Introduction

In light of the burgeoning demand for environmentally benign energy solutions and the imperative of fostering sustainable development, the pivotal role of large-scale energy storage technology in mitigating the intermittency inherent in renewable energy sources cannot be overstated1,2. Aqueous zinc-ion batteries (AZIBs) emerge as a promising avenue within the realm of large-scale energy storage systems and wearable electronics, owing to their prominent attributes encompassing cost-effectiveness, high safety, large power density, and moderate energy density3,4. Notwithstanding, challenges persist, notably pertaining to zinc dendrite formation, corrosion, and hydrogen evolution reaction at the zinc electrode surface5,6. Addressing these challenges has been pursued through various methodologies, including zinc electrode surface coatings7,8,9, zinc electrode structure design10,11,12, electrolyte additive modifications13,14, and hydrogel electrolyte utilization15,16. In fact, these methodologies predominantly target zinc electrode/electrolyte interface, often proximate to the separator17,18. This reflects the critical role of the separator in tackling problems at the zinc electrode surface. In addition to this role, separators in AZIBs should serve two essential functions: (1) preventing the direct contact between positive and negative electrodes to forestall short circuit within the battery, and (2) furnishing channels for electrolyte storage and ionic transport19,20. The glass fiber (GF) separators widely used at present are expensive, have excessive thickness (typically >200 μm), and cannot effectively resist zinc dendrites21,22. Consequently, there is a pressing need to optimize AZIB separators. Despite various strategies proposed to address these issues, the reduction of separator thickness and the improvement of dendrite suppression effect often cannot be achieved simultaneously23,24,25. It is worth noting that excessive separator thickness would dramatically sacrifice energy densities of AZIBs.

Increasing the modulus of separator may be an effective way to resolve the contradiction between low separator thickness and good dendrite-tolerance ability. In the field of lithium metal batteries (LMBs), it has been confirmed that the modulus enhancement of polymer electrolytes and separators can effectively suppress the growth of lithium dendrites26,27,28. For instance, Ding et al. reported a polyimine aerogel separator with an average modulus of 141 MPa and a thickness of ~50 µm for LMBs28. This separator can effectively mitigate the risks associated with the formation of large-size dendrites, enabling Li||Li symmetric cell to operate stably for over 450 h at 1 mA cm−2 and 1 mAh cm−2, significantly surpassing that utilizing traditional polypropylene separator (only 218 h). Given that the modulus of zinc metal is tens of times higher than that of lithium metal, the modulus of separators used in AZIBs should be elevated to a considerably higher level. Yet, the modulus of separators for AZIBs has received inadequate attention to date. Recently, high-modulus hydrophilic polyvinylidene difluoride separator (named as VVLP) was demonstrated to suppress zinc dendrite growth and extend the life span of Zn||Zn cell to 2400 h under 3 mA cm−2 and 3 mAh cm−2 29. Nevertheless, Young's modulus of VVLP separator (137.4 MPa) is insufficient.

To maximize the separator modulus along the dendrite growth direction, this work proposes the adoption of wood-inspired biomimetic anisotropic architecture. Previous reports have confirmed that such architecture can impart improved mechanical properties along the orientation direction30,31. For instance, an anisotropic poly(vinyl alcohol) (PVA) hydrogel with oriented honeycomb-like pores was successfully established through directional freezing and salting-out strategies, achieving an obvious augment in tensile strength (23.5 MPa) and toughness (210 MJ m−3) along the preferential direction30. Besides, the anisotropic separator can provide a low tortuosity (τ), which can be represented by Eq. (1), in which L0 represents the straight-line distance between two points, while L denotes the actual path length required for electrolyte ions to traverse between the same two points32.

$$\tau={\left(\frac{L}{{L}_{0}}\right)}^{2}$$
(1)

Typically, the τ exhibits an inverse relationship with ionic conductivity33. Consequently, the anisotropic separator is expected to significantly enhance ionic conductivity along the oriented direction. For example, nearly 1.5 times higher ionic conductivity along the oriented direction was achieved for anisotropic PVA-based separator, compared to its isotropic counterpart34. Nevertheless, the limited studies on anisotropic separators for batteries have not focused on the effect of modulus in the orientation direction35. In this study, we introduce a biomimetic anisotropic separator in the field of AZIBs, and systematically examine how the separator's components influence its properties and the resulting battery performance. The optimized anisotropic separator (abbreviated as V-NFC-CS), consisting of nanofibrillated cellulose (NFC) and chitosan, can overcome the challenge of achieving both a reduced thickness (23 μm) and effective dendrite suppression, while resolving the trade-off between high modulus (7.3 GPa) and large ionic conductivity (20.5 mS cm−1). This study also unveils the importance and effect of modulus enhancement for battery separators. Besides, the V-NFC-CS separator, featuring aligned vertical channels, can be readily fabricated using a straightforward directional freezing method, and exhibits good biodegradability and hydrophilicity. The experimental results and theoretical calculations confirm that the V-NFC-CS separator can homogenize current density field distribution, facilitate Zn2+ ion migration, enhance electrochemical kinetics, and effectively suppress zinc dendrite formation and adverse parasitic reactions. Consequently, a significant improvement in the zinc stripping/plating reversibility is realized, contributing to significant performance improvement of full batteries.

Results

Construction and confirmation of anisotropic architecture

As illustrated in Fig. 1a, the fabrication of V-NFC-CS separator involves a directional freezing technique, wherein a mixed aqueous dispersion comprising NFC and chitosan was poured onto the upper surface of a copper ingot. The lower segment of the ingot was submerged in a bath of liquid nitrogen. This arrangement can facilitate the vertical growth of ice crystals along the z-axis owing to the exposure of copper ingot to liquid nitrogen. Consequently, the unfrozen portions, encompassing chitosan and NFC constituents, would be squeezed. Subsequent volatilization of ice crystals via freeze drying would yield vertically aligned channels, thereby producing an anisotropic architectural configuration36. Interestingly, this architecture bears a striking resemblance to the longitudinal section of wood, where the modulus along the z-axis surpasses that of other axes. Furthermore, analogous to the rapid transport phenomena observed within the channels of wood for water, inorganic salts, and organic nutrients, the anisotropic separator herein can exhibit comparable characteristics. Additionally, an applied pressure of 50 bar along the z-axis can further enhance the modulus in that direction. The designations of the obtained products, denoted as V-NFC-CS (10%), V-NFC-CS (20%), and V-NFC-CS (30%), correspond to varying mass ratios of chitosan to NFC of 1:10, 2:10, and 3:10, respectively. It is noted that unless expressly specified, the V-NFC-CS stands for a mass ratio of 20% for chitosan.

