Recent advances in flexible aqueous zinc-based rechargeable batteries

Electrospun freestanding anodes for metal-ion batteries: structural design and application

With the rapid development of flexible electronic devices, flexible metal-ion batteries have attracted considerable interest. One-dimensional (1D) nanofiber materials fabricated through electrospinning are regarded as excellent candidates for flexible freestanding anodes due to their high specific surface area, short electron transport paths, and excellent flexibility. They demonstrate impressive application potential in meeting the demand for deformation and outstanding electrochemical performance. This comprehensive review delves into their structural design, such as porous, core-shell, hollow, and composite structures, with particular detail on the approaches, polymer combination, and post-treatment methods. We focus on the contribution of different structures to stability, reversible capacity, long-term cycling, and rate performance during the charge/discharge process of the freestanding nanofibrous anodes. We introduce the combination of commonly used silicon-based materials, alloys, metal oxides, and metal sulfides with multi-structure nanofibers used in anodes. The paper explains how this combination overcomes the difficulties encountered by active materials in different types of metal-ion batteries. Finally, the paper concludes and discusses the challenges and prospects of electrospinning for enhancing freestanding anode and flexible metal-ion batteries.

Dextran stabilised hematite: a sustainable anode in aqueous electrolytes

During the last decades, the use of innovative hybrid materials in energy storage devices has led to notable advances in the field. However, further enhancement of their electrochemical performance faces significant challenges nowadays, imposed by the materials used in the electrodes and the electrolyte. Such problems include the high solubility of both the organic and the inorganic anode components in the electrolyte as well as the limited intrinsic electronic conductivity and substantial volume variation of the materials during cycling. The present work focuses on the fabrication of novel and sustainable anode electrodes for use in energy storage devices, utilizing cross-linked oxidized dextran (Ox-Dex) as the binder and hematite (α-Fe2O3) cubes as the active component. The ion diffusion mechanism within the anode electrode materials, as well as their cycling stability, were studied via cyclic voltammetry measurements, using Li+, Zn2+ and Al3+ aqueous electrolytes. The hybrid iron oxide electrodes exhibited the highest electrochemical performance in the Al2(SO4)3 electrolyte (3000 mA g-1), followed by ZnSO4 (2000 mA g-1) and Li2SO4 (800 mA g-1). The differences in the performance of the anodes for the three investigated electrolytes were attributed to the ionic radii of Li+, Zn2+ and Al3+, which affect the rate of ion diffusion within the material lattice exhibiting the highest diffusion coefficient of 4.64 × 10-9 cm2 s-1 in Al3+. Notably, the hybrid anodes demonstrated superior cycling performance (with the lowest variance percentage of 1.3% for hybrid compared to 38.1% for the bare in the presence of Zn2+), underlining the pivotal role of the natural binder. This was attributed to hydrogen bonding interactions, which increase the contact points between the inorganic and polymeric components, resulting in a more uniform network structure. Additionally, the cross-linking of Ox-Dex promotes stability and tolerance to the volume expansion of the electrodes. These results underscore the immense potential of the proposed hybrid electrodes in the field of energy storage.

Stabilizing zinc powder anodes via bifunctional MXene towards flexible zinc-ion batteries

Flexible zinc (Zn) batteries have gained considerable attention as wearable energy storage devices because of their inherent safety and high theoretical capacity. However, conventional Zn anodes suffer from dendrite growth, high rigidity, and poor cycling stability issues, hindering their practical application in flexible zinc-ion batteries. Herein, a dendrite-free and flexible Zn anode is designed using direct ink writing (DIW) printed MXene as a flexible and highly conductive current collector and MXene-wrapped Zn powder (ZnP) as the active material by carefully optimising the rheological properties of MXene-based dispersion. As a result, the synergistic effects of the MXene-based current collector and the MXene protective layer promoted dendrite-free Zn deposition and prevented side reactions, achieving an outstanding cycling performance that exceeded 130 h at a high depth of discharge of 30%. When paired with a Vanadium pentoxide (V2O5)-based cathode, the flexible full cell demonstrated stable electrochemical performance under mechanical deformation and can power electronic devices, presenting a promising pathway for the development of flexible zinc-ion batteries.

