10 mAh cm⁻², consistently results in lower polarization voltages for the magnetized electrolyte, highlighting the suppression of dendrite formation and parasitic reactions. These observations confirm that magnetic field treatment significantly improves the reversibility and long-term stability of Zn plating/stripping processes. To further substantiate this mechanism, XRD and SEM analyses were conducted on Zn electrodes after 400 h of plating/stripping. XRD results reveal that under 0 T conditions, Zn deposition predominantly occurs along the (101) plane, which is typically associated with unstable, dendrite-prone growth. In contrast, Zn electrodes cycled under a 3 T magnetic field exhibit a distinct transition to the (002) crystal orientation (Fig. 7c), indicative of enhanced structural stability. SEM imaging corroborates these findings: Zn deposited from the blank electrolyte presents a rough, irregular morphology with clear dendritic features, whereas Zn deposited using the magnetized electrolyte forms a much denser and more uniform structure (Fig. 7d, e). Together, these results demonstrate that magnetic field treatment modulates the Zn deposition pathway by promoting preferential (002) plane growth and suppressing dendrite formation, thereby significantly extending the Zn plating/stripping lifespan of Zn||Zn symmetric cells. The observed improvements in deposition morphology and reduced polarization voltage underscore the effectiveness of the magnetized electrolyte in regulating Zn plating/stripping behavior. This effect can be attributed to the magnetic-field-induced reconfiguration of the SO₄²⁻ hydration shell and the associated hydrogen-bond network, which is consistent with the structural evolution revealed in Fig. 5e–j. Under 3 T magnetic field conditions, the DDAA → DDA transition stabilizes SO₄²⁻ hydration, optimizes Zn²⁺ solvation, and facilitates controlled Zn²⁺ migration—ultimately enabling preferential (002) growth and enhancing Zn deposition reversibility and interfacial stability. To further confirm the efficacy of magnetic-field-treated electrolytes in enhancing battery performance, we conducted cycling tests on Zn||δ-MnO₂ full cells using a 2 M ZnSO₄ electrolyte magnetically pretreated at 3 T. As shown in Fig. 7f, the cell with the magnetized electrolyte retained a high specific capacity of 228 mAh g⁻¹ after 1000 cycles, whereas the capacity of the control cell with untreated electrolyte sharply declined to 85 mAh g⁻¹. This significant improvement clearly illustrates the beneficial impact of magnetic field treatment on long-term cycling stability. Furthermore, the magnetized electrolyte maintained a coulombic efficiency close to 100% throughout cycling, indicating highly reversible Zn plating/stripping processes. In contrast, the coulombic efficiency of the untreated cell exhibited notable fluctuations and remained consistently lower, reflecting irreversible Zn losses and side reactions, consistent with the observed rapid capacity decay. Post-cycling XRD analysis of Zn electrodes (Fig. 7g) further revealed a distinctly enhanced (002) crystallographic orientation under magnetic field conditions. This preferential orientation arises from the magnetic field-induced reconfiguration of the hydrogen-bond network in the ZnSO₄ electrolyte, promoting Zn deposition preferentially along the (002) plane and facilitating selective oxygen adsorption (Fig. 3d, e). These synergistic mechanisms effectively suppress the HER and inhibit the formation of ZnO byproducts, thereby enhancing the reversibility of Zn deposition/dissolution, improving electrode structural stability, and achieving higher capacity retention.

Fig. 7: Magnetized electrolyte-induced uniform Zn deposition for enhanced cycling stability and battery performance.

a Electrochemical performance of Zn||Zn symmetric cells using ZnSO₄ (2 mol/L) blank electrolyte. b Electrochemical performance of Zn||Zn symmetric cells using the magnetized electrolyte. c XRD patterns of Zn deposits collected from the electrodes of Zn||Zn symmetric cells after 400 h of plating/stripping. d Scanning electron microscopy (SEM) image of Zn deposits from the electrodes of Zn||Zn symmetric cells cycled in the blank electrolyte after 400 h of Zn plating/stripping. e SEM image of Zn deposits from the electrodes of Zn||Zn symmetric cells cycled in the magnetized electrolyte after 400 h of Zn plating/stripping. f Charge-specific capacity and efficiency of Zn||δ-MnO₂ full cells during 1000 cycles of Zn plating/stripping. g XRD patterns of Zn deposits collected from the electrodes of Zn||δ-MnO₂ full cells during 1000 cycles of Zn plating/stripping.