Fig. 1: Preparation and characterization of V-NFC-CS separator.
figure 1

a Schematic illustration of the preparation procedure of V-NFC-CS separator. SEM images and corresponding EDX mapping images of V-NFC-CS separator: b in the xz plane and c in the xy plane. d FTIR spectra and e tensile stress–strain curves of V-NFC, V-CS, V-NFC-CS, and NFC-CS separators. f Force-displacement curves of NFC-CS and V-NFC-CS separators. DMT modulus distributions of g NFC-CS separator and h V-NFC-CS separator. DMT modulus distributions of zinc electrodes after a zinc plating process of 10 mAh cm−2: i using coin-cell configuration and V-NFC-CS separator and j using electrolytic cell configuration without any separator.

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The reported techniques used for fabricating separators of AZIBs are summarized in Supplementary Table 1. Some earlier studies modified commercial separators such as GF separators, whereas the inherent drawbacks of GF separators (i.e., high price of ~USD $500 m–2 and excessive thickness of at least 200 μm) remain problematic37. Besides, common fabrication methods like vacuum filtration and electrospinning are not well-suited for the rapid production of separators. In this study, the directional freezing technique that is scalable and capable of rapid production is utilized to fabricate V-NFC-CS separator. As presented in Supplementary Fig. 1, the size of V-NFC-CS separator can be easily scaled up to 16 cm × 24 cm. Based on kilogram-scale raw material costs (chitosan: USD $30 kg−1, balsa wood powders: USD $5 kg−1, approximated from alibaba.com) and assuming manufacturing costs account for 90% of the total cost, the estimated cost for V-NFC-CS separator is USD $1.29 m−2. This cost is expected to considerably decrease at larger production scales. However, when scaling up to industrial production, the directional freezing method used in this work will require the redesign and planning of equipment and production lines, as existing setups cannot be used directly. Nevertheless, this should not pose a significant challenge for technicians in the field.

A thinner separator is beneficial to the improvement in battery energy density. As depicted in Supplementary Fig. 2, the V-NFC-CS separator possesses a low thickness of 23 μm, which is considerably lower than that of the majority of separators designed for AZIBs, such as the ones listed in Supplementary Table 1. Nevertheless, the thickness of V-NFC-CS separator is expected to be further reduced in future research efforts, with the goal of achieving an ideal thickness of <10 μm. The microstructure attributes of different separators in the xz and xy planes (refer to Fig. 1a for axis definition) were characterized by scanning electron microscope (SEM). Within the xz plane, the V-NFC-CS separator manifests a discernible arrangement of uniform and parallel channels (Fig. 1b and Supplementary Figs. 3a, b, and  4a), concomitant with abundant pores (ends of channels) in the xy plane (Fig. 1c and Supplementary Fig. 3c, d). It is also observed that there are some fibers within the channels of V-NFC-CS separator (Supplementary Fig. 4b). These fibers are ascribed to NFC, which resides in the channels because of their good hydrophilicity. Specifically, the freezing process of water fails to entirely expel NFC from the ice crystals due to the robust interaction between water and NFC, thereby leaving a portion of NFC in the channels. To highlight the benefits of anisotropic architecture, a traditional freezing method (i.e., freezing in a refrigerator) was employed to fabricate an isotropic NFC/chitosan composite separator denoted as NFC-CS. Examination of this separator reveals no obvious difference between the xz and xy planes (Supplementary Fig. 5a, b), verifying the absence of anisotropic characteristic for NFC-CS separator. For better comparison, the preparation process almost same as that of V-NFC-CS separator was employed to prepare V-CS and V-NFC separators, comprising solely chitosan and NFC, respectively. Evidently, the V-CS separator also owns anisotropic architecture (Supplementary Fig. 5c, d), while the V-NFC separator lacks such structural attribute due to the aforementioned hydrophilic effect (Supplementary Fig. 5e, f). To further elucidate the critical role of directional freezing in the formation of anisotropic structures, a conventional freezing method was employed to prepare CS and NFC separators. As shown in the SEM images in Supplementary Fig. 6, this conventional method fails to produce the anisotropic structure, highlighting the necessity of directional freezing for achieving the desired alignment.

The crystallization characteristics of four different separators were investigated through X-ray diffraction (XRD) analysis (Supplementary Fig. 7). Evident in the XRD patterns were a broad peak at 22.5° corresponding to cellulose and a distinctive peak at 10.2° indicative of chitosan. Fourier transform infrared (FTIR) spectroscopy was utilized to detect the functional groups within these separators (Fig. 1d). The characteristic bands at 3284 and 3358 cm−1 originate from amino group, and the bands at 1540, 1312, and 1016 cm−1 come from N–H stretching vibration, C–N bond, and C–O–C bond, respectively38. These chemical bonds have been confirmed by previous studies to restrict H2O activity, facilitate the desolvation process, and homogenize Zn2+ ion flux, hence promoting uniform zinc deposition39,40,41. These observations also substantiate the combination of chitosan and NFC in the V-NFC-CS separator. The transverse tensile strength of different separators along the x-axis or y-axis direction was assessed (Fig. 1e). In this regard, the V-NFC separator exhibits the largest strength of 23.8 MPa, benefiting from good mechanical properties of NFC20. The reinforcing effect of NFC considerably augments the strength V-NFC-CS separator (13.8 MPa) compared to V-CS separator (7.5 MPa). It is also found that the strength of V-NFC-CS separator is 14.8% lower than that of NFC-CS separator, suggesting a sacrifice in strength along the non-oriented direction due to the anisotropic architecture, albeit not to a considerable extent.