Blocking Interfacial Proton Transport via Self-Assembled Monolayer for Hydrogen Evolution-Free Zinc Batteries

Aqueous Zn-ion batteries (ZIBs) are promising next-generation energy storage devices, yet suffer from the issues of hydrogen evolution reaction (HER) and intricate side reactions on the Zn anode surface. The hydrogen (H)-bond networks play a critical role in interfacial proton transport that may closely relate to HER but are rarely investigated. Herein, we report a self-assembled monolayer (SAM) strategy which is constructed by anchoring ionic liquid cations on Ti3C2Tx substrate for HER-free Zn anode. Molecule dynamics simulations reveal that the rationally designed SAM with a high coordination number of water molecules (25-27, 4-6 for Zn2+) largely reduces the interfacial densities of H2O molecules, therefore breaking the connectivity of H-bond networks and blocking proton transport on the interface, by which the HER is suppressed. Then, a series of in situ characterizations demonstrate that negligible amounts of H2 gas are collected from the Zn@SAM-MXene anode. Consequently, the symmetric cell enables a long-cycling life of 3000 h at 1 mA cm-2 and 1000 h at 5 mA cm-2. More significantly, the stable Zn@SAM-MXene films are successfully used for coin full cells showing high-capacity retention of over 94 % after 1000 cycles and large-area (10×5 cm2) pouch cells with desired performance.

Electrolyte Additives for Stable Zn Anodes

Zn-ion batteries are regarded as the most promising batteries for next-generation, large-scale energy storage because of their low cost, high safety, and eco-friendly nature. The use of aqueous electrolytes results in poor reversibility and leads to many challenges related to the Zn anode. Electrolyte additives can effectively address many such challenges, including dendrite growth and corrosion. This review provides a comprehensive introduction to the major challenges in and current strategies used for Zn anode protection. In particular, an in-depth and fundamental understanding is provided of the various functions of electrolyte additives, including electrostatic shielding, adsorption, in situ solid electrolyte interphase formation, enhancing water stability, and surface texture regulation. Potential future research directions for electrolyte additives used in aqueous Zn-ion batteries are also discussed.

Strategies Toward Stretchable Aqueous Zn-based Batteries for Wearable Electronics from Components to Devices

Recently, aqueous Zn-based batteries (AZBs) are receiving increased attention in wearable and implantable electronics due to the low cost, high safety, high eco-efficiency, and relatively high energy density. However, it is still a big challenge to develop stretchable AZBs (SAZBs) which can be conformally folded, crumpled, and stretched with human body motions. Although a lot of efforts have been dedicated to constructions of SAZBs, a comprehensive review which focuses on summarizing stretchable materials, device configurations and challenges of SAZBs is needed. Herein, this review attempts to critically review the latest developments and progress in stretchable electrodes, electrolytes, packaging materials and device configurations in detail. Furthermore, these challenges and potential future research directions in the field of SAZBs are also discussed.

Recent Advances in Bioinspired Hydrogels: Materials, Devices, and Biosignal Computing

The remarkable ability of biological systems to sense and adapt to complex environmental conditions has inspired new materials and novel designs for next-generation wearable devices. Hydrogels are being intensively investigated for their versatile functions in wearable devices due to their superior softness, biocompatibility, and rapid stimulus response. This review focuses on recent strategies for developing bioinspired hydrogel wearable devices that can accommodate mechanical strain and integrate seamlessly with biological systems. We will provide an overview of different types of bioinspired hydrogels tailored for wearable devices. Next, we will discuss the recent progress of bioinspired hydrogel wearable devices such as electronic skin and smart contact lenses. Also, we will comprehensively summarize biosignal readout methods for hydrogel wearable devices as well as advances in powering and wireless data transmission technologies. Finally, current challenges facing these wearable devices are discussed, and future directions are proposed.

Photocorrosion-Based BiOCl Photothermal Materials for Synergistic Solar-Driven Desalination and Photoelectrochemistry Energy Storage and Release

Solar-driven interfacial evaporation is one of the most promising desalination technologies. However, few studies have effectively combined energy storage with evaporation processes. Here, a novel multifunctional interfacial evaporator, calcium alginate hydrogel/bismuth oxychloride/carbon black (HBiC), is designed, which integrates the characteristics of interfacial evaporation and direct photoelectric conversion. Under illumination, the Bi nanoparticles which were produced by photoetching of BiOCl and its reaction heat are simultaneously used for the heating of water molecules. Meanwhile, part of the solar energy is converted into chemical energy through the photocorrosion reaction and stored in HBiC. At night, Bi NPs undergo autooxidation reaction and an electric current is generated during this process (like a metal-air battery), in which the maximum current density is more than 15 μA cm^-2. This scientific design cleverly combines desalination with power generation and provides a new development direction for energy collection and storage.