Discussion

In summary, we have demonstrated the significant impact of magnetic pretreatment on the anionic solvation structure and dynamic processes, proposing an interfacial water reorientation strategy to enhance the stability of Zn metal negative electrodes for use in Zn-ion batteries. To leverage the Paschen–Back effect on the O–H stretching mode, a magnetic field was applied perpendicular to the circulation velocity. The Lorentz force disrupts the DDAA hydrogen-bonded water structure, leading to charge redistribution and localizing excess charge on SO₄²⁻, thereby establishing single-HB acceptor configurations (DDA). This reorientation causes interfacial water molecules to align with their H → O bonds directed toward the Zn electrode, significantly stabilizing the DDA water molecules, inhibiting the 2D diffusion of Zn²⁺ ions, and preventing dendrite growth while enhancing corrosion resistance. Our approach enhances the stability of Zn metal negative electrodes. This study investigates how magnetic field-induced modulation of water molecule configurations influences the electrolyte/electrode interface performance. It further examines the relationship between the Paschen–Back effect and the local environments of water molecules, highlighting the critical role of DDA water molecule interactions with SO₄²⁻ in reducing the onset potentials for proton and water reduction, thus suppressing H₂ evolution in various application environments, thereby improving electrode structural stability, and achieving higher capacity retention. This understanding provides insights into achieving uniform zinc metal deposition for dendrite-free structures, offering potential for optimizing the interfacial microenvironment in liquid flow batteries.

Methods

Chemicals

Zinc sulfate heptahydrate (ZnSO₄·7H₂O, Aladdin, 99.995%) and all other reagents were used as received without further purification. Titanium foil (purity ≥99.7%, thickness: 0.1 mm), zinc foil (purity ≥99.99%, thicknesses: 150 μm and 20 μm), and platinum foil (purity ≥99.95%, thickness: 0.5 mm) were obtained from CeTech Co., Ltd. (China). All aqueous solutions were prepared using deionized water (18.2 MΩ cm) obtained from an ultrapure purification system (Aqua Solutions).

Preparation of the magnetically treated electrolyte

The generated magnetic field was an adjustable uniform magnetic field, with the field strength precisely regulated between 0 and 3 T. The magnetic field strength was controlled by adjusting the distance between the magnetic poles using a precision screw mechanism, with an error of ±0.002 T, and monitored in real time using a teslameter to ensure stability throughout the experiment. The magnetic field was aligned parallel to the plane perpendicular to the electrolyte flow direction to ensure uniform magnetic interactions along the flow path. A 2 mol/L ZnSO₄ electrolyte was circulated through the magnetic field using a recirculating pump at a stable flow rate of 100 mL/min, providing an optimal interaction time between the electrolyte and the magnetic field while avoiding turbulence. Each batch processed in the magnetic field had a volume of 200 mL, with the treatment time automatically controlled to maintain consistency across all trials and ensure reproducibility. The circulation tubing passing through the magnetic field was made of titanium to ensure chemical compatibility with the ZnSO₄ electrolyte and prevent corrosion. Titanium was selected for its relative magnetic permeability (${{{\rm{\mu }}}}/{{{{\rm{\mu }}}}}_{0}$) of 1.00018, which is close to the permeability of vacuum. This matching ensures that the tubing does not interfere with the uniform distribution of the magnetic field. Additionally, the use of titanium prevents contamination of the electrolyte, enhancing the reliability of the experimental results. The experimental system was designed to maintain consistent magnetic treatment conditions. Key parameters such as the magnetic field intensity, electrolyte flow rate, and treatment time were precisely controlled by an automated control system to minimize human error and ensure repeatability across multiple experiments. This experimental setup provides a robust framework to explore the influence of a magnetic field on the ZnSO₄ electrolyte. The precise control of the magnetic field intensity, electrolyte flow rate, and tubing material ensures accurate and reliable results, enabling a thorough evaluation of the effects of the magnetic field on the electrolyte dynamics.