Modulus and ionic conductivity evaluation

As discussed earlier, the mechanical properties along the z-axis direction are of greater significance. Nanoindentation measurements were conducted to study these properties (Fig. 1f). The V-NFC-CS separator displays Young's modulus and hardness of 4.5 and 0.44 GPa, respectively, both markedly superior to those of NFC-CS separator (1.8 and 0.16 GPa, respectively). Notably, the modulus of V-NFC-CS separator is much larger than that of previously reported VVLP separator (45.8 MPa) for AZIBs and those separators featuring high modulus for LMBs42,43. Atomic force microscope (AFM) technique was utilized to further elucidate the modulus disparity, as presented in Fig. 1g, h and Supplementary Fig. 8a, b. The average Derjaguin–Muller–Toporov (DMT) modulus of V-NFC-CS separator (7.3 GPa) is 3.3 times that of NFC-CS separator (2.2 GPa). To better underscore the importance of separator modulus, the modulus of zinc electrodes was also evaluated (Fig. 1i, j and Supplementary Fig. 8c, d). Following a zinc plating process of 10 mA cm−2 for 1 h, the average modulus of zinc electrode within coin cells reaches a substantial value of 15.7 GPa with the use of V-NFC-CS separator. When a configuration of electrolytic cell is used in the absence of any separator, the average modulus is even larger at 42.8 GPa. These findings disclose the imperative and advantageous effects of enhancing separator modulus for AZIBs.

The anisotropic structure of V-NFC-CS separator can introduce oriented channels aligned along the z-axis direction. This is evident from the light emitting diode (LED) illumination tests displayed in Supplementary Fig. 9. When the LED lamp is positioned beneath the xy plane with the light mainly directed along the z-axis, most of the light can effectively penetrate V-NFC-CS separator, whereas light transmission through NFC-CS separator is considerably diminished. The vertically aligned channels within V-NFC-CS separator can facilitate low tortuosity for ionic transport33, as illustrated in Fig. 2a. In sharp contrast, the disordered pore structure of NFC-CS separator results in tortuous pathways for ionic transport (Supplementary Fig. 10). To validate this, the ionic conductivity of four different separators along the z-axis direction was assessed through electrochemical impedance spectroscopy (EIS) measurements (Supplementary Fig. 11a)44. Thanks to the anisotropic architecture in the V-NFC-CS separator, its ionic conductivity (20.5 mS cm−1) dramatically surpasses that of NFC-CS separator (11.8 mS cm−1) and V-NFC separator (10.8 mS cm−1), as shown in Fig. 2b and Supplementary Fig. 11b. Besides, the ionic conductivity of V-NFC-CS separator is lower than that of V-CS separator (21.7 mS cm−1), attributable to the presence of NFC inside the channels of the former. Despite that, the difference in ionic conductivity between these two separators is very small. NFC and CS separators prepared by conventional freezing method were also examined, as shown in Supplementary Fig. 12. Lacking oriented channels, they exhibit low ionic conductivities of 10.5 and 12.8 mS cm−1, respectively, further substantiating the significant role of the anisotropic structure in promoting ionic transport along the z-axis direction.

Fig. 2: Properties of V-NFC-CS separator and electrochemical performance of Zn||Zn cells.
figure 2

a Illustration of fast ionic transport path within V-NFC-CS separator. b Contact angle and ionic conductivity of V-NFC-CS and NFC-CS separators (the error bars represent the standard deviation calculated from five in-parallel tests). c CA curve of the Zn||Zn cell with V-NFC-CS separator and corresponding Nyquist plots to determine tZn2+. d Arrhenius curves and calculated Ea values with the use of two different separators. e Overpotential values with respect to specific current and corresponding i0 values and f GCD profiles at 5 mA cm−2 and 25 mAh cm−2 of Zn||Zn cells when using two different separators. g Current-dependent Sand’s capacity with the use of V-NFC-CS separator. h GCD profiles of Zn||Zn cells with two different separators at 10 mA cm−2 and 2 mAh cm−2.

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The temperature-dependent ionic conductivity values of V-NFC-CS and NFC-CS separators, based on EIS measurements at varying temperatures (Supplementary Fig. 13a, b), are plotted in Supplementary Fig. 13c. According to the fitting results through Arrhenius equation, the ionic conduction activation energy within V-NFC-CS separator is merely 0.061 eV, which is 47.0% lower than that within NFC-CS separator. This confirms that ionic transport is significantly more efficient along the z-axis in the presence of oriented channels. To evaluate the wetting properties of different separators with respect to 2 M ZnSO4 aqueous electrolyte, contact-angle tests were carried out (Supplementary Fig. 14). Owing to the markedly better hydrophilicity of NFC than chitosan, the V-NFC separator shows the lowest contact angle of 43.8° when the electrolyte was just dropped, while the V-CS separator manifests the highest contact angle of 86.8°. After a duration of 30 s, the contact angles for V-NFC-CS and V-NFC separators decline to 0°, due to the vertical channels within the former that can allow water to rapidly penetrate and good hydrophilicity of NFC. Conversely, owing to the relatively inferior hydrophilicity of chitosan, the contact angle for the V-CS separator remains a large value of 55.2° after 30 s. As for the NFC-CS separator, characterized by the absence of vertical channels and the presence of chitosan, the contact angle remains nearly unchanged after 30 s. The heightened wettability of V-NFC-CS is conducive to the access of aqueous electrolyte.

Investigation on Zn||Zn cells

After 7 days of storage in a Zn||Zn cell (prior to any electrochemical testing), the zinc electrodes were taken out for XRD measurements (Supplementary Fig. 15). Almost no signals apart from those of metallic zinc can be detected when using V-NFC-CS separator. However, an obvious diffraction peak at around 8.0° is visible when using NFC-CS or GF separator. This peak corresponds to the (001) plane of Zn4SO4(OH)6·5H2O (ZSH, JCPDS 78-0246)45, which is formed due to the corrosion of zinc metal. These results indicate that the V-NFC-CS separator can effectively suppress the corrosion issue of zinc electrode. According to the chronoamperometry (CA) curves and corresponding Nyquist plots of Zn||Zn cells with different separators, the Zn2+ ion transference number (tZn2+) can be determined46, as presented in Fig. 2c and Supplementary Fig. 16. The tZn2+ with V-NFC-CS separator (0.67) considerably exceeds that obtained with NFC-CS separator (0.51). This discrepancy arises from two primary factors. On one hand, the relatively large size of hydrated zinc ion ([Zn(H2O)6]2+, 8.6 Å in diameter) makes its transport susceptible to obstruction by the separator's framework. Thus, the obstruction encountered in NFC-CS separator, which has longer ionic transport paths, is greater than that in V-NFC-CS separator, which features oriented channels. On the other hand, NFC and chitosan dispersions exhibit zeta potential values of −31.4 and 26.7 mV, respectively. The negative charge of NFC facilitates Zn2+ ion transport, while the positive charge of chitosan inhibits it. By combining the results from Supplementary Figs. 12 and 17, it is evident that Zn2+ ion conductivity through NFC separator is ~20% higher than that through CS separator. In the context of using V-NFC-CS separator, Zn2+ ion transport primarily occurs through the vertical channels, where NFC is present and chitosan is absent, therefore contributing to improved Zn2+ ion transfer. EIS tests were also performed on Zn||Zn cells at various temperatures ranging from 30 to 70 °C (Supplementary Fig. 18). Based on these results, the desolvation activation energy (Ea) can be estimated (Fig. 2d)47. Obviously, the Ea associated with the use of V-NFC-CS separator (Ea = 38.0 kJ mo−1) is lower than that using NFC-CS separator (Ea = 49.0 kJ mo−1), indicating that the former can effectively promote the desolvation process of hydrated Zn2+ ions, hence enhancing zinc plating kinetics and inhibiting water-induced side reactions48.