Facile and effective defect engineering strategy boosting ammonium vanadate nanoribbon for high performance aqueous zinc-ion batteries

Vanadium-based oxides have gained widespread attention as promising cathode materials for aqueous zinc-ion batteries (AZIBs) due to their abundant valences, high theoretical capacity and low cost. However, the intrinsic sluggish kinetics and unsatisfactory conductivity have severely hampered their further development. Herein, a facile and effective defect engineering strategy was developed at room temperature to prepare the defective (NH₄)₂V₁₀O₂₅·8H₂O (d-NHVO) nanoribbon with plenty of oxygen vacancies. Owing to the introduction of oxygen vacancies, the d-NHVO nanoribbon possessed more active sites, excellent electronic conductivity and fast ion diffusion kinetics. Benefiting from these advantages, the d-NHVO nanoribbon as an aqueous zinc-ion battery cathode material exhibited superior specific capacity (512 mAh g^-1 at 0.3 A g^-1), excellent rate capability and long-term cycle performance. Simultaneously, the storage mechanism of the d-NHVO nanoribbon was clarified via comprehensive characterizations. Furthermore, the pouch battery based on the d-NHVO nanoribbon was fabricated and presented eminent flexibility and feasibility. This work provides a novel thought for simple and efficient development of high- performance vanadium-based oxides cathode materials for AZIBs.

Rational Design of Flexible Zn-Based Batteries for Wearable Electronic Devices

The advent of 5G and the Internet of Things has spawned a demand for wearable electronic devices. However, the lack of a suitable flexible energy storage system has become the "Achilles' Heel" of wearable electronic devices. Additional problems during the transformation of the battery structure from conventional to flexible also present a severe challenge to the battery design. Flexible Zn-based batteries, including Zn-ion batteries and Zn-air batteries, have long been considered promising candidates due to their high safety, eco-efficiency, substantial reserve, and low cost. In the past decade, researchers have come up with elaborate designs for each portion of flexible Zn-based batteries to improve the ionic conductivities, mechanical properties, environment adaptabilities, and scalable productions. It would be helpful to summarize the reported strategies and compare their pros and cons to facilitate further research toward the commercialization of flexible Zn-based batteries. In this review, the current progress in developing flexible Zn-based batteries is comprehensively reviewed, including their electrolytes, cathodes, and anodes, and discussed in terms of their synthesis, characterization, and performance validation. By clarifying the challenges in flexible Zn-based battery design, we summarize the methodology from previous investigations and propose challenges for future development. In the end, a research paradigm of Zn-based batteries is summarized to fit the burgeoning requirement of wearable electronic devices in an iterative process, which will benefit the future development of Zn-based batteries.

Ultrafast Synthesis of Metal-Layered Hydroxides in a Dozen Seconds for High-Performance Aqueous Zn (Micro-) Battery

Efficient synthesis of transition metal hydroxides on conductive substrate is essential for enhancing their merits in industrialization of energy storage field. However, most of the synthetic routes at present mainly rely on traditional bottom-up method, which involves tedious steps, time-consuming treatments, or additional alkaline media, and is unfavorable for high-efficiency production. Herein, we present a facile, ultrafast and general avenue to synthesize transition metal hydroxides on carbon substrate within 13 s by Joule-heating method. With high reaction kinetics caused by the instantaneous high temperature, seven kinds of transition metal-layered hydroxides (TM-LDHs) are formed on carbon cloth. Therein, the fastest synthesis rate reaches ~ 0.46 cm2 s-1. Density functional theory calculations further demonstrate the nucleation energy barriers and potential mechanism for the formation of metal-based hydroxides on carbon substrates. This efficient approach avoids the use of extra agents, multiple steps, and long production time and endows the LDHs@carbon cloth with outstanding flexibility and machinability, showing practical advantages in both common and micro-zinc ion-based energy storage devices. To prove its utility, as a cathode in rechargeable aqueous alkaline Zn (micro-) battery, the NiCo LDH@carbon cloth exhibits a high energy density, superior to most transition metal LDH materials reported so far.