Characterization

¹⁷O NMR and ¹H NMR data were recorded with Bruker Advance III (400 MHz) spectrometers. A coaxial insert containing deuterium oxide (D₂O), a standard NMR solvent, was carefully positioned within the NMR tube to facilitate precise measurements of electrolyte samples subjected to varying magnetic field intensities, while fully preserving their pristine microstructures. This setup effectively isolated the electrolyte sample from the NMR solvent, completely preventing unintended interactions and thereby enabling accurate characterization of the intrinsic interactions between water molecules and SO₄²⁻ ions. Raman spectroscopy was performed using a LabRam HR800 UV NIR with 532-nm laser excitation and a 50$\times$ lens. The Raman spectra of the magnetically treated electrolytes were recorded by dripping each electrolyte into a capillary. IR and ATR-IR spectra were collected with a PerkinElmer Spectrum II FTIR spectrometer. The crystal structure was studied by X-ray diffraction (Bruker AXS, Inc.) using Cu Kα as the radiation source under 40 kV and 40 mA. AFM images were acquired in tapping mode using a Dimension Icon AFM (Bruker). For in situ electrochemical Raman experiments, a custom-designed Raman electrochemical cell was employed, with a Ti electrode as the working electrode, a zinc counter electrode, and an Ag/AgCl reference electrode. Ti working electrodes were sequentially cleaned using ultrapure Milli-Q water (18.2 MΩ cm), 0.5 M H₂SO₄, and ethanol. The electrodes were then sonicated in these solutions three times to ensure complete cleaning. The electrochemical potential was controlled using an Autolab PGSTAT30 potentiostat (Metrohm).

Electrochemical measurements

All electrochemical experiments were performed using a CHI760E electrochemical workstation equipped with a three-electrode configuration, maintained at 298 K. Zinc foil was precisely cut into square electrodes (10 mm × 10 mm) to serve as the working electrode. A saturated Ag/AgCl electrode and platinum foil acted as reference and counter electrodes, respectively. Chronoamperometry (CA) tests were carried out using asymmetric Ti-Zn cells. Tafel plots were obtained using an in-house fabricated three-electrode cell composed of zinc foil for both working and counter electrodes, with Ag/AgCl as the reference. Cyclic voltammetry (CV) measurements were performed in Zn||Ti cells, scanning within a potential window from −0.4 V to 0.8 V at a scan rate of 10 mV s⁻¹. Electrochemical impedance spectroscopy (EIS) was measured at approximately −0.96 V versus Ag/AgCl in a 2 mol·L⁻¹ ZnSO₄ electrolyte. Frequency was varied from 100 kHz down to 0.01 Hz with a small AC perturbation amplitude of 5 mV. Prior to each EIS measurement, the cell was stabilized at open-circuit voltage for 10 min to ensure quasi-steady-state conditions. The impedance spectra obtained were fitted and analyzed using EC-Lab software (ZSimpWin 3.6). Linear sweep voltammetry (LSV) was performed on asymmetric Pt-Zn cells at a controlled scan rate of 1 mV s⁻¹. All electrochemical data presented herein are reported without compensation for internal resistance (iR drop).