The impact of separator on zinc plating/stripping behavior was explored through galvanostatic charge/discharge (GCD) measurements49. As shown in Supplementary Fig. 19, the Zn||Zn cell with V-NFC-CS separator exhibits a reduced voltage hysteresis spanning from 100 to 240 mV as the specific current escalates from 0.5 to 10 mA cm−2, in comparison with that employing NFC-CS separator (from 180 to 364 mV). According to these overpotential values, the exchange current density (i0) can be calculated (Fig. 2e)50. It can be clearly seen that the i0 is improved with the use of V-NFC-CS separator, indicative of enhanced electrochemical kinetics. The long-term cycling stability of Zn||Zn cells with different separators was evaluated at a specific current of 1 mA cm−2 and an areal capacity of 1 mAh cm−2 (Supplementary Fig. 20). Compared to V-NFC-CS (10%) and V-NFC-CS (30%) separators, the V-NFC-CS (20%) separator demonstrates better performance, with a prolonged life span exceeding 2000 h. In sharp contrast, the Zn||Zn cells with NFC-CS and V-NFC separators can only be stably operated for approximately 500 and 360 h, respectively. As for the use of V-CS separator, the overpotential is rather large and the cell voltage fluctuates heavily, implying cell failure49.

To examine the viability of employing V-NFC-CS separator under harsh conditions, the assembled Zn||Zn cell was run at 5 mA cm−2 and a huge areal capacity of 25 mAh cm−2, corresponding to an enormous depth of discharge (DOD) of 85.4% (Fig. 2f). Under these conditions, the cell with NFC-CS separator fails during the initial cycle51. In striking contrast, the cell with V-NFC-CS separator is stable for at least 300 h. Furthermore, the Sand's capacity, defined as the point at which severe dendrite formation has commenced, was evaluated under various specific currents (Supplementary Fig. 21, Fig. 2g with the light blue zone indicating severe dendrites)52. It is not surprising that the Sand's capacity declines with the increase of specific current. Nonetheless, the Sand's capacity still reaches ~10 mAh cm−2 at a large specific current of 10 mA cm−2. Under the condition of 10 mA cm−2 and 2 mAh cm−2, the Zn||Zn cell incorporating V-NFC-CS separator can still offer stable operation for over 1000 h (Fig. 2h). In contrast, the cell with NFC-CS separator suffers from rather large overpotential and dramatic voltage fluctuations. This disparity further confirms positive impact of the anisotropic architecture of separator on the zinc electrode/electrolyte interfacial stability. Besides, the electrochemical stability with the use of V-NFC-CS separator is drastically superior to that using conventional GF separator (Supplementary Fig. 22). As compared in Supplementary Fig. 23 and Supplementary Table 1, the life span and corresponding cumulative zinc plating capacity of Zn||Zn cell with V-NFC-CS separator in this work outperform those employing other separators, such as polymer-matrixed zeolite separator (SZ)53, sulfonated cellulose separator (CF-SO3)54, and molecular-sieve membrane23.

Zinc stripping/plating reversibility

In-situ EIS tests were employed to assess the impedance variations of Zn||Zn cells during the 4th cycle (Supplementary Fig. 24). The acquired Nyquist plots were then translated into distributions of relaxation time (DRT), as depicted in Fig. 3a, b. The signals observed at the time scale of 10−3–1 s are related to the charge transfer impedance (Rct), while those beyond 1 s can be attributed to the diffusion impedance of Zn2+ ions within the zinc deposition electrode55. With the use of V-NFC-CS separator, not only can the impedance values be decreased, but also can the zinc stripping/plating reversibility be significantly enhanced, in comparison with those using NFC-CS separator. To gain deeper insights into zinc stripping/plating reversibility, XRD measurements were conducted on the Zn electrodes after varying numbers of cycles in Zn||Zn cells operated at 10 mA cm−2 and 2 mAh cm−2 (Fig. 3c and Supplementary Fig. 25). Obviously, the (001) peak of ZSH byproduct at the zinc electrode following cycling with V-NFC-CS separator is markedly weaker than that with NFC-CS separator. The formation of ZSH is closely related to hydrogen evolution reaction, which increases the local concentration of OH− near the zinc electrode surface. To assess hydrogen evolution, the thickness of Zn||Zn cells before and after the measurements in Fig. 2h was compared (Supplementary Fig. 26). It can be seen that the thickness expansion rate using V-NFC-CS separator is merely 0.60%, substantially lower than the 21.7% and 32.0% observed with NFC-CS and GF separators, respectively. To better evaluate hydrogen evolution, the thickness variations of pouch-type Zn||Zn cells (electrode dimensions: 4 cm × 4 cm) were measured after cycling at 2 mA cm−2 and 2 mAh cm−2 for 60 h, as illustrated in Supplementary Fig. 27. When utilizing the GF separator, the cell thickness exhibits a substantial increase of 3.89 mm, corresponding to a volume expansion of ~6.22 cm3. This volume change is primarily attributed to hydrogen evolution. In the case of using NFC-CS separator, the amount of hydrogen evolution declines, though it remains relatively large. In contrast, with the use of V-NFC-CS separator, the increase in cell thickness is significantly diminished. These findings demonstrate the V-NFC-CS separator can effectively inhibit hydrogen evolution.

Fig. 3: Zinc stripping/plating reversibility and separator biodegradability evaluation.
figure 3

DRT profiles of Zn||Zn cells during the GCD process at the 4th cycle: a with V-NFC-CS separator and b with NFC-CS separator. c XRD patterns of the pristine Zn electrode and Zn electrodes after the measurements in Fig. 2h. d, e SEM images and f, g AFM images of the Zn electrodes after the measurements in Fig. 2h: d, f with V-NFC-CS separator and e, g with NFC-CS separator. h Photos of V-NFC-CS and GF separators after being embedded into soil for different time.