A strategy for anode modification for future zinc-based battery application

In the past several years, rechargeable zinc batteries, featuring the merits of low cost, environmental friendliness, easy manufacturing, and enhanced safety, have, attracted much attention. Zinc (Zn) anodes for zinc metal batteries play an important role. In this review, the fundamental understanding of these batteries and modification strategies to deal with the problematic issues for Zn anodes, including dendrite growth, corrosion, and the hydrogen evolution phenomenon will be summarized. The practical application of Zn anodes can still lead to Zn dendrites, various side reactions, and serious safety risks. Therefore, metal-free anodes for "rocking chair" zinc ion batteries to replace Zn anodes are systemically reviewed. The performance and the zinc storage mechanism of metal-free anodes will be discussed. Subsequently, a "rocking chair" zinc ion battery prototype selected as a recent example is assessed to explore the merits and demerits of Zn anodes and metal-free anodes. To conclude, a perspective on the future of zinc metal batteries and "rocking chair" zinc ion batteries is presented. It is hoped that this review may provide for further improvement of commercial rechargeable zinc batteries.

Sub-1 nm MoC Quantum Dots Decorating N-Doped Graphene as Advanced Electrocatalysts of Flexible Hybrid Alkali-Acid Zn-Quinone Battery

The development of flexible energy devices is envisaged to revolutionize the next generation of the wearable electronics industry, the practical application yet faces critical issues of low power density, poor cycling stability, and low energy density. Herein, the authors report a newly flexible hybrid Zn-quinone battery (h-ZnQB) with acidic gel in the cathode and alkaline gel in the anode, in which proton (H⁺ ) and hydroxide ions (OH^- ) are served as the ion charge carriers for acidic quinone cathode and alkaline Zn anode. To this end, the nanohybrids of sub-1 nm MoC quantum dots decorating nitrogen-doped ultrathin graphene (MoC QDs/NG) are developed as the advanced cathode electrocatalysts toward redox conversion between quinone and hydroquinone (H₂ Q/Q). Comprehensive characterization studies and density functional theory (DFT) calculations reveal that high valent Mo species originating from the size-effects serve as the active sites for the conversion of H₂ Q/Q, contributing to the impressive catalytic performance. The as-developed flexible h-ZnQB displays a high open-circuit voltage of 1.74 V with a specific capacity of 223.3 mAh g^-1 and an energy density of 350 Wh kg^-1 at 0.2 A g^-1 , thanks to the fast kinetics of charge carriers (H⁺ and OH^- ), the high activity of the catalyst, and the elaborate design of alkali-acid gel electrolytes.

Research Progresses and Challenges of Flexible Zinc Battery

Flexible zinc batteries have great potential in wearable electronic devices due to their high safety, low cost, and environmental friendliness. In the past few years, a great deal of work on flexible zinc batteries has been reported, with exciting results. Therefore, many solutions have been proposed in electrode design and electrolyte preparation to ensure the desired flexibility without sacrificing the capacity. This paper reviews the recent progress of flexible zinc batteries. We discuss the differences between various anode materials, cathode materials, and electrolytes, introduce the differences of electrode preparation methods of active materials on flexible substrates and their influence on the performance of the battery. Finally, the challenges and future research trends of flexible zinc batteries in capacity and mechanical properties are pointed out.

Smart Solar-Metal-Air Batteries Based on BiOCl Photocorrosion for Monolithic Solar Energy Conversion and Storage

Herein, a BiOCl hydrogel film electrode featuring excellent photocorrosion and regeneration properties acts as the anode to construct a novel type of smart solar-metal-air batteries (SMABs), which combines the characteristics of solar cells (direct photovoltaic conversion) and metal-air batteries (electric energy storage and release interacting with atmosphere). The cyclic photocorrosion processes between BiOCl (Bi³⁺ ) and Bi can simply be achieved by solar light illumination and standing in the dark. Upon illumination, the device takes open-circuit configuration to charge itself from the sunlight. Notably, in this system, the converted solar energy can be stored in the SMABs without the need of external assistance. In the discharging process in the dark, Bi⁰ spontaneously turns back to Bi³⁺ producing electrons to induce the oxygen reduction reaction. With an illumination of 15 min, the battery with an electrode area of 1 cm² can be continuously discharged for ≈3000 s. Taking elemental Bi as the calculation object, the theoretical capacity of the SMABs is 384.75 mAh g^-1 , showing its potential application in energy storage. This novel type of SMABs is developed based on the unique photocorrosive and self-oxidation reaction of BiOCl to achieve photochemical energy generation and storage.