Preparation of MnO₂ electrode

δ-MnO₂ powder (Sigma-Aldrich) was used as the active material and mixed with conductive carbon black (Super P, 99%, Alfa Aesar) and polyvinylidene fluoride (PVDF, 99%, Sigma-Aldrich) in a mass ratio of 7:2:1. The components were thoroughly blended, and N-methyl-2-pyrrolidone (NMP, battery grade, purity ≥99.9%) was added dropwise to form a homogeneous slurry. This slurry was subsequently subjected to ball milling at 400 rpm for 12 h. The resulting mixture was uniformly coated onto a 50-µm-thick graphite foil and placed in a vacuum oven. The coated electrode was first dried at 60 °C for 4 h, followed by drying at 80 °C for 12 h, yielding a positive electrode sheet with an active material loading of approximately 1 mg cm⁻².

Battery assembly and testing

Symmetric cells were assembled using 150-µm-thick Zn foil as both the working and counter electrodes, with either the blank electrolyte or the magnetically treated electrolyte. The Zn plating/stripping stability of the symmetric cells was evaluated using a Neware CT-4008T-5V 10 mA battery testing system at an area capacity of 1 mAh cm⁻² under current densities of 1, 2, 5, and 10 mA cm⁻². For the full-cell configuration, the positive electrode was the MnO₂ electrode prepared as described in the “Preparation of MnO₂ electrode” section, and the negative electrode was a 150-µm-thick Zn foil. Zn negative electrodes with an effective area of 2 × 2 cm were employed in Zn||δ-MnO₂ full cells assembled with a low N/P ratio of 0.77. A commercially available AZ2270P separator was utilized, featuring a single-layer structure with a thickness of 220 μm and lateral dimensions of 3 × 3 cm. This separator exhibited a porosity of 353% and possessed a hierarchical pore structure composed of mesopores (2–50 nm, ~60%) and macropores (>50 nm, ~40%). The cells were custom-assembled with external dimensions of 5 × 5 cm. The casing and spring components were constructed from acrylic and silicone rubber, respectively. No specific spring constant was measured. The working electrode was single-sided, coated with an effective area of 2 × 2 cm, and each cell contained one electrode. During assembly, 2 mL of liquid electrolyte was injected using a syringe. Neither pipettes nor pipette tips were employed for electrolyte handling, and no special wetting procedure for the separator was conducted prior to cell assembly. The cells were assembled using either the blank electrolyte or the magnetically treated electrolyte. Long-term Zn plating/stripping performance was evaluated over 1000 cycles at current densities of 0.1 A g⁻¹ and 1 A g⁻¹ using the same battery testing system.

MD simulations

MD simulations were performed using large-scale parallel atomic/molecular simulation software (LAMMPS23)^57,58. During the MD simulations, the all-atom (OPLS-AA) force field⁵⁹ was used to describe the interactions between atoms. The cell structure was constructed using PACKMOL software, and the water molecule model was set as TIP3P^60,61, with 10,000 water molecules and 100 zinc sulfate molecules. Prior to the MD simulations, the energy of the initial model was minimized using the steepest descent algorithm⁶². Then, under the NpT ensemble (T = 298 K, and p = 1000 Pa), structural relaxation was performed for 100 ps (with a time step of 0.1 fs) to bring the model to equilibrium, and the temperature was controlled by the Nose‒Hoover thermostat. During the MD simulations, the NVT ensemble (T = 298 K) was employed, and MD simulations of 2000 ps with a 0.1 fs time step were carried out. The calculated results were visualized and plotted using OVITO software⁶³.

In our MD simulations, the system consisted of 10,000 water molecules and 200 zinc sulfate (ZnSO₄) molecules. Each zinc sulfate molecule contained 1 Zn²⁺ ion and 1 SO₄²⁻ ion, so the system included 200 Zn²⁺ ions and 200 SO₄²⁻ ions. Additionally, the water molecules were represented by the TIP3P model. The interactions between H, O, Zn²⁺, and SO₄²⁻ were described using the all-atom (OPLS-AA) force field. The initial model was constructed using PACKMOL software and was energy-minimized using the steepest descent algorithm. To investigate the orientation of interfacial water on different crystal facets, we used atomic coordinates to statistically analyze the distributions of H and O atoms relative to the Zn bulk surface. The detailed method is as follows:

Obtainment of atomic coordinates: The coordinates of the H and O atoms were obtained through MD simulations. In the simulation, the structure of the Zn surface was obtained by classical MD, and then, the distributions of H and O atoms were analyzed.