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Additionally, with an increasing number of cycles, the ratio of the diffraction intensity of Zn (002) peak to that of Zn (101) peak gradually increases when using V-NFC-CS separator, whereas this ratio decreases with the use of NFC-CS separator. As zinc deposition orientations along the (002) and (101) planes correspond to horizontal and vertical growth behaviors, respectively56,57,58, it can be inferred that the V-NFC-CS separator possesses beneficial effect on promoting horizontal zinc deposition. To corroborate the above observations, SEM was employed to examine the surface morphology of zinc electrodes after the measurements in Fig. 2h, as presented in Fig. 3d, e and Supplementary Fig. 28. The utilization of V-NFC-CS separator results in a flat zinc electrode surface devoid of dendrite formation after cycling, while evident protrusions are discerned at the zinc electrode surface with NFC-CS separator. These protrusions pose a risk of piercing the separator, easily leading to a series of issues such as short circuit. AFM technique was further used to intuitively observe the surface characteristics of cycled Zn electrodes, revealing that the surface roughness of Zn electrode with V-NFC-CS separator is markedly lower than that with NFC-CS separator (Fig. 3f, g). This distinction primarily stems from the inhibition effect of high-modulus V-NFC-CS separator against vertical deposition of zinc metal and possible formation of ZSH byproduct.

The preceding electrochemical tests were conducted at ~25 °C. To further validate the effectiveness of V-NFC-CS separator, the cycling performance of Zn||Zn cells was evaluated at elevated temperatures. As illustrated in Supplementary Fig. 29a, at 70 °C, the life span of the cells employing different separators is significantly shortened to <16 h at 10 mA cm−2 and 2 mAh cm−2. Despite this, the use of V-NFC-CS separator still offers the best stability. After 16 h of testing, all the coin cells using different separators suffer from severe swelling accompanied by cell cracking (Supplementary Fig. 29b), and the cycled zinc metal electrodes exhibit rough surface and intense diffraction peaks ascribed to ZSH (Supplementary Fig. 29c, d), indicative of pronounced hydrogen evolution at 70 °C. When the test temperature is 50 °C (Supplementary Fig. 29e), the cycling stability of the cells is significantly better than that at 70 °C. Among three types of cells, the use of V-NFC-CS separator achieves the longest life span of 1000 h at 50 °C. Besides, V-NFC-CS and GF separators were embedded into soil to evaluate biodegradability. The GF separator retains intact after 60 days (Fig. 3h). In sharp contrast, the V-NFC-CS separator disappears due to complete decomposition, unveiling that this separator owns biodegradable and environmentally friendly attributes59. It should be noted the fast degradation of V-NFC-CS separator occurs in soil, not in the electrolyte, as the soil provides more ideal conditions (e.g., rich microbial community) for the decomposition of biomass materials. This can be confirmed by the fact that there is no obvious change for the V-NFC-CS separator after 60 days of immersion in 2 M ZnSO4 aqueous electrolyte (Supplementary Fig. 30). In addition, the anisotropic architecture of V-NFC-CS separator can be maintained after electrochemical measurement (Supplementary Fig. 31). As shown in Supplementary Fig. 32, the chemical bonds within V-NFC-CS separator still exist after the measurement in Fig. 2h.

Finite element simulations

Finite element simulations were carried out using COMSOL software to better understand the role of anisotropic separator. The outcomes, depicted in Fig. 4a, b, Supplementary Fig. 33, and Supplementary Movie 1, reveal that the current density field with the implementation of V-NFC-CS separator is more homogeneous at the local sites near the surface of deposited zinc metal compared to that using NFC-CS separator. The Zn2+ ion concentration distributions were also simulated, as displayed in Fig. 4c, d, Supplementary Fig. 34, and Supplementary Movie 2. Evidently, the employment of V-NFC-CS separator contributes to a significantly higher concentration of Zn2+ ions at the surface of deposited zinc metal, along with a more uniform Zn2+ ion distribution along the z-axis direction, compared to the use NFC-CS separator. These benefits are mainly derived from the unique architecture of V-NFC-CS separator, which effectively promotes the transport of Zn2+ ions along the z-axis direction. Concurrently, the deposited zinc metal with the use of V-NFC-CS separator exhibits a much more uniform morphology than that with NFC-CS separator. To further comprehend the effect of the mechanical properties of separator on the morphology of deposited zinc metal, a mechano-electrochemical model was established to simulate zinc plating morphologies with two different separators, as presented in Fig. 4e, f, Supplementary Fig. 35, and Supplementary Movie 3. Evidently, zinc metal prefers to be vertically deposited with the use of NFC-CS separator. Fortunately, this tendency toward vertical zinc deposition can be considerably suppressed by using V-NFC-CS separator.

Fig. 4: Finite element simulation results and illustration of zinc deposition process.
figure 4

a, b Current density field distributions at the surface of Zn electrode, c, d Zn2+ ion concentration distributions at the surface of Zn electrode, and e, f simulated zinc plating morphologies after 24 s: a, c, e with NFC-CS separator and b, d, f with V-NFC-CS separator. Graphic illustration of zinc plating behaviors: g with NFC-CS separator and h with V-NFC-CS separator.

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Based on the results in previous sections, the zinc deposition morphologies are demonstrated in Fig. 4g, h. Accompanied by the uneven current density field and Zn2+ ion concentration distribution at the surface of zinc metal electrode with the use of NFC-CS separator, Zn2+ ions tend to migrate toward pristine protuberances and existing nucleation sites, leading to vertical zinc deposition. Due to the low modulus of NFC-CS separator, the vertically deposited zinc metal would evolve into severe dendritic growth, which would exacerbate parasitic reactions such as ZSH formation. On the contrary, these unfavorable effects can be circumvented by employing V-NFC-CS separator. In one respect, the high modulus of V-NFC-CS separator along the z-axis direction can effectively resist the vertical growth trend of zinc metal and ZSH byproduct. In another respect, fast Zn2+ ion transport along the aligned vertical channels of V-NFC-CS separator can alleviate Zn2+ ion concentration polarization at the zinc metal electrode surface, thereby suppressing hydrogen evolution reaction. These benefits of V-NFC-CS separator in both respects arise from the anisotropic architecture, which is anticipated to be advantageous in other battery systems as well.