Recent Advances in Electrolytes for "Beyond Aqueous" Zinc-Ion Batteries

With the growing demands for large-scale energy storage, Zn-ion batteries (ZIBs) with distinct advantages, including resource abundance, low-cost, high-safety, and acceptable energy density, are considered as potential substitutes for Li-ion batteries. Although numerous efforts are devoted to design and develop high performance cathodes and aqueous electrolytes for ZIBs, many challenges, such as hydrogen evolution reaction, water evaporation, and liquid leakage, have greatly hindered the development of aqueous ZIBs. Developing "beyond aqueous" electrolytes can be able to avoid these issues due to the absence of water, which are beneficial for the achieving of highly efficient ZIBs. In this review, the recent development of the "beyond aqueous" electrolytes, including conventional organic electrolytes, ionic liquid, all-solid-state, quasi-solid-state electrolytes, and deep eutectic electrolytes are presented. The critical issues and the corresponding strategies of the designing of "beyond aqueous" electrolytes for ZIBs are also summarized.

Metal organic complexes as an artificial solid-electrolyte interface with Zn-ion transfer promotion for long-life zinc metal batteries

Metal organic complexes as an artificial solid-electrolyte interface (MOC-SEI) have been generated via in situ coordinative polymerization between Zn²⁺ and organic ligand molecules. Compared to conventional anodes, the MOC-SEI coated anode significantly prolongs the lifespan from 100 h to 1450 h for the Zn||Zn symmetrical cells and increases the reversible capacity up to 160 mA h g^-1 after 1100 cycles for the Zn||V₂O₅ full-cells.

Engineering Hierarchical Co@N-Doped Carbon Nanotubes/α-Ni(OH)2 Heterostructures on Carbon Cloth Enabling High-Performance Aqueous Nickel-Zinc Batteries

Searching for high-performance Ni-based cathodes plays an important role in developing better aqueous nickel-zinc (Ni-Zn) batteries. For this purpose, herein, we demonstrate the design and synthesis of ultrathin α-Ni(OH)₂ nanosheets branched onto metal-organic frameworks (MOFs)-derived 3D cross-linked N-doped carbon nanotubes encapsulated with tiny Co nanoparticles (denoted as Co@NCNTs/α-Ni(OH)₂), which are directly supported on a flexible carbon cloth (CC). An aqueous Ni-Zn battery employing the hierarchical CC/Co@NCNTs/α-Ni(OH)₂ as the binder-free cathode and a commercial Zn plate as the anode is fabricated, which displays an ultrahigh capacity (316 mAh g^-1) and energy density (540.4 Wh kg^-1) at 1 A g^-1 as well as excellent rate capability (238 mAh g^-1 at 10 A g^-1) and superior cycling performance (about 84% capacity retention after 2000 cycles at 10 A g^-1). The impressive electrochemical performance might benefit from the rich active sites, rapid electron transfer, cushy electrolyte access, rapid ion transport, and robust structural stability. In addition, the quasi-solid-state CC/Co@NCNTs/α-Ni(OH)₂//Zn batteries are also successfully assembled with polymer electrolyte, indicating the great potential for portable and wearable electronics. This work might provide important guidance for constructing carbon-based hybrid materials directly supported on conductive substrates as high-performance electrodes for energy-related devices.