Definition of the Zn bulk surface: To calculate the distance of H and O atoms relative to the Zn bulk surface, we first defined a reference position for the Zn surface. This reference surface could be defined by the crystallographic planes of the Zn atoms. Typically, an atomic plane related to the Zn crystal structure was selected as the reference.

Calculation of the distances of H and O from the Zn surface: By obtaining the spatial coordinates (x, y, z) of H and O atoms and the coordinates of Zn surface atoms, we calculated the vertical distance between these atoms and the Zn surface. The distance was computed based on the normal distance between each H or O atom and the Zn surface via the following equation:

$${{d}}=|{{{z}}}_{{{{\rm{H}}}}\,or\,{{{\rm{O}}}}}-{{{z}}}_{{{{\rm{Zn}}}}\,{{{\rm{surface}}}}}|$$

(12)

where ${{{z}}}_{{{{\rm{H}}}}\,or\,{{{\rm{O}}}}}$ and ${{{z}}}_{{{{\rm{Zn}}}}\,{{{\rm{surface}}}}}$ represent the z-coordinates of the H (or O) atoms and Zn surface atoms, respectively.

Statistical analysis of the distance distributions: We statistically analyzed the distances of all H and O atoms relative to the Zn surface and presented their distributions to reveal the spatial arrangement of H and O atoms near the Zn surface. This analysis provides detailed information on the adsorption or binding positions of H and O on the Zn surface.

DFT simulations

ESP and binding energy calculations were performed using Gaussian 09 software. The geometries of the molecules were optimized using the B3LYP hybrid functional with the 6–31 G + (d, p) basis set⁶⁴. The ESP diagrams were calculated with Multiwfn 3.8 software⁶⁵, and the atomic models and ESP diagrams were visualized using VMD 1.9 software⁶⁶, with an isosurface value of 0.03. The DFT-D₃ dispersion correction method was applied to account for weak interactions between cations and anions. The binding energy was defined as the energy difference between the total energy of the complex (e.g., H₂O + Zn²⁺ or SO₄²⁻ + Zn²⁺) and the sum of the energies of the isolated components (e.g., H₂O, SO₄²⁻, and Zn²⁺). The binding energy of the system (${{{{\rm{E}}}}}_{BE}$) was calculated by Eq. (13):

$${{{E}}}_{BE}={{{E}}}_{AB}-{{{E}}}_{A}-{{{E}}}_{B}$$

(13)

where ${{{E}}}_{AB}$ is the total energy of the system (i.e., the energy of the complex, e.g., H₂O + Zn²⁺ or SO₄²⁻ + Zn²⁺), ${{{E}}}_{A}$ is the energy of component A (e.g., H₂O or SO₄²⁻), and ${{{E}}}_{B}$ is the energy of component B (e.g., Zn²⁺). Additionally, the binding energy of H₂O and H⁺ can be defined as:

$${{{E}}}_{B{E}_{({H}_{2}O+{H}^{+})}}={{{E}}}_{{H}_{2}{O}_{(DDAA)}}-{{{E}}}_{{H}_{2}O}-{{{E}}}_{{H}^{+}}$$

(14)

where ${{{E}}}_{{H}_{2}{O}_{(DDAA)}}$ is the total energy of the complex formed by H₂O and H⁺. ${{{E}}}_{{H}_{2}O}$ is the energy of an isolated water molecule (H₂O). ${{{E}}}_{{H}^{+}}$ is the energy of an isolated proton (H⁺). Equation (13) calculates the binding energy of the system formed by water molecules (H₂O) and Zn²⁺ or SO₄²⁻ ions. Equation (14) represents the binding energy for the interaction of water molecules with protons (H⁺). The binding energy reflects the strength of the interaction between the components, with a higher binding energy indicating a more stable complex.