The crucial factor for attaining highly durable AZIBs lies in the high reversibility of zinc stripping/plating. To evaluate this aspect, Zn||Cu cells incorporating V-NFC-CS or NFC-CS separator were subjected to Coulomb efficiency (CE) testing, aiming to discern their impact on the reversibility of zinc-negative electrodes60. As depicted in Fig. 5a, the initial CE with V-NFC-CS separator stands at 79.04%, and then the CE stabilizes at ~99.0% from 20th to 600th cycles. In contrast, the use of NFC-CS separator results in a considerably lower initial CE of 62.96%, with short circuit issue arising before 255 cycles. Notably, the life span of the Zn||Cu cell with V-NFC-CS separator (1200 h) is longer than that of Zn||Cu cells with different separators in previous reports, as compared in Supplementary Table 2. Meanwhile, the Zn||Cu cell with V-NFC-CS separator manifests a diminished voltage gap (46 mV, between charge and discharge plateaus, Fig. 5b), compared to that using NFC-CS separator (148 mV, Supplementary Fig. 36), indicating that the electrochemical kinetics can be significantly enhanced by the V-NFC-CS separator61. By analyzing the initial voltage–capacity curves of Zn||Cu cells, the nucleation overpotential values can be estimated (Fig. 5c). This value equals 41 mV for the V-NFC-CS separator, considerably lower than that for the NFC-CS separator (71 mV). A lower nucleation overpotential implies mitigated nucleation barrier of zinc metal, hence reducing the size of Zn grains and promoting homogeneous zinc deposition62,63.

Fig. 5: Electrochemical behaviors of Zn||Cu cells and Zn||MnO2 batteries.
figure 5

a CE vs. cycle number of Zn||Cu cells with two different separators at 1 mA cm−2 and 1 mAh cm−2. b Voltage–capacity curves of Zn||Cu cell with V-NFC-CS separator at different cycles. c Initial voltage–time curves of Zn||Cu cells with two different separators at 1 mA cm−2. d Rate performance (N/P ratio: 11.0) and e cycling performance (N/P ratio: 16.4) at 1 A g−1 of Zn||MnO2 batteries with two different separators (CNT/MnO2: 1.8 mg cm−2). f Cycling performance of Zn||MnO2 batteries with two different separators under a low N/P ratio of 2.06 at 1 A g−1 (CNT/MnO2: 8.2 mg cm−2, zinc metal: 3.9 mg cm−2). Photos of g powering a LED light strip and h powering a LED panel by a pouch-type Zn||MnO2 cell with V-NFC-CS separator. The aforementioned N/P ratios are derived from the initial cycle when using V-NFC-CS separator.

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Electrochemical performance of full batteries

Figure 5d and Supplementary Fig. 37 illustrate the rate performance of Zn||MnO2 batteries with V-NFC-CS or NFC-CS separators. The battery incorporating V-NFC-CS separator delivers specific discharge capacity of 288.7 mAh g−1 at the 10th cycle of 0.2 A g−1. Subsequent increments in specific current to 0.5, 1, 2, and 5 A g−1 yield specific discharge capacities of 240.6, 195.1, 147.6, and 104.1 mAh g−1, respectively, at the 10th cycle of each specific current. These capacity values are obviously larger than those employing NFC-CS separator or conventional GF separator (Supplementary Fig. 38). This enhancement is likely attributed to the accelerated electrochemical reaction kinetics facilitated by V-NFC-CS separator, which significantly enhances ionic transports and reduces Rct (Supplementary Fig. 39)64. The cyclability is a critical parameter for batteries. The Zn||MnO2 battery with V-NFC-CS separator can still give a large specific capacity of 190.9 mAh g−1 after 1000 cycles at 1 A g−1 (Fig. 5e), corresponding to a large capacity retention of 96.2%. Such capacity retention is superior to many previously reported Zn||MnO2 batteries using different separators, such as the ones listed in Supplementary Table 3. In contrast, the use of NFC-CS separator can only provide 119.3 mAh g−1 after 1000 cycles with a much lower capacity retention of 63.6%, while the Zn||MnO2 battery with GF separator experiences much faster capacity fading (Supplementary Fig. 40). H11Al2V6O23.2 (HAVO) was also employed as the positive electrode material, as displayed in Supplementary Fig. 40. The utilization of V-NFC-CS separator contributes to significantly enhanced rate capability and cycling stability, compared to the use of other separators. The cyclability of the Zn||HAVO battery with V-NFC-CS separator also exceeds that of many previously reported AZIBs using various separators and V-based positive electrode materials, as presented in Supplementary Table 4. To better reveal the advantages of V-NFC-CS separator, a zinc ion hybrid supercapacitor (ZHS) was assembled with activated carbon (AC) as the positive electrode material. This ZHS achieves a large capacity retention of 99.2% after 5000 cycles at 1 A g−1 (Supplementary Fig. 42). Instead, the use of NFC-CS separator results in drastic capacity attenuation after 2600 cycles, accompanied by a much greater fluctuation in CE.