Electrochemical Generation of Hydrated Zinc Vanadium Oxide with Boosted Intercalation Pseudocapacitive Storage for a High-Rate Flexible Zinc-Ion Battery

With the surging development of flexible wearable and stretchable electronic devices, flexible energy-storage devices with excellent electrochemical properties are in great demand. Herein, a flexible Zn-ion battery comprised by hydrated zinc vanadium oxide/carbon cloth (ZnVOH/CC) as the cathode is developed, and it shows a high energy density, superior lifespan, and good safety. ZnVOH/CC is obtained by the in situ transformation of hydrated vanadium oxide/carbon cloth (VOH/CC) by an electrochemical method, and the intercalation pseudocapacitive reaction mechanism is discovered for ZnVOH/CC. The co-insertion/deinsertion of H⁺/Zn²⁺ is observed; the H⁺ insertion dominates in the initial discharge stage and the high-rate electrochemical process, while Zn²⁺ insertion dominates the following discharge stage and the low-rate electrochemical procedure. An ultrastable reversible capacity of 135 mAh g^-1 at 20 A g^-1 is obtained after 5000 cycles without capacity fading. Moreover, the as-assembled flexible zinc-ion battery can operate normally under rolled, folded, and punched conditions with superior safety. It is capable to deliver a high discharge capacity of 184 mAh g^-1 at 10 A g^-1 after 170 cycles. This work paves a new way for designing low-cost, safe, and quick-charging energy-storage devices for flexible electronics.

Boosting the Cycling Stability of Aqueous Flexible Zn Batteries via F Doping in Nickel-Cobalt Carbonate Hydroxide Cathode

Cathodes of rechargeable Zn batteries typically face the issues of irreversible phase transformation, structure collapse, and volume expansion during repeated charge/discharge cycles, which result in an increased transfer resistance and poor long-term cycling stability. Herein, a facile F doping strategy is developed to boost the cycling stability of nickel cobalt carbonate hydroxide (NiCo-CH) cathode. Benefiting from the extremely high electronegativity, the phase and morphology stabilities as well as the electrical conductivity of NiCo-CH are remarkably enhanced by F incorporation (NiCo-CH-F). Phase interface and amorphous microdomains are also introduced, which are favorable for the electrochemical performance of cathode. Benefiting from these features, NiCo-CH-F delivers a high capacity (245 mA h g^-1 ), excellent rate capability (64% retention at 8 A g^-1 ), and outstanding cycling stability (maintains 90% after 10 000 cycles). Moreover, the quasi-solid-state battery also manifests superior cycling stability (maintains 90% after 7200 cycles) and desirable flexibility. This work offers a general strategy to boost the cycling stability of cathode materials for aqueous Zn batteries.

An Overview and Future Perspectives of Rechargeable Zinc Batteries

Aqueous rechargeable zinc-based batteries have sparked a lot of enthusiasm in the energy storage field recently due to their inherent safety, low cost, and environmental friendliness. Although remarkable progress has been made in the exploration of performance so far, there are still many challenges such as low working voltage and dissolution of electrode materials at the material and system level. Herein, the central tenet is to establish a systematic summary for the construction and mechanism of different aqueous zinc-based batteries. Details for three major zinc-based battery systems, including alkaline rechargeable Zn-based batteries (ARZBs), aqueous Zn ion batteries (AZIBs), and dual-ion hybrid Zn batteries (DHZBs) are given. First, the electrode materials and energy storage mechanism of the three types of zinc-based batteries are discussed to provide universal guidance for these batteries. Then, the electrode behavior of zinc anodes and strategies to deal with problems such as dendrite and passivation are recommended. Finally, some challenge-oriented solutions are provided to facilitate the next development of zinc-based batteries. Combining the characteristics of zinc-based batteries with good use of concepts and ideas from other disciplines will surely pave the way for its commercialization.

A Long-Cycling Aqueous Zinc-Ion Pouch Cell: NASICON-Type Material and Surface Modification

Aqueous zinc-ion batteries (ZIBs) have become the highest potential energy storage system for large-scale applications owing to the high specific capacity, good safety and low cost. In this work, a NASICON-type Na₃ V₂ (PO₄ )₃ cathode modified by a uniform carbon layer (NVP/C) has been synthesized via a facile solid-state method and exhibited significantly improved electrochemical performance when working in an aqueous ZIB. Specifically, the NVP/C cathode shows an excellent rate capacity (e. g., 48 mAh g^-1 at 1.0 A g^-1 ). Good cycle stability is also achieved (e. g., showing a capacity retention of 88% after 2000 cycles at 1.0 A g^-1 ). Furthermore, the Zn²⁺ (de)intercalation mechanism in the NVP cathode has been determined by various ex-situ techniques. In addition, a Zn||NVP/C pouch cell has been assembled, delivering a high capacity of 89 mAhg^-1 at 0.2 A g^-1 and exhibiting a superior long cycling stability.