The realization of a low negative/positive electrode capacity (N/P) ratio constitutes a pivotal aspect in evaluating practical application potential65. Herein, the mass loading of carbon nanotube (CNT)/MnO2 positive electrode material was augmented to 8.2 mg cm−2, while a Cu foam electrodeposited with 3.9 mg cm−2 zinc metal was utilized as the negative electrode. When the V-NFC-CS separator is used, the assembled Zn||MnO2 battery, featuring a low N/P ratio of 2.06, can still maintain 172.1 mAh g−1 after 200 cycles at 1 A g−1, in accordance with a large capacity retention of 90.9% (Fig. 5f). Conversely, the utilization of NFC-CS separator leads to a continuous decline in capacity, with merely 131.3 mAh g−1 retained after the same number of cycles. The improved cyclability with the use of V-NFC-CS separator can also be reflected by more stable CE compared to the use of NFC-CS separator. Besides, the rate performance of the Zn||MnO2 battery with V-NFC-CS separator is obviously superior to that with NFC-CS separator under a low N/P ratio (Supplementary Fig. 43). When considering the total mass of positive electrode active material, zinc metal, and separator, the energy density of the coin-cell-type battery with V-NFC-CS separator is estimated to be 205.6 Wh kg−1 at the last cycle of 0.2 A g−1. To further substantiate the applicability of V-NFC-CS separator, flexible pouch-type Zn||MnO2 batteries were constructed with electrode dimensions of ~3 cm × 3.5 cm and a large positive electrode active material mass loading of 11.8 mg cm−2, using aluminum plastic packaging film (Supplementary Fig. 44a). In this configuration, the pouch-type battery with V-NFC-CS separator can still offer 144.3 mAh g−1 after 300 cycles with a large capacity retention of 77.8%, which is considerably higher than that with NFC-CS separator (53.9%, Supplementary Fig. 44b). Moreover, when two Zn||MnO2 batteries connected in series are encapsulated into a single pouch-type cell, the cell is able to power an LED light strip both in a normal state and under bending, as shown in Fig. 5g. In addition, the pouch-type Zn||MnO2 cell can successfully power a LED panel with a rated voltage of 3 V and a rate power of 2 W (Fig. 5h). These results disclose high energy density of Zn||MnO2 battery with V-NFC-CS separator and its good capability to withstand external strain. Furthermore, a pouch-type Zn||I2 battery with a large mass loading of 12.5 mg cm−2 for the I2 positive electrode active material was constructed using V-NFC-CS separator. As displayed in Supplementary Fig. 45, this battery can still offer 85.5% of its initial capacity after 1500 cycles.

Discussion

In summary, a wood-inspired thin anisotropic separator (V-NFC-CS, 23 μm thickness), consisting of nanocellulose and chitosan, is developed via directional freezing and compression reinforcement, aiming to address severe dendrite issues in AZIBs. Benefiting from the biomimetic design, the mechanical properties along the oriented direction can be considerably improved and Zn2+ ion transport can be significantly facilitated within the vertically arranged channels. Therefore, the V-NFC-CS separator simultaneously manifests substantial modulus of 7.3 GPa and large ionic conductivity reaching 20.5 mS cm−1 along the z-axis direction. Besides, this separator owns good biodegradability and hydrophilicity. Both theoretical calculations and experimental results confirm that the V-NFC-CS separator can effectively suppress the vertical deposition of zinc metal, contributing to dendrite-free characteristic and dramatically inhibited parasitic reactions. Concomitantly, the V-NFC-CS separator imparts fast stripping/plating kinetics and good reversibility to zinc electrodes. Consequently, the Zn||Zn cell with V-NFC-CS separator delivers reduced overpotential and prolonged life span of 1000 h at 10 mA cm−2 and 2 mAh cm−2, and sustains reliable operation even under rather high areal capacity of 25 mAh cm−2 and large DOD of 85.4%. Moreover, in the context of Zn||MnO2 batteries, the use of V-NFC-CS separator realizes large capacity retention of 96.2% after 1000 cycles and great rate capability. The beneficial effects of the V-NFC-CS separator can also be observed under low N/P ratio condition and in the configurations of pouch-type battery, Zn||HAVO battery, and ZHS device. This study not only proposes a biomimetic concept for high-performance AZIBs but also highlights the importance of modulus enhancement for separators.

Methods

Materials

Acetic acid (AR), H2O2 solution (AR), HCL solution (AR), and I2 (99.99%) were purchased from Sinopharm Chemical Reagent Co., Ltd. Chitosan (200–400 mPa·s), Na2SO3 (≥98.0%), Al(NO3)3·9H2O (99%), MnSO4·H2O (99%), ZnSO·7H2O (99%), and N-methy1-2-pyrrolidone (NMP, 99.5%) were acquired from Aladdin. NaOH (≥98%) was obtained from Macklin. V2O5 was sourced from Sigma-Aldrich. Carbon black (CB) was bought from Alfa Aesar. KMnO4 (AR) was ordered from Nanjing Reagent. Zn(CF3SO3)2 (99%) was attained from Tokyo Chemical Industry. Polyvinylidene fluoride (PVDF) and aluminum plastic packaging film were supplied by Canrd. CNT and AC were provided by Nanjing XFNANO Materials Tech Co., Ltd. Zn and Ti foils were procured from Qinghe Haoxuan Metal Materials Co., Ltd.

Preparation of NFC

Two grams of balsa wood powders was immersed into 60 mL aqueous solution containing 0.15 mol NaOH and 0.023 mol Na2SO3, followed by thermal treatment with oil bath at 80 °C for 4 h. Then, the product was washed with deionized (DI) water, immersed in 8.5 wt% H2O2 aqueous solution, and then treated at 110 °C for 3 h utilizing oil bath. After washing and drying, cellulose was obtained and then dispersed in DI water at a weight ratio of 1:5. The obtained dispersion was sonicated at 450 W for 3 h, resulting in the formation of NFC.

Preparation of V-NFC-CS separator

Two grams NFC was dispersed in 20 mL DI water to obtain dispersion A, while 1 g chitosan and 400 μL acetic acid were dissolved in 40 mL DI water to obtain solution B. A certain amount of solution B was added into dispersion A, and then stirred to form a homogeneous dispersion. Four milliliters of the above mixed dispersion was poured onto the top of a copper ingot, approximately half of which was immersed in liquid nitrogen. After 5 min, a thin membrane was produced, which was then freeze dried and pressed at 50 bar for 5 min. When 0, 8, 16, and 24 mL solution B was used, the obtained separators were abbreviated as V-NFC, V-NFC-CS (10%), V-NFC-CS (20%), and V-NFC-CS (30%), respectively. For comparison, V-CS separator was prepared by adding 16 mL solution B to 20 mL DI water, while other conditions remained unchanged. In addition, isotropic NFC-CS separator was prepared by a same procedure as V-NFC-CS (20%) except for that the mixed dispersion was poured into a mold, which was frozen in a refrigerator.

Synthesis of positive electrode materials

The CNT/MnO2 positive electrode material was prepared via a facile hydrothermal method. Typically, 0.45 g KMnO4 and 30 mg CNT were added to 40 mL DI water and stirred for 30 min. Then, 1 mL HCl solution (37%) was added into the above dispersion under stirring. After 1 h stirring, the dispersion was transferred into a Teflon-lined stainless-steel (SS) autoclave, which was maintained at 120 °C for 16 h. After washing and drying, black product (i.e., CNT/MnO2) was obtained. A 60 mL aqueous dispersion containing 4 mmol V2O5, 1 mmol Al(NO3)3·9H2O, and 1 wt% H2O2 was sealed in a Teflon-lined SS autoclave, which was maintained at 180 °C for 16 h. After washing and drying, HAVO was produced. For the preparation of AC/I2 positive electrode material, AC and I2 powders were mixed and then sealed in a Teflon-lined SS autoclave, which was maintained at 90 °C for 6 h.

Materials characterization

XRD, SEM, and FTIR measurements were carried out on Rigaku Ultima IV using Cu Kα radiation, Hitachi Regulus 8100, and Thermo Electron Nicolet-360, respectively. The tensile properties and electrolyte wettability of different separators were evaluated by SANS UTM2502 universal testing machine and Dataphysics OCA15EC contact angle meter, respectively. The modulus and hardness of separators were characterized by iMicro nanoindenter. The modulus and surface roughness of separators and zinc electrodes were evaluated by Bruker Dimension ICON AFM. The zeta potential values were collected by Malvern Zetasizer Nano ZS instrument.

Electrochemical measurements

In total, 70 wt% CNT/MnO2 (140 mg), 20 wt% CB (40 mg), and 10 wt% PVDF (20 mg) were homogeneously dispersed in 2 mL NMP through magnetic stirring in an ambient air atmosphere at ~25 °C and then pasted onto a Ti foil. After drying in an oven and cutting into desired shapes, CNT/MnO2 positive electrodes were obtained. Similarly, HAVO and AC positive electrodes were prepared. The AC/I2 positive electrodes were also prepared using a similar process, with the exception that the AC/I2 accounts for 80 wt%. Unless specified, CR2016 coin-cell configuration was utilized and 100 μL liquid electrolyte was added to each coin cell. Zn||MnO2 batteries were assembled by using CNT/α-MnO2 positive electrode, zinc foil negative electrode, and 2 M ZnSO4 + 0.2 M MnSO4 aqueous electrolyte. Zn||HAVO batteries were assembled by using HAVO positive electrode, zinc foil negative electrode, and 3 M Zn(CF3SO3)2 aqueous electrolyte. Zn||AC ZHSs were assembled by using AC positive electrode, zinc foil negative electrode, and 2 M ZnSO4 aqueous electrolyte. Pouch-type Zn||I2 batteries were constructed by using AC/I2 positive electrode, zinc foil negative electrode, and 2 M ZnSO4 aqueous electrolyte. The specific current and specific capacity of Zn||I2 batteries were calculated based on the mass of I2. Zn||Zn symmetric and Zn||Cu asymmetric cells were constructed by using 2 M ZnSO4 aqueous electrolyte and zinc foil negative electrode. Fifty micrometers-thick zinc foils and 200-μm-thick zinc foils were used for the measurements in Fig. 2f, g, respectively. In other cases, 10-μm-thick zinc foils were employed. CA and EIS measurements were conducted on Bio-Logic VSP-300 multichannel electrochemical workstation. During the EIS measurements, the potentiostatic mode was employed with frequencies ranging from 1 MHz to 100 mHz and a sinus amplitude of 10 mV, and the data collection method involved capturing 8 points per decade of frequency in logarithm spacing. Unless otherwise specified, all EIS measurements were conducted at open circuit potential prior to initiating the electrochemical process. GCD tests were performed on LAND CT2001A battery testing systems. Unless otherwise specified, all electrochemical measurements were carried out at ~25 °C without the use of climatic chambers. For the ex-situ measurements, the electrodes were collected by disassembling the coin cells, after which the electrodes were removed and washed with DI water, followed by natural drying in an ambient air atmosphere.

Ionic conductivity measurements

The ionic conductivity (σ) values of the separators (infiltrated with 2 M ZnSO4 electrolyte) were estimated by EIS tests using SS||SS symmetric cells. The σ (mS cm−1) could be calculated through the following equation:

$$\sigma=\frac{L}{{RS}}$$
(2)

where L is the thickness of separator, S is the area of SS electrode, and R (Ω) represents the bulk resistance acquired from the intercept of Nyquist plots with the real axis.

Measurements of t Zn 2+

The tZn2+ was determined through CA and EIS tests on Zn||Zn symmetric cells and calculated by the following equation:

$${t}_{{{\rm{Zn}}}^{2+}}=\frac{{I}_{{\rm{S}}}(\Delta V-{I}_{0}{R}_{0})}{{I}_{0}(\Delta V-{I}_{{\rm{s}}}{R}_{{\rm{s}}})}$$
(3)

where I0 and Is are the initial and steady-state current, respectively; ΔV is the applied constant potential (10 mV); and R0 and Rs are the initial and steady-state interfacial impedances of the cells estimated by EIS tests, respectively.

Finite element simulations

Finite element simulations were performed using COMSOL Multiphysics 6.2 software with the “Tertiary Current Distribution” and “Phase Field” modules. A transient simulation of the process was carried out in a zone filled with electrolyte. The Zn2+ ion transfers were simulated by Fick's law. The relationship between the diffusion coefficient and the electric mobility, the equilibrium potential of the electrode surface, and the electrode reaction for the electrode surface were described by the Nernst–Einstein relation, the Nernst equation, and the Butler–Volmer kinetics expression, respectively. To simulate dynamic zinc deposition behaviors, a two-dimensional mechano-electrochemical model was established. The two phases and three components in this system were distinguished by a non-conserved order parameter ξ (electrolyte, ξ = 0; zinc metal negative electrode, ξ = 1) and a concentration set ci (i = Zn, Zn2+, and SO42−, respectively). The local electrostatic potential was denoted as ϕi (i = Zn and e, representing zinc metal electrode and electrolyte, respectively) and the displacement field was represented by u. The total free energy of this system was given by the following equation:

$$F={\int } _{V}\left[ \, {{f}_{{\rm{grad}}}}\left(\xi \right)+{{f}_{\rm{ch}}}\left(\xi,{{c}_{i}}\right)+{{f}_{\rm{elec}}}\left(\xi,{{c}_{i}},{{\phi }_{i}}\right)+{{f}_{\rm{els}}}\left(\xi,u \right)\right]{\rm{d}}V$$
(4)

where \({f}_{{\rm{grad}}}\), \({f}_{\! \! \! {\rm{ch}}}\), \({f}_{\! \! \! {\rm{elec}}}\), and \({f}_{\! \! \! {\rm{els}}}\) represent the local energy density from the gradient, chemical, electrostatic, and elastic contributions, respectively. The other equations used for the simulations in this work referred to those proposed in previous reports66,67.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.